# Planetary Nebulae: Sources of Enlightenment

Karen B. Kwitter  Department of Astronomy, Williams College, Williamstown, MA
01267, USA<EMAIL_ADDRESS>R.B.C. Henry  H.L. Dodge Department of
Physics & Astronomy, University of Oklahoma, Norman, OK 73019, USA
<EMAIL_ADDRESS>
###### Abstract

In this review/tutorial we explore planetary nebulae as a stage in the
evolution of low-to-intermediate-mass stars, as major contributors to the mass
and chemical enrichment of the interstellar medium, and as astrophysical
laboratories. We discuss many observed properties of planetary nebulae,
placing particular emphasis on element abundance determinations and
comparisons with theoretical predictions. Dust and molecules associated with
planetary nebulae are considered as well. We then examine distances, binarity,
and planetary nebula morphology and evolution. We end with mention of some of
the advances that will be enabled by future observing capabilities.

ISM: abundances, planetary nebulae: general, stars: evolution, galaxies:
evolution

##  1 Introduction

In 1764, while observing the sky toward the constellation Vulpecula, the
French astronomer Charles Messier noted a “nebula without star” that “appears
of oval shape” (Messier, 1771), adding it as number 27 in his catalog of non-
stellar objects not to be confused with his main interest, comets; thus was
discovered the first planetary nebula, known today as the Dumbbell Nebula (or
M27 or NGC 6853). Eighteen years later, shortly after beginning his tenure as
Court Astronomer to King George III of England, William Herschel was scanning
the heavens for double stars when he, too, found a curious non-stellar object,
one we now call the Saturn Nebula (or NGC 7009). Herschel dubbed objects like
these “planetary nebulae,” and he puzzled over their nature for the rest of
his life (Hoskin, 2014). We are fortunate nowadays to know much more, though
by no means, all, about them: planetary nebulae (PNe) are ephemeral
manifestations of the dynamic nature of stellar evolution and the ongoing
enrichment of the Galaxy’s reservoir of star-forming matter. They are the
penultimate stage in the lives of multitudes of stars, including, possibly,
the Sun (Boffin & Jones, 2019, p. 94). Fig. 1 is an artistic montage of 22 PNe
displaying some of the variety of their shapes and sizes.

Since the time of Messier and Herschel, PNe have become indispensable tools
for studying stellar evolution, galactic chemical evolution, and the
interstellar medium. Studies of PNe also contribute to a variety of other
astrophysical topics. PNe progenitor stars contribute the majority of the
matter that forms the ISM (Dorschner & Henning, 1995; Edwards, Cox, & Ziurys,
2014). They are also excellent tracers of stellar populations in galaxies
(e.g., Buzzoni & Arnaboldi, 2006; Hartke et al., 2020) and serve as valuable
test particles in studies of galaxy kinematics (Aniyan, Freeman, & Arnaboldi,
2018; Aniyan et al., 2020) and galaxy cluster and merger dynamics (Gerhard et
al., 2007). Furthermore, PNe are fertile sites for detecting important
molecular species: recently the first detection of the cosmologically
significant molecule, HeH+ via its fundamental rotational transition, was
reported in NGC 7027 (Güsten, Wiesemeyer, & Neufeld, 2019), and soon
thereafter, Neufeld et al. (2020, 2021) detected additional rovibrational HeH+
lines, along with CH+ emission seen for the first time in an astronomical
source.

A significant fraction of the high luminosity of PNe is concentrated in the
O++ emission line at 5007Å (see §5.2.1), allowing them to be observed at
extragalactic distances. The first extragalactic PNe were detected by Baade
(1955), who discovered five in M31. Subsequent searches in M31 using
increasingly sensitive detectors revealed 311 PNe (Ford & Jacoby, 1978).
Merrett et al. (2006) found more than 2600 PNe; the latest survey in M31
identifies over 4000 (Bhattacharya, Arnaboldi, & Hartke, 2019). PNe have also
been identified in dozens of external galaxies, including members of the Virgo
and Fornax clusters (Ford, Peng, & Freeman, 2002; Spriggs et al., 2021) at
d$\sim$20 Mpc, and even out to the Coma cluster at d$\sim$100 Mpc (Gerhard et
al., 2005).

How many PNe are there in the Milky Way Galaxy? We don’t know! As of this
writing, the HASH database (Parker et al., 2016) contains 2667 “true,” 447
“likely,” and 681 “possible” PNe; Parker (2020) reviews the status of modern
searches. According to Awang Iskandar et al. (2020), 64% of “likely” and 41%
of “possible” PNe are “true” PNe, predicting a total of 3232. The current
census likely represents only 15 – 30% of the full count (Frew, 2016),
implying a population between roughly 11,000 and 22,000. Jacoby et al. (2010)
discuss various estimates of the total number of PNe (all much larger than the
number detected), and enumerate possible reasons for the shortfall (e.g.,
interstellar dust obscuration, survey biases, poorly searched regions of the
sky). As one example, Hong et al. (2021) report near-infrared observations of
two probable PNe at projected distances $\lesssim$20 pc from the Galactic
center and behind more than 20 magnitudes of visual extinction; these would be
the first detected in the nuclear stellar disk, a disk of stars in rotation
around Sgr A∗. The Galactic distribution of the known PNe is shown in Fig. 2.

There have been several valuable reviews of PNe over the years, such as those
by Kaler (1985), Kwok (1994), Kwitter et al. (2014), and Zijlstra (2015).
Recent IAU Symposia on PNe are #234 (Barlow & Méndez 2006), #283 (Manchado,
Stanghellini, & Schönberner 2012), and #323 (Liu, Stanghellini, & Karakas
2016). Books and monographs concentrating on PNe include Aller & Liller
(1968), Aller (1971), Pottasch (1983), Aller (1987), Gurzadyan (1997), Kwok
(2000), and Osterbrock & Ferland (2006). Frew (2008) provides an excellent,
detailed study of PNe in the solar neighborhood.

In this review/tutorial we will show how PNe reveal the nucleosynthesis
histories of their stars, and examine their important impact on the chemical
evolution of the Milky Way and other galaxies. In §2 we briefly review the
evolution of PN progenitor stars (low-to-intermediate-mass stars: LIMS: 0.8 –
8 M⊙) from the main sequence to the PN stage. Detailed discussion of the
evolution and properties of PN central stars is not included here; we
recommend Weidmann et al. (2015, 2020) for a current overview, and Iben (1995)
for a historical, physics-heavy, deep dive. Werner (2012) and Ziegler et al.
(2012) discuss the evolution of H-poor and H-rich central stars111This
distinction results from the relative timing of the progenitor star’s
departure from the AGB and its last helium-shell thermal pulse; see §2.2.,
respectively, and Hajduk et al. (2015) explore the temporal variability of
nebular fluxes as a way to study young central star evolution. In §3 we
examine in detail the chemical abundances measured in PNe in the Milky Way and
in a selection of Local Group and more distant galaxies. We also discuss the
molecular and dust components of PNe. The extensive nebular astrophysics
involved in calculating these abundances is not included here, but is
comprehensively discussed in excellent recent reviews by Peimbert, Peimbert, &
Delgado-Inglada (2017) and García-Rojas (2020). Then in §4 we discuss radial
abundance gradients in galaxy disks, and go on to compare observed abundances
with theoretical predictions. Distance determinations for PNe are explored in
§5, and in §6 we consider the important question of binarity in PN central
stars. Nebular morphology and evolution are discussed in §7. In §8 we
summarize and touch on anticipated future developments in PN research.
Appendix A contains a list of databases and catalogs of PNe and central stars,
and Appendix B lists references to papers containing model-predicted yields
and surface abundances of LIMS.

##  2 Stellar Evolution and Planetary Nebula Formation

###  2.1 From the Main Sequence to the Asymptotic Giant Branch

The brief summary that follows is designed to get us to the point where we can
discuss how nuclear products get from the stellar interior to the envelope and
then to the interstellar medium. It is drawn from excellent reviews of the
evolution of asymptotic giant branch (AGB) stars by Herwig (2005) and Karakas
& Lattanzio (2014), to which the reader should turn for greater detail. To
gain an historical perspective on the development of this scenario, the reader
should begin with the papers by Iben & Truran (1978) and Renzini & Voli
(1981). The evolutionary stages described below are shown in the context of an
HR diagram in Fig. 3 [adapted from Herwig (2005)], where the evolution of a 2
M⊙ star is illustrated.

When a LIMS exhausts its core H, a H-burning shell surrounding the now-He core
ignites and slowly moves outward, leaving behind its He product. The star’s
outer envelope then expands and cools as the star moves through the
Hertzsprung gap and begins to ascend the red giant branch (RGB) in the HR
diagram. While the energy needed for this expansion may come from the
H-burning shell, there is no firm consensus among specialists regarding the
actual mechanism by which the star expands and becomes a red giant (Miller
Bertolami 2021). Once it reaches the upper end of the RGB, He ignition occurs
in the core, either in a runaway flash under degenerate conditions (if M$<$2
M⊙) or more gently (if M$>$2 M⊙). The star now settles into a relatively
stable giant-like configuration (expanded envelope, dense core), as He is
slowly burned to C and O in the core. Following exhaustion of He in the core,
a He-burning shell surrounding the CO core and interior to the H shell ignites
and begins burning He into C and O, as the star moves up along the AGB track.
The two shells are separated by an intershell region, now rich in He, and it
is at this point that thermal pulses, triggered by degenerate He-burning in
the He shell, commence.

During the evolutionary process just summarized, the He and heavy element
products of nuclear burning are transported to the outer envelope and from
there deposited through mass loss into the interstellar medium, thereby
seeding the next stellar generation with the enriched materials. Transporting
the nuclear products from the stellar interior to the star’s outer envelope is
accomplished by convective processes involving two or three dredge-up events
depending upon the stellar mass. Because opacity is high in the outer envelope
of a giant star, efficient heat transfer to the surface requires convection.
Thus, first dredge-up (FDU) occurs as the evolved star ascends the RGB and the
inner surface of the convective envelope extends downward into the He-rich
intershell region. At that time hydrogen-burning products such as 4He, 13C,
14N are mixed up into the heretofore pristine envelope, thereby enriching it
with these products of H fusion. Interestingly, model predictions of envelope
abundances following FDU in the higher luminosity RGB stars markedly disagree
with observations. For example, the 12C/13C ratio as well as the abundance of
Li are both observed to be significantly lower than the models predict. This
result suggests the occurrence of a process called extra mixing which
transfers additional products from the H-burning shell up into the convective
envelope (see Karakas & Lattanzio, 2014, and references therein).

Following He exhaustion and the subsequent onset of He-shell burning, the star
begins to ascend the AGB. Stars with masses exceeding 3-4 M⊙ undergo a second
dredge-up (SDU) as the convective envelope reaches deep inside the intershell
region to move more of the same H-burning products into the outer atmosphere.
Less massive stars skip the SDU stage.

At this point the stellar structure, moving outward from the center, includes
a carbon-oxygen core, a He-burning shell, a He-rich intershell region, a
H-burning shell, and a convective envelope now polluted by H-burning products
(see Fig. 14 in Karakas & Lattanzio, 2014). As the star proceeds up the AGB,
the gravitational effects associated with the increasing mass of the
contracting core cause the He-shell to become compressed and thermally
unstable. A He flash (thermal pulse) ensues, resulting in envelope expansion
as well as initiation of convection and homogenization within the intershell.

Following the He-shell flash, energy produced by the flash causes the
intershell region to expand and cool, while at the same time, burning in the
H-shell ceases. The increased opacity of the intershell region resulting from
the temperature reduction allows the base of the convective envelope to
penetrate deeply into the region, causing He-burning products, especially 12C,
to be transported to the outer envelope during a series of pulsations of the
AGB star, a process called third dredge-up (TDU). The amount of dredged-up 12C
can be significant, and enough to result in C/O$>$1 in the convective
envelope, i.e., a carbon star.

Such thermal pulses continue through dozens of cycles, with the precise number
dependent upon core mass and metallicity, and each pulse results in further
dredge-up. During the interpulse phase, the base of the convective envelope
lies near or partially within the upper portion of the H-shell where
temperatures can reach $50\times 10^{6}$K in stars of $M\geq 4M_{\odot}$. With
the envelope now containing an increasing amount of 12C from TDU, CNO
processing may ensue, converting 12C to 14N and forcing C/O to values less
than unity, i.e., an O-rich envelope. This process is referred to as “hot
bottom burning” (HBB) and is discussed in more detail in §§3 and 4.

During the post main sequence evolution just described, the star has gone
through phases of both gentle mass loss as well as the punctuated losses that
occur in connection with the thermal pulses. The moment when a star leaves the
AGB to begin the journey to the hot, blue side of the HR diagram (see Fig. 3)
is not obvious. The essence of this milestone is that the thermal pulses
described above have ceased (as have TDU and HBB), profuse mass loss [up to
10-5 M⊙/yr; Decin et al. (2019)] has reduced the envelope mass to a small
fraction of the core mass [$\sim$1%; Miller Bertolami (2016, hereafter
M3B16)], and the envelope has become detached (Lagadec, 2016).

###  2.2 From AGB to Planetary Nebula

Observationally, the early stages of the AGB-PN transition are typically
marked by stellar spectral types of supergiant F or G, if the star can be
seen; more often the star is surrounded by its lost envelope, obscured by dust
of its own making, and optically visible only via scattered light. The dust
composition will be dominated by either carbon or oxygen (silicate) chemistry,
depending on the C/O ratio. As just described, this will be mass dependent:
below $\sim$ 1.5 M⊙222Mass limits for nucleosynthesis processes are
metallicity dependent (see §4); values given here apply at solar metallicity
(Z=0.014). too few thermal pulses occur to modify the surface composition
toward being C-rich. Up to $\sim$5 M⊙, C/O will be enhanced. But above
$\sim$4.5 M⊙ HBB sends the surface C/O ratio back below unity and enhances
surface 14N (see §4.2.2) (Karakas, 2014; Karakas & Lugaro, 2016). Both O-rich
and C-rich stars will have CO in their atmospheres; the less abundant element
will be locked into CO, leaving the more abundant element able to form dust
grains. Dust in PNe is discussed in detail in §3.5.

The time it takes a star leaving the AGB to move across the HR diagram to the
blue depends steeply on the core mass. M3B16 defines the “crossing time” as
the time it takes for the star to evolve from an effective temperature $\sim
10^{4}$ K to its eventual maximum effective temperature $\sim$105 K (see his
Fig. 8). Crossing times range from $\sim$104 years for initially solar-mass
stars to mere decades for stars with initial masses $\sim$4 M⊙. Fig. 4 shows
the crossing time for solar-metallicity stars of varying main sequence masses
based on data from his Table 3.

Depending on the phase of the helium shell flash cycle during which the star
departs the AGB, a final late or very late thermal pulse can occur (Blöcker,
2001; Werner & Herwig, 2006), looping the star back across the HR diagram to
cooler temperatures (see Fig. 3), leading to H-deficiency and born-again
status; see Iben, Kaler, & Truran (1983). Such PNe are rare; in their paper on
the probable binary central star of born-again PN A 30, Jacoby et al. (2020)
list only seven others (A 58, A 78, GJJC-1, Sakurai’s Object, WR72, IRAS
15154-5258, and HuBi 1). Weidmann et al. (2020) find that 2/3 of PN central
stars in their catalog are H-rich and 1/3 are H-poor. Of binary central stars,
almost 80% are H-rich, which may indicate that binary evolution can somehow
disrupt the sequence of events that lead to an H-poor central star. We discuss
central star binarity in §6.

Nomenclature during the blueward HR diagram crossing of a PN-to-be is murky:
post-AGB (pAGB) and pre-PN (PPN) are both used, though the former also applies
to stars that will not produce PNe due to a lack of either sufficiently dense
nebular material or ionizing photons – essentially a mismatch between the
expansion timescale and the evolution timescale (i.e., crossing time; Renzini,
1981). The beginning of the PN stage is fairly easy to define: as the star
heats to $\gtrsim$20,000 K, widespread hydrogen ionization (and thus,
emission) begins in the nebula, and at $\sim$30,000 K, oxygen can be doubly
ionized, producing the signature [O III] 5007Å line in the spectrum of the new
PN.

##  3 Chemical Abundances in Planetary Nebulae

The gas forming a PN is the debris ejected by the progenitor star as it nears
the end of its lifetime. Thus, the abundances of chemical elements in that gas
which are not synthesized by the star provide information about the
composition of the interstellar medium at the time of star formation. At the
same time, abundances of those elements in the ejected gas which are
synthesized within the star supply crucial information regarding the nuclear
processes that have occurred during the star’s lifetime.

Early examples of some of the first work on PN abundances can be found in
Aller & Menzel (1945), Kaler (1970), Peimbert & Torres-Peimbert (1971), and
Peimbert (1978). These important studies illustrated what could be done in a
more challenging period when dependable values for atomic constants as well as
estimations of corrections for unseen ionization stages had only just begun to
become available. While abundance studies of today can take advantage of the
significant evolution that has occurred in these two areas, each of the
earlier studies helped, by their example, to set in motion what has become a
vibrant industry.

We begin the discussion by taking an extensive look at important large surveys
of PNe in the Milky Way Galaxy (MW), initially focusing on elements which are
products of hydrogen and helium burning, i.e., He, C, N, O, Ne, S, Cl333Unlike
He-burning products such as C, O, Ne, Mg, Si, S, and Ar, Cl is not synthesized
directly from alpha reactions. 35Cl, the most abundant Cl isotope, forms when
32S undergoes two neutron captures to produce 34S which in turn captures a
proton. 37Cl, a less abundant species, forms by a $\beta^{+}$ decay of 37Ar,
itself a product of neutron capture onto 36Ar (Clayton, 2003)., and Ar. Next,
we list numerous smaller but important studies of MW PNe where more extensive
work on individual PNe may be found. Following that, we discuss abundance
studies of elements on rows 3 and 4 of the periodic table, including Fe-peak
and s-process elements. Finally, we explore abundances in extragalactic PNe as
well as molecules and dust in post-AGB objects.

Several good review papers have been published recently addressing the
subjects of nebular physics and abundance determinations from recombination
and collisionally excited lines444A labelled sample spectrum from the near-UV
to the near-IR can be found in Dufour et al. (2015); see their Fig. 3. See
also the templates provided on the Gallery of Planetary Nebula Spectra
website: https://web.williams.edu/Astronomy/research/PN/nebulae/legend.php..
Readers who are unfamiliar with these topics or who desire a refresher course
are referred to articles by Kwitter & Henry (2011), Pérez-Montero (2017),
Peimbert, Peimbert, & Delgado-Inglada (2017); Peimbert (2019), and García-
Rojas (2020).

The reader should keep in mind that persistent problems exist regarding the
computation of both ionic and elemental abundances, such as the abundance
discrepancy factor (ADF) and ionization correction factor (ICF). The ADF is
addressed most recently by Peimbert (2019) and García-Rojas (2020) as well as
in an earlier study by Kholtygin (1998) (see also §6.2 here), while the ICF is
most recently treated by Delgado-Inglada, Morriset, & Stasińska (2014) and
Amayo, Delgado-Inglada & García-Rojas (2020, Na, K, Ca).

Finally, a word of caution. The common use of oxygen as the standard
metallicity indicator is increasingly controversial these day, because some
observations and theoretical models imply that this element can be destroyed
or synthesized during AGB evolution. If you desire to explore that problem
before proceeding here, you can find a detailed discussion within the context
of galaxy abundance gradients in §4.1. Otherwise, if you prefer to wait until
you get to that section in the natural order, then just keep reading on here.

###  3.1 Large Elemental Abundance Surveys of MW Planetary Nebulae

The goal of this section is to present an extensive listing of individual PN
abundance surveys in the MW, where each study comprises a relatively large
number of objects (usually $>30$ for disk objects and a bit less than that for
bulge PNe). In addition to sample size, two additional selection criteria for
choosing a survey for analysis here were: 1) the abundances presented in the
paper must have been computed by the paper’s authors; and 2) line strengths
used in the abundance determinations should be those observed and measured by
the authors themselves, or have been adopted from papers in the literature
after the authors have critically evaluated them. These two criteria ensure a
reasonable level of homogeneity within each sample. In addition to the disk
and bulge surveys, we also present a listing of published abundance studies
for each of the 13 documented Galactic halo PNe. Generally speaking, the He
abundances were derived from recombination lines while the abundances of all
other elements were determined from collisionally excited lines. A discussion
regarding the relevance of these results to stellar evolution and
nucleosynthesis is postponed until section 4.2.

####  3.1.1 MW Disk PN Surveys

The surveys chosen for abundance analysis and comparison here, as listed in
Table 1, are those of Barker (1978b), Aller & Czyzak (1983); Aller & Keyes
(1987), Kingsburgh & Barlow (1994), Perinotto, Morbidelli, & Scatarzi (2004),
Stanghellini et al. (2006), Girard, Köppen, & Acker (2007), Pottasch &
Bernard-Salas (2010), Maciel et al. (2017), and Kwitter & Henry (2020,
hereafter KH20). We removed any PNe listed as bulge objects by Chiappini et
al. (2009)555In selecting bulge PNe, Chiappini et al. (2009) used the set of
criteria proposed by Stasińska & Tylenda (1994), i.e., objects must be located
within 10 degrees of the Galactic center, possess an angular diameter smaller
than 20 arcsec, and have radio fluxes at 5 GHz of less than 100 mJy., as well
as known halo PNe, from several of the samples in order to ensure that each
comprised only disk PNe. As stipulated above, the abundances of all PNe within
a sample were determined homogeneously by the authors, i.e. the same
computational method and software were employed consistently across that
sample. Most authors determined elemental abundances by first computing one or
more ion abundances of an element directly from spectral data and then
applying an ionization correction factor that accounts for the unobserved ions
of an element.

The upper portion of Table 1 lists the basic characteristics of each disk
survey that we evaluated, arranged according to publication date from earliest
to latest. The survey name is listed in column 1 and linked to a specific
reference in the footnote. The number of PNe considered in each survey is
given in column 2, while the relevant wavelength range or ranges of the
spectroscopic data upon which each survey was based are listed in column 3.
The medians of elemental number abundances relative to hydrogen are given in
columns 4-11, while solar abundances from Asplund et al. (2009) are provided
in the final row of the table. Survey sizes range from 32 to 230 disk objects.
Six studies derived their abundances based entirely upon spectral coverage
within the optical range, while three extended their coverage into the UV and,
in one case, the IR. Note that with the exception of the surveys by Perinotto,
Morbidelli, & Scatarzi (2004) and Stanghellini et al. (2006) all studies
employed their own observational data to derive their abundances. Perinotto,
Morbidelli, & Scatarzi (2004) and Stanghellini et al. (2006) adopted
previously published line strengths determined by them to be of high quality.

For each survey listed in Table 1, Fig. 5 shows the survey median (filled
circles) for each observed element, presented in log space666The standard
abundance notation $12+\log{X/H}$ is employed, where X/H corresponds to the
specific fraction at the bottom of a column along the horizontal axis.. The
solar abundance for each element is also plotted for comparison purposes.

We see in the table that most of the survey values for any particular element
are remarkably consistent with each other, regardless of the abundance spread
found in each survey777This assessment does not include the published
abundances by Barker (1978b) for N/H, Ne/H, and S/H, which seem to be
consistently lower than the other samples regarding those same elements..
Furthermore, as a measure of the extent of agreement of survey median values
for a particular element, the value of $\log(\bar{X}+\sigma)-\log(\bar{X})$
ranges from a maximum in the case of S/H (0.13 or 35%) to a minimum in the
case of He/H (0.02 or 5%), where $\bar{X}$ and $\sigma$ represent the average
and dispersion of the survey median values for an element, respectively.

Potential reasons for differences among survey medians are numerous. They
include uncertainties in: a) measured line strengths; b) reddening
corrections; c) atomic data used to convert line strengths into ionic
abundances; and d) ionization correction factors or photoionization modeling.
Also, the presence of any radial, azimuthal, or vertical abundance gradients
in the disk will likely cause survey medians to be affected by the
distribution of sample PNe over the disk888Radial abundance gradients
especially in the case of alpha elements (He burning products) such as O, Ne,
S, Cl, and Ar are known to exist in the MW and most spiral galaxies.
Typically, abundances of these elements decrease by a few hundredths of a dex
per kiloparsec with galactocentric distance along the disk. See §4.1.. In
addition, the surveys are arranged chronologically in Table 1 in order to
check for systematic changes over time. Although this collection of disk
surveys extends over approximately four decades in time, reassuringly no
noticeable effects due to advances in instrumentation (e.g. the advent of CCDs
in the early 1980s) or atomic data updates, are present.

We can compare survey results with solar values by scanning down the column of
medians for individual elements in Table 1. In doing so, we see that this
group of surveys collectively seems to indicate the following: 1) He, C, N are
enhanced by a few tenths of a dex, likely the result of nucleosynthetic
processes in LIMS (see §2.1); 2) O, Ne, and Ar levels are close to solar; and
3) S and Cl tend to be subsolar – S abundances are often found to be depleted
in PNe relative to values expected based upon their metallicity as measured by
O/H (the “sulfur anomaly”) for reasons that are not currently understood
(Henry et al., 2012). In the same manner, Cl abundances are consistently found
to be sub-solar in surveys of PNe, e.g., see Milingo et al. (2010, Fig. 3),
although to our knowledge this behavior has not been investigated previously.

####  3.1.2 MW Bulge PN Surveys

Surveys of bulge PNe analyzed here are from Aller & Keyes (1987), Webster
(1988), Ratag et al. (1997), Stasińska et al. (1998), Exter et al. (2004),
Wang & Liu (2007), Chiappini et al. (2009), and Cavichia et al. (2010, 2017).
As in the case of the disk, we chose samples based upon homogeneity regarding
data acquisition and abundance analysis. For all but the Cavichia et al.
sample of southern PNe, objects not listed in the large compilation of
northern bulge PNe found in Table A1 of Chiappini et al. (2009) were excluded
from consideration. For the Cavichia sample, we considered only the PNe in
their list which satisfied the criteria listed in Stasińska et al. (1998).

The bottom portion of Table 1 shows the results for the eight surveys cited
above, where again the surveys are ordered time wise beginning from oldest to
most recent. To indicate the level of agreement among the surveys, the
dispersion of median values around their average for the bulge surveys ranges
from 0.03 dex (6.3%) for He/H to 0.19 dex (56%) for Ar/H. (Cl is discounted
since only three of the surveys reported an abundance for this element.) Thus,
for heavy elements there appears to be slightly more disagreement regarding
their abundances among the bulge surveys compared with disk PN studies. This
result is likely due to the larger distances and associated reddening effects
for the bulge objects. And as in the disk, we see no evidence of temporal
variations of survey medians for any element.

A comparison of disk and bulge abundance results in Table 1 suggests a
similarity between disk and bulge PNe in relation to solar abundances of
several elements. For example, we see supersolar He/H and N/H but roughly
solar O/H and Ar/H in both Galactic regions. At the same time, the Ne/H
abundance is generally higher by about 30% in the disk than in the bulge,
while Cl/H abundance is roughly two times higher in the bulge. As in the disk,
S/H in bulge PNe shows significant dispersion, with medians usually well below
the solar level in both systems. Finally, as we saw for the disk, Fig. 6
demonstrates that bulge PN abundances qualitatively follow the solar pattern
as expected.

####  3.1.3 MW Halo Studies

There are currently 13 PNe that are generally recognized as belonging to the
halo of the MW. Four of these objects, BoBn1, DDDM1, H4-1, and K648, have been
well-studied by five or more research teams each. The relevant studies are
listed in Table 2 and stretch over three to four decades in time. For each
object identified in the left column we list each paper by first author name
and year which is keyed to a reference provided in the table footnote. Columns
3-10 contain number abundances relative to hydrogen for each element.
Abundance results for the remaining nine halo PNe, each associated with one to
four studies, are also featured in Table 2 below the first four.

For each halo PN and element, Figure 7 shows the median value of all studies
for that object. Two interesting conclusions can be drawn: 1) O, Ne, S, and
Ar, alpha elements which reflect overall metallicity, have median abundances
below their respective solar values999See the discussion in §4.1.3 regarding
the evidence that O may actually be synthesized in low metallicity AGB stars
following TDU and therefore is not a reliable indicator of the progenitor
star’s metallicity.; 2) He, C, and N exceed solar levels in a few of the halo
PNe; and 3) the range of the median abundance values over the 13 halo PNe is
greatest for C (2.6 dex) and least for Ne (1.2 dex).

We should note that for several PNe listed in Table 2 some uncertainty exists
regarding halo membership. Based on its radial velocity and location, BoBn1
may be a member of the Sagittarius dwarf spheroidal galaxy (Zijlstra et al.,
2006). Further, the relatively small (absolute value) radial velocities of the
following PNe may indicate thick disk membership: NGC2242 (Karachentsev,
Karachentseva, & Huchtmeier, 2004), NGC4361 (Torres-Peimbert, Peimbert, &
Peña, 1990), PNG243.8-37.1 (Boffin, Miszalski, & Jones, 2012), PNG006.0-41.9
(Zijlstra et al., 2006); and possible bulge membership for M2-29 (Durand,
Acker, & Zijlstra, 1998). Improved radial velocity and distance determinations
will be required for definitive classification.

###  3.2 Additional MW Elemental Abundance Studies

Smaller and/or more focused abundance studies published in the last two
decades include Tsamis et al. (2003, 9 MW PNe), Costa, Uchida, & Maciel (2004,
26 MW anticenter PNe), Krabbe & Copetti (2006, 7 MW PNe), Yuan et al. (2011,
3D model of NGC 6153), Dufour et al. (2015, 10 MW PNe), Pagomenos et al.
(2018, 23 MW anticenter PNe), and Miller et al. (2019, 6 MW disk PNe). There
is also a series of 11 papers, each treating an individual PN, by Hyung et al.
(see the last paper in the series, Hyung, Pottasch, & Feibelman (2004), which
provides the references to the previous 10 papers).

Numerous projects providing abundance measurements for a variety of less
studied elements are also available in the literature. Neutron capture
elements, specifically those formed by the s-process, are one important
example. Other elements which have received less attention are those residing
on the third and fourth rows of the periodic table and include F, Na, Mg, Al,
Si, P, K, Ca, Fe, Ni, and Zn. Below we summarize the current picture of
s-process elements and then highlight abundance results of four particularly
interesting elements: F, Mg, Fe, and Zn. These four elements are featured here
because AGB stars are the only observationally confirmed production sites of F
(Karakas & Lattanzio, 2014, §5.2.3); as an alpha element, Mg tracks PN
progenitor metallicity; and while the Fe abundance in PNe is very difficult to
measure directly, Zn has been shown to track it.

####  3.2.1 PN Abundance Studies of Neutron Capture Elements

Many PNe are observed to have s-process elements such as Kr and Se present in
measurable quantities. These post Fe-peak elements with atomic numbers $Z>30$
inhabit the fourth row and beyond of the periodic table. They are produced
when a nucleus (Z,A) first captures a neutron and subsequently undergoes a
beta decay to yield the nucleus (Z+1,A+1). Thus a nucleus of a heavier element
is produced, rather than a different isotope of the original element. In this
instance, the process is termed slow because the local neutron flux is low
enough that beta decay occurs before a second neutron is captured. The
production of s-process elements in AGB stars is discussed in detail by
Karakas & Lattanzio (2014, §3.7). In addition, readers can find a detailed
review of neutron-capture element abundances in PNe in Sterling (2020a). For
now we will briefly summarize the present picture.

Initial observations of emission lines related to s-process elements in PNe
were carried out by Péquignot & Baluteau (1994), covering the spectral region
of 6540-10460 Å101010Earlier NIR observations by Geballe, Burton, & Isaacman
(1991) revealed two unidentified lines later associated with [Kr III] 2.199
$\mu$m and [Se IV] 2.187 $\mu$m. They detected forbidden lines of [Kr III]
$\lambda$6826.9 and [Xe IV] $\lambda$7534.9 in NGC 7027 and proceeded to
estimate the total abundances of Kr/H and Xe/H of $2.74\times 10^{-8}$ and
$3.36\times 10^{-9}$, respectively.

Table 3 provides a listing, from early to recent times, of authors, observed
PNe, spectral coverage, and observed ions covering the time up to this
writing. Note that the atomic number of each element is shown in parentheses
following the element symbol at the top of the table. Papers listed in the
first column are linked to their references in the table footnote. All
transitions except those of Ba II are forbidden. Most of the papers listed
report measurements of the [Kr III] and [Se IV] lines, with lines of Rb and Xe
reported several times as well. Note the significant increase in the number of
observed ions beginning with the paper by Sharpee, Zhang, & Williams (2007).
For the most part, this acceleration in s-process work is due to the advent of
high resolution optical and (especially) infrared instrumentation since that
paper (Sterling, 2020b).

Many of the papers listed in Table 3 used their measured emission line
strengths along with then-available transition energies and probabilities, and
collision strengths to compute ionic and elemental abundances. Researchers
often used ionization correction factors developed within the same
publications through the use of detailed photoionization models.

The resulting element abundances are listed in Table 4. Columns 1 and 2
provide the common object name and paper designation, respectively, where the
latter is defined in a table footnote. When available, abundances reported in
the papers are listed in the next eight columns. At the bottom of the table in
a separate section, we list medians and maximum and minimum values of Se/H (in
68 objects) and Kr/H (in 39 objects) from a survey of 120 PNe by Sterling et
al. (2015). The last line in the table provides the solar abundances by
Asplund et al. (2009) for comparison purposes.

Note that in the cases of Se/H, Kr/H, Rb/H, and Xe/H, many of the abundances
tend to be above their solar values. For instance, recent studies of NGC 7027
by Sterling et al. (2016) and Madonna et al. (2018) indicate supersolar
abundances of Se/H, Kr/H, and Rb. In addition, Sterling et al. (2015)’s large
survey found a median value for the Kr abundance that is roughly four times
the solar value, while the median Se/H level is very close to solar.
Evidently, abundances of certain s-process elements tend to be enriched in
many PNe.

####  3.2.2 Fluorine

The dominant fluorine isotope, 19F, may be partially produced in four steps
summarized by ${}^{14}N+\alpha+p^{+}\rightarrow~{}^{19}F+2\gamma+e^{+}+\nu$ in
the He rich intershell of AGB stars. However, the bulk of 19F in nature is
produced in Type II supernova events when a neutrino (there are a lot of them
produced during core collapse!) impacts a 20Ne nucleus, forcing out either a
proton or neutron, ultimately resulting in the formation of a 19F nucleus
(Clayton, 2003). Zhang & Liu (2005) employed published strengths of the lines
[F II] $\lambda$4789 and [F IV] $\lambda$4060 to determine F abundances in 13
Galactic PNe. Although their median value of $F/H=3.57\times 10^{-8}$ is very
close to Asplund et al. (2009)’s solar value of $3.63\times 10^{-8}$, they
nevertheless find a broad abundance range of $5.54\times 10^{-9}$ to
$2.99\times 10^{-7}$. In the case of NGC 40, $F/F_{\odot}=8.23$, the largest
in the survey, while the lowest value of that same ratio is 0.15, observed in
NGC 2440. The authors also suggest that a positive correlation exists in PNe
between [F/O] and C/O. Otsuka et al. (2008) computed the F abundance in the
low-metallicity halo PN BoBn-1, using their emission measurements of the [F
IV] $\lambda$3997 and $\lambda$4060 lines. They found that F/H$=3.31\times
10^{-7}$, roughly an order of magnitude above the solar value and the median
value observed by Zhang & Liu (2005). Otsuka et al. (2008) invoke a picture
similar to that of Zhang & Liu (2005) regarding the origin of F enhancement in
BoBn-1. Another low metallicity PN, J900, was observed by Otsuka & Hyung
(2020), who measured a value of F/H=$1.45\times 10^{-7}$ or roughly four times
the solar F/H value.

A comprehensive understanding of F in PNe has begun to emerge with the work of
Abia et al. (2019), who observed 11 AGB carbon stars, five SC-type and six
N-type111111The spectral evolution of AGB stars as the number of TDU episodes
increases is M-MS-S-SC-C(N), where C(N) is N-type.. They found that at roughly
solar metallicity, SC and N-type stars possessed nearly equal F abundances. In
the same study, Abia et al. (2019) found an inverse correlation between [F/Fe]
and [Fe/H] for $-2\leq[Fe/H]\leq 0$ (see their Fig. 3). The authors also
showed by plotting theoretical models from Cristallo et al. (2015) that at
constant [Fe/H], [F/Fe] directly increases with the number of thermal pulses.
They conclude from their studies, however, that AGB stars are not the main
contributors of F in the solar neighborhood (core collapse SNe are) in
agreement with chemical evolution models extant in the literature, e.g.,
Kobayashi et al. (2011). Further analysis by this same team presented in
Vescovi et al. (2021) also finds that F abundance in AGB stars is directly
related to the average s-process abundance $<$s$>$ such that [F/Fe] and
[$<$s$>$/Fe] increase together (see their Fig. 2, upper panel). Overall, they
also find that their stellar models better reproduce the F/H abundance
observations when magnetic buoyancy “acts as the driving force for the
formation of the 13C neutron source” in metal-poor AGB stars during TDU.

####  3.2.3 Magnesium

As an alpha element, the Mg found in a PN was likely present in the progenitor
star at the time of its formation. The dominant Mg isotope is 24Mg, which
represents about 79% of all Mg in the Sun (Asplund et al., 2009). 24Mg is a
product of He burning, being produced mainly by the 20Ne($\alpha,\gamma$)24Mg
reaction (Clayton, 2003). Mg is especially interesting because of its moderate
tendency to form dust, with a condensation temperature of 1346 K (Lodders,
2003, fosterite formation) and a general depletion factor121212The depletion
factor of an element X is defined as
$[X_{gas}/H]\equiv\log(X/H)_{gas}-\log(X/H)_{\odot}$. that ranges from
$-$0.270 to $-$1.267 in the ISM, depending upon the line of sight (Jenkins,
2009). These values imply percent depletions of 46% to 95%.

The first observations of Mg emission in a PN were made by Grewing et al
(1978), who measured fluxes of Mg II $\lambda\lambda$2795, 2803 and [Mg V]
$\lambda$2783 in NGC 7027 using the IUE. A photoionization model analysis of
NGC 7027 by Péquignot, Aldrovandi, & Stasińska (1978), using published line
strengths for a range of elements including Mg from a number of sources, found
Mg/H=$3.5\times 10^{-5}$ ($-$0.06)131313The depletion factors corresponding to
the Mg abundances quoted in this paragraph are given in parentheses., a value
very close to Asplund et al. (2009)’s solar value of $3.98\times 10^{-5}$.
Followup work on NGC 7027 by Péquignot & Stasińska (1980) found a Mg negative
radial gradient across the nebula such that the gaseous Mg abundance in the
inner nebula exceeded that of the outer nebula abundance. The authors proposed
that Mg depletion into dust was more likely in the cooler outer nebular
regions where Mg II emission dominated, while Mg precipitated less in the
hotter region closer to the central star dominated by the [Mg V] emission.
Subsequent studies of Mg in PNe included work on IC 418 by Harrington et al.
(1980), Middlemass (1988), and Hyung, Aller, & Feibelman (1994) who found
Mg/H$=2.0\times 10^{-5}(-0.30),4.0\times 10^{-5}$ (+0.002), and $6.91\times
10^{-6}$ ($-$0.76), respectively. Likewise, Mg/H in IC 4997 was measured by
Middlemass (1988) to be $9.12\times 10^{-6}$ ($-$0.64), while Hyung & Aller
(1998) found a subsolar value of $2.0\times 10^{-6}$ ($-$1.30) for NGC 2440.
Finally, Wang & Liu (2007) observed Mg II $\lambda$4481 in six MW bulge PNe
and found the average Mg/H=$4.79\times 10^{-5}$ (+0.08), close to the solar
value of $3.98\times 10^{-5}$ (Asplund et al., 2009). Observationally, then,
Mg depletion in the PNe appears to range from 0% in NGC 7027 to 95% in NGC
2440.

####  3.2.4 Iron

According to Jenkins (2009) and Dwek (2016), the Fe depletion factor in the
ISM has a range of $-$0.951 to $-$2.236, corresponding to percentage
depletions of 89% to 99%, depending upon the line of sight. The Fe observed in
PNe was present in the interstellar material at the time of the formation of
the progenitor star and exists in the nebula in both gas and dust form.
Roughly 92% of Fe is 56Fe, which results from $\beta^{+}$ decay of 56Ni via
56Co to 56Fe. The original 56Ni is produced by explosive Si-burning in single
massive stars (Type II supernovae) or C ignition in a C-O white dwarf member
of a binary stellar system (Type Ia supernovae).

The Fe abundance is difficult to measure in emission nebulae because of its
weak lines due to heavy depletion onto dust. It was first measured in a PN by
Shields (1975), who used previously published optical line strength data to
determine Fe/H in NGC 7027 to be $7.94\times 10^{-7}$. The corresponding solar
value is $3.16\times 10^{-5}$ (Asplund et al., 2009), implying an Fe depletion
factor of $-$1.60 or a percentage depletion of 97%.

In a followup study, again using published data, Shields (1978) repeated
measurements of Fe/H in NGC 7027 and included five additional PNe, NGC 1535,
NGC 2022, NGC 6741, NGC 6886, and IC 2165. In the same year Garstang, Robb, &
Rountree (1978) used optical line strengths published by Kaler (1976) to
determine Fe/H in three PNe, NGC 6720, NGC 7009, and NGC 7662. Finally,
Perinotto et al. (1999) used their own observed optical line strengths to
measure Fe/H values and Fe depletion factors for NGC 7027, NGC 6543, Hu 2-1,
and Cn 3-1.

The numerical results for these three studies are presented in Table 5. Note
that except for the case of NGC 7009, each PN exhibited an Fe depletion of
more than an order of magnitude. In the case of NGC 7027, which was measured
twice by Shields and once by Perinotto, the depletions range from $-$1.51 to
$-$1.90 with an average of $-$1.70. Marked Fe depletion is seen consistently
in these 11 PNe.

More recently, Delgado-Inglada et al. (2009) measured Fe in 33 MW PNe. They
found a range in Fe/H of $3.09\times 10^{-6}$ to $1.86\times 10^{-8}$, a
median value for Fe/H of $7.08\times 10^{-7}$, and a median depletion value of
$-$1.65 or 98%.

Fe/H is an important quantity to determine in nebulae, as it can be compared
with stellar Fe/H measurements in order to contrast metallicities in these two
environments141414Usually nebular metallicity is determined using O/H, while
in stars, Fe/H serves the same purpose.. Alas, its marked depletion makes this
task difficult. But read on!

####  3.2.5 Zinc

As just discussed, estimating the Fe abundance in PNe is difficult because of
its large depletion factor. Zinc, however, is more volatile and has a
depletion factor range of $-$0.059 to $-$0.551 (Jenkins, 2009), corresponding
to depletions of 13% to 72%, respectively. In addition, Zn/Fe is found to
maintain very nearly its solar value of $1.15\times 10^{-3}$ (Asplund et al.,
2009) over the range of $-2\leq[Fe/H]\leq+0.5$ (Saito, Honda, & Takeda, 2009,
Fig. 3). Since stellar metallicities are usually represented by the Fe
abundance, knowing the Zn/Fe ratio and measuring the Zn abundance in PNe
allows a direct comparison to be made with the former.

The stable isotopes of zinc are 64Zn, 66Zn, 67Zn, and 68Zn, where the first
two represent nearly 77% of the total element abundance (Asplund et al.,
2009). These two isotopes can be formed via alpha freezeout following a core
collapse supernova event, explosive Si burning, or the s-process in massive
stars (Clayton, 2003). However, 64,66Zn are also at the beginning of the chain
of s-process elements and can be produced in observable quantities in AGB
stars (Karakas & Lugaro, 2010).

Dinerstein (2001) first identified [Zn IV] 3.625 $\mu$m as an emission feature
in two Galactic disk PNe, NGC 7027 and IC 5117. In the absence of any relevant
Zn collision strengths, accurate abundances could not be determined. However,
the authors concluded that, for reasonable assumptions about values of
collision strengths based on similar transitions in other elements, the Zn
abundance in these two objects is not enhanced.

Smith, Zijlstra, & Dinerstein (2014) measured the strength of the [Zn IV]
3.625 $\mu$m in nine PNe, five of which are located in the Galactic bulge.
With a collision strength now available, they computed Zn abundances and
concluded that Zn/H is subsolar in a majority of their sample objects. Three
years later Smith et al. (2017) observed six additional bulge PNe and updated
their observations of the nine objects observed in Smith, Zijlstra, &
Dinerstein (2014). Values of Zn/H abundance ratios were determined for all 15
objects. The median for both the disk and bulge samples was found to be
$Zn/H=2.00\times 10^{-8}$, a bit less than the solar value of $3.63\times
10^{-8}$(Asplund et al., 2009). They concluded that while Zn is generally
subsolar in both the disk and bulge PNe, their ratios of O/Zn were above solar
and indicated that O is enriched relative to Zn (Smith et al., 2017, Fig. 2).
More generally, if Zn abundances track those of Fe, the inverse correlation of
[O/Zn] vs. [Zn/H] shown in Smith et al.’s Fig. 2 is quite consistent with the
well established decrease of [O/Fe] with increasing [Fe/H] that is seen in the
solar neighborhood and elsewhere in the Galaxy. Kobayashi, Karakas, & Lugaro
(2020, Fig. 5) recently compared chemical evolution model results with
observations to show this behavior between [O/Fe] and [Fe/H], which is likely
due to the delayed contribution of Fe-peak elements to the Galactic
environment by SNIa. The striking similarity between the [O/Zn] vs. [Zn/H] and
[O/Fe] vs. [Fe/H] further supports the assumption that Zn and Fe abundances
change together in lockstep. The next step in research would seem to be to
compare Fe abundances in PNe, inferred from the constant Zn/Fe ratio, with Fe
measurements in central star atmospheres where available.

###  3.3 Extragalactic Planetary Nebula Elemental Abundance Studies

So far we have focused on chemical abundance work pertaining to the MW.
Analogous studies have also been carried out on at least 19 external galaxies.
Just within the Local Group, abundance characteristics of four galaxies, M31,
M33, and the Large and Small Magellanic Clouds have each been studied by
numerous research teams. Other Local Group members receiving less attention
include the spheroidals Fornax, M32, NGC 147, NGC185, NGC 205, and dwarf
spheroid Sagittarius dSph; a barred Magellanic spiral NGC 3109; barred
Magellanic irregulars NGC 4449 and NGC 6822; and Magellanic irregulars IC 10,
Sextans A, and Sextans B. Finally, abundance work on galaxies outside of the
Local Group includes the spirals M81 and NGC 300, as well as the lenticular
galaxy and strong radio emitter NGC 5128 (Centaurus A).

Tables 6A and 6B provide a summary of the important parameters of each
abundance study. For each paper listed in the table, the data were both
collected and analyzed by the authors themselves. The bold-print name of each
galaxy appearing in the center column is followed in square brackets by the
NED classification designation of galaxy type along with the associated T-type
index number, with morphology extending from elliptical through spiral to
irregular galaxies as T values increase. Columns 1-5 list the first author
name and year in a contracted format (see the table footnote for the
associated reference), the number of PNe with abundances reported in that
paper, the elements whose abundances were determined, the spectral range(s) of
the observations from which line strengths were determined, and the median
($\geq$3 objects), average (2 objects) or single (1 object) value of O/H in
the objects observed. Thus,O/H* is a statistical value derived from O/H values
for individual PNe within a single sample. Finally, Column 6 provides comments
where appropriate. As done previously, papers for each galaxy are listed in
order of earliest to latest.

We note that values in Column 5 of Tables 6A and 6B are meant to provide only
a rough gauge of the metallicity levels of the PN samples observed, using O/H*
as the metallicity indicator. Differences in O/H* among studies are partially
related to the measurement uncertainties associated with individual surveys.
Additionally, O/H variations among objects within a single survey may also be
due to the range in progenitor masses of the PNe comprising the survey.
Lastly, in the case of galaxy disk samples, the details of how the PNe are
spread out radially, vertically, and azimuthally in the potential presence of
gradients or any nonuniformity in element distributions over the disk will
also impact the value of O/H*.

Figure 8 is a plot of the logarithmic values of O/H* in Tables 6A and 6B
versus galactic morphological T-type. Individual galaxies listed in the tables
have corresponding color coded symbols defined in the legend, while each O/H*
value listed in the tables for a particular galaxy is shown. For reference
purposes, the crosses at T=4 show the log(O/H∗) values from Table 1 for the MW
disk. We note the trend toward lower metallicity with increasing T-type
between T=3 (the spiral galaxy M31) and T=10 (irregular and dSph galaxies),
although there are too few galaxies with T$<$3 to determine if this trend
extends to earlier objects. This apparent indirect correlation between
metallicity and galaxy type is likely related to the complex interactions of
total stellar mass, metallicity, and star formation history uniquely
associated with each galaxy.

###  3.4 Molecules in Planetary Nebulae

Molecules in both the gas and solid phases represent an important component of
both PPNe and PNe. As an example, in his recent review of molecules in PNe,
Zhang (2017) points out that more than 80 different molecules have been
observed in C-rich AGB envelopes and PPNe. Zhang also lists nearly 30
molecules that have been discovered in PNe alone (see his Table 1). These
molecules range from the simple and abundant two-atom species such as CO, OH,
and H2 to the complex fullerene molecules, C60 and C70. In addition, the
quantitative measurement of molecular mass in the circumstellar envelopes
related to PNe likely explains at least some of the difference between the
combined masses of the central star and ionized nebula and the presumed mass
of the main sequence progenitor star, the so-called “missing mass” (Kwok,
1994; Zhang, 2017).

Because of the significant mass loss that occurs during the AGB phase, a
circumstellar envelope forms and expands radially around the star. This
envelope material is cool enough and of sufficiently high density to permit
stable chemical bonding to occur between two or more atomic species. As a
result, molecules presently observed in PNe are primarily the result of the
chemical processing that occurs beginning with the AGB mass loss phase,
continuing through the intermediate PPN stage, but diminishing when the
central star becomes hot enough to photoionize the circumstellar material to
form the PN with its hotter environment. The post-AGB chemistry may also be
affected by the presence of an external ambient UV radiation field. Brief
reviews of the physics and chemistry of neutral gas in and around PNe are
provided by Dinerstein (1991), Hollenbach & Tielens (1997, §4.6), Kwok (2000,
Ch. 5), Van Winckel (2003), Hasegawa (2003), Bujarrabal (2006), and Zhang
(2017). And for readers in need of a refresher course in the astrochemistry
that is relevant to what follows, Kwok (2007) is a good source of information
concerning molecular orbitals, polycyclic aromatic hydrocarbons, and organic
compounds [see §§§7.3, 8.5, and 11.3, respectively in Kwok (2007)], while
Herbst & van Dishoeck (2009) present a detailed discussion of complex organic
molecules in the interstellar medium.

In the following discussion, we begin by focusing on the first two molecules
to be observed in PNe, CO and H2. After that, we briefly explore many of the
more complex molecules, evidence of which has been observed more recently.

####  3.4.1 CO

The first detection of a molecule in a PN was made by Mufson, Lyon, & Marionni
(1975), who detected 2.6mm emission from the J=1-0 transition of CO in NGC
7027, IC 418, and NGC 6543. The authors made note of the large volume of gas
containing CO and extending beyond the smaller ionized region in NGC 7027.
From this they speculated that the molecular gas was expelled by the PPN
central star as the PN was forming.

In a set of three papers, the team of P.J. Huggins and A.P. Healy measured the
more energetic J=2-1 CO transition at 1.3mm in NGC 7293 (Helix) (Huggins &
Healy, 1986a), NGC 2346 (Huggins & Healy, 1986b; Healy & Huggins, 1988) and
NGC 6720 (Ring) (Huggins & Healy, 1986b) to study the distribution and
kinematics of CO in these objects. For NGC 7293, the authors concluded that a
significant fraction of the matter lost by the stellar wind during the PPN
stage has not been ionized by the central star. Thus, roughly 10% of the
system’s total mass remains in the neutral state. Likewise, relative to its
total mass NGC 2346 has an estimated neutral mass of greater than 40%, while
the estimated neutral mass associated with NGC 6720 is 7% of its total mass.

Huggins & Healy (1989) carried out a survey of 100 Galactic PNe again at 1.3mm
and detected CO in 19 of the objects. The investigators noted that these PNe,
when compared to the 81 objects with no CO detections, appeared to have had
high-mass progenitors, based upon each PN’s relatively high N/O ratio and
strong preference for bipolar morphology. The 19 objects also exhibited a
range in mass of the molecular gas of 10-3 to 1 M⊙. In a second survey study,
Huggins et al. (1996) observed 91 Galactic PNe, 23 of which were found to
harbor CO (three of which they had studied previously).

Table 3 in Huggins et al. (1996) summarizes the observations of 44 PNe with
positive CO detections, where most of the objects were part of the two surveys
cited above while data for an additional few objects were taken from the
literature. The table lists, among other characteristics, the radius of the
ionized nebula, N/O, PN morphological type, total molecular mass Mm (inferred
from the CO mass), and the ratio of total molecular to ionized nebular mass
($M_{m}/M_{i}$). For the 44 PNe, the median value of Mm is 0.031 M⊙, with
minimum and maximum values of $4\times 10^{-4}$M⊙ (J900) and 0.79M⊙ (M1-16),
respectively. Values for $M_{m}/M_{i}$ are 0.47 (median) and $5.4\times
10^{-3}$ (NGC 7008; minimum), and 490 (CRL618; maximum). Thus, for PNe in
which CO is detected, there is a large range in Mm as well as $M_{m}/M_{i}$.

The most interesting finding in Huggins et al. (1996) is illustrated in their
Fig. 11, where a logarithmic plot of the molecular to ionized mass,
$M_{m}/M_{i}$, versus the radius of the ionized nebula (PN) clearly shows an
inverse relation for the objects in which CO is detected. The authors
attribute this correlation to the growth in size of the ionized nebula as
ionizing photons from the central star cause the CO to disassociate and atoms
to become ionized. In their view, this result supports the notion that the
matter comprising the PN was initially neutral and molecular in composition
but became dissociated and ionized by photons as the central star moved
horizontally left on the HR diagram as its temperature rose. The ionization
front moves outward radially at the expense of the molecular gas. Thus, the
inverse correlation between $M_{m}/M_{i}$ and nebular radius represents an
evolutionary sequence. As for those sample PNe in which CO is undetected, the
authors speculate that the molecular gas became rapidly photo-dissociated
either before or during the formation of the visible PN.

Finally, a few recent examples of CO observations of PNe can be found in Doan
et al. (2017), Guzman-Ramirez et al. (2018), and Andriantsaralaza, Zijlstra, &
Avison (2020). Doan et al. (2017) observed the AGB star $\pi^{1}$ Gruis,
confirming the system’s torus-bipolar structure as well as the mass, velocity,
and momentum of the outflow. Guzman-Ramirez et al. (2018) used ESO’s Atacama
Pathfinder Experiment (APEX) radio telescope facilities to survey 93 Galactic
PNe. They detected CO emission in 21 of the objects and measured the column
density and molecular mass in each of them. Andriantsaralaza, Zijlstra, &
Avison (2020) used ALMA to observe three isotopic forms of CO, 12CO, 13CO, and
18CO in the C1 knot of the Helix Nebula, NGC 7293. They determined the total
molecular mass of the globule to be $\approx 2\times 10^{-4}$ M⊙ (much greater
than previously published values) and the mass of the progenitor star to be 2
M⊙.

####  3.4.2 H2

Shortly after the initial observation of CO, H2 was first observed at 2 $\mu$m
in NGC 7027 by Treffers et al. (1976) and followed by H2 observations by
Beckwith, Persson, & Gatley (1978) in five additional PNe. Webster et al.
(1988) later observed H2 in 11 PNe, and concluded that PNe with strong,
excited H2 emission are Type I PNe (see §4.2.2) which also display a toroidal
morphology with faint bipolar extensions. H2 was observed in three PNe by
Zuckerman & Gatley (1988), whose conclusions supported those of Webster et al.
(1988) regarding morphology and spectral type. Further solid reinforcement of
the link among H2 emission, bipolar morphology, and the presence of a toroidal
disk came from the extensive study by Kastner et al. (1996), who searched
roughly 60 PNe and found 23 objects with the 2.122 $\mu$m emission feature.
These same objects also were observed to be located at low galactic latitude.
The authors concluded that the progenitors of the central stars were likely
relatively massive. Kastner et al. (1996) also speculated that instead of
fluorescence, shocks heated the gas to high temperatures and thus colllisional
excitation was more likely to be the excitation mechanism of the 2.122 $\mu$m
emission. Support for this idea was provided by Guerrero et al. (2000), who
presented H2 and Br$\gamma$ narrow band imaging in 15 bipolar PNe, finding a
strong correlation between shock-excitation and bipolar morphology.

Next, García-Hernández et al. (2002) for the first time extended H2 studies to
PN precursors, i.e., late AGBs, PPNe, and young PNe, finding results similar
to those of Kastner et al. (1996) and Guerrero et al. (2000) at earlier
stages, when H2 is shock excited rather than excited by fluorescence. Kelly &
Hrivnak (2005) followed up with a study of 51 PPNe, 16 of which were observed
to exhibit H2 emission. They found that H2 emission is predominantly
associated with bipolar nebulae located at low galactic latitudes. Rosado &
Arias (2003) inferred the total mass of H2 in five PNe, NGC 6720, NGC 6781,
NGC 3132, NGC 2346, and NGC 7048, from the observed mass of shocked H2 gas and
knowledge of initial density obtained from measured 2.12$\mu$m surface
brightness and shock velocities in each object. This was accomplished in each
case by establishing the pre-shock density of the molecular torus from the
observed 2.12$\mu$m surface brightness and shock velocity. In this way, Rosado
& Arias (2003) found a range of 0.1 to 0.8 M⊙ in total H2 mass. Their study
also implied that the major source of excitation of the 2.122 and 2.248 $\mu$m
lines is shock heating. Support for this conclusion was later provided by the
observations by Likkel et al. (2006) of H2 emission in eight PNe, where a few
of their objects displayed H2 line ratios characteristic of shock excitation.

More recent work on H2 in PNe has helped to refine our view of the location
and nature of the molecular hydrogen observed in PNe. Examples of studies that
have been carried out along this line include those by Marquez-Lugo et al.
(2013), Manchado et al. (2015), Akras, Gonçalves, & Ramos-Larios (2017), and
Akras et al. (2020). Using 8$\mu$m images of H2 emission in PNe, Marquez-Lugo
et al. (2013) showed that such emission is not produced exclusively in bipolar
PNe, as had been previously assumed, but can also be associated with
ellipsoidal/barrel PNe. Manchado et al. (2015) used highly resolved H2 images
in the IR of the PN NGC 2346 to show that the H2 gas is composed of knots and
filaments. They speculated that thermal pressure of the ionized gas resulted
in fragmentation of the swept-up shell as the system expands. Akras,
Gonçalves, & Ramos-Larios (2017) employed high resolution images in H2 2.122
and 2.248$\mu$m of two PNe, K 4-47 and NGC 7662, to study low-ionization knots
(internal structures in PNe are discussed in §7.2.1). Their results confirmed
the presence of H2 gas in both fast and slow-moving knots and suggested that
low-ionization structures in PNe are characteristically similar to
photodissociation regions. In their most recent paper on low-ionization
structures, Akras et al. (2020) again employed 2$\mu$m observations of H2 to
study NGC 7009 and NGC 6543. In comparing their own observations and similar
ones found in the literature with extant shock and UV excitation models of H2
emission, the authors were unable to decide definitively which mechanism is
most relevant.

####  3.4.3 Additional Molecules

Evolution of the molecular composition of PNe was the subject of a paper by
Bachiller et al. (1997), who found that molecular abundances in the
circumstellar envelope are altered considerably between the AGB and PN stages.
The same study indicated that as PNe themselves evolve, molecular abundances
remain relatively constant. This latter point was supported by Edwards, Cox, &
Ziurys (2014), who measured abundances of CO, CS, and HCO+ in five PNe
spanning the ages of 900-10,000 years and found the abundances of each of
these molecules tend to be largely constant over time. An additional
correlation with implications for linking molecular chemistry with central
star properties is the discovery by Bublitz et al. (2019, their Fig. 15) that
the HNC/HCN abundance ratio decreases as the UV luminosity of the central star
increases, in a power law relation characterized by a slope of -0.363 and a
correlation coefficient of -0.885.

In a recent conference review paper, Schmidt & Ziurys (2018) presented results
from their decade-long work to detect PN emission of numerous molecules
besides CO and H2. Detections of one or more simple organic compounds were
made in 14 of the 17 objects observed. They concluded that: 1) polyatomic
molecules are observed in PNe of various ages and morphologies; 2) abundances
of the molecules measured appear not to vary with PN age (see their Fig. 2);
and 3) molecules in PNe are located in dense clumps where photodissociation is
minimal due to shielding by dust.

Two of the most interesting molecules found in PNe are C60 and C70, the
largest and most stable molecules ever detected in space. The first
observation of these species was made by Cami et al. (2010), who employed the
IRS aboard the Spitzer Space Telescope in a study of the PN Tc 1, where the
abundance ratio C/O$\approx$3.2. The authors observed what appeared to be a
complete absence of H-containing aliphatic (open chain) molecules such as HCN
and C2H2, as well as polycyclic aromatic hydrocarbons (PAH), i.e., molecules
built around one or more benzene rings. From this they suggested that
fullerene formation requires an H-free environment, a rather rare situation in
PNe.

This picture was challenged by García-Hernández et al. (2010), who showed that
fullerenes are observed in PNe with normal H abundances together with other
H-rich species like PAHs, and suggested the top-down photochemical processing
of hydrogenated amorphous (no crystalline structure) carbon (HAC) dust grains
for fullerene formation. These results were confirmed by IR observations of
more numerous PNe samples [García-Hernández et al. (2011, 2012a), Otsuka et
al. (2014)] and other types of objects (see e.g., García-Hernández (2012b) for
a review). For example, in García-Hernández et al. (2012a) the authors
compiled a total of 263 PNe observed by Spitzer/IRS. Out of this sample, the
16 PNe found to display fullerene spectral features were analyzed in order to
discover the kinds of environments which are favorable for the formation of
these molecules and from what materials do they form. They concluded that
fullerene detection in PNe increases with decreasing metallicity and that
fullerenes (along with PAH and aliphatic species) most likely form from a
carbonaceous compound that is a mixture of aromatic and aliphatic structures
(HAC-like), where the chemical processing is driven by UV radiation from the
hot central star and/or post-AGB shocks (see also Micelotta et al., 2012).
This finding is in agreement with predictions based upon laboratory results
published earlier by Scott, Duley, & Pinho (1997). Interestingly, the idea of
HAC-like starting materials would be consistent with the efficient formation
of non-aromatic carbonaceous molecules in circumstellar environments as
evidenced by recent top-level experiments (Martínez et al., 2020). However,
other starting materials for top-down fullerene formation have been proposed
in the literature; e.g., the photochemical processing of large PAHs (Berné &
Tielens, 2012) or shock heating and ion bombardment of SiC grains (Bernal et
al., 2019), among others. C60 and C70 fullerenes may be just the tip of the
iceberg, and many other fullerene derivatives (see e.g., Omont, 2016) are
potentially present in PNe environments.

Finally, in a more speculative vein, the presence of fullerenes in PNe suggest
that molecules suspected of being precursors of C60,70 might also be
observable. One such candidate is graphene, C24. [An example of a proposed
mechanism for forming fullerene from graphene was suggested by Chuvilin et al.
(2010).] García-Hernández et al. (2011, 2012a) observed IR emission features
located at 6.6, 9.8, and 20$\mu$m in five PNe in the Magellanic Clouds as well
as in the Galactic PN K 3-24. These three transitions correspond to the
strongest ones associated with C24 that were previously predicted from theory
by Kuzmin & Duley (2011), implying the presence of graphene in these six PNe.
Recently, Li, Li, & Jiang (2019) have inferred an upper limit of graphene
abundance in the ISM of 20 ppm, based upon the absence of a 2755 Å graphene
absorption feature in the interstellar extinction curve. Thus, the presence of
graphene in PNe and the ISM remains uncertain.

So for the final exam, what are the main points to know about molecules in
PNe? They are: 1) PNe with detectable CO and H2 appear to have relatively
massive progenitors and tend to possess a bipolar morphology; 2) the ratio of
molecular to ionized gas mass is inversely proportional to the radius of the
ionized region (the PN); 3) although the abundances of a variety of molecules
relative to H2 change with respect to each other during the PPN stage, they
tend to remain constant after PN formation; and 4) fullerenes in PNe form top-
down through a still unknown starting material and a rich family of fullerene
derivatives is likely present.

###  3.5 Dust in Planetary Nebulae

Early recognition of the possibility that PNe harbor dust came from IR
photometric studies by Gillette, Low, & Stein (1967); Gillette, Merrill, &
Stein (1972), Persson & Frogel (1973), and Willner (1972) that showed the
presence of IR excess beyond what was estimated to have come from atomic
processes. Several years later, Moseley (1980) observed 13 PNe in the far-IR
(37-108 $\mu$m) and concluded that all but one object (IC 418) have roughly
the same dust masses. Natta & Panagia (1981) then employed the IR data from
Moseley (1980) to show that the dust/gas ratio, grain size, and internal
optical depth decreased with increasing values of nebular radius relative to
that of NGC 7027. The authors speculated that these trends were the result of:
1) an inhomogeneous distribution of nebular dust resulting from an increase in
the concentration of dust as the AGB stellar mass loss progressed; or 2) the
partial destruction of grains over time. Finally, an estimation of the total
PN contribution of interstellar dust to the Galactic ISM of
10-6M${}_{\odot}yr^{-1}$ was made by Gehrz (1989). Such were the results of
the early explorations of dust in PNe. More general discussions and reviews of
dust in PNe may be found in Kwok (2000, Chapter 6), Kwok (2007, Chapters
10-13), Gail & Sedlmayr (2014), Kwitter et al. (2014, §9), and García-
Hernández (2015). For the following discussion, we employ the notation for the
various dust types used by García-Hernández & Górny (2014), namely,
Featureless (F), C-rich (CC), O-rich (OC) and mixed dust or dual-dust (DC).

Dust studies of relatively large samples of PNe have been carried out by
Stanghellini et al. (2007, 2012), Bernard-Salas et al. (2009), García-
Hernández & Górny (2014), and García-Hernández (2015). Stanghellini et al.
(2007) used the Spitzer Space Telescope with its IR spectrograph between 5-40
$\mu$m to observe 41 PNe, 25 located in the LMC and 16 located in the SMC.
Twenty of their sample objects (9 in the LMC and 11 in the SMC) possessed
broad CC dust features, three displayed broad OC features, and the remaining
18 PNe lacked broad dust features altogether. For each PN, the authors then
compared the inferred dust type with its previously published C/O value as
determined from collisionally excited lines. They found that C/O$>$1 for
objects with CC dust and C/O$<$1 for objects with OC dust. The latter case was
attributed to the effects of HBB, with its associated conversion of C to N via
the CNO cycle. The authors also found that their CC PNe were all
morphologically symmetric, while the OC objects appeared highly asymmetric
with a tendency toward harboring more massive central stars. In a later and
much larger dust study of 150 Galactic bulge and disk PNe, Stanghellini et al.
(2012) found the relative population by dust type to be 17% F, 25% CC, 30% OC,
and 28% DC. Furthermore, the CC group was found to comprise two molecular
types, i.e., aromatic and aliphatic, while the OC group was split into two
structural groups, i.e., crystalline and amorphous.They found that: 1) DC PNe
favor locations closer to the Galactic center; 2) aliphatic chemistry was
favored in CC PNe, while amorphous structure was preferred in OC PNe; 3)
Nebular radii of CC PNe scaled inversely with both dust temperature and IR
luminosity; and 4) CC PNe significantly outnumber OC PNe in the Magellanic
Clouds in contrast to their relative populations in the Galaxy. This last
point is likely the result of both the greater efficiency of TDU and the
heightened effectiveness of increasing the C/O ratio at the low metallicities.

Bernard-Salas et al. (2009) performed a low resolution spectroscopic study of
dust features of 18 LMC and 7 SMC PNe using the Spitzer Space Telescope. PAH
emission features, appearing at 6.2, 7.7, 8.6, and 11.2 $\mu$m were seen in 14
of the PNe151515C-rich PAH molecules in gaseous form are often present in CC
environments, and the former are usually taken as evidence of the presence of
the latter. However, Cohen & Barlow (2005) observed the 7.7 $\mu$m feature of
PAH in NGC 6302 and Hu 2-1, two objects in which C/O was found to be 0.31 and
0.48, respectively. In addition, Guzman-Ramirez et al. (2011) studied 40
Galactic bulge PNe and found DC dust chemistry and evidence of PAH in 30
objects. They concluded that the DC chemistry is related to hydrocarbon
chemistry occurring in the presence of UV radiation within dense tori.
Therefore, the link between PAH and CC dust chemistry is not absolute., while
nine PNe displayed broad SiC and MgS emission at 11 and 25 $\mu$m,
respectively. All of these features are indicative of a CC environment. At the
same time, the authors detected amorphous silicate emission, usually
associated with an OC environment, in only two of their sample objects. Again,
as found by Stanghellini et al. (2012), the CC environment appears to be
favored at the low metallicity that is characteristic of the Magellanic
Clouds.

García-Hernández & Górny (2014) presented a sample of 131 Galactic bulge and
disk PNe for which both optical and IR spectroscopic data were available. The
authors used Spitzer IR spectral data from Gutenkunst et al. (2008), Perea-
Calderón et al. (2009), and Stanghellini et al. (2012), coupled with optical
spectrophotometric data of their own or critically chosen from the literature,
to determine dust type and gas phase chemical abundances for each PN in order
to explore how the two properties are connected.

Fig. 9 is a column plot of data contained in Table 5 of García-Hernández &
Górny (2014) showing the percentage of the total number of bulge or disk PNe
that belong to the indicated dust types. We can see that while the bulge and
disk exhibit roughly the same proportions of F and OC PNe, the disk has a
significantly greater proportion of CC PNe and a much smaller proportion of DC
PNe. In fact, roughly half of the bulge PNe belong in the DC category. For
further comparison, we have added data from Table 6 of Stanghellini et al.
(2012) for the Magellanic Clouds. In this case we can see that roughly half of
the PN sample belong to the CC group, two-fifths to the F group, and only a
relatively small number in OC group.

Values from García-Hernández & Górny (2014) listed here in Table 7 link the
median gas phase abundances of He, N/O, and Ar/H to the four dust types for
both the Galactic bulge and disk PNe, where Ar/H is taken by the authors as
the metallicity indicator. For comparison, solar abundances from Asplund et
al. (2009) are provided in the last row of the table. The values in Table 7
indicate clearly that in both the bulge and disk: 1) the He/H ratio in PNe of
all dust types is about 25% greater than the solar value; 2) the ratio of N/O
is significantly greater in DC PNe than in the other three dust types; and 3)
the metallicities of DC PNe are markedly greater than the levels seen in both
CC and OC PNe. Regarding alpha elements other than Ar, Figs. 8 and 9 in
García-Hernández & Górny (2014) show that in both the bulge and disk, Ne and S
abundances in OC and DC objects appear to increase in lockstep with O as is
observed in HII regions. But curiously, in the case of CC PNe, the S
abundances are consistently below what is expected from their O abundances.
This is perhaps related to the sulfur anomaly described in (Henry et al.,
2012), although it is interesting that the effect seems to be limited to CC
PNe.

García-Hernández & Górny (2014) also compared their median abundances for each
of the several dust types with published stellar evolution models by Karakas
(2010). Given that DC PNe are observed to have solar or supersolar
metallicities and elevated N/O values, the authors concluded that DC PNe
likely had relatively massive progenitor stars ($>$3-5 M⊙) that experienced
HBB during the AGB phase of their evolution. On the other hand, CC and OC PNe
with unevolved (amorphous and aliphatic) dust tend to have subsolar
metallicities and significantly lower N/O values, and are likely descended
from progenitor stars having masses of less than 3 M⊙. However, in a
subsequent study of a small subsample of DC PNe for which C/O ratios from
faint optical recombination lines161616Delgado-Inglada & Rodríguez (2014)
present a comparison of C/O ratios determined from both collisionally excited
lines and optical recombination lines. They find that the agreement is
generally good but caution that in some objects the difference is large. could
be measured, García-Rojas et al. (2018) showed that updated AGB nucleosythesis
predictions could explain abundances in some DC objects with progenitor masses
of $\leq$ 1.5 M⊙, suggesting that DC PNe are not necessarily associated
exclusively with massive progenitors.

Finally, although each element’s total relative abundance is conserved
throughout the evolution of the post-AGB nebula, the form in which the element
exists, i.e., ion, atom, or molecule (gas or solid, including dust), changes
as local conditions such as temperature, density, and the presence of UV
radiation change. Therefore, when considering elemental abundance measurements
that are most commonly made by analyzing spectra of the ionized gas in a PN,
we need to be aware of how the elements are partitioned in the different
phases. For example, how much carbon is actually tied up in molecules and dust
grains instead of the observable ionic and atomic stages?

Alas, this is a difficult question to answer. According to García-Hernández
(2021), a complete knowledge of the full inventory of the molecular and dust
species in PNe or their immediate AGB or post-AGB precursor stages is
presently unknown, in spite of having identified a few molecules convincingly
in the optical, infrared, and radio domains [see e.g., Table 1 in Zhang
(2017)]. In addition, instead of definitive identifications of species from
which spectral features arise, researchers in this area mostly have candidate
carrier species for the several dust features seen in CC PNe (e.g., SiC, MgS,
HAC, or even mixed aromatic-aliphatic species with O, N, and S impurities) and
OC PNe (e.g., amorphous/crystalline silicates with different Fe, Si, and Mg
content). As an example, Volk, Sloan, & Kraemer (2020) have recently reviewed
the problems and ambiguities encountered when attempting to definitively match
carriers to the solid state spectral features located at 30 $\mu$m and 21
$\mu$m in C-rich objects. According to these authors, the 30 $\mu$m feature is
usually aligned with MgS, although they provide reasons to doubt that
association, most notably a debate about whether there is enough MgS to
explain the measured intensity. Even less certain is the feature at 21 $\mu$m,
as its detection in PNe is “tentative at best” according to the authors. Thus,
for these several reasons, the prospect of making a significant step forward
in the near future regarding how elements are partitioned among the several
physical phases is unlikely.

However, in the absence of positive spectroscopic identifications of molecular
and dust species, one possible path around this problem is illustrated in the
recent analysis by Gómez-Llanos et al. (2018) [see also Otsuka et al. (2017)]
of the PN IC 418. This team developed a detailed photoionization model of both
the ionized and photodissociated regions of the PN by varying the dust types,
amounts and distributions relative to the distance to the central star. They
were able to match the observed IR emission spectrum from 2-200 $\mu$m by
using graphite, amorphous carbon, MgS, and SiC as dust ingredients. Their
model results showed that refractory elements such as Mg, Si, and S were
noticeably depleted from the gas phase, while C, N, O, and Ne remained
undepleted. Such models enable estimates of the amount of depletion of an
element, an amount which can then be added to the observed gas phase abundance
in order to estimate the total elemental abundance in the system.

So what have we learned about dust in PNe to date? Substantial progress has
been made over the past 15 years in identifying specific dust species as well
as in understanding the nature of dust in PNe, thanks in large part to the
availability of quality IR spectrophotometric data obtained by the Spitzer
Space Telescope. Observed dust features in the IR coupled with nebular gas
abundance studies, mostly in the optical and UV, suggest that dust chemistry
is largely determined by the value of the C/O abundance ratio within the
environment in which the dust forms. For example, C-rich dust probably forms
when C/O$>$1\. Such a rich C environment is likely the result of TDU, in which
C is transported from the AGB’s He-burning shell into the stellar atmosphere
and ultimately ejected. On the other hand, an O-rich environment can result
either when the progenitor star is not massive enough for TDU to occur, or in
the case of massive progenitors, TDU does occur but HBB converts the C to N.
Challenges remain before we can claim a thorough understanding of dust in PNe.
As already pointed out, we cannot yet confidently identify the carriers of
many observed dust features. In addition, without knowledge of the relative
masses of dust and gas in a PN system we cannot uncover details of dust
production through modeling. Such a condition leaves room for numerous PhD
theses in the future!

##  4 What Can We Glean From PN Abundance Studies?

It is now time to ask what the outcomes of the numerous PN abundance studies
reviewed above can teach us about both stellar and galactic chemical
evolution. In §4.1 we consider how disk PN abundances, when combined with
their galactocentric distances, can shed light on disk formation. Then in §4.2
we compare elemental abundance information from §3 with stellar evolution
model predictions in an attempt to learn about stellar nucleosynthesis.

###  4.1 Disk Galaxy Abundance Gradients from Planetary Nebula Abundances

Measurements of chemical abundances in H II regions, PNe, Cepheids, and open
clusters in the disk of the MW and other galaxies indicate that the
metallicity generally decreases with increasing radial distance from the
center of a galaxy. Recent reviews regarding abundance gradients in galaxies
include those by García-Rojas (2018) & Maciel & Andrievsky (2019). Chemical
evolution models of disk galaxies strongly indicate that the slope of an
abundance gradient is closely tied to the temporal and spatial variation of
the infall rate of external gas, the star formation efficiency, and radial gas
flows [(Fu et al., 2009; Marcon-Uchida, Matteucci, & Costa, 2010; Spitoni &
Matteucci, 2011; Grisoni, Spitoni, & Matteucci, 2018)]. Even slope differences
of the order of a few hundredths of a dex/kpc can readily distinguish between
models with different input parameter values.

PNe play an important role in ascertaining the abundance gradient slope in
galactic disks, as they are visible at large distances and the abundance
determination process is relatively straightforward. The chemical composition
of a PN is determined by the local conditions at the time of progenitor star
formation as well as the contribution of nuclear products synthesized by the
star during its lifetime. These two factors must be kept in mind, for example,
when using abundance gradients based upon PNe to constrain chemical evolution
models.

####  4.1.1 The Milky Way Gradient

Examples of PN gradient studies that have been carried out for the MW disk
include those by Maciel & Köppen (1994); Maciel & Quireza (1999), Henry et al.
(2010), Maciel, Costa, & Cavichia (2015), and Stanghellini & Haywood (2018).
What follows is a brief summary of the three most recent papers concerning the
MW gradient.

Henry et al. (2010): The PN sample containing both Peimbert Types I and II
objects171717Peimbert Types are defined in §4.2 as part of the discussion of
Fig. 11. employed in this study comprised 124 PNe whose galactocentric
distances $R_{g}$ were derived from heliocentric distances published by Cahn
et al. (1992) and Stanghellini et al. (2008, SSV) and ranged from 0.9-21 kpc,
assuming a solar distance of 8.5 kpc. The O/H values came entirely from the
authors’ own observations and computations. Using the Cahn et al. distances,
they computed a gradient for 12+log(O/H) versus $R_{g}$ by also considering
the uncertainties in both distance and abundance and found a value of
$-0.058\pm.006$ dex/kpc, with a correlation coefficient of $r=-0.54$. A second
regression using the SSV distances resulted in a flatter gradient of
$-0.042\pm.004$ dex/kpc. In addition, no correlation was found between O/H and
vertical height from the Galactic plane.

Maciel, Costa, & Cavichia (2015): These authors combined their own O/H
abundance data (Maciel & Costa, 2013) with like measurements from Stanghellini
& Haywood (2010a) to form a PN sample of 263 objects. Object distances were
determined using the SSV distance scale, assuming a solar distance of 8.0 kpc.
Objects in the combined sample had a range of $<1$ to roughly 15 kpc
(estimated from their Fig. 2). They obtained a gradient value of
$-0.025\pm.004$ dex/kpc and a correlation coefficient of $r=-0.357$. An
additional study was made in order to check for a correlation between O/H
abundance and vertical distance from the Galactic plane. By dividing their
sample into two groups having either $Z\leq 1000$ pc or $Z\geq 1000$ pc, the
authors computed a linear fit to each group and then compared their intercept
and slope values. The group closer to the plane had a 12+log(O/H) intercept
value roughly 0.17 dex (47%) greater and a gradient that was steeper by -0.007
dex/kpc than the respective values for the more distant group.

Stanghellini & Haywood (2018): This recent abundance study of disk PNe in the
MW included abundances of He, N, O, Ne, and Ar. The sample for PN O/H
measurements comprised 248 disk objects carefully selected from high quality
observational results published by numerous authors. Radial distances were
determined using the SSV distances and ranged from less than 1 kpc to roughly
28 kpc. A linear fit that included uncertainty considerations for both
distance and O/H yielded a gradient of $-0.021\pm.008$ dex/kpc181818An attempt
to understand the cause of the slope differences among the Henry et al.
(2010), Maciel, Costa, & Cavichia (2015), and Stanghellini & Haywood (2018)
gradients proved unsuccessful.. Two groups were then formed from their
complete sample, one comprising PNe with progenitor stars younger than 1 Gyr
and the other with progenitor stars older than 7.5 Gyr, as determined by
comparing abundances with stellar model predictions of final surface
abundances. The younger group was found to have a gradient of -0.027 dex/kpc,
while the older group’s gradient was -0.015 dex/kpc, i.e., shallower than that
of the younger group. The authors also found that the radial gradient 1)
becomes flatter between distances of 10 and 13.5 kpc; and 2) is steeper near
the disk plane compared with its value at greater vertical distances, in
qualitative agreement with Maciel, Costa, & Cavichia (2015).

####  4.1.2 Metallicity Gradients in External Galaxies

Gradients of O/H, Ne/H, and Ar/H have been measured using PNe in the disks of
M31, M33, NGC 300, and M81. The gradient in M31 has been recently studied by
Kwitter et al. (2012), Balick et al. (2013), and Sanders et al. (2012).
Magrini et al. (2004); Magrini, Stanghellini, & Villaver (2009b); Magrini et
al. (2010), Stasińska et al. (2005), and Bresolin et al. (2010) have similarly
studied M33, while Stasińska et al. (2013) and Stanghellini et al. (2010b)
have determined gradients for NGC 300 and M81, respectively.

The results for M31, M33, and NGC 300, along with the MW, have recently been
reviewed by Peña & Flores-Durán (2019). In their paper, required abundances
were collected from the numerous extant literature sources, where in most
cases the abundances were computed using relevant electron temperatures, i.e.,
the direct method. Separate from the analysis by Peña & Flores-Durán (2019),
Stanghellini et al. (2010b) used their own optical spectra to determine
abundance gradients of O/H, Ne/H, and S/H in M81. The results of these two
studies are presented in Table 8, where gradient values pertaining to combined
samples of Type I and non-Type I PNe are provided. Note that each gradient has
been normalized to the relevant photometric radius, $R_{25}$191919R25 is the
radial distance at which the blue surface brightness (mB) falls to 25 mag per
arcsec2., to allow a direct comparison among galaxies possessing different
disk radii.Here we can appreciate especially the relative flatness of the M31
gradients with respect to those gradients of the remaining four galaxies,
while M81 possesses by far the steepest gradients. Balick et al. (2013) have
suggested that M31’s flat gradient is the result of a starburst that occurred
roughly 2 Gyr ago in a metal-rich ISM in the outskirts of the disk following
an encounter with M33 approximately 3 Gyr ago. Given the reported
uncertainties, we also see relatively close agreement among the O/H, Ne/H, and
Ar/H gradients of any one galaxy; this is likely a reflection of the well
known lockstep behavior of alpha elements that is consistently seen in PN
abundance studies and is discussed in §4.2.1 below.

####  4.1.3 Does Oxygen Really Track Metallicity?

An interesting wrinkle in the abundance gradient picture produced by PNe that
has slowly developed over the past two decades involves the reliability of
using the O/H ratio as a measure of metallicity. Péquignot et al. (2000)
studied two PNe in the metal-poor Sagittarius dwarf galaxy and found that
values of Ne/O, S/O, and Ar/O were smaller than the corresponding values found
in the MW. The authors suggested that He burning followed by TDU in low mass
stars ($M<2M_{\odot}$) might produce an elevation of both 12C and 16O in the
PNe that eventually form. Then Wang & Liu (2008) compiled published data for
both PNe and H II regions in the MW and several external galaxies and reported
that in metal-poor galaxies (Z$<$0.004) both Ne/H and O/H were enhanced in
PNe, which they ascribed to synthesis of these two elements by LIMS.

Delgado-Inglada et al. (2015) chose 20 Galactic PNe located in the halo, bulge
and disk, all falling within $\pm$0.25 dex of the solar oxygen abundance and
for which both optical and IR data were available. They then divided the
sample into two groups, i.e., those possessing CC dust and those with OC dust,
and plotted log values of O/Cl versus O/H. In contrast to the PNe that were
associated with OC dust (as well as a small sample of H II regions also
included in the study) seven of the eight PNe with CC dust were offset as a
group from the other objects, exhibiting greater O/Cl values (see their Fig.
3), thereby supporting the conclusion of Péquignot et al. (2000) mentioned
above. Since another of their plots indicated strict lockstep behavior between
Ar and Cl, the authors suggested that either of these two elements (they
preferred Cl) should be used instead of O to gauge metallicity in PNe.

So what does stellar evolution theory have to say about this matter? As
pointed out by García-Rojas (2020), AGB stars can synthesize O via He burning
and TDU or via HBB and the CNO cycle. For example, the stellar evolution
models of Pignatari et al. (2016) include convective boundary mixing or
overshooting to move He shell burning products 12C and 16O into the He-rich
intershell region and ultimately into the outer atmosphere. They found that
the final O mass fraction in the outer envelope of stars of mass 2-3 M⊙
becomes roughly twice what it was in the original material that formed the
progenitor star. The key to enhanced O here seems to be the inclusion of
overshooting in the models at the boundary between the He-burning shell and
He-rich intershell above it. In addition, results of stellar evolution models
by Ventura et al. (2017) indicated that when Z$<$0.004, HBB in massive stars
destroys oxygen, while TDU in low mass stars causes an increase in oxygen. On
the other hand, when Z$>$0.004, O/H in AGB stars shows a tight correlation
with metallicity. Thus, at low metallicities, O/H may not be a reliable
indicator of stellar metallicity. This is a problem which is sure to receive
much more attention in the future.

###  4.2 Measured Elemental Abundances of Planetary Nebula versus Theoretical
Predictions

The principal nucleosynthetic products of LIMS are He, C, N, F, and numerous
s-process elements. Thus, the abundance measurements of these elements in PNe,
as described in §3, serve as valuable constraints on LIMS models that make
predictions of element levels in the nebular gas. At the same time, while O
and perhaps Ne may be synthesized in low-metallicity AGB stars during He-
burning and brought to the surface by TDU (see §4.1.3), generally speaking,
the abundances of alpha elements O, Ne, S, Cl, and Ar observed in PNe reflect
the amounts that were originally present in the star-forming gas of the
progenitor star. This abundance dichotomy allows PNe to play a second role,
that of establishing the metallicity of the ISM at the time and location of
the formation of PN progenitor stars. We shall address these two features in
reverse order.

####  4.2.1 Planetary Nebula Abundances As Tests of Alpha Element Lockstep
Behavior

In §3.2.4, we briefly described the difficulty of using Fe, the usual
indicator of metallicity in stars, to establish metallicity in nebulae such as
PNe. On the other hand, gauging metallicity in PNe is customarily done by
measuring abundances of O (usually) or other alpha elements such as Ne, S, Cl,
or Ar. Since the bulk of these elements is mostly synthesized via He burning
in massive stars and expelled during Type II supernova events, their
interstellar abundances are expected to increase in lockstep.

A direct method for exploring this lockstep behavior using PNe is to form
element-versus-element plots of alpha element abundances determined for a
large survey and then to look for strong linear correlations between element
pairs. Observed abundance data from KH20 are shown with open circles in Figure
10 for Ne/H, S/H, Cl/H, and Ar/H versus O/H, where we have used the standard
logarithmic form of 12+log(X/H) and X and H are number abundances. The error
bars in the lower right corner of each panel indicate the average uncertainty
expressed logarithmically. We also show least-squares fits in each panel,
where the solid line represents the fit to the PN data. In the cases of Ne, S,
and Ar, the dashed line shows the fit to a collection of published abundances
for H II regions and blue compact galaxies (H2BCG) compiled by Milingo et al.
(2010, Table 6). The analogous fit for Cl was inferred from a study of
Galactic disk H II regions by Esteban, García-Rojas, & Pérez-Mesa (2015).
Table 9 displays the regression parameters and uncertainties, i.e.,
y-intercept, slope, correlation coefficient, and number of sample objects
considered for each line. The lockstep behavior of alpha elements O, Ne, S,
Cl, and Ar in the ISM, as probed by the H2BCG, is clearly demonstrated by the
near-unity slope values and correlation coefficients. The PN results are a bit
messier (no pun intended!), although with the exception of Ne/H, the slopes
are strongly suggestive of lockstep behavior. The larger amount of scatter
demonstrated by the PNe for all the alpha elements may be due in part to the
generally higher levels of ionization within the gas, which can complicate
corrections for unobserved ions when determining total elemental abundances. A
different explanation may be that one or more of the original alpha element
abundances at the time of star formation were subsequently altered by
nucleosynthetic processes within the star during its lifetime as just
discussed in §4.1.3.

Another way of using PNe to confirm the direct abundance relation among alpha
elements is to compare the slopes of abundance gradients of these elements in
galactic disks, where PNe that are positioned over a wide range of
galactocentric distances are used as abundance probes. Using this method, good
agreement among gradient values for O/H, Ne/H, and Ar/H has been illustrated
by Bresolin et al. (2010) for PNe in the disk of M33 and by Stanghellini &
Haywood (2018) for Galactic disk PNe. Similarities of alpha element gradient
slopes in galactic disks are also predicted by chemical evolution models such
as those published by Chiappini, Matteucci, & Gratton (1997).

To summarize, with the possible exception of low metallicity regimes (Miller
Bertolami, 2021), alpha element abundances appear to evolve in lockstep in the
ISM, a pattern which is then observed in PNe that form from that gas.

####  4.2.2 Gauging LIMS Nucleosynthesis With Planetary Nebulae

We now consider elements which are synthesized by LIMS during their lifetime
and subsequently ejected into the ISM. Stellar models predict both the total
contribution of such elements to the local environment over the star’s
lifetime, i.e., the yield, as well as the abundances of these elements in the
stellar envelope (surface abundances) just prior to ejection and subsequent PN
formation. A comparison of PN abundance measurements with predicted surface
abundances serves as a constraint on the stellar models. A successful model
then not only implies the progenitor star’s mass and element yields, but it
also helps to confirm the role of the physical processes that were part of the
model calculation. Therefore, the back and forth comparison of models and PN
abundance observations teaches us much about the contributions that LIMS make
to the chemical evolution of galaxies. (See Appendix B for a list of
publications of model-predicted stellar yields and surface abundances of
LIMS.)

In this subsection we present and discuss plots of observed values of He/H,
C/O, and N/O in MW disk PNe. Following that, we compare the observations with
updated predictions of the final AGB surface abundances made by the same four
codes featured and compared in detail in Henry et al. (2018), i.e., MONASH
[Karakas & Lugaro (2016); Karakas et al. (2018)], LPCODE (Miller Bertolami,
2016), ATON [Ventura et al; (2020) and Marini et al. (2021)], and FRUITY
[Cristallo et al. (2011); Piersanti, Cristallo, & Straniero (2013); Cristallo
et al. (2015, 2016)].

Observed abundance ratios of He/H, C/O, and N/O for the MW disk PNe contained
in KH20 are displayed with circles in each of the panels of Figs. 11 and 12.
In the upper panels of Fig. 11 filled circles represent objects whose C
abundances were strictly based upon UV data (C III] 1909Å and C IV 1549Å),
while open circles indicate those objects where only optical data (C II 4267Å)
were used instead because UV data were unavailable. The sample error bars in
the left-most panels show median values of the observational uncertainties. In
the bottom panels, the upper right quadrant marked off by a pair of dashed
lines shows the region occupied by Type I PNe. This classification was
originally introduced by Peimbert (1978), who noted that objects in this group
had noticeably enhanced abundances of He and N, favored bipolar morphology,
and resided in the MW disk202020Peimbert (1978) also defined types II, III,
and IV for PNe characterized by intermediate population, high velocity, and
halo location, respectively. However, most conversations today regarding
Peimbert types are concerned with whether an object is a Type I or non-Type I
object, especially when abundances are of prime interest.. After nearly two
decades, and in light of the availability of many additional abundance results
in the literature, Torres-Peimbert & Peimbert (1997) recommended that MW Type
I PNe be defined abundance-wise by He/H$\geq$0.125 and N/O$\geq$0.5.

The sample of abundance ratios in the bottom panels of Fig. 11 clearly
suggests a direct relation between log(N/O) and He/H. A regression analysis of
the data produces a correlation coefficient of +0.55 between these two
variables with a probability of $<$0.001 of computing such a value from an
uncorrelated sample. One can see a qualitatively similar correlation in both
the Aller & Czyzak (1983) and Kingsburgh & Barlow (1994) data (not shown
here). In view of the discussion presented in §2.1, a log(N/O)–He/H
correlation can be reasonably interpreted as the result of the major
conversion of 12C to 14N via the HBB process at the base of the H-rich
envelope as the He/H ratio rises steadily, where both increases are directly
related to progenitor mass. This last point is clearly illustrated in Fig. 13,
where we have plotted values of predicted surface abundances versus mass from
Karakas & Lugaro (2016); Karakas et al. (2018). In the bottom panel note the
abrupt increase in log(N/O) beginning at roughly 4 M⊙, where HBB becomes
effective, especially under low metallicity conditions. The top panel shows
the predicted steady rise of He/H with progenitor mass. These trends are also
consistent with the notion that Type I PNe result from more massive progenitor
stars (Torres-Peimbert & Peimbert, 1997).

However, the notion that Type I PNe are exclusively associated with massive
progenitors is challenged by other empirical results. For example, Stasińska
et al. (2013) observed several Type I objects in a sample of 26 PNe in NGC
300, while at the same time estimating the masses of their progenitor stars to
be within the range of 2-2.5 M⊙. In addition, assuming that selection effects
are not a significant factor, Type I PNe comprise 30% of the entire KH20
sample presented in Fig. 11, a proportion significantly larger than predicted
by a standard initial mass function if these objects are solely the product of
massive progenitors. Indeed, Stasińska et al. (2013), Karakas & Lattanzio
(2014), and others have suggested that many Type I PNe originate from
progenitor stars less massive than 3 M⊙ in which rotationally induced mixing
on the main sequence may have resulted in elevated N/O following the first
dredge-up. Thus, stars with M$<$3 M⊙ may play a bigger role in influencing PN
nitrogen abundances than previously thought.

Regarding the abundances in the upper panels of Fig. 11, note that the absence
of a correlation between C/O and He/H is confirmed by the presence of a near-
zero correlation coefficient for these points. Again, we examined the data in
the Aller & Czyzak (1983) and Kingsburgh & Barlow (1994) papers and found no
suggestion of a correlation between C/O and He/H in either reference.

Continuing on with the same data set, we have also plotted log(C/O) vs.
log(N/O) in each of four panels of Fig. 12. Symbols in this figure are defined
as they are in Fig. 11. Each panel features a different unique set of model
predictions for our upcoming comparison with the data. Note the absence of a
correlation between the two abundance ratios, which we can confirm by the
presence of a near-zero correlation coefficient for these points. Again, we
checked the data in the Aller & Czyzak (1983) and Kingsburgh & Barlow (1994)
papers and found no suggestion of a correlation between C/O and N/O in either
reference. The absence of a correlation in this case may be related to the
initial increase followed later by a decrease of C/O as progenitor mass
increases, all while N/O increases monotonically with mass.

We now consider the models and what they can tell us about the observed
ratios. The surface abundance predictions of published models of AGB stars
after the final pulse from the MONASH, LPCODE, and ATON groups referenced
above are shown with X symbols in Fig. 11. Models of the same three groups
plus those of the FRUITY group are shown in Fig. 12. Each panel in the two
figures contains three model sets, where all models within a set have the same
metallicity and symbol color, as defined in the legend. Each model within a
metallicity set has a unique progenitor mass (not shown). For each metallicity
set, Table 10 provides details regarding the source of the models,
metallicity, progenitor mass range in solar masses, and the estimated onset
mass of HBB. This last quantity is the progenitor mass at which log(C/O)
reaches its highest value before beginning a steady descent in a plot (not
shown) of log(C/O) versus mass.

Fig. 11 clearly demonstrates that as set metallicity increases (red to green
to blue), set members in each panel collectively tend to shift toward lower
log(C/O) or log(N/O) values and to higher values of He/H. As discussed by
Karakas & Lattanzio (2014, §4.1) and references therein, the efficiency of TDU
is inversely related to metallicity but directly related to progenitor mass.
In the upper panels of Fig. 11, the downward shift of the metallicity sets is
consistent with progressively less C dredge-up (via TDU) as metallicity
increases. In addition, as the O abundance rises with metallicity, the direct
effect of C dredge-up on the value of C/O is likely dampened to a greater
extent. The drop in dredged-up C with increasing metallicity also limits the
amount of that element that can be used to synthesize N through HBB and can
explain the downward shift in log(N/O) in the lower panels.

The rightward shift with increasing metallicity tells an equally interesting
story. Look at the top panel of the MONASH models in Fig. 11 and consider the
low metallicity (red) set for a minute. With rising He/H, and thus the stellar
mass (top panel, Fig. 13 again), we see an initial increase in log(C/O)
followed by an abrupt drop of 0.78 dex at He/H=0.113, a drop presumably due to
the onset of HBB. This behavior is repeated in the two higher-metallicity
model sets but is more difficult to see, due to the density of the observed
data points. In the lower panel of Fig. 11 the abrupt rise in log(N/O) in the
MONASH models coincides with the sudden drop in log(C/O), likely at the point
where HBB begins to ramp up. Note again that the models representing the more
massive progenitor stars appear in the upper right region defined by the Type
I PN abundance parameters. A different but consistent version of the above
scene is played out in Fig. 12. Here we can see how progenitor mass splits
each metallicity set horizontally into two subgroups. The ATON models also
exhibit the trends especially well because their output represents three
distinct values of He/H instead of a continuum.

To summarize: for constant mass, C/O and N/O appear to correlate indirectly
with metallicity but directly with mass when metallicity is held constant.
Thus in Fig. 11, according to the models the greater the vertical and
horizontal distances of a PN from the origin, the lower its metallicity and
greater its progenitor mass is likely to be, respectively. According to our
current understanding of LIMS evolution, as reviewed above, these effects are
most likely due to the sensitivity of both TDU and HBB to each of these two
stellar parameters.

Fiinally, a general point about the models. The areas occupied by the
observations appear to be spanned moderately well by the models in both Figs.
11 and 12. No models were available for He/H$<$0.10 and the region where
He/H$>$0.15 is only sparsely populated with models. Models also appear to be
lacking for log(N/O)$\leq$-0.75. But the main core of observed points falling
between the two He/H extremes appears well covered. This suggests that most if
not all of the observed points may be successfully modeled simply by making
small adjustments in input parameter values and/or internal processes.
Unfortunately, the problem then shifts to assessing the uniqueness of each
model, but so far the collective results are encouraging. At least that’s our
optimistic glass-is-half-full interpretation.

Besides the production of He, C, and N, another significant contribution made
by LIMS to the chemical composition of the ISM includes the group of s-process
elements which were discussed earlier in §3.2.1. According to Karakas &
Lattanzio (2014, §5.2.5), roughly half of the elements beyond the Fe peak are
produced by s-process neutron capture, and AGB stars are responsible for most
of that production. S-process elements are likely produced in the He-burning
shell prior to TDU, where the source of free neutrons is either the
13C($\alpha$,n)16O or 22Ne($\alpha$,n)25Mg reaction, depending upon the local
temperature.

One of several good examples of the predicted impact of AGB stars on the
chemical evolution of s-process elements in the Galaxy is provided by the
recent paper by Prantzos et al. (2018). In their study, the authors provide
results of a detailed one-zone chemical evolution model of the proto-solar
nebula that predicts the abundances of all 285 stable isotopic species from
hydrogen to uranium. Their successful model employed the stellar lifetimes and
metallicity-dependent yields of Cristallo et al. (2015, FRUITY code) for the
mass range 1-7 M⊙ and of Limongi & Chieffi (2018) for stars exceeding 7 M⊙.
The Cristallo yields for LIMS were computed for stars within the metallicity
range for [Fe/H] of -2.4 to 0.2., while the metallicity range over which
massive star yields were computed was -3 to 0 for [Fe/H]. In addition, the
massive star yields included the effects of stellar rotation on internal
mixing. The final model generally reproduced the abundances of the major
isotopes between 12C and 56Fe to better than 15%.

The top panel of our Fig. 14, taken from Prantzos et al. (2018), shows the
mass fraction of the proto-solar abundance (Lodders, Palme, & Gail, 2009, for
t = -4.5 Gyr) of s-process isotopes that are produced by LIMS only (blue open
circles), or LIMS and either non-rotating (green crosses) or rotating (red
filled circles) massive stars as a function of mass number A. The blue
vertical error bars show the 1$\sigma$ observational uncertainties, while the
dotted lines show the 10% and 50% deviations from the solid line representing
the proto-solar abundances. For orientation purposes, the atomic mass numbers
of the observed s-process elements discussed in §3.2 and listed in our Table 3
range from 70-134 (Ge to Xe).

Since the vertical gap between the blue symbols and the proto-solar line above
them represents the contribution to the total abundance that is made by LIMS,
it is clear that this contribution rapidly increases between A=70 and A=95;
after that point, the s-process element production appears to be completely
dominated by LIMS, according to the model predictions. We also note that below
about A=85, rotating massive stars have a large impact on the abundance of
these elements. The middle panel illustrates the same results by explicitly
showing the fraction of the total s-process production of an isotope
represented by LIMS. For A$\geq$95, the fraction is roughly 95%. The bottom
panel shows the variation of the production factor212121The production factor
is the ratio of the yield to the solar abundance. of a given isotope with
respect to that value for 150Sm.

Finally, considering the broader picture that includes species besides
s-process elements, what does the Prantzos et al. (2018) model suggest about
the impact of LIMS on the chemical enrichment of the ISM? The authors note
that about 1/3 of the total C in their model is contributed by LIMS, while the
remaining 2/3 originates in massive stars. Similarly, LIMS are responsible for
about 45% of N production, while the balance comes from massive stars. (The
authors also found that the total production of N that is necessary to match
observations required the inclusion of rotational effects in massive stars.)
Therefore, the importance of LIMS for creating two basic elements necessary
for nearly all biological life is obvious. Regarding 19F production, Prantzos
et al. (2018) point out that both 14N and 13C are consumed within the He-
burning shell to produce this isotope. In the final accounting, rotating
massive stars are responsible for about 2/3 of total stellar production of
19F, while LIMS make up the remaining 1/3. And if we now add in the
contribution of LIMS to s-process element abundances in the ISM discussed
above, we conclude that stars between 1 and 8 M⊙ are vital sources of
important elements. To borrow a quote from Karakas & Lattanzio (2014),
“Stellar yields are a key ingredient in chemical evolution models. Low- and
intermediate-mass stars are an integral part of galaxies and help shape their
evolution, gas and dust content, as well as their integrated light. Even stars
as low as 0.9 M⊙ can, at low metallicity, contribute to the chemical evolution
of elements. The days of only considering supernovae are over.”

##  5 Planetary Nebula Distance Determinations

To convert many observed properties of PNe into astrophysically useful ones
requires knowledge of the nebular distances. Gaia (GAIA Collaboration et al.,
2018) trigonometric distances are becoming the standard for Milky Way PNe
(except in cases where the central star is too faint), but for completeness
and context we review below the suite of PN distance methods that have been
and continue to be in use. Straightforward in principle, the determination of
accurate distances for PNe has been far from simple. Neither the central stars
of PNe nor the nebulae themselves present as easily characterized standard
candles. Carefully chosen subsamples may exhibit some mean parameter values,
but with significant dispersion, resulting in unsatisfactorily constrained
distances.

Distances for individual Galactic PNe can be derived from central star
properties (e.g., trigonometric parallax, companion spectroscopic parallax,
gravity distance) and/or nebular properties (e.g., reddening, kinematics,
expansion parallax). Membership in a star cluster affords additional
constraints on stellar and nebular parameters, including distance. For PNe in
nearby galaxies, distances are presumed to be known, at least within the
uncertainty of a galaxy’s distance and physical extent along the line of
sight. In §5.1 we discuss numerous methods commonly used to determine PN
distances. In §5.2 we will discuss the related matter of the Planetary Nebula
Luminosity Function (PNLF), whose bright end has been used as an extragalactic
standard candle to establish distances as part of the cosmological distance
ladder.

###  5.1 Methods

Distance methods can be classified as primary or secondary. Primary distance
methods (e.g., trigonometric parallax) do not rely on generic theoretical
models of stars or nebulae and are focused on individual PNe; secondary
methods (e.g., the “Shklovsky method”), in contrast, are statistical in nature
and are based on analysis of the correlated behavior of some property/ies of
the star or nebula, and must be calibrated against PNe whose distances have
been obtained independently using primary methods. Below we summarize the most
important of these methods; a more detailed discussion of measurement error
and systematic bias in various PN distance techniques can be found in Smith
(2015). Frew et al. (2016, hereafter F16) also give a detailed discussion and
assessment of distance measurement methods; their Tables 1-10 list results
(theirs and others’) from the techniques they describe.

####  5.1.1 Primary methods

Trigonometric Parallax of the PN Central Star

Trigonometric stellar parallax is the most direct distance method, yet prior
to Gaia, it was only possible for a small number of nearby PNe: of the 12
objects from the literature listed in Table 1 of F16, 11 are within 750
pc.222222The remaining PN, K3-35 (d = 3900 pc), is thus far the only PN to
have its parallax derived from observations of maser emission (Tafoya et al.,
2011). The fractional error for parallax measurements is typically 15-40% or
more. Harris et al. (2007) carried out a ground-based program at the US Naval
Observatory that yielded parallaxes for 16 objects (their Table 3). Using HST,
Benedict et al. (2009) measured parallaxes for four nearby PNe in Harris et
al.’s sample, finding good agreement.

Fortunately, the advent of Gaia has meant that the number of PN central stars
with measurable parallaxes will continue to grow. Stanghellini et al. (2020)
studied over 400 PN central stars from DR2 (their 2020 Table 1). Schönberner &
Steffen (2019) used DR2 parallaxes for 11 identified central stars (their
Table 1) to compare with the expansion parallaxes they derived, finding good
agreement (see section on expansion parallaxes, below). Kimeswenger & Barría
(2018) were able to manually identify almost 400 PN central stars in DR2.
González-Santamaría et al. (2019, hereafter GS19) derived distances for 211 PN
central stars with good quality Gaia DR2 data. González-Santamaría et al.
(2021, hereafter GS21) have extended this work with EDR3 data, deriving good
quality distances to 405 PN central stars; comparing distances in common
between the two datasets, good agreement is found. Anticipating the burgeoning
of both the Gaia archives and PN catalogs, Chornay & Walton (2019, 2020, 2021)
devised an automated technique for efficient identification and cross-matching
of PN central stars and rejection of potential contaminants. Applied to the
HASH PN Catalog (Parker et al., 2016), the method yielded more than 1000
likely Gaia PN central stars, more than twice the number from previous manual
matching attempts.

Binary Membership

Binarity provides additional opportunities to ferret out distances of PNe. If
a PN central star has a resolved binary companion of a standard spectral type,
then the established method of spectroscopic parallax can be applied to it,
and a distance determined for the system. PN central stars with resolved
companions represent a minority of PNe with known binary central stars (see §6
on binaries). The best known example is NGC 246. From ground-based photometry
Bond & Ciardullo (1999) concluded that the central star companion, at a
projected separation of 3.8 arcsec, is a G8-K0 main sequence star, implying a
distance of 495 pc, in good agreement with the Gaia EDR3 value of 530 pc (GAIA
Collaboration et al., 2021). Ciardullo et al. (1999) carried out an HST
snapshot survey to search for additional resolved PN pairs and found 10
“likely” and six “possible” binary associations. As one might expect,
calculated distances for these objects range far beyond those for ground-based
parallax measurements, extending to several kpc, with fractional distance
errors averaging around 25% (F16, Table 2). A small number of PNe have
eclipsing binary nuclei (see §6); astrophysical analyses of these systems
offer additional distance estimates (F16, Table 3). González-Santamaría et al.
(2020) found eight wide binaries (including one triple system) among their
good-quality Gaia DR2 distance sample described in GS19. Most recently, GS21
detected three further possible wide binary systems in their EDR3 sample,
including the Ring Nebula (NGC 6720).

Cluster Membership

A PN located in a star cluster is a rare celestial gift. Reliable methods
exist for determining cluster distances: multi-color photometry of cluster
members allows fitting isochrones of appropriate metallicity and age, and
distances based on cluster membership typically have errors around 10% or
better (F16, Table 4). In addition, cluster membership allows the
determination of the PN progenitor mass. What is not always reliable is the
conclusion that a PN is physically associated with a cluster. There are
examples of such associations being claimed, then deprecated, then possibly
re-claimed, on either re-analysis or additional evidence (e.g., NGC 2818 in
the open cluster of the same designation, and Abell 8 in the open cluster Bica
6). The current status of PNe in clusters is summarized by Davis et al.
(2019).

Fragkou et al. (2019a) report the association of a PN, BMP J1613-5406, with
the young ($\sim$90 Myr) open cluster NGC 6067. Two Cepheids in the cluster
indicate a distance of 1.75$\pm$0.10 kpc (Majaess et al., 2013); Gaia DR2
parallaxes for 43 cluster stars yield 1.94$\pm$0.07 kpc. Using the PN
H$\alpha$ surface brightness–radius relation (see see §5.1.2 below). Fragkou
et al. (2019a) derive a distance of 1.71 +0.29/-0.24 kpc, in good agreement
with the other methods. A PN in such a young cluster implies a massive
progenitor, around 5 M⊙; such PNe are rare and of exceptional interest.
Another intriguing example is the distant, intermediate-age ($\sim$0.7 Gyr)
open cluster Andrews-Lindsay 1 containing the PN PHR 1315-6555, most recently
studied by Fragkou et al. (2019b), who derive a distance of 12.0$\pm$0.5 kpc,
a 4% error; they are even able to detect the central star.

As for globular clusters, there are currently four in the Milky Way containing
an identified PN: Ps1 (whose central star is named K648, often used for the PN
as well) in M15 (Pease, 1928), GJJC 1 in M22 (Gillette et al., 1989), JaFu 1
in Palomar 6, and JaFu 2 in NGC 6441 (Jacoby et al., 1997). Recent proper
motion analysis of these PNe support their cluster membership, except for JaFu
1, which still requires more confirmatory data (Bond et al., 2020). Surveying
globular clusters in the direction of the Galactic bulge, Minniti et al.
(2019) identify four “excellent candidates” for PNe, one each in four
clusters. If confirmed, these would double the known number of globular
cluster PNe.

Bond (2015) carried out a largely unsuccessful HST snapshot survey to detect
PNe in the globular clusters of Local Group galaxies; he did, however, find a
PN with a relatively massive central star in an open cluster in M31 (Davis et
al., 2019). Larsen (2008) identified a PN in a globular cluster in the Fornax
dwarf spheroidal galaxy. Searches have been undertaken for PNe in star
clusters belonging to more distant galaxies, with limited success. Out of 80
clusters observed in four galaxies, Larsen & Richtler (2006) detected two PN
candidates in young clusters: one in M83 and one in NGC 3621. Most recently
Sun at al. (2019) identified one PN in a globular cluster in M87.

Self-consistent Nebula + Star Photoionization/Spatiokinematic Modeling

An approach that produces a self-consistent model description of observed and
predicted nebular and stellar properties can be a useful exercise, yielding
distances with errors around 20%. Using photoionization codes like Cloudy
(Ferland et al., 2017) and MOCASSIN (Ercolano et al., 2003) one tries to
construct a self-consistent description of both the star and the nebula. The
method is data-hungry, requiring spatially resolved narrow-band imaging,
spectrophotometry and kinematics, and is more likely to be feasible for nearby
angularly large and bright PNe. The method has been successfully applied to
about a dozen PNe; see F16, Table 7 and references therein.

Gravity Distances

In principle, if both a star’s absolute flux and observed flux are known its
distance can be calculated via the inverse square law. The gravity distance
method uses NLTE model atmospheres to derive a PN central star’s effective
temperature and surface gravity, yielding the absolute flux, which is then
coupled with the observed magnitude and interstellar reddening toward the star
to determine the reddening-corrected observed flux, and thus the distance. The
method is described in detail by Méndez et al. (1988). Despite its apparent
simplicity, the application of this method is challenging and dependent on
model parameters of the stellar atmosphere (see, e.g., Rauch et al., 2007).
F16 list updated gravity distances from the literature for $\sim$60 PNe in
their Table 5; the average distance error is about 30%.

Expansion Parallaxes

This is another method that is simple in principle, but susceptible to
complications. The spectrum of a spherical nebula expanding homogeneously will
exhibit a Doppler shift due to the expansion. Over time, as the nebular radius
increases, its angular growth can be measured. Assuming the angular rate of
change is fueled by the spectroscopically determined radial velocity, the
distance can be calculated. Unfortunately, PNe are rarely spherical, and more
importantly, the observed angular motion of a specific nebular feature does
not necessarily correspond to the expansion of the nebula as a whole, as
described by Mellema (2003). As might be expected, PNe with measurable
expansion parallaxes are bright and within a few kpc.

Schönberner et al. (2018) used spherically-symmetric 1D radiation
hydrodynamical models (see §7.3) to predict the expansion behavior of various
nebular components (shell, rim, shock front), providing correction factors to
be applied in deriving the distance from the measured radial velocities; the