# Down but not out: properties of the molecular gas in the stripped Virgo
Cluster early-type galaxy NGC 4526

Lisa M. Young Physics Department, New Mexico Tech
801 Leroy Place
Socorro, NM 87801, USA  Adjunct Astronomer, National Radio Astronomy
Observatory, Socorro, NM 87801, USA  David S. Meier Physics Department, New
Mexico Tech
801 Leroy Place
Socorro, NM 87801, USA  Adjunct Astronomer, National Radio Astronomy
Observatory, Socorro, NM 87801, USA  Alison Crocker Department of Physics,
Reed College, Portland, OR 97202, USA  Timothy A. Davis School of Physics &
Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24
3AA, UK  Selçuk Topal Department of Physics, Van Yüzüncü Yıl University, Van
65080, Turkey

###### Abstract

We present ALMA data on the 3mm continuum emission, CO isotopologues (12CO,
13CO, and C18O), and high-density molecular tracers (HCN, HCO+, HNC, HNCO, CS,
CN, and CH3OH) in NGC 4526. These data enable a detailed study of the physical
properties of the molecular gas in a longtime resident of the Virgo Cluster;
comparisons to more commonly-studied spiral galaxies offer intriguing hints
into the processing of molecular gas in the cluster environment. Many
molecular line ratios in NGC 4526, along with our inferred abundances and
CO/H2 conversion factors, are similar to those found in nearby spirals. One
striking exception is the very low observed 12CO/13CO(1$-$0) line ratio,
$3.4\pm 0.3$, which is unusually low for spirals though not for Virgo Cluster
early-type galaxies. We carry out radiative transfer modeling of the CO
isotopologues with some archival (2$-$1) data, and we use Bayesian analysis
with Markov chain Monte Carlo techniques to infer the physical properties of
the CO-emitting gas. We find surprisingly low [12CO/13CO] abundance ratios of
$7.8^{+2.7}_{-1.5}$ and $6.5^{+3.0}_{-1.3}$ at radii of 0.4 kpc and 1 kpc. The
emission from the high-density tracers HCN, HCO+, HNC, CS and CN is also
relatively bright, and CN is unusually optically thick in the inner parts of
NGC 4526. These features hint that processing in the cluster environment may
have removed much of the galaxy’s relatively diffuse, optically thinner
molecular gas along with its atomic gas. Angular momentum transfer to the
surrounding intracluster medium may also have caused contraction of the disk,
magnifying radial gradients such as we find in [13CO/C18O]. More detailed
chemical evolution modeling would be interesting in order to explore whether
the unusual [12CO/13CO] abundance ratio is entirely an environmental effect or
whether it also reflects the relatively old stellar population in this early-
type galaxy.

Early-type galaxies (429) – Interstellar molecules (849) – CO line emission
(262) – Molecular gas (1073) – Galaxy evolution (594) – Virgo Cluster (1772)

††facilities: ALMA, CARMA, IRAM

##  1 Introduction

One of the outstanding questions in modern astrophysics is understanding the
origins of the Hubble sequence and the surprising diversity of nearby
galaxies. Fortunately, nearby galaxies preserve some clues to their histories
in their current properties. Cold molecular gas in early-type (elliptical and
lenticular) galaxies is particularly interesting in this context; it falls
outside our simple paradigm that early-type galaxies are quiescent and free of
cold gas. In fact, almost 25% of nearby early-type galaxies have retained some
molecular gas and at least 40% of them host atomic and/or molecular gas (Young
et al., 2014; Davis et al., 2019) at a level of $\gtrsim 10^{-3}$ M⋆.

Detailed studies of the gas in early-type galaxies have provided important
insights into their evolutionary histories. Comparisons between gas and
stellar kinematics reveal frequent kinematic misalignments between the gas and
stars, such that it is not unusual for the cold gas in early-type galaxies to
be counterrotating with respect to the stars. That counterrotating gas cannot
have had a long symbiotic relationship with those stars. Up to 30% – 50% of
the cold gas in early-type galaxies is sufficiently misaligned that it must
have come in from outside after the bulk of the stars were formed (Davis et
al., 2011). More recently, Davis & Young (2019) moved towards using
metallicities as another, complementary set of clues to the evolution of
early-type galaxies. Signatures of gas accretion can be seen in the fact that
the metallicity of the ionized gas in early-type galaxies is occasionally
lower than the metallicity of the stars. Ultimately it would be useful also to
study the isotopic abundance patterns in early-type galaxies as further clues
to their gas accretion and nucleosynthetic enrichment histories, employing the
types of chemical evolution models that are frequently used for the Milky Way
(Romano et al., 2019; Côté et al., 2019).

Beyond their accretion histories, early-type galaxies also allow us to probe
the processing of galaxies in clusters. And because they have generally been
resident in the clusters for a much longer time than the spirals that are more
commonly the subject of ram-pressure stripping studies, they give additional
insights beyond studies of spirals. They sample longer timelines for the
cluster-driven processing.

In this paper we present an exploration of molecular line ratios in the Virgo
Cluster galaxy NGC 4526. The target is an unusually molecule-rich early-type
galaxy with a striking but small silhouette dust disk, 1 kpc in radius. We
focus on new ALMA data for continuum emission, CO isotopologues, and high-
density molecular tracers in the 3mm band, supplemented by archival
12CO(2$-$1) and 13CO(2$-$1) data. We carry out radiative transfer modeling of
the available isotopologue data, coupled with Bayesian inference techniques.
The current data constrain the excitation-corrected [12CO/13CO] and
[13CO/C18O] abundance ratios; we find the former to be roughly constant in the
disk but the latter to have a strong radial gradient, and those patterns
provide clues to the processes driving the abundance gradients. We also
estimate the CO/H2 conversion factors $\alpha_{\mathrm{CO}}$ using the dust
continuum and CO images, providing the first estimate of this type for an
early-type galaxy. This analysis lays the groundwork for future explorations
of isotopic abundances in early-type galaxies, and especially for cluster
members, which should give insights into the evolution of early-type galaxies
and the processing of galaxies in clusters.

##  2 About ngc 4526

NGC 4526 is a Virgo Cluster member whose prominent central dust disk (Figure
1) has long prompted interest in its cold gas content. CO emission was
detected in the galaxy in single dish surveys by Sage & Wrobel (1989) and
Combes et al. (2007); the first resolved images of its CO emission were
published by Young et al. (2008). It is also a member of the ATLAS3D survey
(Cappellari et al., 2011), which provides additional information on its
stellar and ionized gas kinematics (Krajnović et al., 2011), stellar
populations (McDermid et al., 2015), and star formation history (Krajnović et
al., 2020). It is a fast rotator and one of the more massive galaxies in the
ATLAS3D sample, with a stellar mass $\log(M_{\star}/M_{\odot})\sim 11.1$ and
global colors that place it firmly in the red sequence (Young et al., 2014).
As a member of the Virgo Cluster, we assume a distance of 16.4 Mpc (Cappellari
et al., 2011). A more recent measurement based on the tip of the red giant
branch gives 15.7 $\pm$ 0.2 $\pm$ 0.4 Mpc (the uncertainties are statistical
and systematic, respectively; Hatt et al., 2018), which is only 6% smaller
than the distance we have assumed.

Davis et al. (2011) studied the kinematics of gas and stars in the ATLAS3D
sample and noted that field early-type galaxies often display kinematic
misalignments between their gas and stars, suggesting the gas was recently
accreted from some external source. In contrast, the Virgo Cluster early-type
galaxies and those in other dense groups tend to have relaxed and well-aligned
prograde gas. In this respect NGC 4526 is typical of cluster members.

It would have been difficult for NGC 4526 to acquire gas after falling into
the Virgo Cluster, because the relative velocities of typical interactions
(characterized by the velocity dispersion of the cluster) are much larger than
the internal escape velocities of the galaxies themselves. Thus, unlike the
cold gas in many field early-type galaxies, this gas has most likely been in
NGC 4526 for several Gyr and has been processed through a long, continuous
symbiotic relationship with the stars in multiple generations of mass loss and
star formation.

The molecular gas in NGC 4526 is also undergoing star formation with an
efficiency not too different from that of typical spirals. Davis et al. (2014)
estimate a star formation rate of 0.2 M⊙ yr-1 based on 22 µm and FUV emission;
this gives a specific star formation rate (SFR/M⋆) of $10^{-11.8}$ yr-1, a gas
depletion time of 2.6 Gyr, and a star formation rate surface density
$\Sigma_{\rm SFR}\sim 0.09$ M⊙ yr-1 kpc-2. Those values are all averaged over
the whole molecular disk.

Previous observations of the cold gas in the galaxy have revealed some unusual
and extreme properties. For example, Crocker et al. (2012) used the IRAM 30m
telescope to study molecular tracers in a subset of the ATLAS3D early-type
galaxies. They found that, relative to 12CO, NGC 4526 has unusually bright
13CO and HCN and a high HCN/HCO+ line ratio. It is also undetected in HI
emission (Lucero & Young, 2013), which produces a remarkably large H2/HI mass
ratio $>$ 60\. This extreme deficit of atomic gas suggests that the low-
density ISM in NGC 4526 has been stripped by the intracluster medium. Its
molecular properties should therefore give valuable perspective on the effects
of a long residence in a cluster.

Figure 1: NGC 4526. The white circle shows the FWHM of the ALMA field of view
at 110 GHz. The background color image is HST data, provided by ESA/Hubble and
NASA (https://esahubble.org/images/potw1442a/); original image by Judy
Schmidt, with astrometry by LY. Two optical contours are overlaid to highlight
the boxy structure in the galaxy’s bulge.

##  3 Observations

NGC 4526 was observed in ALMA’s compact configurations in band 3, projects
2017.1.01108.S and 2018.1.01599.S, in April 2018 and April 2019. We made use
of the standard pipeline calibrated raw data and carried out continuum
subtraction, imaging, and cleaning ourselves. An additional round of phase
selfcal was not found to offer any improvement in the images because of the
relatively modest signal-to-noise ratios. For continuum subtraction we used
zero-order or first-order fits to the line-free channels in the visibility
domain; for imaging, we made a wide variety of images at varying channel
widths and resolutions as necessary to optimize the resolution or to match
resolutions for resolved line ratios. The times on source, along with fiducial
beam sizes and rms noise levels, are indicated in Table 1 for the detected
spectral lines. Emission was cleaned down to about the 1$\sigma$ level and a
primary beam correction was applied.

We also use 12CO(2-1) observations obtained with the CARMA array (Davis et
al., 2013b). Those observations are relatively high resolution data, and were
initially imaged at 0$\farcs$25 resolution; for the analysis here, we tapered
the visibility data to make a lower-resolution image and smoothed in the image
plane to match the resolution of the ALMA 12CO(1-0) data. Appendix A describes
short-spacing verification and continuum subtraction on the 12CO(2-1) data.

Table 1: Fiducial image parameters for NGC 4526

Line | Time | Beam size | rms | $\Delta v$
---|---|---|---|---
| sec | (′′) | mJy bm-1 | km s-1
12CO(1$-$0) | 1727 | 2.01$\times$1.90 | 0.97 | 15.0
12CO(1$-$0) | 1727 | 1.12$\times$0.82 | 2.0 | 2.54
12CO(2$-$1) |  $\cdots$ aaApproximately 50 hours at CARMA, in four array configurations (Davis et al., 2013b). | 1.12$\times$1.12 | 9.0 | 10.0
CN (N=1$-$0)bbBoth J=3/2$-$1/2 and J=1/2$-$1/2. | 1727 | 1.47$\times$1.14 | 0.19 | 41.3
13CO(1$-$0) | 5443 | 2.01$\times$1.89 | 0.36 | 15.0
HNCO$(5_{0,5}-4_{0,4})$ | 5443 | 2.01$\times$1.90 | 0.36 | 15.0
C18O(1$-$0) | 5443 | 2.01$\times$1.90 | 0.36 | 15.0
CS(2$-$1) | 5443 | 2.32$\times$2.12 | 0.28 | 15.0
CH3OH($2_{k}-1_{k}$)ccFour constituent transitions are blended. | 5443 | 2.35$\times$2.15 | 0.29 | 15.0
HNC(1$-$0) | 3871 | 2.55$\times$2.38 | 0.26 | 15.0
HCO+(1$-$0) | 3871 | 2.60$\times$2.40 | 0.28 | 15.0
HCN(1$-$0) | 3871 | 2.60$\times$2.41 | 0.29 | 15.0
HNCO$(4_{0,4}-3_{0,3})$ | 3871 | 2.62$\times$2.43 | 0.29 | 15.0
cont. 99.3 GHz |  | 2.00$\times$2.00 | 0.012 |
cont. 99.3 GHz |  | 0.91$\times$0.79 | 0.014 |

Note. — Narrower velocity resolution is available for all the cubes made with
15 km s-1 channels but the faintest lines require binning for improved signal-
to-noise. For simplicity, we sometimes refer to the HNCO transitions as
(5$-$4) and (4$-$3). In most cases, these are the ‘natural’-weighted beam
sizes.

##  4 Continuum

In NGC 4526 we have near-simultaneous observations in the same telescope
configuration, covering frequencies from 87 GHz to 110 GHz (with gaps) with
similar uv coverage and time on source, so these data are suitable for imaging
the continuum intensity and estimating the spectral index of any emission. We
used all of the available line-free frequencies in CASA’s multi-term, multi-
frequency synthesis deconvolver (Rau & Cornwell, 2011), and we solved for two
terms, i.e. the intensity and the spectral slope. When imaged at a relatively
high resolution of 0.9′′$\times$0.8′′, the resulting continuum image at 99.33
GHz shows only a nuclear point source of flux density 4.79 $\pm$ 0.03 mJy and
spectral index $-1.07\pm 0.02$. This nuclear source is clearly synchrotron
emission. Kim et al. (2019) have commented that the galaxy was not previously
known to host an AGN; however, they detect a nuclear X-ray point source, and
combined with a 5 GHz point source (Nyland et al., 2016) and the 99 GHz
synchrotron emission, these data are all consistent with the presence of an
AGN.

Imaging at a lower resolution of 2.0′′ also reveals continuum emission from a
low surface brightness disk, as shown in the contours in Figure 2. The total
flux density associated with NGC 4526 in the 2.0′′ image is 6.68 mJy $\pm$
0.08 mJy (statistical) $\pm$ 0.33 mJy (absolute calibration), of which 4.8 mJy
is the point source and the remaining 1.9 mJy is the disk. The disk emission
is rather faint and uncertainties on its spectral index are large, but
individual pixels have a mean spectral index of $1.8$ and an rms $\approx$
0.7. This strongly rising spectral index is confirmed by individual images at
the extreme frequencies. Using a high resolution image (as described above) to
isolate the flux density of the point source from that of the extended dust
disk, we find the dust disk to have a flux density of 1.60 $\pm$ 0.15 mJy at
90.30 GHz, 1.98 $\pm$ 0.12 mJy at 101.69 GHz, and 2.46 $\pm$ 0.20 mJy at
108.33 GHz. The disk and nuclear continuum flux densities are also shown in
the broadband spectrum in Figure 3, where they can be compared to the FIR flux
densities and modified black body fit from Dustpedia (Nersesian et al., 2019);
additional details are in Section 8. The 3mm dust disk’s flux density
measurements are remarkably close to the long-wavelength extrapolation of the
modified black body fit.

Star-forming galaxies show a combination of free-free and dust emission at 3mm
(Peel et al., 2011), and if we interpret the disk flux densities above as a
combination of flat-spectrum free-free emission and dust with an effective
spectral index of 4.0, we infer that the disk’s flux density at 3mm should be
roughly half free-free and half dust. On the other hand, the accuracy of the
extrapolation in Figure 3 suggests that the 3mm emission might be mostly dust.
The good match in Figure 3 could also be a coincidence, if the dust emissivity
is overestimated at 3mm and a free-free contribution masks the overestimate.
We infer that somewhere between half and all of the disk’s 3mm flux density is
attributable to thermal dust emission. This fraction is somewhat larger than
would be usual for starburst and spiral galaxies (e.g. Bendo et al., 2015,
2016), but as this is an early-type galaxy, the dust emission might be more
strongly driven by heating from an old stellar population than by young stars.
More precise interpretations of the 3mm continuum emission in NGC 4526 will
require additional data at $\approx$ 200 to 300 GHz and/or 30 GHz, to help
constrain the spectral energy distribution.

Figure 2: 3mm continuum emission. The greyscale is an unsharp-masked HST WFPC2
image in the F555W filter. The contours show the continuum emission at 2.0′′
resolution and contour levels are $\pm$2, 4, 8, 16, 64, and 256 times the rms
noise (0.0125 mJy beam-1). The bright star that is present here but absent in
Figure 1 is SN1994D.  Figure 3: Radio - FIR spectrum of NGC 4526. The FIR data
do not have adequate angular resolution to permit decomposition into a disk
and a nucleus, so the FIR flux densities are attributed entirely to the star-
forming disk. The blue line is the modified black body fit to the FIR data
from Nersesian et al. (2019).

##  5 Gas Distribution and Kinematics

Figure 4 presents an integrated 12CO(1$-$0) intensity image, produced by
masking regions containing real emission and then integrating within the mask.
The mask is made using CASA’s auto-multithresh algorithm, which clips each
channel at 3$\sigma$ and then extends the clipping region spatially by about a
beamwidth. The molecular gas distribution observed here is consistent with the
results shown in Davis et al. (2013b) and Utomo et al. (2015), who studied
12CO(2$-$1) at higher resolution (0$\farcs$3) and lower sensitivity. We find a
poorly-resolved central peak, which they showed is a fast-rotating disk or
ring with a radius of about 0.5′′ (40 pc). Outside the nuclear peak is a dip
in the surface brightness, a bright molecular ring at $r=2$′′ to 7′′ (160 to
550 pc), and lower column density emission extending to about 15′′ (1.2 kpc).
The bright molecular ring is just interior to some recent star formation
activity that is visible as blue stars in Figure 4 or as white regions in the
unsharp-masked image in Figure 2. The peak 12CO(1$-$0) integrated intensities
are 2.71 Jy bm-1 km s-1 in the central peak and 2.74 Jy bm-1 km s-1 in the
molecular ring, when measured at 1.1$\times$0.8′′ resolution. Assuming a
standard conversion factor of 2.0$\times 10^{20}$ cm-2 (K km s-1)-1 or 4.3 M⊙
pc-2 (K km s-1)-1, including He, and deprojecting to face-on assuming an
inclination of 78° (discussed below), these values correspond to 240 M⊙ pc-2.

Figure 4: Integrated intensity of 12CO(1$-$0) emission at 1.1$\times$0.8′′
resolution; the beam size is indicated in the lower right corner. A cross
indicates the position of the nuclear continuum source. One contour is shown
at a level of 0.05 Jy bm-1 km s-1 = 4.5 M⊙ pc-2 (deprojected to a face-on
surface density). For context, the inner portion of the HST image from Figure
1 is reproduced at the same scale in the lower panel.

The peak brightness temperature in 12CO(1$-$0), at 1.1$\times$0.8′′ (75 pc)
resolution, is 6.1 K; it is found in the molecular ring at a radius of 5.9′′.
Somewhat lower brightness temperatures are found in the outer disk, with
values of 1.0 to 3.5 K at radii of $\approx$ 12′′. Peak brightness
temperatures are also quite low (1.0 to 1.5 K) in the nucleus of the galaxy,
though the column densities there are high because of the large linewidths.

We created velocity fields for the molecular gas in NGC 4526 using two
different methods, one using an intensity-weighted mean velocity and another
by fitting 4th order Gauss-Hermite functions (i.e. including skew and
kurtosis) to the spectrum at each location. Significant beam-smearing effects
mean that the skew and kurtosis terms are necessary to accurately reproduce
the line profile shapes and identify the peak in each spectrum. Figure 5 shows
a CO velocity field and Figure 6 shows the velocity dispersion.

Figure 5: 12CO(1$-$0) velocity field, based on the velocity of the maximum in
the Gauss-Hermite profile fitted to the spectrum at each position. The
kinematic major axis and its perpendicular are indicated in dashed lines.
Velocity contours are $\pm$(0, 50, 100, 150, 200, 250, 300, and 335) km s-1
with respect to systemic. Figure 6: Velocity dispersion of 12CO(1$-$0) at
1.1′′ $\times$ 0.8′′ resolution. The dispersion is measured from a Gauss-
Hermite profile fitted to the spectrum at each position. Contour levels are
10, 15, and 22.5 km s-1. Towards the nucleus the velocity dispersions range
from 250 to 300 km s-1, and the kinematics there are better modeled by Davis
et al. (2013b).

In this paper we do not focus on detailed kinematic and dynamic analysis of
the gas disk, but we still need estimates of the kinematic position angle and
inclination for deprojection and analysis of radial trends in the molecular
properties. For this purpose we use a kinemetric analysis of the 12CO(1$-$0)
velocity field, based on the code of Krajnović et al. (2006).111A python
implementation of kinemetry is available from
www.davor.krajnovic.org/software. The galaxy shows a well-defined kinematic
center that is coincident with the 3mm continuum peak to better than 0.05′′.
The kinematic position angle exhibits a slight twist from 292.2° $\pm$ 0.2° at
$r=2$′′ to 293.8° $\pm$ 0.1° at $r=12.6$′′. The fitted inclination varies only
from 79.0° $\pm$ 0.2° at $r=3$′′ to 76.3° $\pm$ 0.3° at $r=12.6$′′. Thus,
tilted-ring models should be highly accurate for both deprojection and
dynamical analysis.

##  6 Line fluxes and ratios

Figure 7: Integrated spectra of the detected lines in NGC 4526. The blue lines
use the entire disk region at every velocity; the orange lines use a velocity-
dependent mask that follows the rotation of the gas, as defined by the regions
with 13CO emission. The CN lines are blends of multiple components at
different frequencies, and they have poorer velocity resolution, so the strict
masking based on 12CO or 13CO does not work well for them. CN(3/2$-$1/2) is
shown with the solid line and CN(1/2$-$1/2) is dashed. The HNCO(5$-$4) line
partly overlaps C18O(1$-$0) so its spectrum is meaningless without the
velocity-dependent mask. Table 2: Integrated line fluxes in NGC 4526

Line | Flux |  12CO(1$-$0)/X
---|---|---
| Jy km s-1 |
12CO(1$-$0) | 141.82 $\pm$ 0.95 | $\cdots$
12CO(2$-$1) | 221.1 $\pm$ 5.5 | 2.56 $\pm$ 0.07
13CO(1$-$0) | 38.13 $\pm$ 0.25 | 3.40 $\pm$ 0.03
C18O(1$-$0) | 6.50 $\pm$ 0.17 | 19.8 $\pm$ 0.5
CN(N=1$-$0, J=3/2$-$1/2) | 8.08 $\pm$ 0.31 | 17.0 $\pm$ 0.7
CN(N=1$-$0, J=1/2$-$1/2) | 5.80 $\pm$ 0.13 | 23.5 $\pm$ 0.5
CS(2$-$1) | 2.51 $\pm$ 0.09 | 40.8 $\pm$ 1.6
CH3OH($2_{k}-1_{k}$) | 1.21 $\pm$ 0.08 | 83 $\pm$ 6
HNC(1$-$0) | 3.46 $\pm$ 0.11 | 25.4 $\pm$ 0.8
HCO+(1$-$0) | 3.00 $\pm$ 0.08 | 28.3 $\pm$ 0.8
HCN(1$-$0) | 7.44 $\pm$ 0.15 | 11.3 $\pm$ 0.2
HNCO$(4_{0,4}-3_{0,3})$ | 0.93 $\pm$ 0.08 | 86 $\pm$ 6
HNCO$(5_{0,5}-4_{0,4})$ | 1.34 $\pm$ 0.13 | 93 $\pm$ 9

Note. — Line ratios are computed in K km s-1 units (e.g. Mangum & Shirley,
2015). The uncertainties include only statistical effects, not absolute
calibration. Standard flux calibration procedures for ALMA data are usually
assumed to be accurate to $\approx$ 5% to 10% (e.g. Andrews et al., 2018;
Martín et al., 2019; Remijan et al., 2019), and ratios between lines observed
at different times (see Table 1) will have these additional calibration
uncertainties.

Figure 7 shows integrated spectra of the galaxy in all the detected lines, and
Table 2 gives the corresponding integrated line fluxes and line intensity
ratios. The line fluxes presented here are consistent with, though
significantly higher resolution and signal-to-noise than, the corresponding
values for 12CO, 13CO, C18O, CS, HCN, HCO+, and CH3OH measured with the BIMA
and IRAM 30m telescopes by Young et al (2008), Davis et al (2013) and Crocker
et al (2012). Table 6 also gives the peak column density estimates for the
various molecular species, assuming LTE at excitation temperatures of 20 K and
10 K (Section 7). Column densities are calculated using the methodology in
Mangum & Shirley (2015) equation 80, with molecular data from the LAMDA
database.

Table 3: LTE column density estimates for 2.6′′ resolution

Species | Intensity | log N (20 K) | log N (10 K)
---|---|---|---
| (Jy bm-1 km s-1) | ( cm-2) | ( cm-2)
12CO | 14.59 $\pm$ 0.09 | 17.388 $\pm$ 0.003 | 17.258 $\pm$ 0.003
13CO | 3.83 $\pm$ 0.03 | 16.881 $\pm$ 0.003 | 16.746 $\pm$ 0.003
C18O | 1.02 $\pm$ 0.03 | 16.31 $\pm$ 0.02 | 16.17 $\pm$ 0.02
CN | 1.24 $\pm$ 0.05 | 13.98 $\pm$ 0.02 | 13.85 $\pm$ 0.02
CS | 0.44 $\pm$ 0.03 | 13.67 $\pm$ 0.03 | 13.57 $\pm$ 0.03
CH3OH | 0.23 $\pm$ 0.03 | 13.85 $\pm$ 0.06 | 13.74 $\pm$ 0.06
HNC | 0.61 $\pm$ 0.03 | 13.52 $\pm$ 0.02 | 13.37 $\pm$ 0.02
HCO+ | 0.52 $\pm$ 0.03 | 13.26 $\pm$ 0.02 | 13.10 $\pm$ 0.02
HCN | 1.18 $\pm$ 0.03 | 13.38 $\pm$ 0.01 | 13.23 $\pm$ 0.01
HNCO | 0.20 $\pm$ 0.03 | 13.90 $\pm$ 0.06 | 13.80 $\pm$ 0.06

Note. — Intensities come from the peaks in the integrated line intensity
images, all smoothed to match the lowest-resolution line at 2.6′′ (210 pc).
For 12CO, the intensity in column 2 refers to the J=1$-$0 transition, and for
HNCO, it refers to $(4_{0,4}-3_{0,3})$. Uncertainties reflect only statistical
(signal-to-noise) effects. All lines are assumed to be optically thin for this
calculation, even though some lines are known to be thick. The CN optical
depth in the nucleus is $\tau\geq 4.5$ (Section 7), and correcting for optical
depth would increase the column density by at least 0.66 dex. HCN, HNC, and
HCO+ are probably thicker yet.

Figure 8: Integrated intensities of the detected lines in NGC 4526. These
integrated intensities are computed using a velocity-dependent mask that
follows the rotation of the gas, as defined by the regions with 12CO or 13CO
emission. Each line’s beam is indicated by the gray ellipse in the top left
corner, and the colors are scaled to the minimum and maximum of each image.
The colorbar shows integrated intensity values in Jy bm-1 km s-1. Dotted white
contours indicate the regions where the emission is detected at a signal-to-
noise ratio $>3.$ The last panel shows the effects of our masking and
integrating procedures on a line-free cube with a rest frequency of 90.0 GHz.

Integrated line intensity images (Figure 8) show that the distributions of all
the detected molecules in NGC 4526 are broadly similar, and the molecules
differ mainly in their signal-to-noise ratio and degree of central
concentration. For example, the position-velocity slice in Figure 9 shows that
HCN is more centrally concentrated than 12CO, as the 12CO/HCN ratio increases
with radius.

We quantify the radial variations in the line ratios using three main
techniques which all give similar answers. One method is to construct matched-
resolution major axis position-velocity slices (e.g. Figure 9), integrate over
radial regions, and compute the ratios of the corresponding sums in radial
bins. Uncertainties for this method can be estimated from standard error
propagation on the number of independent data points in the bin and also by
varying the clip threshhold used to select pixels with signal. (We always use
the same data volumes for both lines, to eliminate biases related to different
line strengths.) Another method is to construct integrated spectra by summing
the data cube over elliptical annuli of the appropriate position angle and
inclination. We then carry out a least-squares optimization modeling a fainter
line’s annular spectrum as a multiple of the brighter line. This technique
works because the distributions of all the species are broadly similar, so
that the corresponding annular spectra all have the same shape. The
uncertainty in the ratio can be characterized with standard $\chi^{2}$
goodness-of-fit criteria. Finally, we also create matched-resolution
integrated intensity images, compute a line ratio directly for every pixel,
and use the orientation and inclination of the disk to associate each pixel
with its deprojected radial distance. Figures 10 and 11 show comparisons of
these methods for the CO isotopologue ratios and for a few other selected line
ratios, indicating good agreement for all of them. Figures 12 and 13 show
radial trends in other line ratios.

In this section we present a large-scale overview of the relative intensities
of the molecular lines in NGC 4526 with some qualitative comments on unusual
aspects. In Section 7 we undertake more quantitative analysis of the physical
conditions in the molecular gas. To summarize the qualitative aspects, we note
that NGC 4526 is relatively bright in 13CO and the high-density tracers (HCN,
HCO+, HNC, CN, and CS), when compared to many spirals. It has relatively faint
emission in the shock tracers CH3OH and HNCO, though it should be noted that
existing observations of those species are biased towards active and
starbursting galaxies. All of the line ratios between 12CO and other
molecules, with the singular exception of 13CO, show strong radial gradients
of factors of two to four over 1 kpc in radius. In contrast, there is limited
or unmeasurable radial variation in 12CO(1$-$0)/13CO(1$-$0) and the line
ratios of any two high density tracers, such as HCN/HCO+, HCN/HNC, HCN/CS,
HCO+/CS, HCN/HNCO, and CH3OH/HNCO.

Figure 9: Major axis position-velocity slice showing the 12CO(1$-$0)/HCN
intensity ratio. The 12CO emission is smoothed to 2.6′′ resolution, to match
HCN, and the slit is 2.0′′ wide.

Figure 10: Colored circles indicate line ratios computed at each pixel from
the integrated intensity images; fainter symbols have lower signal-to-noise
ratio. In this figure, 12CO is always (1$-$0). Pixels are plotted at their
deprojected radius. Black filled symbols with error bars correspond to ratios
computed from the position-velocity slices and black open symbols with error
bars show ratios computed from the annular spectra (see text). Grey lines
indicate the surface brightness profile of the molecular gas, based on a
folded major axis slice of the high resolution 12CO(1$-$0) integrated
intensity image, arbitrarily scaled for visibility. The dotted vertical line
marks the approximate location of the local surface brightness peak in the CO
ring.  Figure 11: Similar to Figure 10, for additional selected ratios. The
dashed horizontal line indicates the theoretical optically thin LTE ratio of
the two CN blends. Figure 12: Radial variations in some line ratios in NGC
4526. As in Figure 10, filled symbols are ratios computed from the position-
velocity slices and open symbols are from the annular spectra. Small radial
offsets are added to some points for clarity. ‘CN32’ refers to the
(J=3/2$-$1/2) blend.

Figure 13: Radial variations in more molecular ratios. Lines and symbol types
have the same meanings as in Figure 10 and 12; ratios are grouped into these
figures purely for purposes of dynamic range and legibility. In this figure,
12CO is always the (1$-$0) transition. 12CO/CN here uses only the
CN(J=3/2$-$1/2) blend, and HNCO uses the $(4_{0,4}-3_{0,3})$ line.

###  6.1 CO Isotopologues

The 12CO(1$-$0)/13CO(1$-$0) ratio observed in NGC 4526 is $3.4\pm 0.3,$ which
is one of the lowest values observed outside of the Local Group (Figure 14).
Beyond the Milky Way, such low values are rare and noteworthy; some examples
include NGC 4429 and NGC 4459 (two other Virgo Cluster early-type galaxies)
and parts of resolved galaxies like the SMC and LMC, Centaurus A, and IRAS
04296+2923 (citations in Figure 14 and Meier et al., 2014). Spatial variations
in 12CO/13CO in NGC 4526 are also remarkably small, being less than 5% and
smaller than the corresponding statistical uncertainties. Resolved studies of
12CO/13CO within spiral galaxies usually show greater variation than that,
sometimes increasing with radius and sometimes decreasing (Cao et al., 2017;
Cormier et al., 2018; Topal, 2020), though usually over larger radial ranges.

The 13CO/C18O line ratios in NGC 4526 are not particularly unusual, as they
range from 4.7$\pm$0.3 to 8.7$\pm$1.8, and they fall near the median of the
values observed in other nearby galaxies (Figure 15). But unlike 12CO/13CO,
the 12CO/C18O and 13CO/C18O line ratios have significant radial structure.
Figure 10 shows that the ratios involving C18O rise by a factor of 1.8 over
this compact disk. The figure also identifies the location of the bright
molecular ring, and the gradients in the C18O ratios are markedly larger
exterior to the ring than they are interior to the ring. Thus the rise from
13CO/C18O = 5 to 9 occurs over the radial range of 0.4 to 1.0 kpc. For
comparison, the same rise in the Milky Way 13CO/C18O(1$-$0) line ratios occurs
over a radial range of about 6 to 12 kpc (Wouterloot et al., 2008). Additional
comparisons to other spiral galaxies are discussed in more detail in Section
9.2.

Resolved measurements of the 12CO(2$-$1)/(1$-$0) line ratio mostly range
between 0.4 and 0.7 (Figure 11). These values are very typical for spiral
galaxies (Leroy et al., 2021). Indeed, the star formation efficiency of the
molecular gas in NGC 4526 is consistent with values in many of those spiral
galaxies even though its gas content is lower than most of them. Evidence for
any spatial variations in the (2$-$1)/(1$-$0) line ratio is not compelling;
the ratio might be slightly elevated towards the nucleus, but because of the
uncertainty associated with continuum subtraction in the (2$-$1) data
(Appendix A), the issue should be re-evaluated with new data.

Figure 14: A compilation of observed 12CO/13CO line ratios, in the same spirit
as Figure 1 of Zhang et al. (2018) and Young et al. (2021). NGC 4526 is
highlighted in blue and other early-type galaxies are orange; other galaxy
types are grey. Data are drawn from Davis (2014), Jiménez-Donaire et al.
(2017), Brown & Wilson (2019), Cormier et al. (2018), Henkel et al. (2014),
Braine et al. (2017), Heikkilä et al. (1999), Zhang et al. (2018), Israel et
al. (2003), Méndez-Hernández et al. (2020), Crocker et al. (2012), Alatalo et
al. (2015), and Israel (2020). For early-type galaxies, the largest error bar
belongs to Cen A (McCoy et al., 2017) and it shows a range in measured values
rather than an uncertainty.  Figure 15: A compilation of observed 13CO/C18O
line ratios, after Figure 1 of Zhang et al. (2018). Data are also drawn from
Johansson et al. (1994), Wang et al. (2009), and works noted in Figure 14. For
NGC 4526, the error bars represent the range of values observed in our data
(since that range is larger than the uncertainties).

###  6.2 High Density and PDR tracers

The range of 12CO/HCN values we measure in NGC 4526 is 8.0$\pm$0.5 to
30$\pm$8\. The values in the outer disk of NGC 4526 are comparable to those in
the spirals in the EMPIRE survey (Jiménez-Donaire et al., 2019), but only a
handful of points in the spirals have bright enough HCN to match the center of
NGC 4526. Of course, it is worth noting that the EMPIRE data have lower
resolution that we are using here (1 to 2 kpc compared to 200 pc). Similar
results also hold for CN and CS. 12CO/CS in NGC 4526 ranges from 27$\pm$2 to
51$\pm$6; the spirals in Gallagher et al. (2018) have typical values of
12CO/CS $\sim$ 90 in their central kpc. For 12CO/CN ratios (isolating just the
J=3/2$-$1/2 blend), we measure values ranging from 11.4$\pm$0.2 to 49$\pm$10,
or 17$\pm$0.7 for a global line ratio. Other global 12CO/CN ratios measured by
Wilson (2018) range from 20 to 150. In short, the high density tracers in NGC
4526 are not exceptionally bright in comparison to 12CO but, especially for
CS, they are factors of roughly 2 brighter than the median values for nearby
spirals.

The CN radical is expected to be formed through photodissociation of HCN
and/or through reactions involving C and C+, so it should be enhanced in
regions with strong radiation fields. It may also be particularly enhanced in
XDRs (Boger & Sternberg, 2005; Meijerink et al., 2007). Ledger et al. (2021)
find some supporting evidence for factors of two enhancements in CN/HCN ratios
towards the nuclei of some starbursting galaxies and ULIRGs. In contrast, we
find no such evidence for variations in CN/HCN in NGC 4526, or in CN/CS or
HCN/HCO+ for that matter, even though there is an AGN in the center of the
galaxy and a faint X-ray point source as well (Kim et al., 2019). The AGN in
NGC 4526 may simply be faint enough that its effects on molecular line ratios
are restricted to regions smaller than our current resolution.

In the light of evidence that CS emission is enhanced in PDRs (e.g. Lintott et
al., 2005; Meier & Turner, 2005), it has been suggested that CS might trace
star formation activity even better than a standard dense gas tracer such as
HCN. For example, Davis et al. (2013a) found that CS is enhanced relative to
HCN in galaxies whose ionization is more strongly dominated by star formation
activity than by AGN. That study used unresolved single-dish measurements of
the molecular lines and traced star formation activity through integrated [O
III]/H$\beta$ line ratios. With our new ALMA data we can also test whether
this trend applies in an internal, spatially-resolved manner. NGC 4526
displays a wide range of [O III]/H$\beta$ values (Figure 16), from log([O
III]/H$\beta$) = $-0.85$ in its northwest quadrant to $-0.2$ in its nucleus
and even higher values outside the molecular disk. However, we find no
evidence of variable CS/HCN ratios anywhere in the galaxy, and no significant
difference between the northwest quadrant and other parts of the galaxy. While
the integrated measurements in NGC 4526 are consistent with a trend between
low [O III]/H$\beta$ and high CS/HCN, the internally resolved measurements do
not follow such a trend.

The above discussion also highlights the fact that it is not yet clear whether
internal variations of [O III]/H$\beta$ in NGC 4526 trace stochasticity in the
star formation rate in the last $\sim$ 10 Myr, shocks, metallicity variations,
or something else. The lowest [O III]/H$\beta$ ratios are on the receding side
of the galaxy, which is the side with brighter CO emission (Figure 7).
However, the asymmetry in [O III]/H$\beta$ is not reflected in the 3mm
continuum emission or in the 24µm dust emission (Young et al., 2009).
Additional work on other star formation tracers will be required before NGC
4526 can give a clear conclusion about CS/HCN and star formation activity or
about internal variations in the star formation efficiency.

Figure 16: 3mm continuum emission contours, overlaid on the [O III]/H$\beta$
line ratio from the SAURON/ATLAS3D data (Sarzi et al., 2006). Contours are as
in Figure 2. The prominent [O III]/H$\beta$ minimum is coincident with young
blue stars but not with any enhanced continuum; these observations may support
our interpretation that the 3mm continuum is mostly dust rather than free-free
emission.

###  6.3 CH3OH and HNCO – shock tracers

Our new measurements of 12CO/CH3OH in NGC 4526 broadly confirm the single-dish
measurements of Davis et al. (2013a). NGC 4526 is relatively faint in CH3OH
emission compared to the other early-type galaxies in that sample. We find
hints that the distribution of CH3OH in NGC 4526 may be different from that of
the other molecules; the integrated intensity (Figure 8) suggests a broader
extent of CH3OH in the minor axis direction than that of the other species, so
the 12CO/CH3OH ratios in the galaxy are systematically higher on the major
axis ($\sim$ 110) than on the minor axis ($\sim$ 40). But CH3OH is very faint
and this suggestion should be verified with higher sensitivity data.
Similarly, there are hints that some tracers such as CH3OH and HNCO(5$-$4) are
brighter in the far-receding and near-approaching quadrants of the galaxy than
in the other two quadrants, suggestive of a bar structure, and those features
will be explored in a future paper.

Meier & Turner (2005) have argued that HNCO is also a shock tracer, like
CH3OH. At present there are few other HNCO detections in early-type galaxies,
but for comparison purposes we note that the 12CO/HNCO(4$-$3) and
HCN/HNCO(4$-$3) line ratios in NGC 4526 have similar values to those found in
the nearby starburst galaxy NGC 253 (Meier et al., 2015) and in the early-
types NGC 4710 and NGC 5866 (Topal et al., 2016). Interestingly, NGC 253 also
suggests that the low-J transitions of HNCO might be anticorrelated with
vigorous star formation activity; Meier et al. (2015) found a central deficit
in HNCO(4$-$3), which they interpreted as a signature of excitation effects in
high-temperature molecular gas and/or photodissociation of HNCO in the
vicinity of the starburst. In NGC 4526, in contrast, we find higher
HNCO(4$-$3) intensities (relative to 12CO) in the center of the galaxy, but
constant HCN/HNCO(4$-$3) ratios. The interpretation of this radial trend is
not entirely clear. If the majority of the star formation activity is just
exterior to the molecular ring, as suggested by the young blue stars and the
[O III]/H$\beta$ ratios, then the lower HNCO intensities in the outer disk of
NGC 4526 could be consistent with high-temperature and/or photodissociation
effects in PDRs. But the constancy of HCN/HNCO(4$-$3) instead suggests that
PDR effects are not the dominant drivers of the radial behavior of HNCO in NGC
4526.

##  7 Physical conditions in the molecular gas

###  7.1 CO isotopologues

We have spatially resolved data on four CO isotopologue transitions [
12CO(1$-$0), 12CO(2$-$1), 13CO(1$-$0), and C18O(1$-$0) ] plus a single-dish
measurement of the 12CO(2$-$1)/13CO(2$-$1) line ratio (4.6$\pm$0.7; Crocker et
al., 2012), and we use these data to explore the physical conditions in the
CO-emitting gas. We use the RADEX code (van der Tak et al., 2007) to compute
predicted line ratios for a variety of physical conditions and a Markov chain
Monte Carlo sampler (Foreman-Mackey et al., 2013) to estimate maximum
likelihood parameters with their uncertainties. The details are in Appendix B,
and we summarize the results here.

The conditions in the CO-emitting gas of NGC 4526 are most tightly constrained
in the molecular ring. There we estimate the column density of 12CO to be log
N(12CO) [cm-2] = $18.0\pm 0.3.$ (Strictly speaking, RADEX constrains the ratio
of the column density to the linewidth, $N/\Delta v.$ We assume a linewidth of
30 km s-1 in this part of the galaxy, based on the velocity dispersions along
the major axis in Figure 6.) The quoted uncertainty contains 68% of our
inferred probability distribution. We also find the H2 volume density to be
log $n_{\mathrm{H}_{2}}$[cm-3] = $2.4\pm 0.4$ and the kinetic temperature to
be Tkin $>10$ K. The density and temperature are still not particularly well
constrained since we do not have observations of the (2$-$1) transitions in an
optically thin line. Despite that limitation, the isotopologue abundances can
be constrained. We find the [12CO/13CO] abundance ratio to be
$7.8^{+2.7}_{-1.5},$ an unusually low value; values between 20 and 60 are much
more common for nearby spirals (Section 9.1). We find the optical depth of
13CO(1$-$0) to be a relatively high value of $\tau_{13}=1.1^{+0.9}_{-0.5}$.
The derived value of the [13CO/C18O] abundance ratio in the molecular ring is
$6.2^{+0.8}_{-0.6}$.

We also find strong evidence for a radial gradient in [13CO/C18O], as we we
infer values of 5.7${}^{+0.7}_{-0.6}$ in the nucleus ($r\lesssim 2$′′) and
9.2${}^{+1.0}_{-1.0}$ at the outer edge of the disk. Those abundances are
approximately 15% larger than the corresponding observed line intensity ratios
because of the optical depths in 13CO(1$-$0).

We find no particularly strong evidence for a gradient in [12CO/13CO]. Our
inferred value for the outer disk is $6.5^{+3.0}_{-1.3},$ which is entirely
consistent with the measurement in the ring. This abundance ratio is more
poorly constrained in the nucleus because of the lower brightness temperatures
and the broader allowed range of kinetic temperatures, but the marginalized
probability distribution peaks at [12CO/13CO] $\sim 6.3$ in the nucleus. The
lack of a gradient in [12CO/13CO] is a bit surprising, as there is some
expectation for lower [12C/13C] ratios in the centers of galaxies.
Measurements and models for the Milky Way are presented by Romano et al.
(2019), for example. Further discussion of abundance ratio gradients is in
Section 9.

As is commonly found in other galaxies, the conditions that reproduce the CO
isotopologue intensities in NGC 4526 do not reproduce the observed intensities
of the high-density tracers. For example, using the density, temperature, and
column density appropriate to the molecular ring, and typical abundances of
[CO/H2] $\approx 10^{-4}$ and [HCN/H2] $\approx 10^{-8}$ (Meier et al., 2015),
we predict HCN(1$-$0) intensities on the order of 1 mK. The observed
intensities are roughly 0.5 K. Thus, these data are consistent with the usual
paradigm that the high-density tracers arise in a significantly different
“phase” of molecular gas from that traced by the CO isotopologues.

###  7.2 HNCO

We detect two transitions of HNCO, $(4_{0,4}-3_{0,3})$ and
$(5_{0,5}-4_{0,4})$, whose rest frequencies are 87.925237 GHz and 109.9057490
GHz respectively. They provide some constraints on the excitation temperature
of the high-density molecular gas. The (5$-$4) transition requires careful
treatment as it is close to C18O(1$-$0), and the velocity width of NGC 4526
necessitates careful masking.

The HNCO (5$-$4)/(4$-$3) line ratio measured from the global spectra (Figure
7) is 0.92 $\pm$ 0.11. There is no evidence for significant radial variation
(Figure 13). In optically thin LTE, that ratio implies excitation temperatures
in the range of 7.4 K to 12.5 K (Mangum & Shirley, 2015, Eq 27 and 32). Simple
estimates of the HNCO optical depths suggest that they are probably around 1,
as we discuss in Section 7.4; if this assumption is accurate, the allowed
temperatures fall in a slightly expanded range from 5.4 K to 13.4 K. Of
course, higher temperatures are required if the density is too low to
establish LTE.

This excitation temperature estimate from HNCO is consistent with the
conditions inferred from CO above, which were Tkin $>10$ K. Lapham & Young
(2019) also found an excitation temperature of 15.7 $\pm$ 2.0 K from the [C I]
(1$-$0) and (2$-$1) lines in NGC 4526, and the dust temperature from the far-
IR spectral energy distribution in Figure 3 is 25.1 $\pm$ 0.8 K (Nersesian et
al., 2019). As noted by Hacar et al. (2020), we might expect somewhat higher
temperatures inferred from CO or [C I] than from a high-density tracer like
HNCO, as CO and [C I] should be preferentially emitted from the lower
extinction, warmer outer regions of clouds. Our temperature estimates in NGC
4526 confirm this general picture.

###  7.3 HCN/HNC

HCN/HNC line ratios in NGC 4526 are consistent with a constant value
everywhere in the disk; of the pixels with detections in both lines, the
median ratio is 2.4 and the dispersion is 0.5. Binned measurements range from
2.06 $\pm$ 0.02 to 3.2 $\pm$ 0.6 at $r<12$′′. These values are not unusual for
extragalactic sources. The critical densities of the two species are similar,
so we do not expect substantial differences in their excitations.

Several authors (e.g. Hirota et al., 1998; Graninger et al., 2014; Hacar et
al., 2020) have argued that the primary driver of variations in HCN/HNC line
ratios, for typical interstellar molecular conditions, will be abundance
variations caused by preferential destruction of HNC at warmer temperatures.
At the low temperatures relevant here, the mechanism should be gas-phase
reactions of HNC with neutral atoms. Hacar et al. demonstrate that HCN/HNC
line ratios are an effective indicator of the gas kinetic temperature, and
they provide a calibration relating the observed line ratio to the
temperature. For the line ratios measured in NGC 4526 the inferred
temperatures are 20 to 24 K over most of the disk.

The calibration in Hacar et al. is derived from studies in Orion, and it is
also roughly consistent with results from other molecular clouds (Jin et al.,
2015) and protoplanetary disks (Graninger et al., 2015). The molecular disk of
NGC 4526 obviously includes a wide variety of environments and it is therefore
not obvious that a calibration derived from individual molecular clouds should
be extended to a full galactic disk. And at face value, the temperatures
inferred from the HCN/HNC thermometer are roughly a factor of 2 larger than
those inferred from the HNCO transitions. In principle, the HNCO measurement
is less susceptible to systematic uncertainties as it utilizes two transitions
from the same molecule. On the other hand, in our observational setup, the
HNCO measurement is more susceptible to calibration uncertainties as the lines
are fainter and they were not observed simultaneously like HNC and HCN were.
But all the available estimates suggest relatively low temperatures for the
molecular gas in NGC 4526, with little to no evidence for radial trends.

###  7.4 CN hyperfine blends and implications for the other high-density
tracers

The 3mm ($N=1-0$) spectral lines of CN consist of a set of hyperfine
components which are grouped into two main blends, one with
$J=\frac{3}{2}-\frac{1}{2}$ around 113.49 GHz and one with
$J=\frac{1}{2}-\frac{1}{2}$ around 113.19 GHz. The ratios of these two blends
can be used to infer the optical depths of the CN lines; the optically thin
limit in LTE is I($J=\frac{3}{2}-\frac{1}{2}$)/I($J=\frac{1}{2}-\frac{1}{2}$)
= 2.0, so deviations from that value imply significant optical depths (e.g.
Tang et al., 2019). Previous observations suggested that most observed 12CN is
optically thin (Wilson, 2018, and references therein), though Tang et al.
(2019) found optical depths in the $J=\frac{3}{2}-\frac{1}{2}$ component as
high as $\tau_{3/2}=1.9$ in their sample of three starburst galaxies.

Here we find even lower line ratios and higher optical depths in the center of
NGC 4526. Figure 11 shows values for this CN blend ratio as low as 1.12 $\pm$
0.16 in individual pixels in the center of the galaxy, or 1.16 $\pm$ 0.06
computed from the position-velocity slices, rising to values consistent with
2.0 (the optically thin limit) at $r>5$′′.

In the LTE assumption, the low CN hyperfine blend ratios require
$\tau_{3/2}\geq 4.5$ in the nucleus of NGC 4526. For typical abundances and
column densities, the CN ratio also suggests an excitation temperature $\leq
20$ K in the nucleus of NGC 4526; higher temperatures depopulate those low
energy levels and the transitions become optically thin. This low temperature
is also roughly consistent with the temperatures inferred from CO, [C I] and
HNCO. If the excitation temperature is constant with radius, as suggested by
the HNCO(5$-$4)/(4$-$3) line ratio, then the radial decrease in CN optical
depth requires radial decreases in $n_{\mathrm{H}_{2}}$ of a factor of 30, or
in N(CN) of a factor of 100, or some combination of both. If we also take the
HCN/HCO+ ratio to be an indicator of density, then its constancy with radius
suggests the CN optical depth changes should be attributable mostly to the CN
column density, and perhaps to variations in the CN abundance.

Large optical depths in CN in the center of NGC 4526 also imply large optical
depths in other high-density tracers. For example, if the abundance ratio
[CN/HCN] falls in the range of 1 to 5 (e.g. Liszt & Lucas, 2001; Meier et al.,
2015), and if LTE applies, then we expect the optical depth of HCN(1$-$0) to
be between 1.2 and 6 times that of the CN 113.49 GHz blend. In other words, we
expect the optical depth of HCN(1$-$0) to be at least in the range of 5 to 30.
Similar comments apply to HCO+ and HNC. High optical depths might explain the
unusual lack of radial trends in any of the ratios involving two high-density
tracers. Implications for the use of an HCN/HNC thermometer such as that in
Hacar et al. (2020) are not clear, since that proposed thermometer is based on
a purely empirical calibration. In contrast, if [CN/HNCO] is $\sim$ 1 (Meier
et al., 2015), the optical depth of the HNCO(5$-$4) and (4$-$3) transitions
should be between 0.2 and 0.4 times that of CN. Thus, the HNCO lines are
probably somewhat thick ($\tau\sim 1$) in the nucleus of NGC 4526 and the HNCO
temperature estimate from section 7.2 should still be reliable.

##  8 Dust and CO/H2 conversion factors

With an assumed dust emissivity and a gas-to-dust mass ratio, the total dust
and H2 masses can be obtained from dust continuum emission (e.g. Hildebrand,
1983; Leroy et al., 2011, and many others). In the case of NGC 4526, we have
argued (Section 4) that at least half of the 3mm continuum is dust emission,
so the image in Figure 2 can give loose constraints on the resolved H2 column
density estimates and CO/H2 conversion factors. Here we assume all of the
extended 3mm continuum is dust emission. We use the modified black body
emissivity model for NGC 4526 from the Dustpedia results (Nersesian et al.,
2019): they find a dust temperature of 25.1$\pm$0.8 K and a mass of
(4.38$\pm$0.58)$\times 10^{6}$ M⊙, assuming a distance of 15.35 Mpc. These
values derive from an emissivity of 0.640 m2 kg-1 $(250\mu m/\lambda)^{1.79}$,
which also predicts 7.4$\times 10^{-3}$ m2 kg-1 at 99 GHz and gives a
remarkably accurate prediction of the observed 3mm flux density. We also
assume a H2/dust mass ratio of 100, based on the results of Cortese et al.
(2016) for Virgo Cluster and/or HI-deficient galaxies of stellar mass above
$10^{10.5}$ M⊙.

Figure 17: Colored points are individual pixels’ 12CO(1$-$0)/H2,
13CO(1$-$0)/H2, and C18O(1$-$0)/H2 conversion factor values, calculated from
the ratio of the matched-resolution dust continuum image to the integrated
intensity line images as described in the text. Fainter symbols have lower
signal-to-noise ratio. Black error bars show the median and mean absolute
deviation in radial bins. As in Figures 10 through 13, these are deprojected
radii. A typical Milky Way value is also indicated (e.g. Leroy et al., 2011).

Figure 17 shows the resolved CO-to-H2 conversion factors $\alpha_{X}$ inferred
for the three isotopologues under the assumptions detailed above. Table 4 also
gives representative statistics for all of the pixels that have 3mm continuum
emission detected at a signal-to-noise ratio $>3,$ and that are free of
synchrotron contamination (projected radius $r>2.6$′′, which is
$1.3\times\mathrm{FWHM}$). Our estimated $\alpha_{\mathrm{CO}}$ value for
12CO(1$-$0) in NGC 4526 is 5.6$\pm$1.2 M⊙ pc-2 (K km s-1)-1, which is just 30%
larger than a “standard” Milky Way value of 4.3 in the same units (e.g. Leroy
et al., 2011). The result suggests that 12CO emission in NGC 4526 is just a
bit fainter than usual, for a given H2 surface density. Estimated values for
$\alpha_{\mathrm{CO}}$ under different assumptions may be scaled by noting
that it is proportional to the gas/dust ratio and the fraction of the
continuum intensity that is assumed to be dust, and that it is inversely
proportional to the dust emissivity. As a consistency check, Utomo et al.
(2015) found that an $\alpha_{\mathrm{CO}}$ value of 4.4 M⊙ pc-2 (K km s-1)-1
suggests that most of the molecular clouds in NGC 4526 are in virial
equilibrium.

Furthermore, as the RADEX/MCMC analysis gives confidence intervals on the
species’ column densities, the H2 column density can be used to infer the
species’ abundances. In a continuum image at 99.33 GHz and 2.0′′ resolution,
the surface brightness at $r=5$′′ is 0.12 $\pm$ 0.01 mJy beam-1. Using the
dust emissivity and gas/dust ratio described above, this specific intensity
corresponds to an H2 column density of 1.4$\times 10^{22}$ cm-2, or 300 M⊙
pc-2 (including helium). Both of those values have been deprojected to face-on
column densities assuming an inclination of 78$\arcdeg$ (Section 5). The dust-
derived H2 column densities then give the CO isotopologue abundances listed in
the last column of Table 4. For 12CO, the inferred abundance ranges from
[12CO/H2] $\approx$ 8$\times 10^{-6}$ to 3$\times 10^{-5}$, roughly factors of
3 to 10 lower than the “standard” Milky Way abundance of 8.5$\times 10^{-5}$
(Frerking et al., 1982). The inferred 12CO abundance is proportional to the
dust emissivity but is inversely proportional to the gas/dust ratio and to the
fraction of the continuum that is assumed to be dust. Thus, for example, if
only half of the 3mm continuum emission came from dust, the 12CO abundance
would be closer to the Milky Way value.

Our quoted 12CO abundance in NGC 4526 is farther away from the “standard”
Milky Way value than one might expect, given that $\alpha_{\mathrm{CO}}$ is
fairly close to the Milky Way value. In this context it is worthwhile to note
that the 12CO abundance calculation takes optical depths into account, because
it is based on the RADEX/MCMC results. In contrast, the $\alpha_{\mathrm{CO}}$
calculation uses the raw line intensities and does not account for variations
in optical depth. Lower-than-usual 12CO optical depths in NGC 4526 might
explain relatively normal $\alpha_{\mathrm{CO}}$ values despite low 12CO
abundances.

We do not place much significance on the differences between the
$\alpha_{\mathrm{CO}}$ and [12CO/H2] values for NGC 4526 and the Milky Way,
because the uncertainties associated with this analysis are very large. In
Section 4 we suggest that a free-free contribution at 100 GHz might mean that
the dust surface brightnesses are half of the observed intensities. Dust
emissivities are also highly uncertain at these wavelengths (Cigan et al.,
2019); the slightly different modified black body parameters of Auld et al.
(2013) produce a difference of a factor of 3 in the inferred $\alpha_{X}$
values and the H2 column density, and Clark et al. (2019) also find evidence
for variations in the dust emissivity within an individual galaxy. The
RADEX/MCMC column densities are also, strictly speaking, not as well
constrained as the ratios N$/\Delta v,$ and we have used line widths $\Delta
v$ estimated from the outer part of the disk where there is little kinematic
beam-smearing affecting the line widths. Finally, estimates of gas/dust mass
ratios find wide variations of at least a factor of 30, and sometimes 100,
between different galaxies (Cortese et al., 2016; Lianou et al., 2019), and it
is difficult to know how much of that variation is real and how much is noise.
Recent theoretical work suggests that much of it may be real (Whitaker et al.,
2021).

In the context of these uncertainties, we simply comment that the inferred
$\alpha_{X}$ values and CO isotopologue abundances found here are roughly
consistent with the values assumed in Section 5, and they are similar to the
spirals of the Local Group (Leroy et al., 2011), and at our 150 pc resolution
there is little to no evidence for strong internal variations within the disk
of NGC 4526.

Table 4: Estimated CO/H2 conversion factors and abundances

Species | $\alpha_{X}$ | log N | [X/H2]
---|---|---|---
|  | (cm-2) |
12CO | 5.6$\pm$1.2 | 17.7 — 18.2 | 7.7($-6$) – 2.6($-5$)
13CO | 19.3$\pm$4.1 | 16.9 — 17.3 | 1.1($-6$) – 2.8($-6$)
C18O | 108$\pm$29 | 16.1 — 16.5 | 1.9($-7$) – 4.4($-7$)

Note. — The values of $\alpha_{X}$ are quoted for the (1-0) transitions in
units of M⊙ pc-2 (K km s-1)-1. They represent the medians and mean absolute
deviations of the selected pixels, as described in the text. Column densities
$N$ are 68% confidence intervals from the RADEX/MCMC analysis (Section 7 and
Appendix B) for conditions in the molecular ring, and abundances [X/H2] are
similarly propagated ranges. Column densities quoted in this table have not
been deprojected to face-on values.

##  9 Discussion

###  9.1 Whole-galaxy integrated properties

Most of the molecular line ratios we have measured in NGC 4526, along with the
inferred molecular abundances and CO/H2 conversion factors, are similar to
those found in nearby spirals. In that broad sense, the molecular gas
properties of NGC 4526 are consistent with the idea that at some time before
it entered the Virgo Cluster it may have looked very much like a spiral
galaxy. (In this discussion we make the underlying assumption that it didn’t
acquire gas after entering the cluster, so whatever gas it contains now is gas
that it either carried into the cluster upon entry or regenerated internally
from stellar mass loss.)

One striking exception to the above analogy with spirals is the very low
12CO(1$-$0)/13CO(1$-$0) line ratio and the low inferred abundance ratios
[12CO/13CO] = $7.8^{+2.7}_{-1.5}$ and $6.5^{+3.0}_{-1.3}$. For comparison,
estimated [12C/13C] abundances in nearby spirals and the Milky Way tend to
range from 20 to 60 (e.g. Romano et al., 2019; Tang et al., 2019; Martín et
al., 2019; Teng et al., 2021). In this regard, NGC 4526’s status as a
longtime, virialized resident of the Virgo Cluster is particularly relevant.
Crocker et al. (2012) and Alatalo et al. (2015) noticed that Virgo Cluster
early-type galaxies have systematically lower 12CO/13CO line ratios than field
early-type galaxies or spirals; Crocker et al. (2012) suggested these low
ratios might be caused by ram pressure stripping, which could remove a
diffuse, optically thin component of the molecular gas. In the case of NGC
4526, the HI deficit (Section 2) is also consistent with such stripping. Our
analysis confirms that the 13CO(1$-$0) emission is quite thick, with
$\tau_{13}=1.1^{+0.9}_{-0.5}$. It is not yet clear whether the low abundance
ratio [12CO/13CO] $\approx 7$ was established before or after NGC 4526 entered
the cluster. It would be interesting to compare that ratio to the expected
nucleosynthetic yields, as NGC 4526 has much older stellar populations than
the star-forming galaxies that commonly feature in isotopic analyses.

In contrast to 12CO/13CO, the 13CO/C18O line ratios and abundances in NGC 4526
are similar to those found in spirals. Zhang et al. (2018) recently suggested
that 13CO/C18O line ratios might be used as indicators of the initial mass
function (IMF), as 18O originates in more massive stars than 13C, and both
isotopologues are expected to have optically thin transitions. Our analysis of
NGC 4526 offers a cautionary note, since the optical depth in 13CO(1$-$0)
might be as large as 2.0. Romano et al. (2019) also note that uncertainties in
nucleosynthetic yields, especially for 18O, make it difficult to arrive at
firm conclusions regarding the IMF. Qualitatively and generally speaking,
though, we would expect that recent star formation activity should drive down
the [13CO/C18O] ratio, which should then creep back upwards over several Gyr.
This general idea seems to suggest that NGC 4526 ought to have higher
[13CO/C18O] ratios than spirals, as it has a lower specific star formation
rate, but quantitative models will be needed for a testable hypothesis.

###  9.2 Structures within NGC 4526

Outside of the nucleus, the most prominent structure in the molecular gas
distribution of NGC 4526 is the ring at $r\sim 5.3$′′ (400 pc); the peak
12CO(1$-$0) and (2$-$1) intensities in the ring match those in the galaxy
nucleus. Here we refer to the region interior to the ring as the inner disk
and to the exterior as the outer disk. Until further kinematic studies are
done, the origin of the ring and its possible dynamical significance are not
clear. However, we note that the most prominent star formation activity in NGC
4526, as traced by blue stars (Figure 4) and low [O III]/H$\beta$ ratios
(Figure 16), is found just outside the molecular ring. Figure 11 shows that
the CN emission is optically thick in the inner disk and thin in the outer
disk, but at present it is not clear whether the change in optical depth is
directly driven by the star formation activity or whether it is unrelated.
Optical depth estimates in other high-density species would also be
interesting in this regard.

The resolved data in this paper also show strong radial gradients in all of
the line ratios between 12CO and other non-CO species. In this regard, there
doesn’t appear to be a qualitative difference between the inner disk and the
outer disk. However, there may be a qualitative difference between the inner
disk and the outer disk in terms of the CO isotopologues. Figure 10 and
Appendix B suggest that 13CO and C18O are well mixed in the inner disk, and
the majority of the radial variation (a factor of 1.6 in abundance, or 1.8 in
the line ratio) occurs only in the outer disk at $r>400$ pc. In this
subsection we discuss some of the plausible interpretations of the [13CO/C18O]
abundance gradient and the different behaviors in the inner and outer disks.

For comparison, Jiménez-Donaire et al. (2017) have presented data on resolved
13CO/C18O line ratios in a small handful of nearby spiral galaxies. They
analyze line ratios, not abundances, but they argue their lines are probably
optically thin so that the line ratios are good proxies for abundances. Most
of their nearby spirals show large-scale radial gradients in 13CO/C18O, with
generally rising profiles that have values of 4 to 6 in their centers and
values of 10 to 20 at $\approx$ 6 kpc. On smaller scales, their ALMA data
sometimes show strong local variations within the inner 3 kpc; two interesting
cases show 13CO/C18O rising by a factor of two and then falling again,
producing a local maximum at about 700 pc. Clearly, nearby galaxies show a
variety of behaviors in these isotopic line ratios, and the line ratios should
be sensitive diagnostics of conditions within their disks.

Isotope-selective photodissociation is frequently mentioned as a possibility
for explaining spatial variations in isotopic line ratios. Jiménez-Donaire et
al. (2017) dismiss it in their cases on quantitative grounds. In NGC 4526, the
sense of the [13CO/C18O] abundance gradient is such that explaining it with
isotopic-selective photodissociation would require stronger UV fields in the
outer part of the molecular disk. That might be plausible in a spiral whose
colors become increasingly bluer at large radii, but it seems unlikely for an
early-type galaxy. Furthermore, isotope-selective photodissociation should
also produce an increase in [12CO/13CO] with radius, and we do not observe
that effect.

Another astrochemical process that can affect isotopologue abundances is
fractionation; in regions where the temperature is fairly low but C+ is still
available for ion-molecule reactions, the CO molecules can be preferentially
enhanced in 13CO relative to 12CO. Langer et al. (1984) find the process is
important for $T\lesssim 35$ K, and the higher ionization potential of oxygen
means this process affects the C isotopes but not the O isotopes. Thus the
effect would be expected to produce mirror-image radial trends in [12CO/13CO]
and [13CO/C18O]; if the one increases with radius, the other should decrease.
Jiménez-Donaire et al. (2017) favor this process as an explanation for the
large-scale rising 13CO/C18O line ratios they observe over several kpc in
spiral galaxy disks, but they do not yet have the corresponding [12CO/13CO]
abundance estimates to test the hypothesis. In the case of NGC 4526, our
temperature estimates from CO, HNCO and [C I] are all low enough to make the
fractionation process relevant. However, the dramatic radial increase in
[13CO/C18O] is not mirrored by a similarly strong decrease in [12CO/13CO].
Thus it also seems unlikely that fractionation alone drives the [13CO/C18O]
gradient in NGC 4526.

It is also possible that the steep radial gradient in [13CO/C18O] in the outer
disk of NGC 4526 reflects a compression effect driven by the galaxy’s presence
in the Virgo Cluster. Specifically, Tonnesen & Bryan (2009) note that
hydrodynamical interactions between a spinning galaxy disk and the non-
rotating intracluster medium (ICM) must inevitably result in angular momentum
transfer from the rotating gas disk to the ICM, causing the disk gas to
gradually spiral inward. In their simulated case with the highest ICM thermal
pressure, this effect makes the outer edge of gas disk creep inward from 20
kpc to 12 kpc over 1 Gyr, even in the absence of any ram pressure stripping.
If the gas annuli creep inward at similar radial velocities, this process
could compress the gas disk while maintaining pre-existing abundance
gradients. It is interesting to speculate, therefore, whether the [13CO/C18O]
gradient in the disk of NGC 4526 represents several kpc worth of typical
spiral galaxy abundance pattern gradients, radially compressed into the
current 1 kpc disk. Any compression on that scale must also have been
accompanied by ram pressure stripping, though, as the gas surface densities
and volume densities are not unusual (Sections 5 and 7.1). Furthermore,
secular evolution within the disk of NGC 4526 has probably been complicated by
the presence of a bar (Michard & Marchal, 1994; Ferrarese et al., 2006); the
bar has been identified based on boxy/peanut-shaped isophotes (Figure 1), and
it might have driven the formation of the molecular ring.

Finally, the radial gradient in [13CO/C18O] in NGC 4526 might be driven by
recent star formation activity in the inner disk, increasing the 18O abundance
there. A detailed test of this idea would benefit from a higher-resolution
image of an extinction-free or at least extinction-corrected star formation
tracer, and from analysis of the gravitational instabilities in the molecular
disk. At the moment we simply note that the most obvious blue stars and low [O
III]/H$\beta$ ratios are located not in the inner disk, where the [13CO/C18O]
abundance is lowest, but just exterior to the molecular ring. The displacement
is reminiscent of features sometimes seen in spiral arms, where the blue stars
are displaced downstream of the arm ridgeline traced by molecular gas. In
general, early-type galaxies are not obvious targets for detailed studies of
the star formation process. However, NGC 4526’s long residence in the Virgo
Cluster (its interactions with the ICM) and its very deep internal potential
well (its unusually large circular velocity) make it an interesting target for
star formation and chemical evolution studies.

##  10 Summary

We present new ALMA observations of continuum emission and several molecular
species in the dusty disk of the Virgo Cluster early-type galaxy NGC 4526; the
species include CO and its isotopologues, CN, CS, HCN, HCO+, HNC, HNCO, and
CH3OH.

The 3mm continuum emission shows a nuclear point source with a spectral index
of $-1.07\pm 0.02,$ which is clearly synchrotron emission from an AGN that is
also detected in X-rays and in lower frequency radio emission. We also find
low surface brightness continuum emission from an extended disk; this disk
emission has a strongly rising spectral index, and its flux density is a
remarkably good match to the long-wavelength extrapolation of a modified black
body that fits the FIR flux densities. We therefore estimate that 50% to 100%
of this extended 3mm continuum is dust emission, and the remainder is probably
free-free emission.

The resolved molecular disk structure shows a nuclear peak and a bright ring
at $r\sim 5$′′ (0.4 kpc); assuming a CO/H2 conversion factor of 4.3 M⊙ pc-2 (K
km s-1)-1, the deprojected molecular surface densities in the nucleus and in
the ring are 240 M⊙ pc-2 at 75 pc resolution. The molecular disk also shows
modest asymmetries, kinematic disturbances, and evidence for a bar, and those
kinematic features will be discussed in a future paper.

The 12CO(1$-$0)/13CO(1$-$0) line ratio in NGC 4526 is one of the lowest ever
observed outside of the Local Group, at 3.5 $\pm$ 0.35, and it is remarkably
constant throughout the disk. In contrast, 13CO(1$-$0)/C18O(1$-$0) shows
typical values but an unusually steep gradient; it is nearly constant within
the molecular ring ($r<5$′′) but exterior to that it rises by almost a factor
of two over only 0.6 kpc in radius.

We carry out RADEX modeling of the CO isotopologues and employ Bayesian
analysis with a Markov chain Monte Carlo sampler to estimate posterior
probability distributions for the physical parameters in the CO-emitting gas.
The current set of transitions strongly constrain the [13CO/C18O] abundance
ratio to be 5.7${}^{+0.7}_{-0.6}$ in the inner disk ($r<2$′′) and
9.4${}^{+1.1}_{-0.9}$ at a radius of 1 kpc; those uncertainties are 68%
confidence intervals. The [12CO/13CO] abundance ratio is poorly constrained in
the very inner regions of the disk but is found to be $7.8^{+2.7}_{-1.5}$ at
$r\approx 5$′′ and $6.5^{+3.0}_{-1.3}$ at $r\approx 12$′′, and these values
are a factor of three lower than those typically found in nearby spirals.

We find volume densities $n_{\mathrm{H}_{2}}$ = 250 cm-3 $\pm$ 0.4 dex and
Tkin $>10$ K in the CO-emitting gas. The 13CO(1$-$0) line is moderately
optically thick, with $\tau_{13}\approx 1$ and possibly as high as 2. Our
temperature estimates from the CO lines are consistent with those from the FIR
[C I] transitions and from CN (see below). We also infer temperatures in the
range of 5.4 K to 13.4 K from HNCO(5$-$4)/(4$-$3). These estimates roughly
follow the expected pattern that the high-density tracers should show lower
temperatures than CO or [C I], reflecting the origins of the high-density
tracers in the darker and colder interiors of molecular clouds. The uniformly
low temperatures are also consistent with general expectations based on the
galaxy’s low star formation rate.

NGC 4526 is relatively bright in the high-density tracers HCN, CN, and
especially CS; it is relatively faint in the shock tracers CH3OH and HNCO. We
find no measurable enhancements in high-density ratios like CN/HCN or HCN/HCO+
(or indeed anything else) towards the AGN, when measured at 150 pc resolution.
The one possible exception to that statement is a tentative rise in
12CO(2$-$1)/(1$-$0) towards the nucleus, but that analysis is complicated by
uncertain continuum subtraction in the (2$-$1) data. It has also been
suggested that CS/HCN might be enhanced in regions of star formation activity,
but we find no evidence for any spatial variations in that ratio either. Line
ratios between any two high-density tracers are remarkably constant within NGC
4526.

NGC 4526 also has an unusually high optical depth in the 3mm CN (N=1$-$0)
lines. We find an extremely low (J=3/2$-$1/2)/(J=1/2$-$1/2) ratio of 1.12
$\pm$ 0.16 in the nucleus, rising to values consistent with 2.0 outside the
molecular ring ($r>5$′′). An assumption of LTE requires temperatures $\leq$ 20
K in order to reproduce the low line ratio in the nucleus, and it suggests the
optical depth in the 3/2$-$1/2 transition is $\tau_{3/2}\geq 4.5.$ For typical
abundance ratios, this value then suggests that HCN(1$-$0), HCO+(1$-$0), and
HNC(1$-$0) should also be very thick, with $\tau_{\mathrm{HCN1-0}}$ in the
range of 5 to 30. Extragalactic observations rarely find such high values, and
it is not clear why NGC 4526 would be unusual in this respect.

Motivated by the good match between the modified black body fit and the
extended 3mm continuum flux density, we assume a dust emissivity and a
gas/dust ratio in order to infer dust-based H2 surface densities and CO/H2
conversion factors $\alpha_{\mathrm{CO}}$. Column density estimates for the CO
isotopologues, from the RADEX/MCMC analysis, then allow us to estimate the
abundances of the CO species. The values have large uncertainties of at least
a factor of a few, but at that level they are consistent with other values
inferred for nearby spirals. We find no particular evidence for internal
variations in $\alpha_{\mathrm{CO}}$ or the gas/dust ratio, though we cannot
estimate those quantities toward the nucleus because of the dominant
synchrotron continuum component there.

In many respects, the molecular properties of NGC 4526 are consistent with it
being a heavily stripped descendant of something that used to look like a
large spiral galaxy. Its unusually low [12CO/13CO] abundance ratios and
typical [13CO/C18O] ratios provoke questions about the processing of its
molecular gas in the Virgo Cluster. Its deep potential well (high circular
velocity) should protect its molecular gas from stripping more effectively
than would be the case in lower-mass spirals, though, so it’s not obvious
whether the galaxies that are currently being stripped in the Virgo Cluster
will end up looking like NGC 4526 in the future. Future work on isotopologues
in other cluster galaxies, in combination with chemical enrichment models,
will be particularly valuable for understanding the history and the processing
of galaxies in clusters.

We thank Martin Bureau for many fascinating and productive conversations about
early-type galaxies.

##  Appendix A Verification of 12CO(2-1) data

The 12CO(2-1) data used here were obtained with the CARMA telescope at a
resolution of 0′′.25 by Davis et al. (2013b). A smoothed version of the data
was also used in the dynamical analysis of Davis & McDermid (2017). As the uv-
coverage of the data is significantly different from that of the other lines
studied here, we check whether the CARMA images might have missed significant
flux by comparing them to a single-dish spectrum from the IRAM 30m telescope
(Combes et al., 2007). We convolve the CARMA data cube to the 12′′ resolution
of the 30m at 230 GHz, ensuring proper flux retention by appropriate
normalization of the convolution kernel. The spectra of the individual pixels
in the convolved cube then simulate what the 30m would have observed if it
were pointed at that location. The technique account can account for both
pointing offsets and the fact that the 30m beam is smaller than the size of
the molecular disk. The results are shown in Figure 18 for a location 1.6′′
northwest of the galaxy nucleus, where the location is chosen by eye to
reproduce the degree of asymmetry in the 30m spectrum. (Larger offsets produce
stronger asymmetry and smaller offsets produce weaker asymmetry.) An offset of
1.6′′ is well within the expected pointing performance of the 30m
telescope.222https://www.iram-institute.org/EN/content-
page-58-7-55-58-0-0.html The good match achievable between the actual 30m
spectrum and the simulated one suggests the CARMA 12CO(2-1) data do not miss
significant flux due to missing short spacings. Indeed, in a source like this
with such strong rotation, the emission in each individual channel is
effectively unresolved in the direction of the local velocity gradient.

A second issue for the 12CO(2-1) images is that continuum subtraction was not
performed on the original data because it was primarily used for kinematic
work, and the limited available bandwidth did not provide enough sensitivity
in line-free channels to detect any continuum emission. But we can now
estimate the strength of the 230 GHz continuum, based on the 100 GHz continuum
and FIR flux density measurements. As described in Section 4, the 99 GHz
continuum image at 2.0′′ resolution (Figure 2) contains roughly 1.9$\pm$0.1
mJy in an extended disk with a spectral index of +1.8 and 4.7$\pm$0.1 mJy in a
nuclear point source with a spectral index of $-1$. Uncertainties in the way
the flux density is partitioned are difficult to estimate because they involve
interpolating the disk under the point source, so the quoted uncertainties may
well be underestimates. Extrapolating those flux densities using their
estimated spectral indices suggests 11 mJy of total continuum emission at 230
GHz, of which roughly 2 to 4 mJy would be the nucleus and the rest would be
the disk. Alternatively, the modified black body fits, which use a steeper
effective spectral index for the disk emission, predict roughly 40 mJy at 230
GHz (Figure 3).

We construct a model 230 GHz continuum image including 30 mJy in an elliptical
Gaussian mimicking the size and shape of the dust disk, plus 4 mJy in a
nuclear point source. This level of continuum emission is below the detection
limits of the CARMA data. We then subtract this model continuum image from the
CARMA data cube and compare analyses with and without the estimated continuum.
The continuum subtraction makes a 10% difference in the integrated 12CO(2-1)
flux (221 $\pm$ 6 Jy km s-1 compared to 245 $\pm$ 6 Jy km s-1). It also makes
a 35% difference in the nuclear peak integrated intensity (8.1 $\pm$ 0.7 Jy
bm-1 km s-1 at 1.12′′ resolution, vs 11.0 $\pm$ 0.7 Jy bm-1 km s-1). Resolved
line ratio measurements outside of the nucleus are indistinguishable in the
two cases, as the disk has low surface brightness and the line emission
outside of the nucleus has a relatively narrow velocity support. The values
presented in the paper are computed after the estimated continuum has been
subtracted.

Figure 18: 12CO(2-1) spectra of NGC 4526. The original CARMA spectrum is
integrated over the full region of emission as defined by 12CO(1-0) and
13CO(1-0) detections in the ALMA data. We show also the original IRAM 30m
12CO(2-1) spectrum and a simulated version of a single-dish spectrum recreated
from the CARMA data cube by convolving and applying a modest pointing offset.

##  Appendix B RADEX + MCMC analysis

We investigate the physical conditions in the CO-emitting gas through the
RADEX non-LTE code, which carries out iterative solutions of the level
populations and the line radiation using an escape probability formalism (van
der Tak et al., 2007). We compute the line intensities and optical depths for
the $J=1-0$ and $2-1$ transitions in 12CO,13CO, and C18O for a grid of
physical conditions, giving the relevant line ratios as functions of those
physical conditions. The grid spans volume densities $n_{\mathrm{H}_{2}}$ = 50
to 106 cm-3 in steps of 0.215 dex, kinetic temperature Tkin = 3.0 to 80 K in
steps of 0.071 dex, and column densities N(12CO) = 8$\times 10^{15}$ to
8$\times 10^{19}$ cm-2 in steps of 0.067 dex. For a fiducial [12CO/H2]
abundance of 8$\times 10^{-5}$ (e.g. Frerking et al., 1982), the corresponding
total column densities are N(H2) = 1$\times 10^{20}$ to 1$\times 10^{24}$
cm-2. We also assume a fixed linewidth of 30 km s-1, which is similar to the
linewidth in the outer parts of the galaxy where there is little beam smearing
(Figure 6). In this context we note that the RADEX calculations in fact depend
only on the ratio of the column density to the line width, so we show fiducial
column densities N(12CO) in the figures but in fact the fundamental parameter
of physical relevance is N(12CO)/$\Delta v$. The corresponding column
densities can be easily calculated for other linewidths with a simple scaling.
The grid also spans [12CO/13CO] abundance ratios from 3.4 to 400 and
[13CO/C18O] from 2.0 to 27, both in steps of 0.067 dex. This grid strategy is
very similar to that employed by Teng et al. (2021), though independently
coded.

We then compare the predicted line ratios to observed quantities and use a
Markov chain Monte Carlo sampler (emcee; Foreman-Mackey et al., 2013) to
estimate posterior probability distributions on the relevant physical
parameters in the molecular gas. Sampling using the adaptive Metropolis
algorithm of Cappellari et al. (2013) produces results that are
indistinguishable from those of emcee. In both cases, the sampler interpolates
in the RADEX grids to evaluate predicted intensities, line ratios, and the
likelihood at each set of physical conditions it explores. We assume flat
priors on the logs of the parameters, over the range of conditions spanned by
the RADEX grids.

The observations we use as constraints are the 12CO(1$-$0) intensity and the
line ratios 12CO(1$-$0)/13CO(1$-$0), 12CO(1$-$0)/C18O(1$-$0),
13CO(1$-$0)/C18O(1$-$0), 12CO(2$-$1)/12CO(1$-$0), and 12CO(2$-$1)/13CO(2$-$1).
As the beam is larger than the typical size of a molecular cloud, beam
dilution may make the observed 12CO(1$-$0) brightness temperature smaller than
the intrinsic radiation temperature for the line. We account for the beam
filling factor by using an asymmetric distribution for the TB contribution to
the model likelihood. Specifically, the other measurements’ contributions to
the model likelihood are symmetric Gaussians, with their measurement
uncertainties characterizing the width of the distributions, but for TB we use
a Gaussian below the measured value and a flat distribution above the measured
value. All predicted line intensities that are larger than the measured value
are thus considered equally likely, allowing for beam filling factors in the
range $0\leq f\leq 1.$ In attempting to reproduce the other line ratios we are
effectively assuming this beam filling factor is the same for all the
isotopologues.

The 12CO(2$-$1)/13CO(2$-$1) line ratio also deserves some comment; it is not
measured using resolved ALMA data, like the other line ratios, but with the
IRAM 30m telescope (Crocker et al., 2012) so it is an average over a 12′′
beam. The fact that the resolved measurements of 12CO(1$-$0)/13CO(1$-$0) and
12CO(2$-$1)/12CO(1$-$0) show no significant radial variation lends confidence
to the assumption that 12CO(2$-$1)/13CO(2$-$1) may also be roughly constant
over the disk of NGC 4526.

We carry out this analysis for three representative sets of conditions in NGC
4526. One set of values corresponds to the nuclear regions ($r\lesssim 2$′′),
where the C18O intensity is relatively high, so the 13CO/C18O intensity ratio
is low, and the 12CO(1$-$0) brightness temperature is lower than elsewhere in
the galaxy (Section 5). Another set corresponds to values measured in the
molecular ring at $r\approx 5$′′, where the 13CO/C18O intensity ratio is still
low like the inner disk but the 12CO(1$-$0) brightness temperature is at its
highest. The third set of values corresponds to the outer disk, where the
13CO/C18O intensity ratio is relatively large and 12CO(1$-$0) brightness
temperatures are intermediate between those of the nucleus and the ring.

Figures 19, 20, and 21 show corner plots for the posterior probability
distributions for these conditions. Figure 19 is for the nucleus; it
illustrates the classic degeneracy between density and kinetic temperature for
driving excitation, due to the limited set of currently available line ratios
and the fact that the 12CO brightness temperature does not provide strong
constraints in the nucleus. The inferred posterior probability distribution
for the [12CO/13CO] abundance ratio peaks at 6.3 in the nucleus, though there
is a long asymmetric tail such that higher values are also permitted. The
inferred [13CO/C18O] abundance ratio is, however, tightly constrained and
almost independent of the other parameters; it is $5.7^{+0.7}_{-0.6}$ (the
quoted uncertainties correspond to a 68% confidence interval). That value is
15% larger than the observed line ratio, due to the optical depth of the
13CO(1$-$0) line.

The conditions in the ring (Figure 20) include higher brightness temperatures,
which give tighter constraints on the excitation. Here the line ratios suggest
relatively low densities for the molecular gas, with $n_{\mathrm{H}_{2}}$
$\sim$ 250 cm-3 $\pm$ 0.4 dex and Tkin $>10$ K. The improved constraints on
$n_{\mathrm{H}_{2}}$ and Tkin also help to constrain the [12CO/13CO] abundance
ratio, where we find $7.8^{+2.7}_{-1.5}$. We also find a [13CO/C18O] abundance
of $6.2^{+0.8}_{-0.6}$, consistent with the value in the nucleus. These
conditions require 13CO(1$-$0) to be moderately optically thick, with
$\tau_{13}=1.1^{+0.9}_{-0.5}$. As a check on the plausibility of those
conditions, we note that the density $n_{\mathrm{H}_{2}}$, column density
N(12CO), and a typical CO abundance of $10^{-4}$ give a line-of-sight
thickness of 12 pc. That value is reasonable for a giant molecular cloud;
additional discussion can be found in Teng et al. (2021). Finally, in the
outer disk (Figure 21) we infer similar $n_{\mathrm{H}_{2}}$, Tkin, and
[12CO/13CO] values to the ring, with [12CO/13CO] = $6.5^{+3.0}_{-1.3},$ but
substantially higher [13CO/C18O] abundances of $9.4^{+1.1}_{-0.9}.$

In short, we find strong evidence for a radial gradient in the [13CO/C18O]
abundance ratio, increasing to larger values at larger radii; the change is a
factor of 1.6 over 1 kpc. The gradient is shallower in the inner disk and
steeper in the outer disk, with the majority or perhaps all of the gradient
occurring exterior to the ring. In contrast, we find no compelling evidence
for a radial gradient in the [12CO/13CO] ratio, as our two inferred values of
$7.8^{+2.7}_{-1.5}$ and $6.5^{+3.0}_{-1.3}$ are consistent with each other
given their uncertainties. However, those [12CO/13CO] abundance ratios are
unusually low. If they reflect an intrinsic [12C/13C] ratio $\approx 7$, then
this isotopologue ratio in NGC 4526 is at least a factor of three lower than
the centers of most nearby spirals (e.g. Martín et al., 2019). Additional
discussion of the implications of these isotopologue measurements is in
Section 9.

Figure 22 also presents ($n_{\mathrm{H}_{2}}$, Tkin) slices of the
5-dimensional RADEX model volume, with contours indicating the measurements we
are attempting to explain. We construct each panel by identifying the most
likely values for the 12CO column density, [12CO/13CO] and [13CO/C18O]
abundance ratios for each set of modeled conditions. (Specifically, we use the
median values of the marginalized posterior probability distributions, as
indicated in the histogram titles in Figures 19 and 20.) The slice locations
are fixed at the closest grid values to the medians in those three parameters.
As usual (e.g. Teng et al., 2021) the maxima in the individual one-dimensional
marginalized distributions do not necessarily correspond to the maximum
likelihood solution in the whole model volume, but they are close enough to be
used as reasonable plausibility checks to illustrate the properties of our
solutions. For improved constraints on the temperature of the gas, and thus on
its density, we suspect that it would be most helpful to have high resolution
measurements of the 13CO(2$-$1) and C18O(2$-$1) lines.

Figure 19: Corner plot (Foreman-Mackey, 2016) for the physical conditions
reproducing the line ratios observed in the nuclear regions of NGC 4526,
$r\lesssim 2$′′. The greyscale intensities and corresponding marginalized
histograms show the density of samples obtained by the MCMC sampler. The label
“log N” refers to the log of the 12CO column density in cm-2, for an assumed
linewidth of 30 km s-1 FWHM; “log n” refers to the H2 density in cm-3; T is
the kinetic temperature in K; “[12/13]” is the [12CO/13CO] abundance ratio;
“[13/18]” is the [13CO/C18O] abundance ratio; and $\tau_{13}$ is the optical
depth of the 13CO(1-0) line. Column densities have not been deprojected to
face-on values. The optical depth is, of course, a dependent parameter rather
than an independent one, and it is shown for reference because it guides our
interpretations of the line ratios. Above the one-dimensional histograms,
titles give the medians of the samples of each parameter and the uncertainties
quoted indicate the range between the 16% and 84% quantiles in the cumulative
distributions (dashed black lines). In the panels showing [13CO/C18O], orange
dashed lines indicate the values derived for the nuclear regions and blue
dashed lines show the values for the outer edge of the disk. The measured
parameters used for this analysis are shown in the upper right corner of the
figure.  Figure 20: Corner plot for the conditions in the molecular ring, at
$r\approx 5$′′. Labels and lines have the same meanings as in Figure 19.
Figure 21: Corner plot for the outer molecular disk of NGC 4526. Labels and
lines have the same meanings as in Figure 19.

Figure 22: Representative slices of the RADEX model volume, corresponding to
the nucleus (left) and the molecular ring at $r\approx 5$′′ (right). Contour
lines mark the conditions that reproduce the measured values. Gray bands
around each contour line are within $\pm 1\sigma$ of the measured line ratios;
for the 12CO(1$-$0) brightness temperature measurement, the pink shaded region
is the allowed region with predicted brightness temperatures higher than the
measured value and an inferred beam filling factor in the range $0\leq f\leq
1$. Darker pixels thus have higher likelihood. Additional information is in
the text.

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