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

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 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.

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.

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.

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 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).

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.

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 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).

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.

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.

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.

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).

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.

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.

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.

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).

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 from the [S II], [Cl III], [Ar IV], N II, and O II lines. However, it is possible to recognize that, at PV coordinates corresponding to the outer part of the main shell, the density is near 5,000 cm^-3, as for the other forbidden lines, and, for the inner part of the main shell, the densities reach 10,000 cm^-3, compatible with the results from the N II and O II lines.

Finally, we consider the PV diagrams of [O III] $\lambda\lambda$4363,4959. These emission lines are the result of three physical processes. The dominant process is collisional excitation, but recombination and charge exchange also contribute. So, we must model and subtract the latter two contributions from the observed PV diagrams to yield PV diagrams for the [O III] $\lambda\lambda$4363,4959 lines due to collisional excitation only. We attribute the contributions from both recombination and charge exchange to the normal nebular plasma, since we assume that the additional plasma component does not emit in O III lines (§3.1, Appendix A).

We model the charge exchange contribution using the O III $\lambda$5592 line. The upper level of the O III $\lambda$5592 line will be dominantly excited by charge exchange, though recombination also contributes a minority ($<10$%; atomic data: Table 1). The lower level of the O III $\lambda$5592 line decays to the upper levels of the [O III] $\lambda$4363 or [O III] $\lambda\lambda$4959,5007 lines (for a useful Grotrian diagram, see Dalgarno & Sternberg, 1989). The upper level may also decay directly to the upper levels of the [O III] $\lambda$4363 or [O III] $\lambda\lambda$4959,5007 lines and it may also decay indirectly to these levels via other intermediate levels.

Since we use the observed PV diagram for O III $\lambda$5592, the scaling to account for the contribution of charge exchange to [O III] $\lambda$4363 requires only the branching ratio from the upper and lower levels of the O III $\lambda$5592 line (the Einstein A-values) for populating the upper level of the [O III] $\lambda\lambda$4363,4959 lines, i.e., the physical conditions are not involved (atomic data: Table 1). We find that the excitation to the upper levels of both lines is at most 48% of the intensity of the O III $\lambda$5592 line.

We use the PV diagram of the O III $\lambda\lambda$3260,3265 lines as the emission pattern for the recombination contribution to the [O III] $\lambda\lambda$4959,5007 lines (atomic data: Table 1), as all of the bright O III lines are enhanced by Bowen fluorescence (often dominated by it) and so cannot be used. However, the O III $\lambda\lambda$3260,3265 lines are just to the blue of our flux calibration limit at 3300 Å. Since the He II $\lambda$3203 line over-estimates the $\mathrm{He}^{2+}/\mathrm{H}^{+}$ ionic abundance (Table 7), the O III $\lambda\lambda$3260,3265 lines may over-estimate the recombination contribution to the [O III] lines.

Figure 35 presents the results for [O III] $\lambda\lambda$4363,4959. Clearly, the contamination due to recombination and charge exchange is minor. Only for [O III] $\lambda$4363 is contamination noticeable, and only in the case of recombination. Although the effect of this contamination upon the total emission from [O III] $\lambda$4363 is minor, it affects the “inside” of the line profile where the flux is lower.

Figure 36 presents the [O III] electron temperature before and after correcting for the contamination due to recombination and charge exchange. Figure 36 also presents the change in temperature and, as expected, it is largest on the “inside” of the line profile, near the systemic velocity and at spatial positions near the central star. Even so, the change is small, amounting to a decrease in the electron temperature of up to 200 K. The final panel in Figure 36 presents the change in temperature over the area covered by the contours at 10%, 20%, …, 90% of the maximum intensity of the [O III] $\lambda$4363 line. The biggest change occurs for the areas enclosed by the lower limiting fluxes. These areas also show the widest range of change. This occurs because these areas of the PV diagram correspond to larger nebular volumes within which there is a greater range of electron temperature, including both the hotter interior of the main shell and the lower temperatures in the diffuse emission at the most redshifted velocities.

In NGC 6153, the effect of recombination and charge exchange upon the electron temperature deduced from the [O III] $\lambda\lambda$4363,4959 lines is small to negligible. In particular, the central volume of the nebula (near the systemic velocity and near the central star) appears to be hotter than the rest. This is very likely due to the extra heating as a result of the presence of He²⁺ ions. Since the appearance of He²⁺ is accompanied by the disappearance of O²⁺, the most important source of nebular cooling, there is good reason to accept that the electron temperature really does increase in the central volume of the nebula.

The two panels in Figure 37 quantify the variation of the [O III] and [Ar III] temperatures (Figures 14 and 15, respectively). The left panel presents the mean and median [O III] temperature computed based upon different limiting intensities of the [O III] $\lambda\lambda$4363,4959 lines. To compute these values, only the temperatures from the pixels whose intensities exceed the indicated intensity relative to the maximum intensity are used. For instance, for a relative intensity limit of 0.1, only the non-zero temperature values from the pixels whose line intensities exceed 10% of the maximum intensity for the indicated line are used ([O III] $\lambda\lambda$4363,4959 in the left panel). The mean and median values of the temperatures are similar, indicating that the temperature distributions are approximately symmetric. For a given line, either [O III] $\lambda$4363 or [O III] $\lambda$4959, the variation of the mean and median temperatures as a function of the limiting line intensity is modest. The right panel in Figure 37 presents the same information for the [Ar III] $\lambda\lambda$5191,7135 lines. (The analogous figure for the temperature based upon the [Ar III] $\lambda\lambda$5191,7751 lines is very similar.)

The mean or median temperatures at different limiting line intensities measure the temperature over very different volumes of the nebula. At the 10% limiting intensity, plasma throughout the entire volume that emits the [O III]/[Ar III] lines is included, but, at the 90% limiting intensity, only part of the plasma seen along the line of sight towards the edge of the nebula’s main shell is included. Thus, the wider distribution of temperature values at lower limiting intensities is not due primarily to signal-to-noise, but to the wider range of physical conditions that occur in the larger volumes included by the lower limiting intensity limits.

In both panels of Figure 37, there is a systematic variation in the difference between the mean/median temperature weighted by the auroral and nebular lines, increasing as the limiting intensity increases. The mean/median values based upon the intensity of the auroral lines ([O III] $\lambda$4363, [Ar III] $\lambda$5191) are systematically higher than those based upon the intensity of the nebular lines ([O III] $\lambda$4959, [Ar III] $\lambda$7135). Since the excitation energy for the auroral lines is more than double that for the nebular lines, it makes sense that the temperatures weighted by the auroral lines are the larger ones since they are excited more easily where the temperature is higher and so will be biased to regions of higher temperature.

Comparing the two panels in Figure 37, there is a systematic difference between the [O III] and [Ar III] temperatures, with the latter being systematically lower. While the volumes occupied by the O²⁺ and Ar²⁺ ions largely coincide, the Ar²⁺ volume is biased towards the outer part of the O²⁺ volume, so it may be cooler. However, exciting the [Ar III] lines requires less energy, so they will also be more easily excited where the temperature is cooler. Figure 38 plots the mean [O III] and [Ar III] temperatures weighted using the [Ar III] $\lambda$7135 line, i.e., averaging over the same volume of the nebula. Again, the [O III] temperature is systematically higher than the [Ar III] temperature. This would appear to be a clear example of the temperature sensitivity of the excitation of forbidden lines affecting the temperature derived from them (Peimbert, 1967). An alternative explanation is that, for some reason, one or both of the [Ar III] or [O III] temperatures are systematically wrong.

Both of the [O III] and [Ar III] temperatures (Figures 14 and 15) are greater than the $\sim 8,000$ K temperature that matches the thermal line widths of the H I, He I, and [O III] $\lambda$4959 lines (Table 9). The lower end of the range allowed by the He I lines also matches the kinematic temperature, though temperatures derived from recombination lines should actually under-estimate the true mean temperature (Peimbert, 1967).