# NGC 6153: Reality is complicated111Based on observations collected at the
European Southern Observatory under ESO programme(s) 69.D-0174(A).

Michael G. Richer Instituto de Astronomía, Universidad Nacional Autónoma de
México, Apartado Postal 106, CP 22800 Ensenada, Baja California, México;
<EMAIL_ADDRESS><EMAIL_ADDRESS>Anabel Arrieta Departamento de Física
y Matemáticas, Universidad Iberoamericana, Prolongación Paseo de la Reforma
880, Lomas de Santa Fe, CP 01210, Ciudad de México, México;
<EMAIL_ADDRESS><EMAIL_ADDRESS>eadolfogalindo@gmail  Lorena
Arias Departamento de Física y Matemáticas, Universidad Iberoamericana,
Prolongación Paseo de la Reforma 880, Lomas de Santa Fe, CP 01210, Ciudad de
México, México<EMAIL_ADDRESS><EMAIL_ADDRESS>eadolfogalindo@gmail  Lesly Castañeda-Carlos Instituto de Astronomía,
Universidad Nacional Autónoma de México, Apartado Postal 70-264, CP 04510
Ciudad de México, México<EMAIL_ADDRESS><EMAIL_ADDRESS>Silvia Torres-Peimbert Instituto de Astronomía, Universidad Nacional Autónoma
de México, Apartado Postal 70-264, CP 04510 Ciudad de México, México;
<EMAIL_ADDRESS><EMAIL_ADDRESS>José Alberto López Instituto
de Astronomía, Universidad Nacional Autónoma de México, Apartado Postal 106,
CP 22800 Ensenada, Baja California, México<EMAIL_ADDRESS><EMAIL_ADDRESS>Adolfo Galindo Departamento de Física y Matemáticas,
Universidad Iberoamericana, Prolongación Paseo de la Reforma 880, Lomas de
Santa Fe, CP 01210, Ciudad de México, México<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We study the kinematics of emission lines that arise from many physical
processes in NGC 6153 based upon deep, spatially-resolved, high resolution
spectra acquired with the UVES spectrograph at the ESO VLT. Our most basic
finding is that the plasma in NGC 6153 is complex, especially its temperature
structure. The kinematics of most emission lines defines a classic expansion
law, with the outer part expanding fastest (normal nebular plasma). However,
the permitted lines of O I, C II, N II, O II, and Ne II present a constant
expansion velocity that defines a second kinematic component (additional
plasma component). The physical conditions imply two plasma components, with
the additional plasma component having lower temperature and higher density.
The [O II] density and the [N II] temperature are anomalous, but may be
understood considering the contribution of recombination to these forbidden
lines. The two plasma components have very different temperatures. The normal
nebular plasma appears to be have temperature fluctuations in part of its
volume (main shell), but only small fluctuations elsewhere. The additional
plasma component contains about half of the mass of the N2+ and O2+ ions, but
only $3-5$% of the mass of H+ ions, so the two plasma components have very
different chemical abundances. We estimate abundances of
$12+\log(\mathrm{O}^{2+}/\mathrm{H}^{+})\sim 9.2$ dex and
$\mathrm{He}/\mathrm{H}\sim 0.13$. Although they are all complications,
multiple plasma components, temperature fluctuations, and the contributions of
multiple physical processes to a given emission line are all part of the
reality in NGC 6153, and should generally be taken into account.

stars: evolution; ISM: abundances; planetary nebulae: individual (NGC 6153);
techniques: spectroscopic

††software: IDL, IRAF (Tody, 1986, 1993), Microsoft Office (Microsoft
Corporation, 2016), Python (Van Rossum & Drake, 2009), PyNeb (Luridiana et
al., 2015), SAOImageDS9 (Joye & Mandel, 2003)

##  1 Introduction

NGC 6153 is a bright, southern planetary nebula that has played an important
part in the abundance discrepancy problem. The abundance discrepancy was first
noted by Wyse (1942), who observed permitted lines of O II and found that they
indicated a much higher oxygen abundance than the forbidden [O III] lines that
originate from the same O2+ ions. Over the decades, study after study has
found that the permitted lines yield systematically larger abundances of C, N,
O, and Ne than do the forbidden lines, which is known as the abundance
discrepancy problem. The abundance discrepancy occurs in both H II regions and
planetary nebulae. Whether it also occurs in active galactic nuclei is unknown
since their kinematics impede investigating it.

Until the 1990’s, the magnitude of the abundance discrepancy was typically a
factor of $2-3$ (the permitted lines indicated abundances $2-3$ times higher
than the forbidden lines). However, as CCD detectors came into common use, it
became clear that many planetary nebulae had abundance discrepancies that were
much higher, e.g., a factor of 5 in NGC 7009 (Liu et al., 1995), 10 in NGC
6153 (Liu et al., 2000), and values in excess of 100 for A46 (Corradi et al.,
2015). In their study of NGC 6153, Liu et al. (2000) proposed their model of a
chemically-inhomogeneous plasma containing hydrogen-deficient clumps as a
possible explanation of the abundance discrepancy. This model and the model of
temperature fluctuations that Peimbert (1967) originally suggested to explain
the factor of 2 abundance discrepancies in H II regions have remained the main
contenders to explain the abundance discrepancy. (Torres-Peimbert et al.
(1990) had shown how a chemically-inhomogeneous model of NGC 4361 could
explain the discrepant C abundances found from permitted and forbidden lines.)

Much of the debate regarding the abundance discrepancy, at least in planetary
nebulae, has focussed upon which of the abundances, derived from permitted or
forbidden lines, are the correct abundance ratios to characterize the chemical
composition of the plasma in planetary nebulae. This has happened even though
evidence for a difference in the spatial distributions of the emission from
the permitted and forbidden lines has long existed, with the permitted
emission being more centrally-concentrated (e.g., Barker, 1982, 1991; Garnett
& Dinerstein, 2001; Tsamis et al., 2008; García-Rojas et al., 2016). Likewise,
chemically-inhomogeneous models demonstrating that the two abundances may not
be contradictory, but instead provide information concerning multiple plasmas
in planetary nebulae have existed almost since the Liu et al. (2000) study of
NGC 6153 (e.g., Péquignot et al., 2002; Ercolano et al., 2003; Tylenda, 2003;
Tsamis & Pèquignot, 2005; Yuan et al., 2011). More recently, the kinematics of
the permitted and forbidden lines are often found to be distinct, with the
permitted lines apparently arising from more highly ionized plasma, i.e., in
agreement with the spatial distribution (Sharpee et al., 2004; Barlow et al.,
2006; Otsuka et al., 2010; Richer et al., 2013, 2017; Peña et al., 2017).
These results as well as the work of Gómez-Llanos & Morisset (2020) strongly
influence our view that the structure of the plasma in planetary nebulae is
more complex than hitherto considered in the analyses of their chemical
abundances.

Given the length of this paper, we provide a general roadmap here, and more
detailed versions at the beginning of each section. In §2, we describe the
observations, their reduction, the construction of position-velocity (PV)
diagrams, and our estimate of the interstellar reddening for NGC 6153. In §3,
we present the results related to the structure of the plasma, with various
lines of evidence indicating the presence of two plasma components. In §4, we
focus upon the complex temperature structure of the nebular plasma and its
consequences concerning the chemical composition of NGC 6153’s nebular shell.
In §5, we present our conclusions. In summary, we analyze spectroscopy of NGC
6153 at high spectral resolution and conclude that the kinematics and physical
conditions of the nebular plasma are consistent with the presence of two
plasma components of different composition, density, and temperature. Ignoring
this complexity inevitably leads to the conclusion that there is a large
abundance discrepancy in NGC 6153.

##  2 The observations, their reduction, PV diagrams, and reddening

We begin this section presenting the data used and their reduction. We then
continue with a description of the construction of the PV diagrams we use to
study the kinematics, physical conditions, and chemical abundances in NGC
6153. We conclude this section with our determination of the reddening for NGC
6153, which also allows us to set a common flux scale for all of the
wavelength intervals. Throughout, we identify the wavelengths of emission
lines rounded to integer values, except when that would allow confusion, in
which cases we provide more precise wavelengths. Generally, we adopt the
wavelengths from Van Hoof (Atomic Line List version v3.00b4;
2018)222https://www.pa.uky.edu/peter/newpage/ and Kramida et al. (National
Institute of Standards and Technology 2021)333https://physics.nist.gov/asd,
but Bowen (1960) for forbidden lines and Clegg et al. (1999) for the fine
structure components of H I. We use a lot of atomic data, which we cite in
Table 1 and refer to as needed.

Table 1: Atomic data used Ion | Atomic data
---|---
H I |  Storey & Hummer (1995); Ercolano & Storey (2006)
He I |  Ercolano & Storey (2006); Porter et al. (2013)
He II |  Storey & Hummer (1995); Ercolano & Storey (2006)
N II |  Nussbaumer & Storey (1984); Péquignot et al. (1991); Fang et al. (2011, 2013); Tayal (2011)
O II |  Zeippen (1982); Nussbaumer & Storey (1984); Wenåker (1990); Péquignot et al. (1991); Wiese et al. (1996); Tayal (2007); Kisielius et al. (2009); Storey et al. (2017)
O III |  Dalgarno et al. (1981); Nussbaumer & Storey (1984); Roueff & Dalgarno (1988); Péquignot et al. (1991); Dalgarno & Sternberg (1989); Liu & Danziger (1993); Storey & Zeippen (2000); Tachiev & Fischer (2001); Froese-Fischer & Tachiev (2004); Storey et al. (2014); Kramida et al. (2021)
S II |  Rynkun et al. (2019); Tayal & Zatsarinny (2010)
Cl III |  Rynkun et al. (2019); Butler & Zeippen (1989)
Ar III |  Muñoz Burgos et al. (2009)
Ar IV |  Rynkun et al. (2019); Ramsbottom & Bell (1997)

###  2.1 The observations and their reduction

The data used here were acquired via programme 69.D-0174A (PI Danziger) on 8
June 2002 using the Ultraviolet and Visual Echelle Spectrograph (UVES; Dekker
et al., 2000) on the Very Large Telescope (VLT) Kueyen (UT2) of the European
Southern Observatory (ESO). We retrieved the raw data from the ESO data
archive. McNabb et al. (2016) previously analyzed this same data.

UVES is a two-arm, cross-dispersed echelle spectrograph with common pre-slit
optics, but independent slit and post-slit optics. The blue and red entrance
slits are 10″ and 13″ long. The detector for the blue arm was an EEV 44-82 CCD
with $2048\times 4096$ 15 $\mu$m pixels. The detector for the red arm was a
mosaic of an EEV 44-82 CCD and a MIT-LL CCID-20 CCD, both of which had
$2048\times 4096$ 15 $\mu$m pixels. For these observations, all detectors were
used in $2\times 2$ binning. Four cross dispersers (CD#1, CD#2, CD#3, and
CD#4) were used to cover the wavelength interval 3043–10655Å (except for three
gaps, see below). The effective spectral resolution ($\lambda/\delta\lambda$)
in all cases was in the neighborhood of 30,000. UVES’ atmospheric dispersion
corrector was not used.

Figure 1: This image from the (red) slit camera shows the slit superposed upon
NGC 6153. The arrows indicate the image orientation. The slit size is
$15.75\arcsec\times 2\arcsec$ and its position angle is 118∘ (N through E).
The decker limits the slit length to 10″(CD1 and CD2) or 13″(CD3 and CD4).
Figure 2: We compare an image (left; Hubble Space Telescope proposal ID 8594)
and PV diagram (right; CD#2) of NGC 6153 in the light of H$\alpha$. The
spectrograph slit is shown on the left. The position of the central star,
whose continuum is subtracted from the PV diagram, would appear at the
position of the horizontal line (right panel; y-coordinate of zero). The main
structure of NGC 6153 is its main shell, which is the origin of the
“$\bigcap$”-shaped structure in the PV diagram (dashed line): The Doppler
effect separates the emission from the approaching and receding sides, except
at the top where the expansion is perpendicular to the line of sight. The
rectangle (right panel) indicates the three rows used to compute the velocity
separation between the approaching and receding sides of the nebula (§3.1).
The systemic velocity is the average radial velocity for the object.

Figure 1 shows the location of the red spectrograph slit superposed upon the
object. The observations of both NGC 6153 and the standard stars CD
$-32^{\circ}$ 9927, LTT 3864, and Feige 56 occurred on 8 June 2002, all at low
airmass ($1.0-1.14$ for NGC 6153; $1.01-1.25$ for the standards). The
observations consist of two standard UVES instrument configurations with
simultaneous coverage of CD#1 and CD#3 and then CD#2 and CD#4. For NGC 6153,
three 1200 s exposures were obtained for all wavelength intervals. In
addition, single short exposures of 60 s (CD#1/CD#3) and 120 s (CD#2/CD#4)
were obtained to avoid saturating the brightest lines. While NGC 6153 was east
of the meridian, the long exposures and then the short for the CD#2/CD#4
configuration were acquired, followed by the long exposures and then the short
exposure for the CD#1/CD#3 configuration as it crossed the meridian. For the
standard stars, all exposures were of 120 s duration. The slit width was 2″
for NGC 6153 and 10″ for the standard stars. The observing conditions were not
photometric, as the fluxes for NGC 6153 and the standard stars varied from
exposure to exposure and between the CD#1/CD#3 and CD#2/CD#4 instrument
configurations.

We reduced the data using the Image Reduction and Analysis Facility
(IRAF444IRAF is distributed by the National Optical Astronomical Observatory,
which is operated by the Association of Universities for Research in
Astronomy, Inc., under cooperative agreement with the National Science
Foundation.; Tody, 1986, 1993). We reduced the images from each of the three
individual CCDs separately, so we work with six wavelength intervals: CD1
(3043–3875Å), CD2 (3759–4987Å), CD3b (4980–5965Å), CD3r (6034–7009Å), CD4b
(7101–8915Å), and CD4r (9050–10655Å; “CD3” and “CD4” are shorthand for
CD3b+CD3r and CD4b+CD4r, respectively). The reduction steps that follow were
applied on a CCD-by-CCD basis. Hence, our data reduction establishes a proper
relative flux scale only _within_ each of the six wavelength intervals. Given
the lack of overlapping spectral coverage between the wavelength intervals
(except CD1 and CD2) and the non-photometric observing conditions, we use the
interstellar reddening to establish a common relative flux scale among all of
the wavelength intervals (§2.3).

The bias images were combined and subtracted from all other images. The flat
field images were processed to remove the scattered light between and within
the spectral orders. All of the spectra were divided by their flat field
images to remove pixel-to-pixel variations, the spectrograph’s blaze function,
and the fringing that occurs in the far-red. The exposure times for the flat
field images were very short (0.44 s for CD1, 1.8 s for CD2, 0.33 s for CD3,
i.e., CD3b and CD3r, and 0.7 s CD4), so we created shutter pattern images
using other flat field images obtained on the same night and used them to
correct the spectra of NGC 6153 and the standard stars. The three long
exposures for each wavelength interval for NGC 6153 were combined and then the
object spectra were extracted. For the short exposures of NGC 6153 and the
standard stars, the object spectra were extracted from the reduced images.
When extracting the spectra, the position of the central star of NGC 6153 was
traced, as was the standard star’s position. Since NGC 6153 filled the slit,
we did not subtract the sky background. Exposures of the ThAr arc lamp were
extracted in the same way as the spectra of NGC 6153 and the standard stars
and used to determine the wavelength solution. For the wavelength calibration
of the CD4 wavelength intervals, we also used the sky lines in the deep
spectra of NGC 6153 (wavelengths from Osterbrock et al., 1996, 1997). We
combined the order-separated echelle spectra of the standard stars into a
single spectrum for each wavelength interval. To derive the system sensitivity
function, we used one spectrum of each of the standard stars in the CD1/CD3
wavelength intervals (the ones with the most signal) and one spectrum of LTT
3864 (most signal) and two of CD $-32^{\circ}$ 9927 (all available) for the
CD2/CD4 wavelength intervals (Hamuy et al., 1992, 1994). We then applied the
system sensitivity function to flux-calibrate the spectra of NGC 6153.

###  2.2 The construction of PV diagrams

We constructed position-velocity (PV) diagrams (or maps) for the emission
lines of interest in NGC 6153 from the two-dimensional spectra, of which
Figure 2 is an example. PV diagrams present the spatial structure within the
slit as a function of radial velocity along the line of sight. At each spatial
coordinate in the PV diagram (vertical position in the slit), the emission
from the plasma appears at its velocity with respect to the observer due to
the Doppler effect. In Figure 2, NGC 6153’s main structure is a shell. There
is a more diffuse structure outside it (left panel). Since the shell is
expanding, the approaching side is shifted to bluer wavelengths (more negative
velocities) while the receding side is shifted to redder wavelengths (more
positive velocities). The expansion of the main shell produces the
“$\bigcap$”-shaped structure in the PV diagram. The approaching and receding
sides merge to the same velocity at the edge of the shell since the expansion
there is perpendicular to the line of sight.

To construct the PV diagrams, we adopt the position of the central star as the
spatial zero point and slice the two-dimensional spectra into a collection of
one-dimensional spectra one pixel high. These slices correspond to spatial
slices of 0.492″ and 0.362″ for the blue and red arms, respectively. The
number of spatial slices varied for each cross disperser setting, but covered
the full extent of the slits in all cases. These spatial slices were then
interpolated in a Python script to construct PV diagrams for each line with a
uniform spatial sampling of 0.36″ per row in all of the PV diagrams and
spanning a common spatial extent for all wavelengths (i.e., we discard the
extra extension of the red slit). When converting the spectra to PV diagrams,
it is necessary to correct the intensities for the change in units from
wavelength to velocity, equivalent to multiplying the intensity by a factor of
$\lambda/c$, where $\lambda$ is the wavelength of the emission line. The PV
diagrams span a velocity range of 130 km/s about the systemic velocity of NGC
6153, which we adopted as 35.0 km/s.

By adopting the position of the central star as the spatial zero point, we
eliminate the effect of atmospheric refraction in the spatial direction within
the slit. However, we cannot compensate for its effect in the direction
perpendicular to the slit. Based upon the tabulated atmospheric refraction for
Cerro Paranal555https://www.eso.org/gen-
fac/pubs/astclim/lasilla/diffrefr.html, the image displacements perpendicular
to slit amount to a maximum of 0.14″, 0.07″, -0.26″, and -0.08″ for the cross
dispersers CD#1, CD#2, CD#3, and CD#4, respectively. Within each wavelength
interval, the maximum image offsets perpendicular to the slit is smaller,
0.10″, 0.02″, 0.10″, and 0.01″for the cross dispersers CD#1, CD#2, CD#3, and
CD#4, respectively. (CD#2/CD#4 are affected less since the refraction vector
was more parallel to the slit.) To the extent possible, we compare emission
lines within a given wavelength interval to minimize the effects of spatial
mis-matches due to atmospheric refraction.

We shall often need to compare two PV diagrams. In these comparisons, small
errors in wavelength calibration or uncertainties in laboratory wavelengths
could introduce spurious structures. To avoid this, we first align the PV
diagrams for the individual emission lines to a common velocity scale. The
simplest means of doing so is to use the measurements of the velocities for
the approaching and receding sides of the nebula, used to determine the
velocity splittings in Table 8, setting the mean value for each emission line
to a common value. This process should be reasonable since we will usually be
comparing PV diagrams for emission lines from ions that arise from the same
plasma.

###  2.3 Interstellar reddening

We use the interstellar reddening to establish a consistent flux scale across
our six wavelength intervals. A common flux scale is required in order to
study the temperature structure or to investigate the contributions of
distinct physical processes to the PV diagrams of a particular transition,
e.g., to understand why the forbidden nebular and auroral lines have different
velocity splitting. For this reason, we include the reddening as part of the
data reductions.

We determine both the interstellar reddening and the scale factors for the six
wavelength intervals using two one-dimensional spectra (spatially-integrated).
The first of these is obtained by summing the one-pixel spatial extractions of
the two-dimensional spectra to simulate a traditional one-dimensional
spectrum. The second spectrum is a “standard” one-dimensional spectrum from
the long exposure spectra of NGC 6153 that was reduced independently. In both
cases, we consider only the spatial extent of the blue slit. The results from
both spectra are equivalent, so we present those for the first spectrum. We
include this spectrum as online data.

We compute the reddening using the H I and He I lines and the Fitzpatrick
(1999) reddening law scaled for a total-to-selective extinction ratio of
$R_{V}=3.07$ (McCall & Armour, 2000). We refer the intensity of the H I lines
to H$\beta$ and that of the He I lines to He I $\lambda$4922 or He I
$\lambda$5876 using the intrinsic intensity ratios supposing an electron
temperature of $10,000$ K and the mean of electron densities of 1,000 and
10,000 cm-3 (atomic data: Table 1). We do not use the H8 line or He I
$\lambda$3889 because the two are blended. We cannot use the He I
$\lambda$5048 line since it is contaminated by charge overflow from [O III]
$\lambda$5007 in the adjacent order. Only for the CD2 wavelength interval is
the wavelength/reddening baseline long enough to establish a secure,
independent value for the interstellar reddening. Hence, our relative flux
calibration among the six wavelength intervals is relative to the long
exposure spectrum for the CD2 wavelength interval. Only the CD1 and CD2
wavelength intervals have emission lines in common that allow checking their
relative flux calibration.

Table 2: The H I and He I lines used for reddening Interval | H I lines | He I lines
---|---|---
CD1 | H9-H25 | 3187, 3614
CD2 |  H$\beta$, H$\gamma$, H$\delta$, | 3965, 4026, 4388, 4438,
| H$\epsilon$, H9-H11 | 4471, 4713, 4922
CD3b |  | 5015, 5876
CD3r | H$\alpha$ | 6678
CD4b | P11-P25 | 7281
CD4r | P7-P9 |

Table 2 presents the H I and He I lines available in each wavelength interval
for which theoretical line intensities exist. The lines shown in boldface are
the reference lines used to calculate the reddening. Table 3 presents the
wavelength interval/order (col. 1; the nomenclature $n$/$x$ implies wavelength
interval CD$n$ and order $x$), line wavelength (col. 2), the observed (col. 4)
and intrinsic (col. 5) relative line intensities for H I lines, the reddening
law from Fitzpatrick (1999) (col. 3; $A_{1}(\lambda)=A(\lambda)/E(B-V)$ for
$E(B-V)=1.0$ mag), and the reddening we find (col. 6). Table 4 presents the
analogous information for the He I lines, with He I $\lambda$4922 used as the
reference line in the top half and He I $\lambda$5876 as the reference line in
the bottom half. All of the line intensities in Tables 3 and 4 are from the
long exposure spectra, except H$\alpha$, which is from the short exposure
spectrum of interval CD3r (3rs in Table 3). We compute the reddening according
to

$E(B-V)=\frac{\log{(F(\lambda)/F(\lambda_{ref}))}-\log{(I(\lambda)/I(\lambda_{ref}))}}{-0.4(A_{1}(\lambda)-A_{1}(\lambda_{ref}))}$

where $F(\lambda)/F(\lambda_{ref})$ are the observed flux ratios, after
scaling if they are not from the CD2 wavelength interval,
$I(\lambda)/I(\lambda_{ref})$ are the intrinsic flux ratios, and
$A_{1}(\lambda)$ is the reddening law (Fitzpatrick, 1999, see above).

Table 3: H I line intensities and reddenings CD/# | line | $A_{1}(\lambda)$ | $\frac{\displaystyle F(\lambda)}{\displaystyle F(\mathrm{H}\beta)}$ | $\frac{\displaystyle I(\lambda)}{\displaystyle I(\mathrm{H}\beta)}$ | $E(B-V)$
---|---|---|---|---|---
| (Å) | (mag) | (obs) | (int) | (mag)
1/127 | 3669.45 | 4.67 | 0.0027 | 0.0041 | 0.40
1/127 | 3671.32 | 4.67 | 0.0031 | 0.0045 | 0.35
1/127 | 3673.81 | 4.67 | 0.0030 | 0.0050 | 0.51
1/127 | 3676.38 | 4.66 | 0.0036 | 0.0056 | 0.43
1/127 | 3679.37 | 4.66 | 0.0038 | 0.0063 | 0.49
1/127 | 3682.82 | 4.66 | 0.0042 | 0.0072 | 0.52
1/126 | 3682.82 | 4.66 | 0.0046 | 0.0072 | 0.44
1/127 | 3686.83 | 4.65 | 0.0053 | 0.0082 | 0.43
1/126 | 3686.83 | 4.65 | 0.0051 | 0.0082 | 0.48
1/127 | 3691.55 | 4.65 | 0.0064 | 0.0095 | 0.40
1/126 | 3691.55 | 4.65 | 0.0058 | 0.0095 | 0.49
1/127 | 3697.16 | 4.64 | 0.0071 | 0.011 | 0.45
1/126 | 3697.16 | 4.64 | 0.0066 | 0.011 | 0.53
1/126 | 3703.86 | 4.64 | 0.0078 | 0.013 | 0.54
1/126 | 3711.98 | 4.63 | 0.0094 | 0.016 | 0.53
1/125 | 3711.98 | 4.63 | 0.0091 | 0.016 | 0.56
1/126 | 3721.95 | 4.62 | 0.018 | 0.020 | 0.07
1/125 | 3721.95 | 4.62 | 0.017 | 0.020 | 0.17
1/125 | 3734.37 | 4.61 | 0.014 | 0.024 | 0.57
1/125 | 3750.15 | 4.59 | 0.020 | 0.031 | 0.46
1/124 | 3750.15 | 4.59 | 0.020 | 0.031 | 0.46
1/124 | 3770.63 | 4.57 | 0.024 | 0.040 | 0.57
1/123 | 3770.63 | 4.57 | 0.023 | 0.040 | 0.59
1/123 | 3797.91 | 4.54 | 0.032 | 0.053 | 0.56
1/122 | 3797.91 | 4.54 | 0.033 | 0.053 | 0.51
1/122 | 3835.40 | 4.51 | 0.045 | 0.073 | 0.56
1/121 | 3835.40 | 4.51 | 0.044 | 0.073 | 0.58
2/124 | 3770.63 | 4.57 | 0.025 | 0.040 | 0.50
2/123 | 3770.63 | 4.57 | 0.023 | 0.040 | 0.60
2/123 | 3797.91 | 4.54 | 0.033 | 0.053 | 0.52
2/122 | 3797.91 | 4.54 | 0.031 | 0.053 | 0.60
2/122 | 3835.40 | 4.51 | 0.048 | 0.073 | 0.49
2/121 | 3835.40 | 4.51 | 0.045 | 0.073 | 0.56
2/118 | 3970.08 | 4.38 | 0.11 | 0.16 | 0.48
2/117 | 3970.08 | 4.38 | 0.11 | 0.16 | 0.52
2/114 | 4101.73 | 4.26 | 0.18 | 0.26 | 0.59
2/114 | 4101.73 | 4.26 | 0.18 | 0.26 | 0.59
2/108 | 4340.47 | 4.05 | 0.38 | 0.47 | 0.45
2/107 | 4340.47 | 4.05 | 0.37 | 0.47 | 0.51
2/96 | 4861.35 | 3.56 | 1 | 1 |
3rs/93 | 6563.00 | 2.30 | 5.00 | 2.86 | 0.49
4b/74 | 8323.42 | 1.57 | 0.0039 | 0.0013 | 0.60
4b/74 | 8333.78 | 1.57 | 0.0045 | 0.0015 | 0.61
4b/74 | 8345.54 | 1.56 | 0.0046 | 0.0016 | 0.56
4b/74 | 8359.00 | 1.56 | 0.0059 | 0.0019 | 0.63
4b/74 | 8374.48 | 1.55 | 0.0059 | 0.0021 | 0.56
4b/74 | 8392.40 | 1.55 | 0.0066 | 0.0024 | 0.55
4b/74 | 8413.32 | 1.54 | 0.0066 | 0.0028 | 0.47
4b/73 | 8413.32 | 1.54 | 0.0067 | 0.0028 | 0.48
4b/73 | 8437.95 | 1.53 | 0.0091 | 0.0032 | 0.56
4b/73 | 8467.26 | 1.52 | 0.011 | 0.0038 | 0.55
4b/73 | 8502.48 | 1.51 | 0.012 | 0.0045 | 0.51
4b/72 | 8545.38 | 1.50 | 0.016 | 0.0055 | 0.56
4b/72 | 8598.39 | 1.48 | 0.019 | 0.0067 | 0.54
4b/71 | 8665.02 | 1.47 | 0.025 | 0.0084 | 0.57
4b/71 | 8750.46 | 1.44 | 0.030 | 0.011 | 0.53
4b/70 | 8862.89 | 1.41 | 0.040 | 0.014 | 0.54
4r/235 | 9229.01 | 1.32 | 0.079 | 0.025 | 0.55
4r/233 | 9545.97 | 1.24 | 0.100 | 0.037 | 0.47
4r/230 | 10049.37 | 1.13 | 0.21 | 0.055 | 0.59
Table 4: He I line intensities and reddenings CD/# | line | $A_{1}(\lambda)$ | $\frac{\displaystyle F(\lambda)}{\displaystyle F(\mathrm{ref})}$ | $\frac{\displaystyle I(\lambda)}{\displaystyle I(\mathrm{ref})}$ | $E(B-V)$
---|---|---|---|---|---
| (Å) | (mag) | (obs) | (int) | (mag)
1/147 | 3187.75 | 5.24 | 0.77 | 3.44 | 0.93
1/146 | 3187.75 | 5.24 | 0.80 | 3.44 | 0.91
1/129 | 3613.64 | 4.73 | 0.11 | 0.42 | 1.16
2/118 | 3964.73 | 4.39 | 0.39 | 0.86 | 0.96
2/117 | 3964.73 | 4.39 | 0.37 | 0.86 | 1.02
2/116 | 4026.19 | 4.33 | 1.22 | 1.73 | 0.45
2/107 | 4387.93 | 4.01 | 0.40 | 0.46 | 0.30
2/106 | 4387.93 | 4.01 | 0.36 | 0.46 | 0.53
2/105 | 4437.55 | 3.96 | 0.05 | 0.06 | 0.48
2/105 | 4471.48 | 3.93 | 2.94 | 3.67 | 0.55
2/104 | 4471.48 | 3.93 | 2.85 | 3.67 | 0.63
2/99 | 4713.15 | 3.70 | 0.37 | 0.44 | 0.86
2/99 | 4713.15 | 3.70 | 0.37 | 0.44 | 0.86
2/95 | 4921.93 | 3.50 | 1 | 1 |
3b/122 | 5015.68 | 3.40 | 1.53 | 2.19 | -4.17
3b/104 | 5875.62 | 2.71 | 15.80 | 10.71 | 0.54
3r/92 | 6678.15 | 2.24 | 5.98 | 3.02 | 0.59
3r/91 | 6678.15 | 2.24 | 5.94 | 3.02 | 0.59
4b/85 | 7281.35 | 1.96 | 0.83 | 0.64 | 0.18
4b/85 | 7281.35 | 1.96 | 0.83 | 0.64 | 0.18
1/147 | 3187.75 | 5.24 | 0.048 | 0.32 | 0.81
1/146 | 3187.75 | 5.24 | 0.050 | 0.32 | 0.79
1/129 | 3613.64 | 4.73 | 0.0071 | 0.039 | 0.92
2/118 | 3964.73 | 4.39 | 0.025 | 0.080 | 0.76
2/117 | 3964.73 | 4.39 | 0.024 | 0.080 | 0.79
2/116 | 4026.19 | 4.33 | 0.077 | 0.16 | 0.49
2/107 | 4387.93 | 4.01 | 0.025 | 0.043 | 0.44
2/106 | 4387.93 | 4.01 | 0.023 | 0.043 | 0.54
2/105 | 4437.55 | 3.96 | 0.0033 | 0.0060 | 0.52
2/105 | 4471.48 | 3.93 | 0.19 | 0.34 | 0.54
2/104 | 4471.48 | 3.93 | 0.18 | 0.34 | 0.57
2/99 | 4713.15 | 3.70 | 0.024 | 0.041 | 0.60
2/99 | 4713.15 | 3.70 | 0.024 | 0.041 | 0.60
2/95 | 4921.93 | 3.50 | 0.063 | 0.093 | 0.54
3b/122 | 5015.68 | 3.40 | 0.097 | 0.20 | 1.16
3b/104 | 5875.62 | 2.71 | 15.80 | 1 |
3r/92 | 6678.15 | 2.24 | 0.38 | 0.28 | 0.69
3r/91 | 6678.15 | 2.24 | 0.38 | 0.28 | 0.67
4b/85 | 7281.35 | 1.96 | 0.053 | 0.060 | -0.18
4b/85 | 7281.35 | 1.96 | 0.053 | 0.060 | -0.18
Figure 3: We plot the reddening, $E(B-V)$, from Tables 3 and 4 as a function of wavelength for H I and He I lines. For the lines indicated as “H I, CD#$X$”, the line ratio is $\mathrm{H}n/\mathrm{H}\beta$ or $\mathrm{P}n/\mathrm{H}\beta$ and plotted at the wavelength of $\mathrm{H}n$ or $\mathrm{P}n$, respectively, the Balmer and Paschen lines originating at upper level $n$. For the reddening computed from the ratio of Paschen to Balmer lines, $\mathrm{P}n/\mathrm{B}n$, the reddening is plotted at the wavelength of the Paschen line. The horizontal dashed line represents the mean value of $E(B-V)$ for the H I lines in the CD2 wavelength interval (reference value). For the He I lines, the squares represent ratios using He I $\lambda$4922 as the reference line while the crosses use He I $\lambda$5876 as the reference line. The reddening computed from the He I $\lambda\lambda$5015/4922 and He I $\lambda\lambda$7281/5876 line ratios fall at negative values (and are not shown). Both lines are apparently much too weak.  Table 5: Flux scale factors Interval | Long exposure | Short exposure | short/long
---|---|---|---
CD1 | 0.95 (0.915-0.974) | $0.778\pm 0.028$ | $1.221\pm 0.023$
CD2 | 1.0 (reference) | $0.991\pm 0.047$ | $1.009\pm 0.047$
CD3b | 2.0 (1.9-2.1) | $1.525\pm 0.091$ | $1.312\pm 0.042$
CD3r | 0.6 (0.57-0.63) | $0.430\pm 0.047$ | $1.40\pm 0.13$
CD4b | 0.5 (0.48-0.51) | $0.515\pm 0.019$ | $0.971\pm 0.021$
CD4r | 0.4 (0.38-0.42) | $0.402\pm 0.020$ | $0.995\pm 0.005$

We cross-check the CD2-referenced reddenings in several ways. We compute the
reddening using the H I $\mathrm{P}n/\mathrm{B}n$ ratios, where $\mathrm{P}n$
and $\mathrm{B}n$ are the Paschen and Balmer lines, respectively, with upper
level $n$. This uses CD1/CD4b and CD2/CD4r line ratios, but not including
H$\beta$. There are no H I lines in the CD3b interval. However, we tie its
calibration more tightly to other intervals by computing the reddening from
the He I lines using He I $\lambda$5876 as the reference line.

When a line is well-detected in adjacent orders, we use both measurements.
Note that the relative line intensities in Tables 3 and 4 already include the
scale factors required to place all six wavelength intervals on a common flux
scale. These flux scale factors are given in column 2 of Table 5 with the
acceptable range for the scale factor in parentheses. These flux scale factors
apply to the PV diagrams. The scale factors between the long and short
exposures (column 4) are determined by comparing line fluxes measured in both
spectra and so are independent of the flux scale factors. The scale factors
for the short exposure spectra (column 3) are the ratio of the two previous
scale factors. Usually, the uncertainty is dominated by the range allowed for
the scale factors of the long exposure spectra.

Figure 3 presents the results, showing the reddening, $E(B-V)$, as a function
of wavelength for the H I and He I lines. For the H I lines, the filled
circles show the line ratio with respect to H$\beta$ with the reddening
plotted at the wavelength of the H I lines (numerator). The open gray
triangles show the reddening computed using the ratios of Paschen and Balmer
lines arising from the same upper level, plotted at the wavelength of the
Paschen lines (the plot is less confusing that way). The horizontal dashed
line is the mean value of $E(B-V)$ for the CD2 wavelength interval. For the He
I lines, the open squares show the reddening computed using He I $\lambda$4922
as the reference line and plotted at the position of each He I line
(numerator). The black crosses present the reddening computed from the He I
lines using He I $\lambda$5876 as the reference wavelength, again plotted at
the wavelength of the He I line in the numerator. For the H I and He I lines
plotted as filled circles and open squares, the colour indicates the
wavelength interval.

For the H I lines, the most anomalous is H I $\lambda$3722, which is blended
with [S III] $\lambda$3722\. For the CD1 interval, the reddening decreases for
the bluest lines. In contrast, the bluest Paschen lines imply slightly higher
extinction. This trend is not apparent when the reddening is computed using
the ratio of Paschen and Balmer lines. This could well be the same effect
noted by Mesa-Delgado et al. (2009) due to $l$-changing collisions causing
departures from Case B theory since its effect will largely disappear when
comparing Paschen and Balmer lines from the same upper level. The He I lines
show considerable scatter. The scatter is more pronounced when using He I
$\lambda$4922 as the reference wavelength, in part because the wavelength
baseline for the blue lines is shorter and also because it is the weaker
reference line. He I $\lambda\lambda$3187, 3614, 3964, 5015 are all apparently
too weak, regardless of the reference line. Since they all have the metastable
2s levels as their lower levels (He I $\lambda$3187 is a triplet state, the
others singlet states), this may be due to radiative transfer effects. He I
$\lambda$7281 is too weak, independent of the reference line we choose, but it
is not clear why. He I $\lambda$6678 has the same lower level and its
intensity is, if anything, slightly too high. Most of the Paschen lines from
the CD4b wavelength interval are not anomalous.

Table 6: Average $E(B-V)$ Interval | H I lines | He I lines
---|---|---
CD1 | $0.496\pm 0.064\ ^{\tablenotemark{a}}$ |
CD1, overlap | $0.560\pm 0.026$ |
CD2 | $0.535\pm 0.053$ | $0.528\pm 0.078\ ^{\tablenotemark{b}}$
CD3b |  | $0.536\ ^{\tablenotemark{b}}$
CD3r | $0.486$ | $0.589\pm 0.005\ ^{\tablenotemark{c}}$
CD4b | $0.561\pm 0.032$ |
CD4b, $\mathrm{P}n/\mathrm{H}n$ | $0.532\pm 0.021$ |
CD4r | $0.536\pm 0.061$ |
CD4r, $\mathrm{P}n/\mathrm{H}n$ | $0.545\pm 0.023$ |

Table 6 presents the mean reddening values for lines in each wavelength
interval by the different means described above. The mean reddening for the H
I lines from the CD2 interval is compatible with that measured for all other
wavelength intervals, and we adopt its value, $E(B-V)=0.535\pm 0.053$ mag, as
our reddening for NGC 6153. Based upon the Fitzpatrick (1999) reddening law,
this is equivalent to $c(\mathrm{H}\beta)=1.424E(B-V)=0.76$ dex.

The reddening we find is lower than that reported by others. Kingsburgh &
Barlow (1994) find $c(\mathrm{H}\beta)=0.96$ dex from their optical spectrum,
Liu et al. (2000) report $c(\mathrm{H}\beta)=1.27\pm 0.06$ and $1.30\pm 0.01$
dex based upon their scanned (entire object) and minor axis optical spectra,
respectively, Pottasch et al. (2003) deduce $c(\mathrm{H}\beta)=1.19$ dex
comparing the observed H$\beta$ flux with various 6 cm radio fluxes, and
McNabb et al. (2016) obtain $c(\mathrm{H}\beta)=1.32$ dex based upon the H I
Balmer lines. It is not obvious why our reddening is different since we
checked that our flux calibrations are similar to the historical calibrations
in the ESO
archives666https://www.eso.org/observing/dfo/quality/UVES/qc/SysEffic_qc1.html.
Also, the Fitzpatrick (1999) extinction law is similar to the Cardelli et al.
(1989) extinction law used by McNabb et al. (2016).

Table 7: He II line intensities and abundances CD/# | line | $A_{1}(\lambda)$ | $\frac{\displaystyle F(\lambda)}{\displaystyle F(\mathrm{ref})}$ | $\frac{\displaystyle I(\lambda)}{\displaystyle I(\mathrm{ref})}$ | $\frac{\displaystyle\mathrm{He}^{+i}}{\displaystyle\mathrm{H}^{+}}$
---|---|---|---|---|---
| (Å) | (mag) | (obs) | (int) |
He I |  |  |  |  |
2/104 | 4471.50 | 3.93 | 5.00 | 6.05 | 0.115
3b/104 | 5875.60 | 2.71 | 26.9 | 17.5 | 0.115
3r/92 | 6678.15 | 2.24 | 9.74 | 5.03 | 0.117
3r/91 | 6678.15 | 2.24 | 9.66 | 4.99 | 0.116
He II |  |  |  |  |
1/146 | 3203.17 | 5.22 | 4.49 | 10.4 | 0.021
1/145 | 3203.17 | 5.22 | 4.01 | 9.26 | 0.019
2/100 | 4685.68 | 3.73 | 15.1 | 16.5 | 0.014
3b/113 | 5411.52 | 3.04 | 1.43 | 1.10 | 0.012
3r/101 | 6074.11 | 2.58 | 0.052 | 0.032 | 0.015
3r/100 | 6074.11 | 2.58 | 0.048 | 0.030 | 0.014
3r/100 | 6118.26 | 2.55 | 0.056 | 0.034 | 0.014
3r/99 | 6170.60 | 2.52 | 0.077 | 0.046 | 0.016
3r/96 | 6406.38 | 2.39 | 0.14 | 0.079 | 0.016
3r/92 | 6683.20 | 2.24 | 0.19 | 0.099 | 0.013
3r/91 | 6683.20 | 2.24 | 0.19 | 0.099 | 0.013
3r/89 | 6890.90 | 2.14 | 0.26 | 0.127 | 0.013
3r/88 | 6890.90 | 2.14 | 0.29 | 0.135 | 0.013

Whether our reddening is correct is less important than whether our intrinsic,
reddening-corrected line intensity ratios are correct. For wavelength
intervals where the density of H I or He I lines is high (CD2, the red end of
CD4b, the blue half of the CD4r), our line ratios corrected for our reddening
must necessarily give the correct intrinsic ratios, because that is how we
determine the reddening. For the same reason, the flux scale in the vicinity
of the He I $\lambda\lambda$5876,6678 and H$\alpha$ lines will also be
correct. To check that there are no problems across the CD3b or CD3r
wavelength intervals where there are few H I or He I lines, Table 7 presents
the $\mathrm{He}^{+}/\mathrm{H}^{+}$ and $\mathrm{He}^{2+}/\mathrm{H}^{+}$
abundances for lines that fall in those wavelength intervals and for He II
$\lambda\lambda$3203,4686 from the CD1 and CD2 intervals. The format of Table
7 is identical to that of Tables 3 and 4, except that the last column presents
the He ionic abundance ratios and the intensity ratios are given on the scale
where $F(\mathrm{H}\beta)=I(\mathrm{H}\beta)=100$. We assume a density of
$10^{4}$ cm-3 and temperatures of 8,000 K and 10,000 K when computing the He+
and He2+ abundances, respectively (atomic data: Table 1). After correcting for
reddening (col. 5), our He I line intensities are very similar to those found
by Liu et al. (2000), as expected given that they are used to derive the
reddening and flux scale factors. Given the constancy of the
$\mathrm{He}^{2+}/\mathrm{H}^{+}$ abundance ratio for the lines in the CD3b
and CD3r wavelength intervals, there is no problem with flux scale. Our only
test of the flux scale across the blue half of the CD4b wavelength interval is
the [Ar III] $\lambda\lambda$7135,7751 lines. Since they indicate very similar
[Ar III] temperatures (Figure 15), it would appear that the shape of the flux
scale in this part of the CD4b wavelength interval is secure, but we have no
objective measure of whether its normalization is correct. (The He II
$\lambda\lambda$7177,7592 lines are badly affected by an instrumental artifact
and atmospheric absorption, respectively.)

So, while we are unable to explain why the reddening we determine for NGC 6153
is different from others, we are confident that our relative line intensities,
once corrected for our reddening, yield the correct intrinsic relative
intensities. Note that the flux calibration does not affect any result based
upon kinematics.

##  3 Results: The plasma structure

The multi-component structure of the plasma in NGC 6153’s nebular shell is the
unifying theme of this section. We first analyze the ionization structure of
NGC 6153 in detail. We consider both the information available in the
morphology of the PV diagrams as well as the more common Wilson diagram, which
presents the velocity splitting as a function of the ionization energy.
Following this, we investigate the physical conditions based upon kinematics,
forbidden lines, and permitted lines. Finally, we show that, by assuming two
plasma components in NGC 6153, we can explain the anomalous [N II] temperature
and [O II] density as the result of excitation of the [N II] $\lambda$5755 and
[O II] lines due to recombination, mostly in the additional plasma component.

Both the kinematics and the physical conditions imply the presence of two
distinct plasma components. One component has the kinematics and physical
conditions typically-associated with planetary nebulae (e.g., as described in
textbooks Aller, 1984; Osterbrock & Ferland, 2006), so we shall refer to it as
the “normal nebular plasma”. The other component has unusual kinematics and is
colder and denser than the former, so we shall call it the “additional plasma
component”.

###  3.1 The ionization structure of NGC 6153

Figure 4: We present the PV diagrams for lines spanning the full range of
ionization energies in NGC 6153: C IV $\lambda\lambda$5801,5811, He II
$\lambda$4686, [Ar IV] $\lambda$4740, [O III] $\lambda$4959, [Ar III]
$\lambda$7135, [N II] $\lambda$6583, and [O I] $\lambda$6300 (top to bottom).
The intensity in each panel is normalized to its maximum value, indicated at
upper left in each panel, below the line identification. The color bar at top
is common to all panels (-5% to 100% of the maximum value; linear scale). We
identify several morphological features that we refer to in the text. There
are clear, continuous, and systematic changes in the shape of the emission
line profile as a function of the ionization energy. Likewise, the difference
in velocity between the approaching and receding sides varies with ionization
energy.

A PV diagram (e.g., Figure 2) is the result of the spatial distribution, the
kinematics, and the physical conditions of the of plasma that emits a given
line within the nebular volume intercepted by the spectrograph’s slit
convolved with the fine structure of that line and the mass of the emitting
ion. Figure 4 presents a gallery of PV diagrams that span the full range of
ionization energies we could usefully study in NGC 6153, from C IV
$\lambda\lambda$5801,5811 (64.5 eV) to [O I] $\lambda$6300 (0 eV). In Figure
4, we indicate features that we shall refer to later, such as the emission
from the nebula’s main shell, the filament, and the diffuse emission, both of
which are beyond the receding side of the main shell. The line that
schematically indicates the velocity ellipse for the main shell is drawn for
the [O III] $\lambda$4959 line and repeated in each panel, making it easier to
appreciate the systematic changes in the extent of the main shell (away from
the central star) or its velocity splitting as a function of ionization
energy. In Appendix A (Figures 44-51), we present a large collection of PV
diagrams of all stages of ionization.

There are clear and systematic changes in the shape of the line emission
profiles as a function of ionization energy in Figure 4. In the most highly
ionized gas (C IV $\lambda\lambda$5801,5811), there is little structure apart
from a round velocity ellipse (the low S/N is an impediment; the central star
also emits in this line; Liu et al. (2000)). In the next most highly ionized
line, He II $\lambda$4686, much more structure is apparent, and the main
shell’s spatial extent increases, creating a profile that is more square in
shape. Then, in [Ar IV] $\lambda$4740, the emission from the main shell
changes, especially on the approaching side, to a more rounded shape, mostly
as a result of a greater velocity difference between the approaching and
receding sides of the main shell, but with little increase in spatial extent.
With [O III] $\lambda$4959, the increasing velocity difference between the two
sides of the main shell continues, but there is also less emission on the
receding side of the main shell along the direction to the central star (the
horizontal line; ordinate value of zero). Continuing to lower ionization
energies, in [Ar III] $\lambda$7135, an extension beyond the main shell on its
receding side begins to appear and there is a dimming of both sides of the
main shell along the line of sight to the central star. Proceeding to [N II]
$\lambda$6583, the emission from the main shell decreases substantially and
the filament is by far the brightest feature. Finally, in the lowest
ionization stage, [O I] $\lambda$6300, the main shell almost disappears while
the filament remains very bright (the other emission is telluric).

Figure 5: These panels present the Wilson diagram, adding details from top to
bottom. The top panel presents the velocity splitting as a function of
ionization energy from all forbidden nebular lines and all permitted lines,
except those of O0, C+, N+, O+, and Ne+. These lines establish a well-defined
relation between velocity splitting and ionization potential. In the second
panel, we add the auroral forbidden lines of N+, O+, O2+, S+, S2+, Ar2+, and
Ar3+ (open squares). For N+, O+, O2+, and Ar3+, these transitions have smaller
velocity splitting than the nebular transitions. In the bottom panel, we add
the permitted lines of O0, C+, N+, O+, and Ne+. Although these lines span a
wide range of ionization potentials, they share a common velocity splitting.
The permitted lines of H0 and He0 and the forbidden lines of O2+ and Ne2+ are
shown in larger symbols since these lines sample the majority of the nebular
volume. The small symbols for Mn4+, Ne3+ (forbidden), and C3+ (permitted)
indicate that they are difficult measurements. The tick marks and labels
indicate the ionization energies.

Figure 5 presents three Wilson (1950) diagrams for NGC 6153 in which we
quantify the foregoing, adding details from top to bottom. For emission lines
arising from different ions and different excitation processes, we compute the
line splitting, measured as the velocity difference between the approaching
and receding sides of the nebula. In Figure 5, we plot the line splitting as a
function of the ionization potential of the “parent” ion, i.e., the ion that
initiates the emission process. For example, O2+ ions are responsible for
initiating the emission of the permitted lines of O II, and the emission of
forbidden [O III] lines. The Bowen fluorescence lines of O III and N III are a
special case. These lines arise due to fluorescence from He II Ly$\alpha$, so
we plot them at the ionization energy of He+ and not the ionization energies
of O2+ and N2+.

We measure the line splitting near the position of central star, within the
three rows of the PV diagram in the rectangle in Figure 2, over the spatial
extent 0.72″–1.80″ NE of the central star. Due to the symmetry with respect to
the line of sight towards the central star, measuring the line splitting in
this region minimizes projection effects. All of the measurements of the line
splittings used to construct Figure 5 are given in Table 8. When several lines
from a given ion and process are available, we plot the average line splitting
and its standard deviation (error bars) in Figure 5. We adopt ionization
energies from Kramida et al. (2021).

Figure 6: These panels present the PV diagrams in the lines of C II
$\lambda$6578, O II $\lambda$4649, N II $\lambda$5680 , and Ne
II$\lambda$3694\. Although the PV diagram for Ne II $\lambda$3694 is of lower
S/N, all of the lines share the same morphology, indicating that they arise
from the same volume of plasma. Note that the morphology of these PV diagrams
is quite different from the morphology of the PV diagrams for [O III]
$\lambda\lambda$4959,5007 and [Ne III] $\lambda$3869 (Figure 4, Figure 47,
Figure 48). They are more similar to the PV diagrams in Figure 46, but their
overall shape is even more circular because of their larger velocity
splitting.

In the top panel of Figure 5, the velocity splitting of the emission lines in
NGC 6153 decreases as the ionization energy for the parent ion increases
(Wilson, 1950). This well-known result arises since the most highly ionized
ions are in the innermost plasma that expands most slowly, i.e., the inner
plasma cannot overrun the plasma outside it. This panel includes all lines due
to forbidden nebular transitions (transitions between the first excited state
and the ground state or ground term), Bowen fluorescence lines of O III and N
III, charge exchange lines of O III, and all permitted lines, except those of
O I, C II, N II, O II, and Ne II. The sequence, from [Ar V], [Ne IV], O III,
and He II at the smallest velocity splitting to [S II], [O II], and [N II] at
the largest, is therefore expected. With the exception of the H I lines, the
permitted and forbidden lines follow a single, continuous ionization
structure. Even lines such as O III $\lambda\lambda$3757,5592 that arise from
charge exchange and the O III and N III Bowen fluorescence emission fall, as
they should, at velocities similar to those for the emission from He II and O
III recombination (higher ionization energies).

In the second panel, we add the auroral forbidden lines (transitions from the
second excited state to the first excited state). For the lines of [O II], [N
II], [O III], and [Ar IV] (Table 8), the auroral lines have smaller velocity
splitting than their nebular counterparts, e.g., [O II]
$\lambda\lambda$7320,7330 have a smaller velocity splitting than [O II]
$\lambda\lambda$3726,3729. The auroral and nebular lines of [S II], [S III],
and [Ar III] differ by of order 1 km/s, which is similar to the typical
dispersion (standard deviation) of the line splitting in Table 8 for many
ions. As we shall see, the cases of [N II] and [O II] arise due to
contamination of the auroral lines from recombination (§3.3), while the
difference for [O III] appears to be real and due to the ionization structure
(§3.3). For the [S III] lines (similar velocity splitting) and the [Ar IV]
lines, atmospheric absorption confuses the issue (details in Appendix A).

In the bottom panel of Figure 5, we add the permitted lines of O I, C II, N
II, O II, and Ne II. Though the lines from these ions span a large range in
ionization energy, they all have similar velocity splitting. In particular,
the O II and Ne II lines arise from O2+ and Ne2+ ions, respectively, as do the
[O III] and [Ne III] lines. Though the Ne II and [Ne III] lines have similar
velocity splitting, the O II and [O III] lines do not. Since we expect all
lines emitted by a given ion to share the same volume of the nebula, the
different velocity splitting for the O II and [O III] lines is striking.
Similarly, the C II and N II lines would normally be expected to present
velocity splittings similar to those of He I, [S III], [Cl III], and [Ar III],
but the velocity splitting for these lines is systematically too low given
their ionization potentials, by $\sim 3-5$ km/s.

The velocity splitting for these lines, $44-45$ km/s, is very similar to that
of the C III, N III, and [Ar IV] lines at $43-44$ km/s. Figure 6 presents
examples of the PV diagrams of the C II, N II, O II, and Ne II lines. It is
notable that the morphology of these PV diagrams differs from the morphologies
of the PV diagrams for [Ar IV] $\lambda$4740 (Figure 4) or those in Figure 46
that have very similar velocity splitting, indicating that they arise from a
different volume of plasma. The PV diagrams illustrate more clearly than the
Wilson diagram (Figure 5) that the kinematics of the C II, N II, O II, and Ne
II lines is different from the kinematics of other lines of either the same
ionization potential or velocity splitting. (See Figures 4 and 47,
respectively, for the PV diagrams of the [O III] $\lambda$4959 and [Ne III]
$\lambda$3869 lines.)

Finally, there is a cluster of permitted lines from H I, O I, and Si II, at
approximately 14 eV and 46 km/s (the auroral lines of [O II] and [N II] also
fall here; middle and bottom panels of Figure 5). The case of H I is the
simplest to understand. Given that it is emitted throughout the whole nebular
volume, its velocity splitting should be similar to that of other lines that
sample the majority of this volume, such as the lines of He I, [O III], and
[Ne III]. Indeed, this is the case, so its deviation from the general trend is
not unexpected.

Second, the O I $\lambda\lambda$7771,9265 lines in question are quintuplet
lines, whose lower level is the meta-stable 3s ${}^{5}\mathrm{S}^{o}$ state
that can decay to the O0 ground state only through a forbidden transition.
Hence, they cannot be excited by fluorescence from the ground state and so are
likely the result of recombination. Figure 7 compares the PV diagrams of these
lines with the emission from O II $\lambda$9982, obtained simultaneously. The
morphology and velocity splitting of the PV diagrams for these O I lines,
especially O I $\lambda$9265 (least affected by sky lines), is very similar to
that of O II $\lambda$9982\. So, it appears that the O I
$\lambda\lambda$7771,9265 lines arise from the same plasma that emits the O II
lines. García-Rojas et al. (2022) find the same result.

Third, the Si II lines involved are Si II $\lambda\lambda$5041, 6347, 6374
from multiplets V5 (5041Å) and V2, respectively, and we detect them with good
S/N (see Figure 51). We suspect that these lines in NGC 6153 are partly
excited by recombination and partly by fluorescence as a minority ion in zones
of higher ionization. So, the velocity splitting from these Si II lines in NGC
6153 may not reflect the kinematics of the volume where Si2+ is the dominant
ionization state, which is how this data point is plotted in Figure 5. We
provide more details in Appendix A.

Figure 7: These panels present the PV diagrams of the O I $\lambda\lambda$
7771, 7774 (7775 to the red), and 9265 lines. In all cases, some sky lines
have been subtracted, which is what produces the faint vertical bands. The
black streak is a cosmic ray. The contours are of the intensity of the
emission of the O II $\lambda$9982 line. In this and following figures, we
plot the contours at 10%, 20%, …, 90% of the maximum intensity. The kinematics
of these O I quintuplet lines are compatible with those of the O II
$\lambda$9982 line.

The general trend of a velocity splitting that decreases as the ionization
energy of the parent ion increases in Figure 5 is the expected one. This trend
defines what we refer to as the _normal nebular plasma_. There are two
novelties though. First, the auroral forbidden lines of [O II], [N II], and [O
III] clearly have lower velocity splitting than their nebular counterparts,
the first two due to contamination from recombination and the last due to real
temperature structure (§3.3). This also occurs for [Ar IV], but may be due to
atmospheric absorption. Second, the lines of O I, C II, N II, O II, and Ne II
share a common velocity despite spanning a large range in the ionization
energy of the parent ions. These lines appear to define a second kinematic
component that does not participate in the general trend and which we call the
_additional plasma component_.

Table 8: Line splitting Parent | $E_{ion}$ | Velocity splitting | Lines
---|---|---|---
| (eV) | (km/s) |
H+ | 13.6 | $47.37\pm 0.48$ | H I $\lambda\lambda$3770, 3797, 3835, 3970, 4101, 4340, 4861, 6563, 9229, 9545, 10049
He+ | 24.6 | $48.51\pm 0.75$ | He I $\lambda\lambda$3187, 3614, 3965, 4026, 4387, 4471, 4713, 4922, 5015, 5876, 6678, 7281
He2+ | 54.4 | $41.09\pm 1.00$ | He II $\lambda\lambda$3203, 4541, 4686, 4859, 5411, 6560, 10123
C0 | 0.0 | $47.23\pm 0.95$ | [C I] $\lambda\lambda$9850 (nebular)
C2+ | 24.4 | $44.48\pm 0.46$ | C II $\lambda\lambda$4267, 5342, 6151, 6461, 6578, 7231, 9903
C3+ | 47.9 | $44.4\pm 1.8$ | C III $\lambda$4647
C4+ | 64.5 | $38.67\pm 0.54$ | C IV $\lambda\lambda$5801, 5811
N+ | 14.5 | $52.72\pm 0.18$ | [N II] $\lambda\lambda$6548, 6583 (nebular)
N+ | 14.5 | $46.4$ | [N II] $\lambda$5755 (auroral)
N2+ | 29.6 | $45.0\pm 1.1$ | N II $\lambda\lambda$4035, 4041, 5666, 5676, 5680, 5686, 5710
N2+ | 54.4 | $43.92\pm 0.29$ | N III $\lambda\lambda$4097, 4103, 4634, 4641 (Bowen fluorescence)
N3+ | 47.4 | $43.26\pm 0.63$ | N III $\lambda\lambda$4379, 5147
O0 | 0.0 | $51.30\pm 0.38$ | [O I] $\lambda\lambda$6300, 6364 (nebular)
O+ | 13.6 | $49.90\pm 0.30$ | [O II] $\lambda\lambda$3726, 3729 (nebular)
O+ | 13.6 | $46.32\pm 0.04$ | [O II] $\lambda\lambda$7319, 7320, 7330, 7331 (auroral)
O+ | 13.6 | $45.1\pm 1.4$ | O I $\lambda\lambda$7771, 7774, 9265
O2+ | 35.1 | $47.2$ | [O III] $\lambda$4959 (nebular)
O2+ | 35.1 | $44.6$ | [O III] $\lambda$4363 (auroral)
O2+ | 35.1 | $44.58\pm 0.96$ | O II $\lambda\lambda$4069.6, 4069.9, 4072, 4076, 4084, 4089, 4317, 4349, 4366, 4591, 4596, 4639,
|  |  | 4649, 4662, 4676, 6500.8, 6501.4, 9982
O2+ | 54.4 | $43.18\pm 0.69$ | O III $\lambda\lambda$3133, 3299, 3312, 3340, 3444, 3754, 3759 (Bowen fluorescence)
O3+ | 54.9 | $42.6\pm 1.2$ | O III $\lambda$3260, 3707
O3+ | 54.9 | $41.43\pm 0.98$ | O III $\lambda\lambda$3757, 3774, 5592 (charge exchange)
Ne2+ | 41.0 | $46.02\pm 0.32$ | [Ne III] $\lambda\lambda$3869, 3967 (nebular)
Ne2+ | 41.0 | $45.68\pm 0.55$ | Ne II $\lambda\lambda$3335, 3568, 3694, 5130, 9096
Ne3+ | 63.5 | $39.3\pm 2.0$ | [Ne IV] $\lambda$4724 (nebular)
Si+ | 8.2 | $50.5$ | S I $\lambda$6486
Si2+ | 16.3 | $46.67\pm 0.60$ | Si II $\lambda\lambda$5041, 6347, 6371
S+ | 10.4 | $53.03\pm 0.50$ | [S II] $\lambda\lambda$6716, 6731 (nebular)
S+ | 10.4 | $52.4$ | [S II] $\lambda$4069 (auroral)
S2+ | 23.3 | $49.6$ | [S III] $\lambda\lambda$9531 (nebular)
S2+ | 23.3 | $50.27\pm 0.37$ | [S III] $\lambda$6312 (auroral)
Cl+ | 13.0 | $49.1\pm 2.7$ | [Cl II] $\lambda\lambda$8578, 9123 (nebular)
Cl2+ | 23.8 | $50.26\pm 0.30$ | [Cl III] $\lambda\lambda$5517, 5537 (nebular)
Cl3+ | 39.6 | $46.27\pm 0.47$ | [Cl IV] $\lambda\lambda$7530, 8045 (nebular)
Ar2+ | 27.6 | $49.02\pm 0.22$ | [Ar III] $\lambda$7135, 7751 (nebular)
Ar2+ | 27.6 | 50.4 | [Ar III] $\lambda$5191 (auroral)
Ar3+ | 40.7 | $43.05\pm 0.21$ | [Ar IV] $\lambda\lambda$4711, 4740 (nebular)
Ar3+ | 40.7 | 38.7 | [Ar IV] $\lambda$7262 (auroral)
Ar4+ | 59.8 | $36.87\pm 0.43$ | [Ar V] $\lambda$6435, 7006 (nebular)
K3+ | 45.7 | $47.78\pm 0.52$ | [K IV] $\lambda\lambda$6101, 6795 (nebular)
Mn4+ | 51.4 | $48.29\pm 0.29$ | [Mn V] $\lambda\lambda$5701, 5861, 6083, 6393

###  3.2 Physical conditions

In the following subsections, we study the temperature and density in the
nebular shell of NGC 6153 based upon a variety of methods. Table 9 summarizes
these results. The temperatures derived from forbidden lines and the He I
lines are substantially higher than the temperatures derived using the
permitted lines of N II and O II. Likewise, a dichotomy exists concerning the
density, with the N II and O II lines indicating higher densities than other
methods. Thus, the physical conditions reflect the results of the kinematics,
i.e., that two plasma components are present.

####  3.2.1 Thermal broadening of line profiles

Ions belonging to the same plasma component should share common spatial,
velocity, density, and temperature structures provided that they occupy the
same (or similar) volume within the nebula. Even so, emission lines from two
ions that share the same volume of the nebula will have different PV diagrams
if they have different intrinsic fine structure or different thermal line
widths. Therefore, we can exploit differences in atomic mass to infer the
plasma temperature for ions that share the same nebular volume if we can
account for the differences in the intrinsic line structure of the two lines
(e.g., Courtès et al., 1968; Dyson & Meaburn, 1971; García-Díaz et al., 2008).
Determining the temperature in this way circumvents issues related to atomic
data, but requires comparing only ions that share the same nebular volume.

We will consider lines arising from ions of H+, He+, and O++. The latter two
are expected to occupy very similar volumes within the nebula, especially
since NGC 6153 is highly ionized and optically thin. The volume of the nebula
occupied by H+ will differ from that occupied by He+ and O++, but the effect
of this difference is predictable and clear: the PV diagrams for lines from H+
will present an excess at low expansion velocities and near the central star
(the He2+ zone) compared to PV diagrams for lines arising from He+ and O++.
The sensitivity of the process depends upon the difference in atomic mass, so
it is most instructive to compare H and He with heavy elements. The case of
O++ allows us to extend our results to the permitted lines of C II, O II, N
II, and Ne II. In order to minimize instrumental and observational effects, we
consider only lines from the CD2 wavelength interval, for which the slit’s
position angle was closest to the parallactic angle, so they suffer least from
differential atmospheric refraction.

The width observed for an emission line will depend upon the velocity
structure of the nebula, the instrumental resolution, the thermal broadening,
and the intrinsic line structure. The thermal and instrumental broadening are
Gaussian or closely so in profile, so we approximate the line width as
$\sigma^{2}=\sigma_{neb}^{2}+\sigma_{ins}^{2}+\sigma_{th}^{2}+\sigma_{fs}^{2}$,
where $\sigma_{neb}$ is the contribution due to the nebula’s kinematic
structure, $\sigma_{ins}$ the instrumental broadening, $\sigma_{th}$ the
thermal broadening, and $\sigma_{fs}$ the fine structure of the emission line
itself.

Figure 8: left panel: This plot presents the line profile for the spatial
interval used to compute the velocity splitting (see Figure 2) for the [O III]
$\lambda$4959 line as well as the models based upon this line for the H$\beta$
and He I $\lambda$4471 lines. Right panel: This plot presents the model of the
H$\beta$ line based upon the [O III] $\lambda$4959 line from the left panel as
well as the profiles of this model after broadening with a Gaussian to match
the thermal line width of the H$\beta$ line for temperatures of 3,000 K, 6,000
K, 8,000 K, and 10,000 K. The latter is the largest modification made to the
[O III] line profile.  Figure 9: These panels present the ratio of H$\beta$
(left column) and H$\gamma$ (right column) with respect to [O III]
$\lambda$4959\. The ratio images assume temperatures of 3,000 K, 6,000 K,
8,000 K, and 10,000 K (top to bottom) when broadening the PV diagram of [O
III] $\lambda$4959\. In the top row, the contours are those of the PV diagram
for [O III] $\lambda$4959\. In the bottom row, the contours are those of
H$\beta$ (left column) and H$\gamma$ (right column). The ratios best
approximate a constant value for a temperature of 8,000 K.  Figure 10: These
panels present the ratio of the He I $\lambda$4922 line with respect to
H$\beta$ (left column) and H$\gamma$ (right column), assuming temperatures of
3,000 K, 6,000 K, 8,000 K, and 10,000 K (top to bottom). The contours are
those of the PV diagram for He I $\lambda$4922 in the top row, but of H$\beta$
(left) and H$\gamma$ (right) in the bottom row. The ratios are most constant
when the assumed temperature to broaden the He I lines is 8,000 K.

The effect of atomic mass appears through the thermal broadening of the lines
emitted by a given ion. The thermal width is given by
$\sigma_{th}=\sqrt{82.5((10^{-4}T_{e})/m_{ion})}$, where $T_{e}$ is the
temperature of the plasma (K) and $m_{ion}$ is the mass of the ion (atomic
mass units; García-Díaz et al., 2008). Thus, the difference in thermal line
width can be accounted for by convolving the PV diagram of the emission line
from the more massive ion with a Gaussian to account for the difference in
atomic mass between it and the ion with lower atomic mass.

The differences in the line structure can always be accommodated if one of the
lines is a single, spectrally-resolved emission component. In that case, we
can modify the PV diagram of the single line to match the line structure of
the other, reflected in its PV diagram: Multiple copies of the single line are
shifted and scaled appropriately to mimic the structure of the line with
multiple components.

The H I and He I triplet lines have substructure that must be taken into
account. The H I Balmer lines have 7 components, spread over a small range in
velocity (Clegg et al., 1999). The seven components divide into two groups
whose spread in velocity is significantly less than the difference in velocity
between the two groups (blue and red). Within the blue group, about 80% of the
total intensity is split between two components while, within the red group, a
single component accounts for about 80% of the total intensity (e.g., Fig. 1
of Clegg et al., 1999). We adopt the fraction of the emission from each group
from Clegg et al. (1999). The He I lines are either triplet or singlet states.
The triplets are formed by three
($n\,^{3}\mathrm{S}-n^{\prime}\,{}^{3}\mathrm{P}$) or six
($n\,^{3}D-n^{\prime}\,{}^{3}\mathrm{P}$) individual transitions; all but one
conform a blue group spread over 1-3 km/s while the last transition falls
10-20 km/s to the red (Van Hoof, 2018). We follow Axner et al. (2004) to
determine the relative intensities of the individual transitions in He I,
finding that the blue group contains 89% of the total intensity. Within the
blue group, two transitions separated by about half of the total spread
account for about 72% of its total intensity.

So, we approximate the H I and He I triplet lines as two components, one
representing the blue group and the other the red line/group. Two copies of
the PV diagram of a single line are created and added together after
appropriately shifting them in wavelength and scaling them in flux according
to the details of the H I or He I line involved. Then, this model PV diagram
is broadened by convolving it with a Gaussian so as to match the thermal width
of the H I or He I line. Matching the thermal width is a process of trial and
error in which we consider electron temperatures between 3,000 K and 15,000 K.
We then compare this model to the observed PV diagram, determining the best
thermal broadening by searching for the PV diagram with the most constant
ratio.

This kinematic temperature is an emission-weighted mean temperature, measured
by the motions of the ions in the plasma. It does not imply that there is a
single, uniform temperature within the plasma emitting in the H I, He I, O II,
and [O III] lines. The plasma may well contain temperature gradients or small-
scale structure, but the PV diagrams inherently reflect the result of that
structure. (Given the thermal width of the H I and He I lines, the kinetic
temperature will not be very sensitive to small-scale structure.) One worry is
that the temperature sensitivity varies among the lines considered. The
intensity of the [O III] lines increases with increasing temperature, but the
intensities of the other lines decreases, an effect that cannot be compensated
exactly. To mitigate the issue, we consider only [O III] $\lambda$4959.

Figure 11: These panels present the ratio of the PV diagram of He I
$\lambda$4471 (left column) and He I $\lambda$4922 (right column) with respect
to [O III] $\lambda$4959\. The ratios assume temperatures of 3,000 K, 6,000 K,
8,000 K, and 10,000 K (top to bottom). In the top row, the contours are those
of the PV diagram for [O III] $\lambda$4959\. In the bottom row, the contours
are those of He I $\lambda$4471 (left) and He I $\lambda$4922 (right). Again,
the ratios are most constant for a temperature of 8,000 K.  Figure 12: These
panels present the PV diagrams for the O II $\lambda$4649 and [O III]
$\lambda$4959 lines and the ratio O II $\lambda$4649/[O III] $\lambda$4959\.
The contours represent the intensity of the O II $\lambda$4649 line. Both
lines are single lines from the CD2 wavelength interval from the same ion, so
there are no corrections for the intrinsic line structure or thermal
broadening (supposing they arise from the same plasma component). The solid
black color at right is due to contamination of the PV diagram of O II
$\lambda$4649 by C III $\lambda$4650\.  Figure 13: These panels present the
ratios of PV diagrams C II, N II, O II, and Ne II lines, as indicated in each
panel. In all panels, the contours are of the intensity of the numerator. No
correction for thermal broadening was applied to any of the PV diagrams. The C
II $\lambda$4267/O II $\lambda$4649 and O II $\lambda\lambda$6509,6510/N II
$\lambda$5680 ratios required modeling multiple C II and O II lines. The
horizontal bands in the O II $\lambda$6509/N II $\lambda$5680 ratio are due to
the poor background subtraction for O II $\lambda$6509\. The ratio of PV
diagrams all approximate a constant value, indicating that these permitted
lines of C II, N II, O II, and Ne II arise from the same plasma component.

Most of the structure in the line profiles for the lines of the heavy elements
is due to the velocity structure of the nebula, not the thermal width of the
line (nor the instrumental resolution). For example, the observed line width
of [O III] $\lambda$4959 is slightly more than 18 km/s FWHM. Of this, the
thermal broadening contributes 5.4 km/s (supposing a temperature of 10,000 K,
less if the temperature is lower), while the instrumental broadening of order
10 km/s. Since these add in quadrature, the broadening due to the velocity
structure dominates, amounting to 14 km/s.

Even so, the substantial modifications required to match the [O III]
$\lambda$4959 line to the H I Balmer lines gives the method good sensitivity.
The left panel of Figure 8 demonstrates that accounting for the line structure
of either H$\beta$ or He I $\lambda$4471 requires only minor modifications.
However, the broadening required to match the thermal line width of a hydrogen
line can be substantial, as shown in the right panel of Figure 8, amounting to
as much as 20.7 km/s for a temperature of 10,000 K. The modifications required
to match the thermal width of a He line to a H line are less important because
of the larger thermal widths of the He lines. Likewise, matching the thermal
width of an O line to a He line also requires less broadening than illustrated
in Figure 8.

Figure 9 compares the PV diagrams of the H$\beta$, H$\gamma$, and [O III]
$\lambda$4959 lines. In the left column, we present the ratio of H$\beta$ with
respect to [O III] $\lambda$4959\. (By “[O III] $\lambda$4959”, we mean the
model of the H$\beta$/H$\gamma$ line constructed with the [O III]
$\lambda$4959 PV diagram.) The four panels consider temperatures of 3,000 K,
6,000 K, 8,000 K, and 10,000 K when broadening the PV diagram for [O III]
$\lambda$4959\. Since the volumes occupied by H+ and O2+ largely coincide, the
ratio should be approximately constant when the appropriate temperature is
used to broaden the PV diagram for [O III] $\lambda$4959\. If the assumed
temperature is too low, the PV diagram for [O III] $\lambda$4959 will not be
sufficiently broadened, and we expect a minimum in the H$\beta$/[O III]
$\lambda$4959 ratio where the emission from [O III] $\lambda$4959 is most
intense. Conversely, if the assumed temperature is too high, the PV diagram
for [O III] $\lambda$4959 will be broadened too much, diffusing its emission
too far, to velocities too far from and too close to the systemic velocity. In
this case, we expect that the H$\beta$/[O III] $\lambda$4959 ratio will
present a maximum where the H$\beta$ emission is most intense. The main
difference in the volumes occupied by H+ and O2+ is that O2+ does not sample
as completely as H+ the innermost volume of the nebular shell occupied by He2+
(closest to the central star and with velocities closest to the systemic
velocity).

The four panels in the left column of Figure 9 present a clear trend. In the
first panel, with [O III] $\lambda$4959 broadened assuming a temperature of
3,000 K, the ratio varies the most. The H$\beta$/[O III] $\lambda$4959 ratio
falls strongly at the velocities and spatial positions where the emission from
[O III] $\lambda$4959 is most concentrated (the contour lines) because the PV
diagram for H$\beta$ is broader than that of [O III] $\lambda$4959\. As a
result, the ratio is too high at the velocities both closest to and farthest
from the systemic velocity. As the assumed temperature increases to 6,000 K
(second row) and 8,000 K (third row), the ratio better approximates a constant
value. For a temperature of 8,000 K, the ratio is very constant. For an
assumed temperature of 10,000 K, we see an increase in the ratio at the
velocities and positions where the H$\beta$ emission is most intense, implying
that the broadening of the [O III] $\lambda$4959 PV diagram has now gone too
far. For a temperature of 10,000 K, the ratio of the H$\beta$/[O III]
$\lambda$4959 decreases at the velocities that most differ from the systemic
velocity, also a result of the [O III] $\lambda$4959 PV diagram being now too
diffuse. Hence, we conclude that a temperature between 6,000 K and 8,000 K is
that which best matches the kinematics of the lines of H$\beta$ and [O III]
$\lambda$4959\. Comparing the last two panels in the left column of Figure 9,
the pattern of the emission from H$\beta$ is also becoming visible in the
third panel, for an assumed temperature of 8,000 K. So, the temperature that
will best characterize the kinematics of both the H$\beta$ and [O III]
$\lambda$4959 lines will be somewhat below 8,000 K (we return to this in
§4.5).

The right column of Figure 9 presents the analogous results for the ratio
H$\gamma$/[O III] $\lambda$4959\. Again, the most constant value of this ratio
occurs for an assumed temperature of 8,000 K, though, again, the best
temperature is likely to be somewhat lower than this.

In Figure 10, we consider the ratio of the He I $\lambda$4922 singlet line
with respect to H$\beta$ and H$\gamma$ for assumed temperatures of 3,000 K,
6,000 K, 8,000 K, and 10,000 K when broadening the He I $\lambda$4922 line.
For 3,000 K, the He I $\lambda$4922/H$\beta$ and He I $\lambda$4922/H$\gamma$
ratios indicate that the He I $\lambda$4922 line is narrower than the H I
lines, since the ratio is high where there is He I $\lambda$4922 emission. To
some extent, this persists at 6,000 K, especially considering the He I
$\lambda$4922/H$\gamma$ ratio. At 8,000 K the two ratios are approximately
constant. At 10,000 K, there is a bright rim in the PV diagram of the He I
$\lambda$4922/H$\beta$ and He I $\lambda$4922/H$\gamma$ ratios and the ratios
are depressed where the emission from H$\beta$ and H$\gamma$ is strong, all of
which indicate that the He I $\lambda$4922 line is too broad in these cases.
Hence, it appears that 8,000 K is the temperature that best permits matching
the He I $\lambda$4922, H$\beta$, and H$\gamma$ PV diagrams. In the first
three rows of Figure 10, there is a depression in the He I
$\lambda$4922/H$\beta$ and He I $\lambda$4922/H$\gamma$ ratios for the
velocities closest to the systemic velocity and spatial positions closest to
the central star because He+ is supplanted by He2+ as the dominant ionization
stage of helium in the innermost part of the nebular shell.

We present the ratios of the PV diagrams of He I $\lambda$4471 (left column)
and He I $\lambda$4922 (right column) with respect to that of [O III]
$\lambda$4959 in Figure 11. These ratios are computed after broadening the [O
III] $\lambda$4959 line assuming temperatures of 3,000 K, 6,000 K, 8,000 K,
and 10,000 K. Regardless of the temperature assumed, there is a depression in
the He I $\lambda$4471/[O III] $\lambda$4959 and He I $\lambda$4922/[O III]
$\lambda$4959 ratios at velocities near the systemic velocity and positions
near the central star. This arises because (1) O2+ is the dominant ionization
stage of oxygen in the central part of the nebula while He+ is not and (2) the
smaller thermal widths better resolve this central region. Outside this
central zone, the He I $\lambda$4471/[O III] $\lambda$4959 and He I
$\lambda$4922/[O III] $\lambda$4959 ratios vary by approximately 10% for
temperatures of 6,000 K and 8,000 K.

Figure 12 presents the PV diagrams for the lines of O II $\lambda$4649 and [O
III] $\lambda$4959 as well as the ratio of these two lines. Both lines arise
from the O2+ ion and are single lines, so there is no correction for either
line structure or thermal broadening, assuming that they arise from the same
plasma component. Hence, the ratio O II $\lambda$4649/[O III] $\lambda$4959 is
of no use in determining the temperature of the plasma from which these lines
arise. However, since this ratio is very non-uniform, it clearly indicates
that the two lines do not arise from the same plasma component.

Figure 14: These panels present the PV diagrams of the [O III]
$\lambda$4363,4959 lines and the [O III] temperature (bottom). The contours in
all panels are those of the intensity of [O III] $\lambda$4363\. The white
colour in the temperature map includes positions with zero values or
unphysical values. There is a mild temperature gradient from the zone close to
the central star (near the systemic velocity and in the middle of the slit) to
zones farther away (the smallest and largest velocities and towards the top of
the slit).

Given that all of these PV diagrams are very similar to O II $\lambda$4649,
the C II, N II, O II, and Ne II lines presumably all arise in the same plasma
component. In Figure 13, we test this hypothesis. All of the panels in Figure
13 present ratios of different C II, N II, O II, and Ne II lines, all of which
yield approximately constant values. In calculating these ratios, we do not
correct for thermal broadening since the broadening involved varies from 0.7
to 1.3 km/s over the $3,000-10,000$ K temperature range. The O II
$\lambda$4662/O II $\lambda$4649 ratio, is a sanity check to test the method.
The two lines are from the same ion and the same spectral order. In four of
the six ratios, the lines are from the same wavelength interval (CD2 in three
cases, CD3 in the other), so differential atmospheric refraction should not be
a problem. In two cases, N II $\lambda$5680/O II $\lambda$4649 and Ne II
$\lambda$3694/O II $\lambda$4649, the ratios compare lines from wavelength
intervals CD3 and CD1 with respect to CD2. These are the cases where the ratio
varies most. The basic result of Figure 13 is that ratios of the lines of C
II, N II, O II, and Ne II produce constant values, as expected if these lines
arise in the same plasma component.

Figures 9-11 argue that the kinematics of H I, He I, and [O III] lines are
compatible with these emission lines arising from the same plasma component
whose temperature is $\sim 8,000$ K. On the other hand, Figure 12 indicates
that the O II $\lambda$4649 does not arise from the same plasma component that
gives rise to the H I, He I, and [O III] lines. Figure 13 indicates that this
line, as well as other lines of C II, N II, O II, and Ne II, have kinematics
that are compatible with an origin in a common plasma component. So, by
extension, all of these lines arise from a different plasma component from
that producing the H I, He I, and [O III] lines.

####  3.2.2 Forbidden lines

Figure 15: These panels present the PV diagrams of the lines of [Ar III]
$\lambda$7135,7751,5191 the [Ar III] temperature from the [Ar III]
$\lambda\lambda$5191/7135 and 5191/7751 line ratios in the right column. The
contours are of the intensity of the [Ar III] $\lambda$7135 line. The color
scale in the right column is the same as used for the [O III] temperature in
Figure 14.  Figure 16: These panels present the PV diagrams of the [S II]
$\lambda\lambda$6716,6731 lines and of the [S II] density. In all panels the
contours are of the [S II] $\lambda$6716 line intensity. The white color in
the PV diagram of the [S II] density represent non-physical values or where
there is no [S II] emission. The color scale for the density spans the range
$0-10,000$ cm-3.  Figure 17: These panels present the PV diagrams of the [Cl
III] $\lambda\lambda$5717,5537 lines and of the [Cl III] density. In all
panels the contours are of the [Cl III] $\lambda$5717 line intensity. The
white color in the PV diagram of the [Cl III] density represent non-physical
values or where there is no [Cl III] emission. The color scale for the density
spans the range $0-10,000$ cm-3.  Figure 18: These panels present the PV
diagrams for the lines of [Ar IV] $\lambda\lambda$4711,4740 and of the [Ar IV]
density. In all panels, the contours are of the intensity of the [Ar IV]
$\lambda$4711 line. The white color in the PV diagram of the [Ar IV] density
represent non-physical values or where there is no [Ar IV] emission. The color
scale for the density spans the range $0-10,000$ cm-3.

We construct PV diagrams for the electron temperature and density diagnostics
from collisionally-excited lines. Since we resolve both the spatial structure
along the slit and the velocity structure along the line of sight, regions
expected to have higher temperatures, such as those close to the central star,
have different PV coordinates from other volumes of the nebula. We compute the
physical conditions using PyNeb (Luridiana et al., 2015) to convert an
intensity ratio into an electron temperature or density.

We consider the electron temperatures derived from the [O III] and [Ar III]
lines as well as the electron densities derived from the [S II], [Cl III] and
[Ar IV] lines. As we shall see (§3.3), the [N II] and [O II] forbidden lines
have an important excitation component due to recombination, in addition to
the usual collisional excitation process, so we defer their discussion for
later. Finally, due to the radial velocity of NGC 6153 at the time of the
observations, the [S III] $\lambda\lambda$9069,9531 lines coincided with
strong telluric absorption lines, so they cannot be used to determine a
reliable electron temperature (Stevenson, 1994).

Figure 14 presents the PV diagrams of the [O III] $\lambda\lambda$4363,4959
lines as well as the PV diagrams of the [O III] temperature. In computing the
[O III] temperature, we adopt an electron density of 4,000 cm-3 (atomic data:
Table 1). The [O III] temperature map presents three regimes. In the main
shell, there is a slight gradient from the outermost parts of the nebula
(largest distance from the central star, largest velocities w.r.t. the
systemic velocity) to the innermost part (spatial positions closer to the
central star, velocities near the systemic velocity), that varies only
slightly $9,000-10,000$ K. Inside the main shell, the plasma is hotter,
$10,000-11,000$ K. In the diffuse emission beyond the main shell at the
largest recession velocities, the temperature is lowest $8,000-9,000$ K.

Figure 15 presents the PV diagrams of the [Ar III] $\lambda\lambda$5191, 7135,
7751 lines as well as the PV diagrams of the temperature based upon the ratios
of [Ar III] $\lambda\lambda$5191/7135 and [Ar III] $\lambda\lambda$5191/7751.
In this case, lines from different wavelength intervals must be used (CD3b and
CD4b). Again, we adopt an electron density of 4,000 cm-3 (atomic data: Table
1). The [Ar III] temperature map is limited to the main shell and the filament
on its receding side. The [Ar III] temperature map is more uniform than the [O
III] temperature, though with larger uncertainties, and slightly lower, by
$\sim 500$ K.

Figure 19: These panels present the intensities of reddening-corrected,
high-$n$ Balmer lines with respect to the intensity of H$\beta$ as a function
of the upper level for assumed electron temperatures of 1,000 K (left) and
10,000 K (right). The implied densities are between $<1,000$ cm-3 and $\sim
10,000$ cm-3.

Figure 20: These panels present the intensities of reddening-corrected,
high-$n$ Paschen lines with respect to the intensity of H$\beta$ as a function
of the upper level for assumed electron temperatures of 1,000 K (left) and
10,000 K (right). The implied densities are of $\sim 1,000$ cm-3 at 1,000 K
and perhaps $\sim 10,000$ cm-3 at 10,000 K.

Turning to the electron density indicators, Figure 16 presents the PV diagrams
of the [S II] $\lambda\lambda$6716,6731 lines and of the [S II] electron
density. To compute the electron density, we assume an electron temperature of
10,000 K (atomic data: Table 1). There is a clear gradient in the electron
density implied by the [S II] $\lambda\lambda$6716/6731 line ratio, with lower
densities towards the periphery of the object, at either the velocities that
differ most from the systemic velocity or at the greatest distance from the
central star. The variation in electron density appears to exceed a factor of
2, from approximately 2,000 cm-3 to $4,000-5,000$ cm-3. The filament on the
receding side of the main shell that is the brightest feature of the [S II]
$\lambda\lambda$6716,6731 PV diagrams is of low density, so it is presumably
bright due to a change in the ionization stage for sulfur. This feature is not
evident in the H$\alpha$ line (Figure 2), so it is presumably of low mass.

Figure 17 presents the PV diagrams of the [Cl III] $\lambda\lambda$5517,5537
lines and the [Cl III] density. Again, we assume an electron temperature of
10,000 K (atomic data: Table 1). The PV diagram of the [Cl III] density is
quite uniform over the entire area that includes [Cl III] emission. There is,
however, a “red border” around the outer edge of the area with [Cl III]
emission, as if the density drops at the outer edge of the Cl2+ zone. By and
large, this is congruent with the variation in the density as traced by the [S
II] lines, since the [S II] lines trace plasma with a lower degree of
ionization. The higher [Cl III] density throughout most of the Cl2+ zone
agrees with the [S II] electron density at the velocities and spatial
coordinates in common. However, one discrepancy is the higher density implied
for the filament on the receding side of the main shell.

Figure 18 presents the PV diagrams of the [Ar IV] $\lambda\lambda$4711,4740
lines and the [Ar IV] electron density (assuming an electron temperature of
10,000 K; atomic data: Table 1). The PV diagram of the [Ar IV] electron
density is very uniform. However, the electron density implied by the [Ar IV]
lines is substantially lower than that found from the [Cl III] or [S II]
lines, even for the velocities and spatial coordinates in common, more like
the low densities found at the periphery from [S II]. Perhaps, a different
atomic data set could resolve the issue. It is unlikely due uncertainty in the
line intensity ratio, since it implies a 20% change, which we think unlikely
for such strong lines.

Based upon the [S II] and [Cl III] densities, the density throughout most of
the main shell of NGC 6153 appears to be approximately $4,000-5,000$ cm-3 with
a lower density region at the extreme velocities and distance from the central
star (Figures 16 and 17). The electron density implied by the [Ar IV] lines is
about a factor of 2 lower throughout the nebular volume in common with the [S
II] and [Cl III] emission.

####  3.2.3 Permitted lines

Figure 21: Top row: These panels present the PV diagrams of the line ratios He
I $\lambda\lambda$4713/4026 (left), He I $\lambda\lambda$4713/4471 (middle),
and He I $\lambda\lambda$4713/5876 (right). The contours show the intensity of
the He I $\lambda\lambda$4026, 4471, and 5876 lines (the denominator of the
ratio). Middle row: These panels present various statistics for the ratios of
the PV diagrams of He I $\lambda\lambda$4713/4026 (left), He I
$\lambda\lambda$4713/4471 (middle), and He I $\lambda\lambda$4713/5876 (right)
as a function of the line intensities in the original PV diagrams of the He I
$\lambda\lambda$4026, 4471, and 5876 lines (denominator). In the top and
middle rows, the line ratios have been corrected for the flux scale factors
(Table 5), but not for reddening. Bottom row: These panels compare the ratio
of the line intensities of He I $\lambda\lambda$4713/4026 (left), He I
$\lambda\lambda$4713/4471 (middle), and He I $\lambda\lambda$4713/5876
(right), now corrected for reddening (Table 6), with the theoretical line
intensities from Porter et al. (2013). We adopt the mean line ratio for all
pixels exceeding 30% of the maximum line intensity of the denominator and the
uncertainty given by the standard deviation. The He I lines are compatible
with temperatures $\log T_{e}=3.91-4.07$ when considering densities up to
$10^{4}\,\mathrm{cm}^{-3}$ (see Figure 22).

The intensities of high-$n$ Balmer and Paschen lines may be used to infer the
electron density, though this requires adopting an electron temperature. We
use the theoretical line emissivities for Case B (atomic data: Table 1) and
the line intensities measured from the 1-D spectrum (Table 3).

Figure 19 presents the intensities of the high-$n$ Balmer lines relative to
the intensity of H$\beta$. We consider temperatures of 1,000 K (left panel)
and 10,000 K (right panel) as illustrative of the range of relevant values.
The H14 line (H I $\lambda$3721) has an anomalously high intensity, presumably
due to contamination ([S III] $\lambda$3721). As the temperature increases, so
does the implied electron density, but the implied range of electron densities
is modest, $<1,000$ to $<10,000$ cm-3 for this temperature range.

Figure 20 presents the intensities of the high-$n$ Paschen lines relative to
the intensity of H$\beta$ (Table 3). We consider the same representative
electron temperatures. In this case, an electron density of 1,000 cm-3 is
found at a temperature of 1,000 K, but the implied electron density is higher
at 10,000 K, with 10,000 cm-3 being perhaps the most representative value,
except for the highest Paschen lines. Given the difficulty of measuring the
intensities of the highest Paschen lines accurately, due to both line crowding
and telluric absorption, we shall give the electron density derived from them
lower weight. Generally, the H I lines appear to indicate densities of
$\lesssim 10,000\,\mathrm{cm}^{-3}$.

Figure 22: Top row: These panels present the PV diagrams of the line ratios He
I $\lambda\lambda$4026/5876 (left) and He I $\lambda\lambda$4471/5876 (right).
The contours show the intensity of the He I $\lambda$5876 line (the
denominator). Middle row: These panels present various statistics for the line
ratios of He I $\lambda\lambda$4026/5876 (left) and He I
$\lambda\lambda$4471/5876 (right) as a function of the line intensities in the
original PV diagram of the He I $\lambda$5876 line (denominator). These line
ratios have been corrected for the flux scale factors (Table 5), but not
reddening. Bottom row: These panels compare the ratio of the lines of He I
$\lambda\lambda$4026/5876 (left) and He I $\lambda\lambda$4471/5876 (right),
now corrected for reddening, with the theoretical line intensities from Porter
et al. (2013). These line ratios are insensitive to temperature, but have some
sensitivity to density and are useful to check the reddening (Table 6). These
He I lines are compatible with densities up to $10^{4}\,\mathrm{cm}^{-3}$.
Figure 23: These panels present the PV diagrams for the lines (left) of N II
$\lambda$4041, N II $\lambda$5666, and N II $\lambda$5680, and for the line
ratios (right) N II $\lambda\lambda$4041/5680 and N II
$\lambda\lambda$5666/5680. The contour lines are of the N II $\lambda$5680
intensity. The spatial coverage of the PV diagram of N II $\lambda$4041 is
less than for the others. Both the temperature- and density-sensitive maps
(4041/5680 and 5666/5680, respectively) are reasonably uniform.

Figure 24: Left: We present the temperature-sensitive N II
$\lambda\lambda$4041/5680 ratio and its uncertainty (the pink region), based
upon an intensity limit at 40% of the maximum intensity and the 90% width of
the distribution of pixel values. This ratio is corrected for both reddening
and the scale factor between the CD2 and CD3b wavelength intervals.
$T_{e}>2,000$ K if the electron density is very low; $T_{e}>5,000$ K for
higher densities. Right: We present the density-sensitive N II
$\lambda\lambda$5666/5680 ratio and its uncertainty (the pink region; same
definitions). The N II $\lambda\lambda$5666/5680 ratio is compatible with high
densities ($3,000-10^{5}$ cm-3) and a wide range of electron temperatures
($500-16,000$ K).

The He I lines also permit us to set limits on the electron temperature and
density in NGC 6153 (atomic data: Table 1). The ratio of
$n\,\mathrm{S}-n^{\prime}\,\mathrm{P}$ transitions to
$n\,\mathrm{D}-n^{\prime}\,\mathrm{P}$ transitions are sensitive to the
electron temperature. The ratios of like transitions,
$n\,\mathrm{S}-n^{\prime}\,\mathrm{P}$ to
$n^{\prime\prime}\,\mathrm{S}-n^{\prime}\,\mathrm{P}$ or
$n\,\mathrm{D}-n^{\prime}\,\mathrm{P}$ to
$n^{\prime\prime}\,\mathrm{D}-n^{\prime}\,\mathrm{P}$, have some limited
sensitivity to density. Here, we use the triplet lines He I $\lambda$4713
($4\,^{3}\mathrm{S}-2\,^{3}\mathrm{P}$) and He I $\lambda\lambda$4026, 4471,
5876 ($n\,\mathrm{D}-2\,^{3}\mathrm{P}$; $n=5,4,3$, respectively) to
illustrate the process. (He I $\lambda$4713 is the faintest of these lines.)

In the top row of Figure 21, we present the ratios of the the PV diagrams of
He I $\lambda$4713 line to the He I $\lambda\lambda$4026, 4471, 5876 lines to
set limits upon the electron temperature. As shown, these line ratios are not
corrected for reddening. The contours are of intensities of the He I
$\lambda\lambda$4026, 4471, 5876 lines (the denominator of the ratio). The
line ratios are generally uniform, except perhaps the emission from the
approaching side of the main shell in the He I $\lambda\lambda$4713/4026
ratio. Note that this part of the He I $\lambda$4026 (4026.2Å) profile suffers
a slight contamination due to the He II $\lambda$4025.6 line that contaminates
the emission from the approaching side of the main shell.

The three panels in the middle row of Figure 21 present statistics for the He
I $\lambda\lambda$4713/4026, He I $\lambda\lambda$4713/4471, and He I
$\lambda\lambda$4713/5876 ratios (left to right) for the pixels that exceed
10%, 20%, …, 90% of the intensity of the maximum intensity in the PV diagrams
of the He I $\lambda\lambda$4026, 4471, 5876 lines, respectively. The error
bars indicate the standard deviation of the distribution of the ratio values
at each threshold level. The crosses indicate the median values at each
threshold level while the dashed lines indicate the values of the 5-th and
95-th percentiles of the distribution, again at each threshold level. All
statistics include only the $0.72\arcsec-9.00\arcsec$ spatial range to exclude
the flat-fielding artefacts in the top few rows of PV diagrams (top row). The
mean and median values do not vary strongly with the threshold level,
indicating that the temperature variation within the plasma emitting these He
I lines is modest. The different threshold levels correspond to different
volumes of the plasma that emit these lines. At the 10% threshold, plasma
throughout the main shell contributes to the statistics of the line ratios in
Figure 21 while, at the 90% threshold, the statistics reflect only the plasma
along the line of sight to the end of the main shell, farthest from the
central star.

Given the limited variation in these line ratios (and temperatures) we adopt
the mean value and its standard deviation for the threshold at 30% of the
maximum intensity as our temperature indicator and its uncertainty (this
sample includes over 500 pixels). The range of values spanned by the standard
deviation at this threshold usually includes almost the entire range of
variation in the mean or median at all threshold values. In the bottom row of
Figure 21, we compare the intensity ratio, now also corrected for reddening
with the theoretical values (atomic data: Table 1). By this measure, the He I
lines imply an electron temperature of $\log T_{e}$ of $3.85-4.05$ (He I
$\lambda\lambda$4713/4026), $3.90-4.07$ (He I $\lambda\lambda$4713/4471), and
$3.89-4.03$ (He I $\lambda\lambda$4713/5876) if electron densities range over
$10^{2}-10^{6}\,\mathrm{cm}^{-3}$.

In Figure 22, we present the He I $\lambda\lambda$4026/5876 and He I
$\lambda\lambda$4471/5876 line ratios, which have some sensitivity to the
electron density. The three rows present the same information as in Figure 21.
Here, only the He I $\lambda\lambda$4026/5876 ratio provides additional
information, restricting the electron density to values of
$10^{4}\,\mathrm{cm}^{-3}$ or lower. Considering this restriction, the
previous electron temperatures are restricted to the temperature ranges of
$\log T_{e}$ of $3.91-4.05$ (He I $\lambda\lambda$4713/4026), $3.97-4.07$ (He
I $\lambda\lambda$4713/4471), and $3.93-4.03$ (He I $\lambda\lambda$4713/5876)

Figure 25: In the left column, these panels present the lines of O II
$\lambda$4089, O II $\lambda$4662, and O II $\lambda$4649\. In the right
column, the panels present the PV diagrams of the line ratios O II
$\lambda\lambda$4089/4649 and O II $\lambda\lambda$4662/4649. The contours in
the right panels are the intensity contours from the PV diagram of the O II
$\lambda$4649 line (bottom left). The bright fringe at the top of the PV
diagrams is due to imperfect subtraction of the nebular continuum. A cosmic
ray contaminates the PV diagram of the O II $\lambda$4662 line.

Figure 26: Left: We present the temperature-sensitive O II
$\lambda\lambda$4089/4649 ratio and its uncertainty as a function of the
temperature (the pink band), based upon an intensity limit at 40% of the
maximum intensity and the 90% width of its distribution of pixel values. The
temperature implied is rather low, $\log T_{e}=3.25-3.7$ dex, unless the
density is very low. Right: We present the observed value of the density-
sensitive ratio O II $\lambda\lambda$4662/4649 and its uncertainty as a
function of the electron density (the pink band; same definitions). The
observed O II $\lambda\lambda$4662/4649 ratio implies high densities
($10^{4}-10^{5}$ cm-3) at lowest temperatures ($<2,500$ K) and densities of
$5,000-30,000$ cm-3 at higher temperatures.

Finally, we can also use the N II and O II lines to compute the electron
temperature and density. Figure 23 presents the PV diagrams for the N II
$\lambda\lambda$4041, 5666, 5680 lines as well as the N II
$\lambda\lambda$4041/5680 (temperature) and N II $\lambda\lambda$5666/5680
(density) line ratios. The PV diagram for N II $\lambda$4041 is the one with
the worst S/N and is from a different wavelength interval. Even so, the N II
$\lambda\lambda$4041/5680 ratio is decently uniform. Certainly, there is no
clear evidence of gradients or large-scale changes. The N II
$\lambda\lambda$5666/5680 line ratio is very uniform, especially where the
intensity of the lines is strong.

In Figure 24, we plot the N II $\lambda\lambda$4041/5680 line ratio as a
function of temperature (left panel) and the N II $\lambda\lambda$5666/5680
line ratio as a function of density (right panel). For both line ratios, we
use all of the pixels that exceed 40% of the maximum intensity in the PV
diagram of the N II $\lambda$5680 line. The shaded region indicates the mean
value and the range allowed by 90% of the distribution (from the 5th to the
95th percentiles). The theoretical ratio (atomic data: Table 1), is shown for
different values of the electron temperature (left panel) and density (right
panel). The N II $\lambda\lambda$4041/5680 line ratio implies an electron
temperature of $\log T_{e}=3.3-4.2$ dex. The N II $\lambda\lambda$5666/5680
line ratio implies an electron density of $\log N_{e}>3.5$ dex and is
compatible with electron temperatures of $\log T_{e}=2.7-4.2$ dex. Combining
the restrictions from the two N II line ratios, they are nominally compatible
with $\log T_{e}=3.7-4.2$ dex and $\log N_{e}>3.5$ dex (and up to 5.0 dex
given the atomic data available).

Figure 25 presents the PV diagrams of the O II $\lambda\lambda$4089, 4649,
4662 lines (left column) and of the O II $\lambda\lambda$4089/4649
(temperature) and O II $\lambda\lambda$4662/4649 (density) line ratios (right
column). The PV diagrams for all of the lines have good S/N. The temperature-
(top right) and density-sensitive (middle right) line ratios are both quite
uniform. Hence, there is no evidence for any large scale variations in the
temperature or density of the plasma emitting in the O II lines.

Figure 26 compares the O II $\lambda\lambda$4089/4649 and O II
$\lambda\lambda$4662/4649 line ratios (left and right panels, respectively)
with the theoretical values for different physical conditions (atomic data:
Table 1). The pink shaded region indicates the observed value and the range
containing 90% of the distribution of values using all of the pixels that
exceed 40% of the maximum intensity in the O II $\lambda$4649 PV diagram
(denominator). The temperature-sensitive O II $\lambda\lambda$4089/4649 line
ratio (Figure 26; left panel) implies $\log T_{e}=3.2-4.2$ dex, considering
all densities. The density-sensitive O II $\lambda\lambda$4662/4649 line ratio
(Figure 26; right panel) implies $\log N_{e}>3.7$ dex and an electron
temperature of $\log T_{e}=2.8-4.4$ dex. Combining the two O II line ratios
implies $\log T_{e}=3.2-3.7$ dex and $\log N_{e}>3.7$ dex (and up to 5.0 dex).

For both the N II and O II lines, the density-sensitive indicator is
compatible with temperatures substantially lower than the temperature-
sensitive line ratio. The density-sensitive line ratios are sufficiently close
in wavelength that they are independent of the reddening correction and the
scale factors between wavelength intervals, but one (O II) or both (N II)
corrections are important for the temperature-sensitive ratios. The density-
sensitive line ratios also have higher S/N. If the density-sensitive line
ratios are considered alone, they are in excellent agreement, implying that
the electron temperature may be as low as $\log T_{e}=2.7-2.8$ dex ($\sim 500$
K). All things considered, we conclude that the N II and O II lines imply a
“low” electron temperature of $\log T_{e}\sim 3.2-3.7$ dex and a “high”
electron density of $\log N_{e}>3.7$ dex (and up to 5.0 dex given the atomic
data available). If so, the N II and O II lines imply different physical
conditions compared to the H I, He I, and forbidden lines. Again, this argues
for the presence of two plasma components.

###  3.3 Contamination in forbidden lines

Figure 27: We present the emissivities per ion and per electron for the lines
required to decompose the PV diagram of [N II] $\lambda$5755 (top left), [O
III] $\lambda$4363 (top right), and [O II] $\lambda\lambda$7319,7320 (bottom).
The emissivity for charge exchange is per ion and per hydrogen atom. The
legends indicate the transition wavelength in brackets. The line style
indicates the physical process that excites the line: solid for radiative
recombination, dashed for dielectronic recombination, dotted for collisional
excitation, and dot-dashed for charge exchange. Atomic data: See Table 1.

Many emission lines may be excited by multiple processes. Here, we consider
the effects of excitation mechanisms other than collisional excitation on the
[N II] $\lambda$5755, [O II] $\lambda\lambda$7319,7320, and [O III]
$\lambda$4363 lines. We shall call these additional excitation channels
“contamination”, though Nature does not see it that way. The contamination is
severe in the first two cases (Liu et al., 2000), but it has a minimal effect
on [O III] $\lambda$4363 in NGC 6153. We choose these examples deliberately
because they are little affected by collisional de-excitation .

§3.1 and §3.2 indicate that there are two sets of physical conditions that
apply to two kinematical components. One set of physical conditions applies to
the H I, He I, and forbidden lines (the normal nebular plasma), where the
electron temperature is $\sim 8,000$ K and the electron density is $\sim
4,000-5,000$ cm-3. For the normal nebular plasma, we adopt the physical
conditions of $T_{e}=8,000$ K and $N_{e}=5,000\,\mathrm{cm}^{-3}$. The second
set of physical conditions applies to the N II and O II lines (the additional
plasma component), where the temperature is lower, $T_{e}\sim
1,600-5,000\,\mathrm{K}$, and the density higher,
$N_{e}>5,000\,\mathrm{cm}^{-3}$, possibly as high as
$10^{5}\,\mathrm{cm}^{-3}$. For the additional plasma component, we adopt the
physical conditions of $T_{e}=2,000$ K and $N_{e}=10,000\,\mathrm{cm}^{-3}$.
Thus, we shall decompose the PV diagrams for the [N II] $\lambda$5755, [O II]
$\lambda\lambda$7319,7320, and [O III] $\lambda$4363 lines, assuming that
there are two plasma components in NGC 6153, each with distinct physical
conditions.

The goal of the decomposition is to obtain PV diagrams of the forbidden lines
with _only_ the contribution due to collisional excitation, the only
excitation process considered by the standard nebular analysis. Thus, we need
models or patterns of the emission due to recombination from the normal
nebular plasma and the additional plasma component that we may subtract from
the observed PV diagrams, leaving only the contribution due to collisional
excitation. To do this, we must scale the patterns of the PV emission using
the emissivities of the lines involved for the physical conditions found in
each of the plasma components. The three panels of Figure 27 present the
emissivities of the relevant lines due to H+, N+, O+, and O2+ as a function of
the electron temperature (atomic data: Table 1).

Figure 28: We compare the PV diagrams of the forbidden [N II]
$\lambda\lambda$5755,6583 lines (top and middle, respectively) and of their
ratio. The contour lines are of the emission in the N II $\lambda$5680 line
(Figure 29/Figure 6). The main shell is notably brighter, compared to the
filament on its receding side, in the [N II] $\lambda$5755 line, as is the
emission from the permitted N II $\lambda$5680 line. The ratio of the
forbidden lines presents an excellent correspondence between the excess
emission in the [N II] $\lambda$5755 line and the emission from N II
$\lambda$5680\.  Figure 29: These panels present the PV diagrams of the N II
$\lambda$5680 line as observed (top), the model of the recombination in this
line from the normal nebular plasma (middle), and the difference between the
previous two (bottom), which is interpreted as the recombination in this line
due to the additional plasma component. The contours in the three panels
correspond to the contours for the N II $\lambda$5680 line (top panel). The
three panels share the same intensity scale.  Figure 30: The left and right
columns present the PV diagrams of [N II] $\lambda$5755 and [N II]
$\lambda$6583, respectively. In the top row, we present the observed PV
diagrams of these lines. In the second and third rows, we present the models
of the permitted emission in these lines due to recombination in the normal
nebular plasma and the additional plasma component, respectively. In the
bottom row, we present the difference between the observed PV diagram and the
sum of the permitted emission, yielding what should be the emission due to
collisional excitation only from the normal nebular plasma. The maximum of the
intensity/color scale is given at upper right in each panel (constant on the
left; variable on the right). The contour lines are of the intensity of the N
II $\lambda$5680 line (Figure 29/Figure 6). Clearly, the fractional
contribution of recombination from both plasma components, but especially the
additional plasma component, is much greater for [N II] $\lambda$5755\.
Figure 31: These PV diagrams present the [N II] temperature. Top panel: We use
the observed PV diagrams of the [N II] $\lambda\lambda$5755,6583 lines. Middle
panel: We decompose the [N II] lines using the atomic data as published
(Figure 30). Bottom panel: We scale the recombination coefficients (atomic
data: Table 1) by a factor of 1.2 when decomposing the [N II] lines. In all
panels, the temperature scale spans the range $6,000-16,000$ K and the
contours are of the intensity of the N II $\lambda$5680 line (Figure 29).
After correcting for the recombination contribution to the [N II] lines
(middle), the [N II] temperature is a much better approximation of the [O III]
and [Ar III] temperatures, but may still be too high in the innermost regions.
The [N II] temperature map in the bottom panel is nearly as uniform as the [O
III] (Figures 14/36) and [Ar III] temperatures (Figure 15).  Figure 32: These
PV diagrams present the [O II] $\lambda$3726 and [O II]
$\lambda\lambda$7319,7320 lines (top row) and the O II $\lambda$4649 and O II
$\lambda$9982 lines (bottom row). The contours on the PV diagrams in the top
row are of the intensity of the PV diagrams in the bottom row. The morphology
of the PV diagrams for the [O II] lines are very different. For the [O II]
$\lambda$7320 line, the main shell is the brightest feature and its emission
matches very closely that from O II $\lambda$9982\. Also, the velocity
splitting for [O II] $\lambda$3726 is greater than that for O II $\lambda$4649
whereas the velocity splitting for [O II] $\lambda$7320 is the same as for O
II $\lambda$9982\.

First, we consider [N II] $\lambda$5755\. Figure 28 compares the PV diagrams
of the forbidden [N II] $\lambda\lambda$5755,6583 lines. The bright filament
is the brightest feature in both PV diagrams, but the contrast between it and
the main shell is very different for the two lines, with the main shell being
relatively much brighter in the [N II] $\lambda$5755 line. The velocity
splitting of [N II] $\lambda$6583 is greater than in the [N II] $\lambda$5755
line, 52.7 km/s versus 46.2 km/s. Finally, there is an excellent
correspondence between the emission from the main shell in the [N II]
$\lambda$5755 line and the emission from the permitted N II $\lambda$5680 line
(contours). All of these lines are from the CD3 wavelength intervals. The
bottom panel in Figure 28 presents the [N II] $\lambda\lambda$5755/6583 ratio
and it is clear that the excess emission in the [N II] $\lambda$5755 line
correlates with the emission from the N II $\lambda$5680 line (contours).

Hence, in NGC 6153, the [N II] $\lambda$5755 line appears to be contaminated
due to an additional excitation mechanism whose PV distribution is similar to
that of the N II $\lambda$5680 line. The N II $\lambda$5680 line may be
excited directly via recombination, but also indirectly by fluorescence in the
He I $\lambda$509 lines in the He+ zone or by starlight in the N+ zone
(Grandi, 1976; Escalante, 2002; Sharpee et al., 2004). Were N II $\lambda$5680
excited primarily by fluorescence, its PV diagram should be very similar to
that of [N II] $\lambda$6584 (Figure 4; N+ zone) or He I $\lambda$4471 (Figure
47; He+ zone), as occurs for He II $\lambda\lambda$3203,4686 and the Bowen
fluorescence lines of O III $\lambda$3444 and N III $\lambda$4634 (Figure 45).
So, in NGC 6153, fluorescence is unlikely to be the main excitation mechanism
for the N II $\lambda$5680 line. The contamination pattern like N II
$\lambda$5680 in the [N II] $\lambda$5755 line would thus appear to be due to
recombination.

Since the upper level of the [N II] $\lambda$5755 line is a singlet state,
fluorescence from the ground state (triplet) cannot excite it. Although the
excitation of singlet states via recombination is disfavored relative to the
triplet states, it is possible (Rubin, 1986; Liu et al., 2000). The appearance
of contamination with a PV pattern similar to that of a recombination line in
[N II] $\lambda$5755 is therefore not unreasonable. If so, in the model of two
plasma components previously outlined, both components will contribute to the
observed PV diagrams of both [N II] $\lambda\lambda$5755,6583 via
recombination while the normal nebular plasma will contribute the collisional
excitation, i.e., there are three contributions to the [N II]
$\lambda\lambda$5755,6583 lines.

The key to decomposing the PV diagrams of [N II] $\lambda\lambda$5755,6583 is
to decompose the observed PV diagram of N II $\lambda$5680 in terms of the
recombination from each of the plasma components. The parent ion that gives
rise to the N II lines is N2+, which occupies a volume in the nebula very
similar to O2+ (e.g., Figure 9 from Richer et al., 2013). Since [N II]
$\lambda$5755 is from the CD3b wavelength interval, we use the PV diagram of
[O III] $\lambda$5007 as a template for the PV pattern of the emissivity of
the recombination contribution from the normal nebular plasma. We estimate the
N II $\lambda$5680 emission due to the normal nebular plasma by scaling the PV
diagram of [O III] $\lambda$5007 by the abundance ratio (we adopt
$\mathrm{N}^{2+}/\mathrm{O}^{2+}=0.5$; Liu et al., 2000; McNabb et al., 2016),
and then by the ratio of the emissivities of the two lines at 8,000 K (Figure
27; adopting the atomic data for $N_{e}=10,000\,\mathrm{cm}^{-3}$ for N II
$\lambda$5680). We subtract this model of the recombination contribution from
the normal nebular plasma from the observed PV diagram of N II $\lambda$5680
to obtain the PV diagram of the N II $\lambda$5680 emission from the
additional plasma component. Mathematically, if, $I(\lambda)_{x}$ indicates
the PV diagram of the emission line at wavelength $\lambda$ due to
recombination as observed ($x=o$), from the normal nebular plasma ($x=n$), or
from the additional plasma component ($x=a$), the foregoing implies that the
PV diagram of the N II $\lambda$5680 due to the additional plasma component is

$I(5680)_{a}=I(5680)_{o}-I(5680)_{n},$

where

$I(5680)_{n}=\frac{N(\mathrm{N}^{2+})}{N(\mathrm{O}^{2+})}\frac{\epsilon(5680)_{n}}{\epsilon(5007)_{n}}I(5007)_{o}$

with $N(X)$ being the abundance of ion $X$ and $\epsilon(\lambda)_{x}$ the
emissivity of line $\lambda$ at the temperatures previously indicated for each
plasma component (subscript).

Figure 29 demonstrates the decomposition of the PV diagram of the N II
$\lambda$5680 line. Clearly, the contribution from the normal nebular plasma
is a small fraction of the total observed emission. However, its PV emission
pattern differs from that of the additional plasma component.

We use the two PV patterns of the recombination emission in the bottom two
panels of Figure 29 to subtract these contributions from the PV diagrams of
the [N II] $\lambda\lambda$5755,6583 lines. The scale factors are the ratios
of the emissivities of the [N II] $\lambda\lambda$5755,6583 lines with respect
to that of the N II $\lambda$5680 line at the temperatures of the two plasma
components. For the [N II] $\lambda$5755 line,

$I(5755)_{a}=\frac{\epsilon(5755)_{a}}{\epsilon(5680)_{a}}I(5680)_{a}$
$I(5755)_{n}=\frac{\epsilon(5755)_{n}}{\epsilon(5680)_{n}}I(5680)_{n}$
$I(5755)_{c}=I(5755)_{o}-I(5755)_{a}-I(5680)_{n}$

where $I(5755)_{c}$ indicates the PV diagram of [N II] $\lambda$5755 due to
collisional excitation only. (The process for [N II] $\lambda$6583 is
equivalent.) Figure 30 presents the result. While the contamination due to
recombination is completely negligible for [N II] $\lambda$6583, this is not
the case for [N II] $\lambda$5755, since the additional plasma component makes
a very significant contribution to its PV diagram. Even the normal nebular
plasma contributes noticeable emission due to recombination. The morphologies
of the PV diagrams for the [N II] $\lambda\lambda$5755,6583 lines in the
bottom row are now much more similar.

Figure 31 presents the PV diagrams of the [N II] temperature before and
aftercorrecting for the recombination contributions to the [N II]
$\lambda\lambda$5755,6583 lines. Clearly, the result after removing the
recombination contributions is much more like the [O III] and [Ar III]
temperature maps (Figures 14-15). Even so, the [N II] temperature still
exceeds the [O III] and [Ar III] temperatures in the innermost regions. The
bottom panel in Figure 31 is an experiment to estimate the maximum
contribution of recombination to the [N II] $\lambda\lambda$5755,6583 lines in
which the recombination contributions are arbitrarily increased by 20% with
respect to the values based upon the existing atomic data. The resulting PV
diagram of the [N II] temperature is nearly as uniform as the maps of the [O
III] and [Ar III] temperatures.

Therefore, decontaminating the [N II] lines using the nominal atomic data
yields an electron temperature much more similar to those found using the [O
III] or [Ar III] lines. Though it might be argued that the nominal correction
may underestimate the contamination due to recombination, the basic lesson is
that using the raw PV diagrams (or line intensities) of the [N II] lines leads
to erroneous results in NGC 6153.

The previous procedure differs from that employed by others (e.g., Liu et al.,
2000; Corradi et al., 2015; Ruiz-Escobedo & Peña, 2022; García-Rojas et al.,
2022). Those analyses suppose that the additional plasma component emits all
of the permitted emission whereas we find that the additional plasma component
contributes 76% of the total N II $\lambda$5680 emission (and 84% of the total
O II $\lambda$4649 emission), which is not a great difference. Our method may
be applied when two-dimensional data are available, whether in PV or spatial
coordinates.

Turning now to [O II], Figure 32 compares the PV diagrams of [O II]
$\lambda$3726, [O II] $\lambda\lambda$7319,7320, and O II
$\lambda\lambda$4649,9982. The morphologies of the PV diagrams of the [O II]
lines are very different (considering only one line of the [O II]
$\lambda$7319,7320 doublet). For [O II] $\lambda$3726, the filament on the
receding side of the main shell is by far the brightest feature, but, in the
auroral lines, the brightest feature is the brightest part of the main shell!
The contour lines superposed on both panels are those of the O II lines with
the same spatial coverage and they are an excellent approximation to the
emissivity of the main shell in [O II] $\lambda$7320\. This suggests that,
like [N II] $\lambda$5755, the [O II] $\lambda\lambda$7319,7320 lines suffer
very significant contamination due to recombination.

Figure 33: These panels present the decomposition of the [O II]
$\lambda\lambda$7319,7320 line profiles (top row, both columns). The middle
row presents the total permitted emission in both lines using O II
$\lambda$4649 (left) and O II $\lambda$9982 (right) as models. The bottom row
is the difference between the observations (top) the models (middle). All
panels share a common intensity scale. The model based upon the O II
$\lambda$4649 line accounts for _almost all_ of the emission from the main
shell in the [O II] $\lambda\lambda$7319,7320 lines.

We model the [O II] $\lambda\lambda$7319,7320 lines since their critical
densities for collisional de-excitation are well above the densities found for
the normal nebular plasma in NGC 6153. (This is not the case for [O II]
$\lambda\lambda$3726,3729.) We begin by decomposing the O II
$\lambda\lambda$4649,9982 lines to obtain the recombination contributions from
the two plasma components, as we did for [N II] $\lambda$5680\. We use the [O
III] $\lambda\lambda$4959,5007 lines to model the recombination contribution
from the normal nebular plasma (emissivities in Figure 27). We use [O III]
$\lambda$5007 to match the spatial extent of the O II $\lambda$9982 line,
though it was not obtained simultaneously with the other lines and may suffer
from a slightly different slit placement. As for N II $\lambda$5680, the
additional plasma component contributes the majority of the emission due to
recombination. We construct models of the recombination contribution to each
of the [O II] $\lambda\lambda$7319,7320 lines based upon each of the O II
$\lambda\lambda$4649,9982 lines. We subtract the sum of the models from the
observed PV diagram of the [O II] $\lambda\lambda$7319,7320 lines to obtain
the PV diagram of the emission due to collisional excitation only.

Figure 33 presents the result of this decomposition for the [O II]
$\lambda\lambda$7319,7320 lines. The observed PV diagram is in the top row
(both columns). The middle row presents the model of the permitted emission,
based upon the O II $\lambda$4649 (left) and O II $\lambda$9982 lines (right).
The two models differ, with that based upon O II $\lambda$9982 having
approximately two thirds of the flux of the model based upon O II
$\lambda$4649\. The models also differ because the shapes of the O II
$\lambda$4649 and O II $\lambda$9982 PV diagrams differ slightly, with the
latter being somewhat “taller”, likely due to the longer slit used in the red
arm of the spectrograph. The taller O II $\lambda$9982 line profile is a
better match to the shape of the [O II] $\lambda$7319,7320 PV diagram.

The bottom row in Figure 33 presents the difference between the observed
emission and the modeled permitted emission, again using the models based upon
the O II $\lambda$4649 and O II $\lambda$9982 lines. The PV diagrams in the
bottom row in Figure 33 should include only the emission due to collisional
excitation. Evidently, collisional excitation dominates the [O II]
$\lambda\lambda$7319,7320 emission from the filament, but recombination
provides the overwhelming majority of the [O II] $\lambda\lambda$7319,7320
emission from the main shell itself, as expected given the comparison of the
PV diagrams for [O II] $\lambda$3726 and [O II] $\lambda\lambda$7319,7320 in
Figure 32. The PV diagram of the [O II] $\lambda\lambda$7319,7320 at bottom
left is very similar to the PV diagrams of the [N II] $\lambda$6583, [S II]
$\lambda$6716 or [Cl II] $\lambda\lambda$8578,9123 lines (Figure 49).

On the other hand, the PV diagram of the [O II] $\lambda\lambda$7319,7320
lines after subtracting the model based upon O II $\lambda$9982 (Figure 33,
bottom right) still has significantly more emission from the main shell than
those of the [N II] $\lambda$6583, [S II] $\lambda$6716 or [Cl II]
$\lambda\lambda$8578,9123 lines (Figure 49). (The emission in the filament is
unaffected.) In order to obtain a PV diagram for [O II]
$\lambda\lambda$7319,7320 similar to those using the model of the permitted
emission based upon O II $\lambda$9982, the emissivity for this line from
Storey et al. (2017) should be multiplied by a factor of about 1.5. Storey et
al. (2017) note the limitations of their calculations for the
$2\mathrm{s}^{2}2\mathrm{p}^{2}\,(^{3}\mathrm{P})4f$ and $5f$ configurations.
Since the upper level of the O II $\lambda$9982 transition,
$(^{3}\mathrm{P}_{2})\,5g[6]_{13/2,11/2}$ (Wenåker, 1990), is even higher in
energy, within 2.2 eV of the ionization limit (O${}^{2+}\
{}^{3}\mathrm{P}_{2}$), a discrepancy of $\sim 50\%$ in its emissivity is
perhaps not unexpected.

We suppose that the decontamination of the [O II] $\lambda\lambda$7319,7320
lines using the model based upon O II $\lambda$4649 (Figure 33) is the more
reliable result. However, the most important lesson is that recombination
contributes the majority of the emission in the [O II]
$\lambda\lambda$7319,7320 lines for the main shell of NGC 6153 regardless of
which model we use. Hence, were the [O II] $\lambda\lambda$7319,7320 emission
to be analyzed as if due to collisional excitation, the result would be
erroneous for the main shell (but not the filament). Although Figure 33
concerns the [O II] $\lambda\lambda$7319,7320 lines, recombination undoubtedly
contributes to the emission in the [O II] $\lambda\lambda$3726,3729 lines as
well. All of the recombination contribution to the [O II]
$\lambda\lambda$7319, 7320, 7330, 7331 lines will contribute to the excitation
of the [O II] $\lambda\lambda$3726,3729 lines as will direct recombination to
the upper levels of the [O II] $\lambda\lambda$3726,3729 lines, as has been
argued elsewhere (e.g., Liu et al., 2000; Wesson et al., 2018).

Figure 34: We present the PV diagram of the density derived from the [O II]
$\lambda\lambda$3726,3729 lines. The contours are those of the intensity of
the emission in the O II $\lambda$4649 line (see Figure 6). Overall, the
density implied by the [O II] lines is higher than implied by the [S II], [Cl
III], or [Ar IV] lines. In addition, there is a similar structure of high
densities where the [N II] $\lambda\lambda$5755/6583 ratio is high (Figure
28).  Figure 35: These panels present PV diagrams for [O III] $\lambda$4363
(left) and [O III] $\lambda$4959 (right) of the observed emission (top), the
contamination due to recombination (second), the contamination due to charge
exchange (third), and the emission due to collisional excitation (bottom). The
PV diagrams in the bottom row are the result of subtracting those in the
second and third rows from the PV diagrams in the top row. Since the emission
due to recombination and charge exchange is so faint, the normalization value
for the intensity/color scale varies in the middle two rows by factors of
$10-1,000$ with respect to the top and bottom rows. While recombination makes
a small contribution to the [O III] $\lambda\lambda$4363,4959 PV diagrams,
charge exchange is much less relevant.

Figure 36: The top two panels present the [O III] electron temperature using
the raw PV diagrams and those corrected for contamination due to recombination
and charge exchange. The third panel presents the PV diagram of the difference
map between the corrected and raw temperature maps. In all panels, the
contours are of the [O III] $\lambda$4363 intensity. At bottom, we plot the
mean and median for the difference map as a function of the relative intensity
in the [O III] $\lambda$4363 line. The error bars span from the 5-th to 95-th
percentiles.

Even though the [O II] $\lambda\lambda$3726,3729 lines are contaminated by
recombination excitation, they remain a useful density indicator. However, the
[O II] $\lambda\lambda$3726/3729 ratio will sense the density in the two
plasma components. Given the low critical densities for the [O II]
$\lambda\lambda$3726,3729 lines, $\sim 1,000$ and 4,000 cm-3 at 9,000 K,
respectively (atomic data: Table 1), the [O II] $\lambda\lambda$3726,3729
lines will suffer more collisional de-excitation in the additional nebular
plasma. Where a given plasma component dominates the emission in these lines
in the PV diagram, the [O II] $\lambda\lambda$3726/3729 ratio will reflect the
density in that plasma component. Necessarily, there will be PV coordinates
where the two plasma components will contribute and the density will not
represent either component. Figure 34 presents the density computed from the
ratio of these lines, assuming an electron temperature of 10,000 K. Its
structure is more complicated than the PV diagrams for the densities computed