factors are greater than 1, implying larger distances. Their Table 7 lists
expansion distances for 15 PNe, with average quoted errors around 20%.
Schönberner & Steffen (2019) compared results for 11 of these objects that
have Gaia DR2 trigonometric parallaxes: the agreement is very good as shown in
their Table 1 and Figure 2: Schönberner (2021) reports that Gaia EDR3 (GAIA
Collaboration et al., 2021) agreement is even better, with most errors under
10% and less than those for the expansion parallaxes, though some outliers
remain.

Distance Mapping

The distance mapping technique (Akras & Steffen, 2012) is a hybrid process
combining the expansion parallax method along with model-derived 3D morpho-
kinematics. Gómez-Gordillo et al. (2020) used an updated version of this
method to derive distances and for several bright PNe, including NGC 6302, NGC
6543, and BD+30 3639. Their values agree well with previous determinations
from the literature, though for Gaia comparisons, they cite the difficulty of
accounting for the source-dependent zero-point offsets in the Gaia DR2
parallaxes.

Extinction Distances and Kinematic Distances

These methods take advantage of the Galactic environment and line-of-sight to
the PN. Extinction distances are estimated by comparing the extinction of the
nebula and/or central star with angularly nearby stars whose independently
determined distances bracket that of the PN. This is practical only for PNe
within a few degrees of the Galactic plane; at higher latitudes the dust
distribution thins and becomes less predictable. Smith (2015) concludes that
individual extinction distances are generally unreliable. F16 lists 31
extinction distances for PNe in their Table 9, with objects selected for
individual reported errors $<$20%.

To understand the concept of a kinematic distance, consider a PN moving with
the general Galactic circular rotational velocity at its location, and having
only a small peculiar velocity. These constraints automatically restrict the
method to young, disk PNe, most likely of Type I (see §4.2), originating from
progenitors of higher mass than bulge or halo PNe. For any given Galactic
rotation curve and PN sky position, there will be a relationship between the
PN’s distance from the Galactic center (and from us), and its observed radial
velocity. Distance uncertainties from this method derive primarily from
uncertainties in the assumed rotation curve and from the size of the velocity
dispersion for sources of the appropriate age (Phillips, 2001). F16 list 20
objects with kinematic distances in their Table 8; the quoted errors are
around 30%.

####  5.1.2 Statistical Methods

Prior to Gaia, the vast majority of MW PNe were not amenable to direct
distance methods and astronomers developed statistical techniques that related
measurable PN parameters to infer a distance. The continuing value of these
methods lies in their potential to reveal characteristics of different
populations of PNe. Statistical techniques have varying degrees of robustness;
the main difficulty lies in the inherent variation among PNe as well as in
evolutionary effects. Methods that attempt to account for these tend to be
more reliable. Statistical methods must be calibrated using PNe that do have
direct distances available. Over the last several decades, differences in
calibration efforts led to scales dubbed “long” (e.g., Zhang, 1995) and
“short” (e.g., Cahn et al. (1992, hereafter CKS) with distance values
disagreeing by up to a factor of three.

The first widely applied statistical method was developed by Shklovsky (1956).
Assuming that all PNe contain the same mass of ionized material (he assumed
0.2 M⊙), there is a relationship between a PN’s (extinction-corrected)
H$\beta$ surface brightness (SB) and its linear size, so as the nebula
expands, its electron density (which regulates the surface brightness)
decreases. Amassing SB and angular size measurements for a set of target PNe,
then calibrating with PNe having independent distance determinations allows
the distances for the target PNe to be calculated. The assumed nebular mass
actually has a relatively small effect on the resulting distance, which goes
only as M0.4. Variations on the Shklovsky method have included substituting
H$\alpha$ (Abell, 1966) or 5 GHz radio fluxes (Daub, 1982) for H$\beta$, as
well as eliminating the assumption of a fixed ionized mass, and allowing for
consideration of both optically thin and optically thick PNe (e.g., CKS;
Stanghellini et al., 2008).

Frew (2008) first presented a statistical scale based on the SB in H$\alpha$
and the nebular radius. The astronomical observables required are the angular
size of the nebula and the extinction-corrected total H$\alpha$ flux. The
method, refined by F16, includes calibration PNe over a wide range of surface
brightness along with distances determined by an array of methods; the lack of
such broad inclusivity had hampered previous statistical methods, leading to
the conflicting distance scales, and increasing the chances of Malmquist bias
affecting the results.232323Analysis of a flux-limited sample may be subject
to Malmquist bias (Malmquist, 1924), where only brighter objects are detected
at large distances, leading to erroneously higher average luminosity with
increasing distance. A related effect is the Lutz-Kelker bias (Lutz & Kelker,
1973), where increased distance uncertainties result in statistically
underestimated distances, thereby affecting derived distance-scale slopes
(see, e.g., Bensby & Lundström (2001)). They give the best-fit relation
between H$\alpha$ SB and nebular radius for their full sample as:

$log~{}S_{H\alpha}=-3.63(\pm 0.06)log~{}r-5.34\pm 0.05$ (1)

where $S_{H\alpha}$ is in units of erg cm-2 s-1 sr-1 and $r$ is in pc. F16
also give SB-r relations for specific nebular subsamples, e.g., known
optically thick or optically thin, bulge, and extragalactic PNe. In his
analysis of multiple statistical methods and the resulting distance scales,
Smith (2015) concluded that the F16 scale is the best currently available,
with the only caveat concerning very evolved PNe whose distances seem to be
systematically underestimated. Kimeswenger & Barría (2018) found that the Gaia
distance scale agrees with that of F16 to within $\sim$ 8%.

###  5.2 The Planetary Nebula Luminosity Function

####  5.2.1 Basic Concept

The varied morphologies and wide range in observed brightness of Milky Way
PNe, coupled with their difficult-to-determine distances make them unlikely
candidates for consideration as a standard candle. However, just as Henrietta
Leavitt exploited the fact that all Cepheids in the SMC are at a (very nearly)
identical distance so that apparent differences in brightness reflect absolute
differences, the same can be done with the ensemble of PNe in an external
galaxy. The Planetary Nebula Luminosity Function (PNLF) has become a valuable
extragalactic distance indicator with the significant advantage that PNe
originate from low- and intermediate-mass stars found in all types of
galaxies, so that the PNLF can be applied in active star-forming systems as
well as in more sedate, quiescent galaxies.

The brightest PNe in each galaxy exhibit similar absolute fluxes in their
strongest emission line, [O III] $\lambda$5007, suggestive of a specific
maximum PN luminosity (the “cutoff”). Models indicate that up to $\sim$10% of
a PN central star’s total luminosity (L⋆$\geq$ $10^{3}$L⊙) can be concentrated
in this nebular line (Dopita et al., 1992; Ciardullo, 2010; Schönberner et
al., 2010), meaning that [O III] surveys can reveal PNe out to large
distances; as mentioned in §1, PNe have been detected out to $\sim$100 Mpc.
These two characteristics (known luminosity and high luminosity) are just what
is required in a standard candle. Further refinement is possible by using not
just the few brightest PNe but all of the PNe observed in a given galaxy
(Jacoby et al., 1988) and fitting the observed magnitude distribution to a
theoretical model function to yield the distance.

####  5.2.2 The Planetary Nebula Luminosity Function

The absolute [O III] magnitude of a PN, M5007, is defined by Jacoby (1989) as:

$M_{5007}=-2.5\log(F_{5007})-13.74$ (2)

where F5007 is the absolute flux of the nebula in the $\lambda$5007 line in
ergs cm${}^{-2}s^{-1}$ when viewed from a distance of 10 pc. Substituting the
observed flux, f5007, yields the apparent [O III] magnitude, m5007. The
relationship between M5007 and m5007 is the same as for any observed vs.
absolute magnitude: $m-M=5\log(d_{pc}/10)$, after correction for foreground
reddening. As a point of reference, the brightest PNe in M31 have m5007
$\sim$20 (Merrett et al., 2006), while those in the Virgo Cluster have m5007
$\sim$26 (Jacoby et al., 1990).

An observed PNLF is constructed as a histogram of the number of PNe per m5007
interval (typically $\sim$0.2 mag) which can then be fit to a numerical
function incorporating the characteristics and evolution of an ensemble of PNe
and their progenitor stars. Based on their observations of PNe in the Small
Magellanic Cloud, Henize & Westerlund (1963) derived an approximate PNLF
assuming a narrow nebular mass range, uniform expansion, and a constant PN
formation rate. In a study of PNe in M31 and its companions, Ciardullo et al.
(1989b) found that they needed to modify the Henize & Westerlund (1963)
formulation to reproduce the sharp cutoff observed at the bright end of the
distribution, leading to the following expression for the empirical PNLF:

$N(M)\propto e^{0.307M}(1-e^{3(M\star-M)})$ (3)

where N(M) is the expected number of PNe in a bin at magnitude M, and
M$\star$, the cutoff magnitude, is the brightest magnitude observed.242424For
a discussion of a generalized form of the PNLF see Longobardi et al. (2013).
The normalization constant will depend on the number of PNe in the sample. The
value of $M\star=-4.54\pm 0.05$ (Ciardullo, 2013) has been shown to be
invariant over stellar populations and galaxy types, with only a slight
dependence on metallicity (e.g., Dopita et al., 1992; Schönberner et al.,
2010). Figure 15 shows the PNLF for M31 out to about 30 kpc from the center.
Note the sharp cutoff at the bright end, at m5007 $\sim$ 20.17. Figure 16
shows the PNLF for five galaxies in the Leo I group (Ciardullo et al., 1989a)
whose distance is $\sim$10 Mpc. Despite the spread in Hubble type from E0 to
SBb — and therefore the stellar populations sampled — the bright-end behavior
of the PNLF is remarkably consistent. This observed consistency across galaxy
types extends down to $\sim$2 magnitudes below the bright end cutoff; at
fainter magnitudes the star formation history of the population comes into
play, causing deviations above or below the empirical formulation (Ciardullo,
2010). In fact, the detailed shape of a galaxy’s (or galactic subpopulation’s)
PNLF carries information about the stellar mass and age of the parent
population, and can, for example, constrain models of merger scenarios
(Bhattacharya et al., 2021).

The PNLF works, but is not completely understood. It was surprising that
models using relatively simple assumptions matched the early PNLF data well
(Jacoby, 1989; Ciardullo, 2010), though the required distribution of central
star masses (see below) was narrow and higher than the mean of known PN
central stars or of white dwarfs. It continues to be true that decades after
its formulation and after application to PNe in dozens of galaxies of
different types, the PNLF works better than it should, given that it still
lacks a firm theoretical underpinning. Ciardullo (2012) presents extensive
discussion on this point, arguing that it should not work in the first place.

Derivations by several investigators of the central star masses required to
populate the bright end of the PNLF have sat stubbornly at or above $\sim$ 0.6
M⊙ (Jacoby, 1989; Marigo et al., 2004; Schönberner et al., 2007). The
accelerated evolutionary tracks of M3B16 used in the PNLF models of Gesicki et
al. (2018) help by allowing lower-mass stars to produce bright PNe. In their
models the bright end of the PNLF is populated by PNe with progenitor masses
from 1.1 – $\sim$2 M⊙ with lifetimes from 1–$\sim$7 Gyr. Recently, Galera-
Rosillo et al. (2021) obtained deep spectrophotometric observations of a
sample of bright PNe in M31’s extended disk. They found that models of the
four M$\star$ PNe in their sample indicated progenitor masses clustered at the
“knee” of the 1.5 M⊙ M3B16 track; these stars, according to Gesicki et al.
(2018), can spend $\sim$ 1000 years at the bright end of the PNLF. Their
average remnant mass is 0.574 M⊙, which, interestingly, agrees with the 0.58
M⊙ “maximum final mass” derived from PNLF simulations by Valenzuela et al.
(2019). However, Davis et al. (2018) analyzed a sample of bulge PNe in M31 and
concluded that after accounting for the dimming effects of circumstellar dust,
the brightest objects at the observed PNLF cutoff are in fact up to 1 mag
brighter than the canonical M$\star$ value (implying even more massive central
stars $\gtrsim$0.66 M⊙). These authors speculate that the constancy of the
bright-end cutoff in the PNLF might be more indicative of higher circumstellar
extinction with increasing central star luminosity than of a constant
luminosity upper limit. Apparently, a comprehensive explanation for the
observed consistency of the PNLF still eludes us.

Though we still do not entirely understand its foundations, the bottom line is
that the PNLF promises to remain a valuable tool. Studies like those by
Gesicki et al. (2018), Valenzuela et al. (2019), and Bhattacharya et al.
(2021) demonstrate the significant potential of the PNLF to study star
formation history and stellar populations. As a distance indicator, the PNLF
is benefitting from new instrumental capabilities and analysis techniques that
provide increasingly accurate and deeper measurements of PNe in distant
galaxies. For example, Roth et al. (2021) used data from the MUSE integral
field spectrograph on the VLT to develop an improved method of measuring PN
brightnesses that can extend the reach of the PNLF to $\sim$40 Mpc, a distance
where it would become an additional cosmological tool.

##  6 Central Star Binarity

Multiple lines of evidence point to binary systems as the birthplaces of many
— if not most, or even all — PNe. Excellent and detailed discussions of the
role of binaries in PN formation, morphology and evolution are found, for
example, in De Marco (2009); Jones & Boffin (2017); De Marco & Izzard (2017);
Frank et al. (2018); and Boffin & Jones (2019). The current tally252525D.
Jones’ website: http://www.drdjones.net/bcspn/ of $\sim$60 confirmed short-
period, $\sim$10 long-period binary central stars, plus a few dozen systems
with IR photometric excesses indicative of low-temperature companions, will
surely grow as observational sensitivity to binary indications sharpens. For
example, a search for new binary CSPN (Central Star[s] of a PN) candidates
using data from TESS (Transiting Exoplanet Survey Satellite; Ricker et al.,
2015), yielded seven out of eight targets showing some kind of photometric
variation (Aller et al., 2020), though the authors note that three of these
could result from contamination by a nearby variable source. In addition, the
intrinsic variability of CSPN winds can be mistaken for evidence of binarity,
so observed variations should be strictly periodic before binarity is claimed.
Using Gaia epoch photometry Chornay et al. (2021) recovered several previously
known binaries, and found several more objects consistent with binarity,
demonstrating promise for future confirmations from Gaia data.262626Despite
the observed non-spherical morphologies and complex structures in PPNe,
searches for close binaries have failed (Hrivnak et al., 2011, 2017), and the
resulting limits on orbital parameters imply separations too large to have
caused the observed features and compatible only with periods on the order of
years. For example, Manick et al. (2021) recently discovered the longest-known
period in a PPN binary: (IRAS 08005-2356, P$\sim$7.3 yr). Hillwig (2018)
concludes that the population of currently-observed PPNe are not the
precursors of PNe with close binary central stars.

###  6.1 Observational and Theoretical Predictions

PNe are predicted as a result of common envelope (CE) evolution (De Marco,
2009). Stars in close binaries can experience a short-lived period during
which the more evolved of the pair expands and overflows its Roche lobe. The
outflowing material increases in angular momentum at the expense of the binary
orbit, which shrinks in response; the secondary star spirals in toward the
primary before the primary’s envelope is ejected and eventually ionized by the
exposed hot core. A related scenario, “grazing envelope evolution,” may occur
in systems where, prior to the secondary being engulfed, an accretion disk
generates jets that efficiently remove mass from the envelope (Soker, 2015),
preventing, or at least delaying, the onset of a CE phase. In wider binaries
(i.e., in non-contact binaries), hydrodynamic simulations of AGB mass loss via
“wind Roche-lobe overflow” (Mohamed & Podsiadlowski, 2012), show that part of
the accelerated stellar wind slingshots around the accreting star toward the
L2 Lagrange point, producing spiral-shaped density enhancements in the orbital
plane resulting in decidedly non-spherical ejecta. Another possible mechanism
for producing a spiral pattern lies in the orbital motion of the binary
(Mastrodemos & Morris, 1999; Mauron & Huggins, 2006). Such spiral patterns
have been observed in, e.g., the carbon star AFGL 3068 (Mauron & Huggins,
2006) and the AGB star R Sculptoris (Maercker et al., 2012).

Binaries may provide a natural explanation for the morphological and
kinematical features seen in many PNe. Only $\sim$20% of PNe can be described
as having the basically spherical morphology expected for an envelope ejected
and formed by interacting winds from a single star (Parker et al., 2006) (see
§7 on morphology). The markedly non-spherical morphology of the remaining 80%
is hard to explain as arising from a star that has never had a companion. For
example, García-Segura et al. (2014) concluded that a single star cannot
achieve the rotation rate necessary to form a bipolar PN, nor can it muster
the magnetic field strength required to break spherical symmetry, whereas
models of common envelope (CE) ejection naturally form bipolar nebulae.
Furthermore, theory predicts that the symmetry axis of the resulting post-CE
nebula should be oriented perpendicular to the binary orbital plane, which is
precisely what has been observed in every close-binary PN for which the data
are available (Hillwig et al., 2016; Munday et al., 2020). Kinematically, the
outflow features in many PNe with binary central stars appear older than the
central regions, which would be possible if these structures originated from
an accretion disk prior to the general envelope ejection forming the PN proper
(e.g., Corradi et al., 2011). Observed physical features such as point
symmetry (morphologically and kinematically similar structures on opposite
sides of the central star), low-ionization microstructures, and collimated
fast outflows (jets), likewise a challenge to single-star evolution, have been
observed among a significant proportion of the OGLE sample of binary PN
central stars (Miszalski et al., 2009b). However, the CE ejection scenario is
not without flaws: it is unable to account for the very small masses ($\sim$
0.01 M⊙) measured for the nebulae, which would have been ejected over a short
timescale during the post-CE phase, long after the main evolved stellar
envelope has had time to diffuse away (Corradi et al., 2015b). Clearly there
is more to be done to understand the relationship between CE binaries and PNe.

Globular cluster PNe (Bond, 2015), which are rare, (4 known, with another 4
candidates; see §5.1.1), may provide another argument for binary origin. The
four known PNe are located in old globular clusters and have central star
masses too high to have originated from a single star (Jacoby et al., 2017). A
PN ejected from a single current post-AGB remnant with a typical mass
$\sim$0.50 M⊙ in a globular cluster will have expanded and dissipated before
the star has heated sufficiently to ionize the nebular gas. Alves et al.
(2000) concluded that K648 (= Ps 1) in M15, the first PN discovered in a
globular cluster, looks like a merger remnant with a mass $\sim$0.6 M⊙, higher
than the typical remnant of a single AGB star. This conclusion was based on
evolutionary tracks by Vassiliadis & Wood (1994) and Schönberner (1983). The
M3B16 tracks, incorporating updated microphysics and improved modeling of TDU
events on the thermally-pulsing AGB, lead to significantly shortened
timescales by as much as a factor of 10. These faster evolutionary rates make
single stars once again tenable as globular cluster PN progenitors, leading to
higher predicted numbers, but they appear inconsistent with the shorter
kinematic ages of the known globular cluster PNe (Jacoby et al., 2017). The
question is far from closed: globular clusters in other Local Group galaxies
appear comparably deficient in PNe (Bond, 2015), so whatever may be the
eventual explanation for the low observed numbers in Milky Way globular
clusters, it is likely applicable more broadly.

###  6.2 Close Binaries: Chemical Abundances and the ADF

Abundance discrepancies between analyses of permitted vs. collisionally-
excited emission lines, where the former imply higher chemical abundances than
the latter, are observed in many PNe. The “abundance discrepancy factor” (ADF)
is the abundance ratio (typically O++/H+) derived from recombination lines to
those from collisionally-excited lines (see §3). Disagreements are found to be
more extreme in PNe with close binary central stars, sometimes exceeding a
value of 100 (Corradi et al., 2015a). A compilation of H II regions and PNe
with measured ADFs is available on R. Wesson’s
website272727https://www.nebulousresearch.org/adfs/. Wesson et al. (2018)
posit that the observed PN ADF distribution in PNe (see Fig. 5.4 in Boffin &
Jones, 2019) consists of two components: one a “baseline” effect (seen in H II
regions as well) of a factor of a few, and a second that arises only (but not
always) in PNe with close binary central stars. One proposed explanation for
these extreme ADFs is the existence of spatially and chemically distinct gas
phases in the nebula (Liu et al., 2000): “normal” gas (emitting collisionally-
excited lines) and cooler, H-deficient gas (emitting mostly recombination
lines), possibly resulting from discrete ejection events (Corradi et al.,
2014). There appears to be a threshold orbital period around 1.2 days, under
which ADFs tend to be larger ($>$5; Wesson et al., 2018), which presumably
relates to the history and timing of ejection events leading to the extreme
ADF values. In addition, several authors have shown that the emitting regions
are also kinematically distinct, in many cases with the H-deficient gas not
following the general outward acceleration seen in the “normal” plasma, e.g.,
Richer et al. (2013); Peña et al. (2017).

###  6.3 Evidence of Mass Transfer

Since the first identification of lines from Kr and Se (Dinerstein, 2001),
many s-process nuclei such as Ge, Se, Br, Rb, Cd, Te and Xe, have been
detected in PN gas. Their origin is straightforwardly understood, as described
in §3.2. As for detection in PN central stars, there is an intriguing class
called “barium stars,” a subset of which are giants, whose spectra show strong
lines of Ba and other s-process nuclei plus carbon, even though the stars have
not evolved sufficiently to produce these elements. It is now believed that
barium stars are members of binaries, and that their enriched material was
accreted via wind Roche Lobe overflow as previously described, when a now-
faint companion white dwarf was an AGB star (Boffin & Jorissen, 1988; Jorissen
et al., 2019). We know of several PN central stars with cool subgiant or giant
barium components in wide binaries (Tyndall et al., 2013; Boffin & Jones,
2019, Table 4.2), providing compelling evidence for a mass-transfer episode
prior to the PN phase. For close binaries, there was no such smoking gun for
mass transfer until the discovery of a carbon-rich dwarf secondary star in the
Necklace Nebula, a post-CE system with a binary period of a little over one
day (Miszalski, Boffin, & Corradi, 2013). So we see firm evidence among both
short- and long-period PN central star binaries for earlier episodes of mass
transfer with the signature of TDU.

###  6.4 Demographics of Binary Companions

The first confirmed PN binary central star was UU Sge, a previously known
variable identified by Bond et al. (1978) as the central star of Abell 63, a
bipolar PN; this system has become an archetype for close-binary CSPN. UU Sge
is an eclipsing binary with a period of 0.465 days (Bond et al., 1978), (more
recently measured to be 0.456 days by Bell et al. (1994)); this is near the
peak of the period distribution of known close binary CSPN (Jones & Boffin,
2017, Fig. 4). With periods clustered around a few hours to a few days, the
distribution exhibits a very sparsely populated longer-period tail. There are
presently only four known long-period spectroscopic binaries with measured
periods, all greater than 3 years (Boffin & Jones, 2019). Discovery is biased
toward shorter periods which are easier to detect, both photometrically and
spectroscopically; De Marco et al. (2004) argue that a significant fraction of
CSPN may be members of intermediate-period spectroscopic binaries. Binarity
may not be the only relevant configuration; Soker (2016) and Bear & Soker
(2017) posit that 1/6 to 1/8 of PNe are “too messy” to have been formed in a
binary, but require interacting triple stars (not wide triples like NGC 246;
Adam & Mugrauer, 2014) to explain their shapes (Soker, 2021).

Of the 60 or so known close-binary central stars, only a dozen or so have
meaningful constraints on their components (Table 3.2 in Boffin & Jones,
2019). Most are found to have late main sequence companions; two of the three
double-degenerate (WD/WD) systems have total masses above the Chandrasekhar
limit (albeit with large uncertainty), along with a merger time shorter than
the age of the universe. These might be candidates for eventual Type Ia
supernova events (see §7.5) .

The total binary fraction of all PN central stars – a zealously sought grail
with implications for both stellar and PN evolution – is unknown. Recent
estimates of the PN post-CE close-binary fraction (periods less than about a
day) from surveys based on data from OGLE and Kepler, cluster around
$\sim$10-20% (e.g., Miszalski et al., 2009a; De Marco et al., 2015; Jacoby,
2019). But estimates of the total binary fraction calculated by various
investigators do not appear to be converging on any kind of consensus at
present (Boffin & Jones, 2019). Interpretation and comparison of observed and
predicted PN central star binary fractions is muddied by the fact that some
merger remnants may not now be identifiable as having had a binary origin. And
if most PNe do come from binaries, then the numbers detected in the Milky Way
and other galaxies agree reasonably well with predictions from evolution of
stellar populations in galaxies. Based on evolutionary models available at the
time, Moe & De Marco (2006) predicted several times the observed number of PNe
if single stars are their presumed progenitors; such an analysis needs to be
redone with the new accelerated tracks of M3B16. Weidmann et al. (2020) find
that roughly half (88 out of 175) of the central stars whose luminosities,
temperatures and gravities they were able to derive imply masses and ages that
are consistent with models of single star evolution using M3B16 tracks. To
account for the number of PNe observed, Jacoby (2006; during discussion at IAU
Symp. #234) posited a multi-channel origin whereby the predominantly non-
spherical, bright PNe are the result of binary interactions, while single
stars produce the less numerous and fainter, extended spherical PNe.

##  7 Morphology and Evolution of PNe

There has been an abiding historical question of how an originally
spherically-symmetric AGB star metamorphoses into a distinctly non-spherical
PPN and ultimately, PN. However, that appears to have been the wrong question,
since evidence has been accumulating that asymmetries may begin while the star
is still on the AGB. MHD (magnetohydrodynamic) models by Pascoli (2020)
indicate that a spherical-appearing AGB star conceals anisotropic structures
that will break out once the fast stellar wind commences. Sahai & Trauger
(1998) carried out an HST H$\alpha$ imaging survey of young PNe and found that
all of their objects exhibited “highly aspherical” morphology, leading them to
conjecture that high-speed jets or collimated outflows (presumably from a
close companion) during the late AGB or early post-AGB phase are responsible
for shaping PNe282828The morphological classification systems for PPNe (Sahai
et al., 2007) and for young PNe (Sahai et al., 2011) cite lobes, waists, and
haloes, presaging that for PNe in general (e.g., Balick & Frank, 2002;
Manchado et al., 2000), as will be seen below.. Guélin et al. (2018)
investigated the three-dimensional envelope structure of the nearby carbon
star IRC+10 216 ($\sim$130 pc; Menten et al., 2012) using VLA millimeter-wave
interferometry, concluding that mass loss modulated by the orbit of a low-mass
binary companion might explain the regularly-spaced shells also observed in
the optical (Leão et al., 2006), as hypothesized by Soker (1998). Decin et al.
(2020) carried out ALMA observations of oxygen-rich AGB stars that also show
evidence of asymmetrical features such as shells, disks, and spirals.

Advances in imaging and spectroscopic capabilities have spurred progress in
observing and modeling the formation and development of nebular structures.
Some examples: Schmid et al. (2017) used the SPHERE adaptive optics system and
ZIMPOL polarimeter at the VLT to image the binary star R Aqr, (consisting of a
Mira variable and a hot companion), and obtained detailed images of its strong
and complex jet. Using the NACO infrared adaptive optics system at the VLT,
Kervella et al. (2014) discovered a dust disk surrounding L2 Puppis, a nearby
(d=64 pc) AGB star. Kervella et al. (2015) then went on to use the
SPHERE/ZIMPOL instrument at the VLT to image the disk in scattered optical
light. A color composite of their polarimetric visible-light images (Fig. 17)
shows the nearly edge-on disk, from which bipolar plumes emerge, along with
indications of the primary and companion star. Using these data, Chen et al.
(2016) performed three-dimensional hydrodynamical simulations and showed that
these outflows could be due to a thermal pulse, by periastron passage of the
companion, or even by planet ingestion. Subsequent modeling by Zou et al.
(2020) demonstrated that it is possible to form young bipolar PPNe with a
variety of shapes. Fig. 1 of Balick et al. (2019) shows scattered-light HST
images of a dozen PPNe with “candle-shaped” lobes presumed to have been carved
by collimated jets plowing into ambient slower AGB wind. And in a recent
series of papers, Balick and colleagues developed hydrodynamic models for the
mass-ejection histories of PPNe, including winds, lobes, jets, and other
structures (see Balick et al., 2020). In that paper they extend their analysis
to explore effects of toroidal magnetic fields; see their Fig. 1 for images of
very compact PPNe whose knots and protrusions along the axis of symmetry
appear to have been shaped by such magnetic fields.

Our understanding of the menagerie of PN shapes has advanced both
theoretically, with the development of evolution and hydrodynamical codes, and
observationally, with the advent of multiwavelength milli-arsecond resolution
plus deep, wide imaging. Combining morphology with other characteristics can
help us better understand nebular history and evolutionary pathways. Below we
describe nebular classification, and then go on to outline ideas about nebular
shaping and evolution.

###  7.1 Morphology and Classification Systems

Given the twin notions of a spherical AGB star expelling its outer atmosphere
via winds originating near its surface, and its hot stellar remnant creating a
canonical Strömgren sphere with isotropic thermal pressure, it is easy to
understand why the archetypal mental model of a PN is round. However, a quick
inspection of any compilation of modern PN images, e.g., Balick’s catalog of
HST images292929faculty.washington.edu/balick/PNIC/, quickly dispels this
misconception. PNe display morphologies encompassing elliptical, bipolar,
multipolar, point-symmetric, multiple-shell, and yes, round shapes in a
fraction ($\sim 20$%) of cases. The origin of this variety is a vigorous area
of current research, involving stellar evolution, binarity, gas dynamics and
nebular astrophysics. Reviews of PN morphology can be found in Balick (1987),
Manchado (2003), and Shaw (2012).

Curtis (1918) was the first to classify PNe into morphological categories,
motivated by the belief that “a collection of illustrations showing the forms
assumed by the planetary nebulae would be of considerable value as
contributing to theories of the structure and life histories of these bodies.”
He was not wrong. And while his categories include familiar descriptors like
halo, annular, and ellipsoidal, he could only dream of the detailed images and
complex features whose interpretations challenge us today.

Investigation of PN morphology specifically as a consequence of shaping by
current and previous stellar winds (see §7.2), was first undertaken by Balick
(1987). Based on the new availability of high-dynamic-range CCD images, he
devised a two-dimensional classification sequence for global morphology (as
shown in his Fig. 15) along the dimensions of shape (round, elliptical,
butterfly) and evolutionary state (early, middle, late). Balick & Frank (2002)
describe the third shape class slightly differently, dividing what they call
bipolar into butterfly and bilobed, (see their Fig. 1). In the former, the
extended lobes converge into the nebular center, while in the latter they
connect to a central elliptical or round component. Other classifications
focus on symmetry properties of the PN (e.g., Manchado et al., 1996a, b)
ranging from reflection symmetries across one or both axes or point-wise
across the nebular center. Manchado et al. (2000) classified 255 northern PNe,
settling on three main classes: round (20%), elliptical (61%) and bipolar
(13%) – see their Fig. 2. Other classification systems have been described in
Corradi & Schwarz (1995); Parker et al. (2006); Manchado (2004) and Sahai et
al. (2011). Some examples of PN morphological classifications are shown in
Figs. 18-20.

Study of the interconnection between nebular kinematics and morphology has
benefitted from the availability of high-resolution, spatially-resolved
spectra. The kinematic catalog compiled by López et al. (2012b) has enabled
such detailed analysis; e.g., López et al. (2012a) constructed three-
dimensional models of the bipolar PNe Hb5 and K3-17, both of which exhibit
evidence of more recent additional lobe formation, possibly leading to future
poly-polar structure.

It is important to bear in mind that the apparent shape and extent of a PN is
dependent on numerous factors, including how it is observed. Observed shapes
are a two-dimensional projection, and apparently different morphologies might
be due to orientation effects (e.g., Balick & Frank, 2002); for example, a
bipolar PN viewed nearly pole-on will look like a ring. Morphology is also
wavelength-dependent; e.g., Kwok (2018) cites bipolar structure in several PNe
seen in the infrared by Zhang & Kwok (2009) but not in the optical. Kinematics
and expansion velocities observed in PNe also depend on the emission line used
(Chu et al., 1984).

Dynamic range limitations and field of view are further issues affecting how a
PN is seen. As an obvious example, multiple outer shells and faint extended
halos have been discovered surrounding many PNe, (e.g., Jewitt et al., 1986;
Chu et al., 1987; Balick et al., 1992; Ramos-Larios et al., 2016; Guerrero et
al., 2020b; Kastner et al., 2020), presumably representing earlier episodes of
mass ejection. An outstanding example is NGC 6543, the Cat’s Eye Nebula, seen
in Fig 21 (Balick et al., 2001). The central nebula is surrounded by no fewer
than nine $\sim$evenly-spaced, concentric shells (projected as rings),
extending out to about twice the main nebular radius. Encompassing all of
this, extending out roughly five times farther still, with an angular radius
of 2.5 arcminutes, is a patchy, but massive, halo (Fig. 22) comprised of
material ejected earlier during the star’s AGB evolution (Villaver, Manchado,
& García-Segura, 2004). Such extensive shell systems are seen in PPNe as well
(Sahai et al., 1998; Balick et al., 2011).

###  7.2 Nebular Shaping: The Interacting Winds Model

The shape of a planetary nebula is the result of multiple factors, beginning
with often-collimated momentum flux in the outflowing matter from the stellar
atmosphere which alters as the star evolves. The physical environment of the
evolving star also plays a significant role in terms of companion objects, as
well as the ambient ISM.

The kernel of current theories describing PN morphology is the interacting
stellar winds (ISW) model, as originated by Kwok et al. (1978) and further
detailed by Kwok et al. (1978), Volk & Kwok (1985) and many others. In this
scenario, the faster, less dense stellar wind from the evolving central star
catches up with and plows into slower gas ejected previously during the AGB
phase, creating a compressed shell of high density observed as the PN. The
essential anatomy of such an interstellar bubble was described by Castor,
McCray, & Weaver (1975) and further elucidated by Weaver et al. (1977). Though
their focus was on nebulae formed by winds from massive early-type stars
blowing bubbles into the ambient ISM, the basic mechanisms and structure are
similar. More recent PN-specific hydrodynamic simulations are discussed below
in §7.3.

A cartoon schematic of a typical established PN bubble is shown in Fig. 23.
The volume nearest the star is filled with free-streaming stellar wind (gray)
with velocity $\sim$1000 km s-1, and mass-loss rate $\sim$10-9 M⊙ yr-1 (e.g.,
Krtička, Kubát, & Krtičková, 2020). This is surrounded by shocked stellar wind
(blue) created by an inward-moving (reverse) shock formed when the wind first
reached the AGB material. This shocked gas can reach temperatures $\sim
10^{7}$ K, capable of producing detectable x-ray emission (Kastner et al.,
2012; Montez et al., 2015), which has been observed in several PNe, including
NGC 6543 (Chu et al., 2001), as seen in Fig. 21, as well as the young PN
BD+30∘ 3639 (Kreysing et al., 1992; Arnaud, Borkowski, & Harrington, 1996),
NGC 7009 (Fig. 27), and others listed in Table 1 of Kastner et al. (2008). One
thing these PNe always have in common is an intact, continuous inner rim that
presumably confines the shocked wind. Radiation-hydrodynamic simulations of
these hot bubbles and their x-ray emission have been carried out by several
groups. Steffen, Schönberner, & Warmuth (2008) and Sandin et al. (2016)
demonstrated the importance of thermal conduction at the interface between the
shocked wind and the nebular gas. Toalá & Arthur (2014, 2016, 2018) performed
high-resolution two-dimensional calculations following the evolution of these
hot bubbles.

The next shell out is composed of the ionized former AGB slow wind (red) that
we see as the PN, with a temperature $\sim$104 K. Between the hot shocked wind
and the cooler nebular gas, a conduction layer (mentioned above) at $\sim$105
K, is expected to produce collisionally-excited O VI emission, which has been
observed by Ruiz et al. (2013). If the PN is radiation-bounded rather than
matter-bounded, neutral swept-up material (tan) will lie outside an ionization
front, and beyond that, the outward-moving leading shock demarcates the as yet
unaffected remnant AGB wind (white).

Since the nebula expands much faster than the sound speed in the displaced
neutral gas, the original ISW formulation assumed momentum conservation, where
the kinetic energy in the fast wind is radiated away and does not contribute
significantly to the acceleration and compression of the swept-up material. It
was able to explain some, but not all observed PN expansion velocities and
masses (Kwok, 2000; Balick & Frank, 2002). Subsequently, Kwok (1982, 1983);
Kahn (1983) and Volk & Kwok (1985) examined the energy-conserving case, and
estimated that typically $\sim$30% of the fast wind’s energy is dumped into
the expanding shell, which is then able to adequately explain PN expansion
velocities. Detailed analysis of the dynamics and energetics of such systems
can be found in the radiation-hydrodynamic models referred to in §7.3 below.

In the original ISW, the general geometry is taken to be spherically
symmetric, but the abundance of aspherical PN shapes requires that this
assumption be relaxed. In the generalized ISW scheme (GISW; Balick, 1987), the
fast stellar wind expands into a pre-existing asymmetrical density
environment, usually framed as a dense equatorial torus, resulting in fast
lobes directed along the axis of the torus. The origin of this “waist” is not
yet completely understood. Rotation in a single star is an unlikely source
(Frank et al., 2018). It may result from extra momentum supplied by a
companion in a post-CE binary system (Lagadec, 2018), or perhaps from
asymmetric AGB mass loss in a single star, mediated by the stellar magnetic
field (García-Segura et al., 2005; Balick et al., 2020). Recently, Kastner et
al. (2020) constructed UV–to–IR panchromatic HST overlay images of the young
PNe NGC 7027 (Fig. 24) and NGC 6302 (Fig. 25) to study and illustrate PN
shaping processes. The new NGC 7027 image reveals the intricacy of the dust
filaments seen against the bright nebular shell, as well as the wispy,
concentric dust rings. For the bipolar NGC 6302, the most conspicuous features
of the new image are the red point-symmetric arcs seen in [Fe II] emission,
which is an indicator of fast shocks.

####  7.2.1 Internal Structures.

About half of PNe, across almost all morphologies, display internal small-
scale structures described by various terms including filaments, knots, jets,
caps, or ansae (Balick, 1987; Corradi et al., 1996; Gonçalves et al., 2001).
These structures are best visualized in the light of low-ionization species
like [O I], [N II], [O II], and [S II], hence they are called “LIS,” for low-
ionization structures. LIS can manifest in various configurations and display
velocities in a wide range from a few to hundreds of km s-1, indicating
different formation and excitation mechanisms (Gonçalves et al., 2001; Akras,
Gonçalves, & Ramos-Larios, 2017; Balick et al., 2020).

NGC 7293 (the Helix Nebula) exhibits a multitude of cometary knots (Fig. 26):
dense, neutral clumps of material in the nebular interior, ionized on their
star-facing side (O’Dell & Handron, 1996). Such knots are also seen in other
nearby PNe, e.g., NGC 6853 and NGC 6720 (O’Dell, Balick & Hajian, 2002).
O’Dell, Henney, & Ferland (2007) found that for NGC 7293 the central star’s
radiation is sufficient to power the near-IR H2 emission observed from the
knots, eliminating the need to appeal to shock excitation. In addition,
Matsuura et al. (2009) found that the H2 associated with the knots is likely a
relic of molecular gas formed while the star was on the AGB, and not formed in
situ (see §3.5 on the molecular content of PNe).

Balick (1987) noted the presence of low-ionization “inclusions” emitting
prominently in the [N II] $\lambda$6584 line in $\sim$ 20% of the bright PNe
he studied. Balick et al. (1994) dubbed these regions “FLIERs” for fast, low-
ionization emission regions due to their supersonic relative velocities
($\sim$50 km s-1). They tend to occur in pairs along the nebula’s symmetry
axis on opposite sides from the center. Examples of PNe with FLIERs are NGC
6826 and NGC 7009 (both in Fig. 27), and also NGC 3242 and NGC 6543 (Fig. 21).
The origin of FLIERs has been difficult to determine. Balick et al. (2020) and
García-Segura, Taam, & Ricker (2020) conclude that they can be explained as
the remnants of slow, dense, collimated jets shaped by a toroidal magnetic
field during the PPN phase (akin to the bullets seen in CRL 618; Balick et
al., 2013), manifesting as shocked gas at the tips of the jets. Guerrero et
al. (2020a) performed a statistical analysis of jets (inclusive of all the
different names for these features) in 58 PNe. They found a bimodal space
velocity distribution, with means of 66 km s-1 (70%; low-speed) and 180 km s-1
(30%; high-speed). The low-speed jets are a challenge to explain, and are
perhaps related to a lighter outflow more vulnerable to deceleration via
interaction with the slow AGB wind.

The data regarding magnetic fields in PNe are, unfortunately, very sparse.
Observations of dust polarization have revealed toroidal fields in only three
PNe: NGC 7027, NGC 6537, and NGC 6302 (Sabin, Zijlstra, & Greaves, 2007).
Zeeman splitting in molecular maser lines is also a probe of magnetic fields
(Hou & Gou, 2020); thus far only four PNe exhibit distinct or possible pairs
of Zeeman lines: IRAS 1633–4807, K3-35 (see footnote 22), IRAS 17393–2727, and
JaSt 23 (Qiao et al., 2016).

####  7.2.2 Binary Effects.

Binary companions can have profound effects on the nebular morphology: post-CE
PNe are invariably bipolar, and have their orbital plane oriented
perpendicular to the nebular symmetry axis (see §6.1). Soker et al. (1998)
presented arguments to explain the correlation between bipolarity and higher-
mass progenitors. Frank et al. (2018) modeled the interaction of fast stellar
wind with previous CE ejecta and were able to recreate bipolar morphology.
Simulations of post-CE systems by García-Segura, Ricker, & Taam (2018)
likewise reproduced bipolar morphology for young PNe, with later transitions
to barrel or elliptical shapes, sometimes including nested lobes. Numerical
simulations of AGB winds in interacting binary systems (Bermúdez-Bustamante et
al., 2020) can serve as the starting point for hydrodynamic simulations of CE
evolution and eventual PN formation.

The PN KjPn8 (López, Vázquez, & Rodríguez, 1995; López et al., 2000) exhibits
precessing “BRETs,” bipolar rotating episodic jets that have carved out the
most extensive bipolar lobes seen in PNe, more than 4 pc end to end. Kwok
(2018) suggests that such bipolar/multipolar lobes represent low-density
cavities formed after outflows breach the dense equatorial torus. López et al.
(2002) describe KjPn8 as a “double planetary nebula,” that could be the result
of a binary system of two relatively massive stars evolving closely in time,
experiencing two separate PN-creating events, each with its own symmetry axis.
Another BRET nebula, Fg 1 (López, Meaburn, & Palmer, 1993), displaying
spectacular S-shaped point-symmetric jets (Fig. 28), was found by Jones et al.
(2014) to contain a post-CE double-degenerate nucleus with a period of
$\sim$1.2 days, strengthening the association of these outflows with binary
evolution. Additional evidence is provided by Guerrero et al. (2021), who have
for the first time directly imaged the jets in NGC 2392, S-shaped like those
in Fg 1, and which they deduce are being actively launched now, rather than
representing remnants of earlier ejections. Also, based on the observed hard
x-ray stellar emission and high level of nebular excitation, they conclude
that the companion to NGC 2392’s central star is a white dwarf, adding to the
short list of double-degenerate systems in PNe. Longer-period systems with
periods between 100 and 1000 days, including “barium star” PNe (§6.3) like
WeBo 1 (Bond, Pollacco, & Webbink, 2003) and A70 (Miszalski et al., 2012),
exhibit similar morphologies, with equatorially-enhanced densities and bipolar
extensions. Outflow speeds in bipolar PNe appear to be “tapered,” i.e., moving
slowest at low nebular latitudes, and fastest in the polar direction (e.g.,
Corradi, 2004). The gas impacted by these outflows is often observed to
exhibit homologous expansion, moving at velocities that increase with distance
from the star (e.g., Corradi et al., 2001).

Planetary-size bodies can also influence nebular morphology by enhancing a
star’s mass-loss rate on the RGB and AGB, and if a planet spirals into the AGB
envelope, it can spin up the envelope causing asymmetrical mass loss (Soker,
2018). In their modeling of the evolution of several exoplanet systems,
Hegazi, Bear, & Soker (2020) concluded that a planet engulfed into an AGB
envelope could lead to an elliptical PN, as posited by De Marco & Soker
(2011).

###  7.3 Expansion and Modeling of PN Evolution

PNe have been known to be expanding at least since Zanstra (1932) noted as
evidence the Doppler doubling of nebular emission lines.303030Earlier papers
exploring the nature of doubled lines and at least flirting with the idea of
expansion are those by Campbell & Moore (1918), Perrine (1929), and Zanstra
himself (Zanstra, 1931). Thanks to A. Zijlstra for these references. Catalogs
of nebular expansion velocities include Sabbadin (1984); Weinberger (1989),
and more recently, the PN kinematic catalog of López et al. (2012b). The GISW
model provides the phenomenological underpinning describing the response of
ejected and surrounding material to the changing winds and radiation field
from the star. The details of nebular expansion and evolution have been
explored in depth by Schönberner and colleagues (Schönberner, Jacob, &
Steffen, 2005; Schönberner et al., 2005b, 2007, 2014, 2018), who used
spherically-symmetric one-dimensional radiation-hydrodynamics simulations to
examine nebular behavior.

Schönberner et al. (2014) detail their high-resolution echelle observations
and models of various nebular components (see their Fig. 1) over time as the
shock fronts produced by ionization and stellar wind advance. Their generated
plots of variables including density, surface brightness, velocity and line
profiles as a function of time allow comparison with observations. Among their
conclusions is that it is the propagation of the outer shell’s shock (outer
edge of the tan ring in Fig. 23) that represents the PN’s actual expansion
velocity. This finding implies that the typical measured Doppler velocity
(traditionally taken to be $\sim$20 km s-1, measured as half the line
splitting in [O III] $\lambda$5007, or half the half-width if
unresolved)313131This is a simplistic view, at best, since it is well known
that velocities depend on the ion observed, as well as the position in the
nebula (e.g., Chu et al., 1984; Gesicki & Zijlstra, 2000). must be augmented
by a factor $\sim$1.3–1.5 (Jacob, Schönberner, & Steffen, 2013; Schönberner et
al., 2018) to more accurately capture the actual expansion rate. Jacob,
Schönberner, & Steffen (2013) calculate a mean true expansion velocity of 42
$\pm$ 10 km s-1 for their sample of 59 PNe within a distance of about 2 kpc.
GS19 find a similar value, 38 $\pm$ 16 km s-1, for their sample of 45 objects
in Gaia DR2; GS21 find 32 $\pm$ 13 km s-1 for their EDR3 sample of 65 PNe, all
three samples agreeing within the uncertainties. As a consequence of larger
expansion velocities, PN distances determined by the expansion parallax method
will likewise be pushed to larger values (see §5.1.1). Combined with ongoing
high-quality imaging and spectroscopic studies of PNe, meticulous
investigations such as those described promise increased understanding of
nebular evolution.

###  7.4 Ages and Sizes of PNe

Together with their distances, observed PN expansion velocities allow us to
estimate kinematic ages (sometimes called “dynamical ages”). GS19’s analysis
of PNe in DR2 also included age estimates for the sample of 45 PNe central
stars for which they have nebular expansion velocities. They found that most
of their objects were under 15,000 years old, though several appear more than
50,000 years old (see their Fig. 10). The average age was found to be
$\sim$24,000 yr; however, the authors acknowledge a likely bias toward smaller
ages, given the easier detectability of younger PNe. The larger EDR3 sample of
GS21 likewise exhibits a majority of young PNe ($<$10,000 yr); the average age
is 17,800 $\pm$ 3000 yr. Strongly bipolar PNe appear to tend younger: from
their 3D models of a sample of bipolar PNe, Gesicki et al. (2016) derived ages
of only a few thousand years.

The physical radii of PNe are straightforwardly calculable from their
distances and angular radii. Fig. 1 is a montage of 22 PNe with well
determined distances, arranged according to relative physical size; the scale
bar indicates 5 light years ($\sim$1.5 pc). The radii of the PNe shown range
from about 0.03 – 0.8 pc. Fig. 8 in GS19 shows the distribution of radii for
206 PNe, calculated with DR2 distances and angular sizes (10% H$\alpha$
isophotes) from the HASH database (Parker et al., 2016). More than half are
under 0.2 pc in radius, though the distribution has a long tail beyond 1 pc
with small numbers of larger PNe up to a maximum radius of almost 2.2 pc (the
PN EGB 6; Ellis, Grayson, & Bond, 1984). In the GS21 sample, 54% of the
objects have nebular radii $<$0.3 pc, while 14% are greater than 1 pc in
radius (see their Fig. 12). The mean radius of their sample is 0.59 pc.

###  7.5 Late Evolution of PNe

As a PN and its central star evolve, the nebular density decreases and the
surface brightness declines toward invisibility. Morphologically, lobes become
washed out and the nebula as a whole tends toward becoming more spherical.
Pereyra, Richer, & López (2014) studied the kinematics of evolved PNe,
finding, not unexpectedly, that the most evolved objects expand most slowly.

Some PNe have shapes that reveal expansion into an inhomogeneous ISM, denser
in some directions than others.323232Note that the ISM surrounding the PN is
not expanding. Studies, both observational (e.g., Tweedy & Kwitter, 1996;
Xilouris, Papamastorakis, & Paleologou, 1996; Kerber et al., 2000) and
theoretical (e.g., Soker, Borkowski, & Sarazin, 1991) have been carried out,
some including interaction with previously-ejected AGB material as well (e.g.,
Villaver, García-Segura, & Manchado, 2003; Villaver, Manchado, & García-
Segura, 2012; Villaver et al., 2014). In their Atlas of Ancient PNe, Tweedy &
Kwitter (1996) found 21 out of 27 objects exhibiting evidence of ISM
interaction. A striking instance of PN-ISM interaction shaping is seen in
Sh2-188 (Fig. 29); the central star is clearly offset from the nebular center
toward the brighter region in the southeast. This PN was analyzed in detail by
Wareing et al. (2006), whose model, incorporating stellar winds plus the
effect of the nebula’s motion through the ISM, was able to reproduce the
nebula’s shape. They found that the nebula’s peculiar velocity (with respect
to the local ISM) is $\sim$125 km s-1, directed toward the brightest part of
the limb in the southeast, consistent with the proper motion of the central
star. Wareing (2010) describes the effect as “rebrightening” when a PN shell
moving through the ISM interacts with a pre-existing bow shock formed earlier
in the star’s evolution. Abell 21 offers another example, as shown in Fig. 30.
Like Sh2-188, it appears much brighter on one side and the central star is
also clearly offset from the nebular center. One more object worthy of mention
here is Sh2-216, the closest PN (d=129 pc; Harris et al., 2007). It is also
one of the largest currently known, angularly as well as physically: 1.6∘=3.8
pc in diameter. Tweedy, Martos, & Noriega-Crespo (1995) constructed deep
mosaics in H$\alpha$ and [N II] that demonstrate that the bright eastern rim,
where ISM interaction appears to be taking place, is part of a much fainter,
nearly round, nebula (see their Figs. 1-4). The central star, a hot DAO white
dwarf (Tweedy & Napiwotzki, 1992), is displaced from the nebula center, and
has a proper motion consistent with such an interpretation (Cudworth &
Reynolds, 1986).

Intriguingly, there is an example of a classical nova occurring inside a PN.
When V458 Vul erupted in 2007, the outburst flash-ionized a pre-existing
bipolar nebulosity that Wesson et al. (2008) conclude is a $\sim$14,000 yr-old
PN produced by CE evolution of the binary central star (see §6.1). Nova Persei
1901 (GK Per) has been suggested as another example of a nova inside an
ancient PN (Bode et al., 2004).

Finally, the fascinating possibility of a Type Ia supernova (thermonuclear
white dwarf cataclysm) exploding inside a pre-existing PN has been explored by
Tsebrenko & Soker (2015a, b). They estimate this to occur in at least
$\sim$20% of Type Ia events, those resulting from a binary merger of a white
dwarf with an AGB core or with another white dwarf. Their three-dimensional
hydrodynamical simulations can explain the observed shapes of some supernova
remnants (SNRs), in particular those resembling elliptical PNe with “ears,”
small, incomplete lobes on opposite sides of the center, like Kepler’s SNR
(Tsebrenko & Soker, 2013) and G1.9$+$0.3 (Tsebrenko & Soker, 2015b). A prime
candidate for such a Type Ia merger event is the halo PN TS 01 (PN
G135.9$+$55.9), whose double-degenerate binary central star has a total mass
very close to the Chandrasekhar Limit (Tovmassian et al., 2010). Another
potential candidate might be V458 Vul, mentioned above, which is thought to
contain two compact stars with a total mass above the Chandrasekhar Limit
(Wesson et al., 2008; Rodríguez-Gil et al., 2010; Corradi, 2012).

##  8 Summary and Outlook

We examined PNe in the context of stellar evolution in §2, as the penultimate
stage in the lives of low- and intermediate-mass stars. In §3 we laid out the
current landscape of chemical abundance determinations, covering PN abundances
in the Milky Way, including disk, bulge and halo samples. We discussed
neutron-capture elements, the less-abundant elements fluorine, magnesium, iron
and zinc, as well as the molecular and dust content of PNe. We then described
abundance studies of PNe in more than a dozen external galaxies in and beyond
the Local Group. In §4, we presented an analysis of radial abundance gradients
in the Milky Way and external galaxies. Next, the observed elemental
abundances in PNe were compared with those predicted from theoretical models.
In §5, we described techniques for determining distances to PNe, and discussed
the Planetary Nebula Luminosity Function. Central star binarity and its
consequences were considered in §6. Nebular morphology, shaping, and evolution
were explored in §7.

Our understanding of PNe has advanced significantly, but numerous open
questions remain. Areas ripe for future investigations have been pointed out
by, e.g., Kwitter et al. (2014), including: exploiting non-optical wavelengths
for detection of new PN candidates; better characterization of AGB mass loss,
especially as it relates to metallicity; improved atomic data for abundance
determinations, especially in the case of s-process elements; continued
efforts at resolving the ADF; the formation and fate of dust and molecules
around PNe; and improved understanding of the effects of binarity. Existing
observing facilities (e.g., ALMA, Gemini, the VLT and GTC) continue to provide
vital data to address such issues. Future telescopes and instrumentation
promise to extend these capabilities. Guerrero (2020) discusses future x-ray
missions, including eROSITA, which will produce an all-sky survey with a
sensitivity capable of detecting the hot gas in the interior of hundreds of
PNe, thereby improving the statistics of x-ray emitting PNe. In the near- to
mid-IR JWST will enable detection of lower-mass companions in PN central star
binaries and dusty disks in PNe, along with high-resolution mapping of UV-
irradiated knots to probe the evolution of molecules and dust grains in the PN
environment (Sahai, 2020). Lagadec (2020) anticipates contributions from the
ELT’s first instruments, imager/spectrometers and IFUs, that will map dust and
molecule distributions, velocity fields and abundances at high spatial
resolution. Bojic̆ić et al. (2021) make the case that radio continuum surveys
like ASKAP333333Australian Square Kilometre Array Pathfinder (Joseph et al.,
2019) will enable determination of accurate angular diameters for PNe,
including compact objects as well as those suffering heavy optical extinction.
Finally, the capabilities of the ngVLA will allow determinations of light-
element abundances, measurement of precise nebular proper motions, and studies
of close binary interactions in PN central stars (Kastner et al., 2018), as
well as investigations of molecular lines to study the AGB–PN transition.

In this review/tutorial we have seen how the observed properties of planetary
nebulae disclose the workings of stellar evolution, nucleosynthesis, and time.
It is fitting to end with a quote (Aller, 1971) from the late Lawrence H.
Aller, renowned scholar of planetary nebulae and mentor to one of us (KBK):
“They are wreaths placed by Nature around dying stars.”

##  Appendix A A listing of some PN catalogs and databases

###  A.1 Nebulae

The Strasbourg-ESO Catalogue of Galactic Planetary Nebulae. Parts I, II
Acker, A., Marcout, J., Ochsenbein, F., Stenholm, B., Tylenda, R., Schohn, C.,
1992 European Southern Observatory, Garching (Germany), 1992

Planetary Nebula Image Catalog
Balick, B.; http://faculty.washington.edu/balick/PNIC/

New Galactic Planetary nebulae selected by radio and multiwavelength
characteristics
Fragkou, V., Parker, Q.A., Bojic̆ić, I.S., & Aksaker, N. 2018, MNRAS, 480,
2916

Planetary nebulae in the UWISH2 survey
Gledhill, T.M., Froebrich, D., Campbell-White, J., & Jones, A.M. 2018, MNRAS,
479, 3759

An Atlas of Images of Planetary Nebulae
Górny, S.K., Schwarz, H.E., Corradi, R.L.M. & Van Winckel, H. 1999, A&AS, 136,
145

The coordinated radio and infrared survey for high-mass star formation– IV. A
new radio-selected sample of compact galactic planetary nebulae
Irabor, T., Hoare, M.G., Oudmaijer, R.D., et al.2018, MNRAS, 480, 2423

A Catalog of Relative Emission Line Intensities Observed in Planetary Nebulae
and Diffuse Nebulae
Kaler, J.B. 1976, ApJS, 31, 517

Version 2000 of the Catalogue of Galactic Planetary Nebulae
Kohoutek, L. 2000, A&A, 378, 843

Gallery of Planetary Nebula Spectra
Kwitter, K. B. & Henry, R.B.C.; tinyurl.com/63ed7tx

Catalog of Intensities, Analysis & Abundances in Galactic Planetary Nebulae
Kwitter, K. B. & Henry, R.B.C.; tinyurl.com/PN-analysis

The IAC Morphological Catalog of Northern Galactic Planetary Nebulae
Manchado, A., Guerrero, M.A., Stanghellini, l, & Serra-Ricart, M. 1997, IAU
Symp. No.180, 24

The Macquarie/AAO/Strasbourg H$\alpha$ Planetary Nebula Catalogue: MASH
Parker, Q.A., Acker, A., Frew, D.J., et al. 2006, MNRAS, 373, 79

HASH: the Hong Kong/AAO/Strasbourg H$\alpha$ planetary nebula database
Parker, Q.A., Ivan S Bojic̆ić, I.S., & and Frew, D.J. 2016 J. Phys.: Conf.
Ser. 728 032008; http://vizier.u-strasbg.fr/vizier/MASH/

A catalogue of 108 extended planetary nebulae observed by GALEX
Pradhan, A.C., Panda, S., Parthasarathy, M., Murthy, J., & Ojha, D.K. 2019,
Ap&SS. 364, 181; https://arxiv.org/pdf/1910.05543.pdf

The SPM Kinematic Catalogue of Planetary Nebulae & Extragalactic Planetary
Nebulae
Richer, M. G., López, J. A., Díaz-Méndez, E., et al. 2010, Rev. Mexicana
Astron. Astrofis., 46, 191
http://kincatpn.astrosen.unam.mx

First deep images catalogue of extended IPHAS PNe
Sabin, L., Guerrero, M.A., Ramos-Larios, G., Zijlstra, A.A., Awang Iskandar,
D.N.F. 2021, arXiv:2108.13612

First release of the IPHAS catalogue of new extended planetary nebulae
Sabin, L., Parker, Q.A., Corradi, R.L.M., et al. 2014, MNRAS, 443, 3388

An evolutionary catalogue of galactic post-AGB and related objects
Szczerba, R., Siódmiak, N., Stasińska, G., & J. Borkowski, J. 2007, A&A, 469,
799
https://www.ncac.torun.pl/postagb

The Fornax3D project: Planetary nebulae catalogue and independent distance
measurements to Fornax cluster galaxies
Spriggs, T.W., Sarzi, M., Galán-de-Anta, P.M., et al. 2021, A&A, in press

An imaging and spectroscopic study of the planetary nebulae in NGC 5128
(Centaurus A)
Walsh, J.R., Rejkuba, M., & Walton, N.A. 2015, A&A, 574, A109

###  A.2 Central Stars

VizieR Online Data Catalog: Central stars of planetary nebulae in Gaia DR2
Chornay, N & Walton, N.A. 2020, A&A, 638, 103

One star, two star, red star, blue star: an updated planetary nebula central
star distance catalogue from Gaia EDR3
Chornay, N & Walton, N.A. 2021, arXiv:2102.13654v1

All Known Binary CSPN
DeMarco 2009 PASP, 121, 316

Planetary Nebulae in Gaia EDR3: Central Star identification, properties and
binarity
González-Santamaría, I., Manteiga, M., Manchado, A., Ulla, A., Dafonte, C., &
López Varela, arXiv:2109.12114v2

Binary central stars of planetary nebulae identified with Kepler/K2 Jacoby,
J., Hillwig, T., Jones, D., Martin, K., DeMarco, O., Kronberger, M., Horowitz,
J., Crocker, A., & Dey, J., 2021, MNRAS, 506, 5223

Post-CE Binary Central Stars of PNe
D. Jones; https://www.drdjones.net/bcspn/

Catalogue of central stars of planetary nebulae: Expanded edition
Weidmann, W.A., Mari, M.B., Schmidt, E.O., Gaspar, G., Miller Bertolami, M.M.,
Oio, A.G., Gutiérrez-Soto, L.A., Volpe, M.G., Gamen, R., & Mast, D. 2020, A&A,
640, A10

##  Appendix B Model-Predicted Yields And Surface Abundances Of Low And
Intermediate-Mass Stars

A stellar element yield is the total amount of that element that is
synthesized by the progenitor star during its lifetime and ultimately expelled
into the ISM. Examples of early estimates of LIMS yields can be found in
Renzini & Voli (1981), van den Hoek & Groenewegen (1997), Buell (1997), and
Marigo (2001). Karakas & Lattanzio (2014, Table 2) provide a listing of 16
sources of model-predicted yields and surface abundances published between
2004 and 2014. For each reference, the stellar mass and metallicity ranges are
noted as well as whether or not s-process predictions are included. More
recent papers containing AGB yields and surface abundance information include
Miller Bertolami (2016), Karakas & Lugaro (2016), Karakas et al. (2018),
Ventura et al. (2018), Marini et al. (2021), and numerous results relevant to
the model output provided at the FRUITY website (http://fruity.oa-
teramo.inaf.it/modelli.pl). Each reference provides details and specifications
regarding the models along with the assumptions that went into them. While we
shall not review or critique these papers here, we urge the interested reader
to delve into them in order to appreciate the differences in treatments of
processes such as extra mixing, mass loss, third dredge-up, hot bottom
burning, and formation of 13C pockets, just to mention a few.

We are deeply indebted to the referee, Albert Zijlstra, for his thorough and
meticulous reading of this manuscript. We gratefully acknowledge the wisdom,
helpful advice, quick answers, and generous data sharing of many colleagues
during the preparation of this manuscript, including Sergio Cristallo, Amanda
Karakas, Maxwell Moe, Angela Speck, Letizia Stanghellini, and Paolo Ventura.
Special thanks go to those individuals who also read and commented on specific
sections: Bruce Balick, Marcelo Miller Bertolami, Howard Bond, Robin
Ciardullo, Anibal García-Hernández, George Jacoby, Walter Maciel, Miriam Peña,
and Nick Sterling. K.B.K. is grateful to Jim Kaler for career-long friendship
and mentorship. R.B.C.H. is grateful to Dr. Stephen J. Shawl, Emeritus
Professor of the University of Kansas, for his mentorship and steadfast
support from day one and many years afterwards. Both authors wish to
acknowledge the many years of scientific colleagueship and comradeship of the
late Reggie Dufour. K.B.K. thanks the Dean of Faculty Office at Williams
College for financial support; R.B.C.H. thanks the University of Oklahoma for
valuable resources and IT support. The authors have made use of the NASA/IPAC
Extragalactic Database (NED), which is funded by the National Aeronautics and
Space Administration and operated by the California Institute of Technology;
they have also made extensive use of NASA’s Astrophysics Data System.

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Table 1: MW Planetary Nebula Abundance Surveys: Sample Sizes, Spectral Ranges, & Abundance Medians SourceaaSource references: Aller83=Aller & Czyzak (1983), Aller87=Aller & Keyes (1987), Barker78=Barker (1978b), Cavichia10=Cavichia et al. (2010), Cavichia17=Cavichia et al. (2017), Chiappini09=Chiappini et al. (2009), Exter04=Exter et al. (2004), Girard07=Girard, Köppen, & Acker (2007), Kingsburgh94=Kingsburgh & Barlow (1994), KH20=Kwitter & Henry (2020), Maciel17=Maciel et al. (2017), Perinotto04=Perinotto, Morbidelli, & Scatarzi (2004), Pottasch10=Pottasch & Bernard-Salas (2010), Ratag97=Ratag et al. (1997), Stanghellini06=Stanghellini et al. (2006), Stasińska98=Stasińska et al. (1998), Wang07=Wang & Liu (2007), Webster88=Webster (1988). | Number |  $\lambda$ Range (Å) | He/H | C/HbbThe Aller83+87 and KH20 samples comprise a mix of PNe whose carbon abundances were measured using either optical recombination lines or UV collisionally excited lines. The remainder of the samples used strictly UV collisionally excited lines. | N/H | O/H | Ne/H | S/H | Cl/H | Ar/H