Dense Gas, Dynamical Equilibrium Pressure, and Star Formation
in Nearby Star-forming Galaxies
Molly J. Gallagher
1
, Adam K. Leroy
1
, Frank Bigiel
2
, Diane Cormier
2,3
, María J. Jiménez-Donaire
2
, Eve Ostriker
4
,
Antonio Usero
5
, Alberto D. Bolatto
6
, Santiago García-Burillo
5
, Annie Hughes
7,8
, Amanda A. Kepley
9
,
Mark Krumholz
10
, Sharon E. Meidt
11
, David S. Meier
12
, Eric J. Murphy
9
, Jérôme Pety
13,14
, Erik Rosolowsky
15
,
Eva Schinnerer
11
, Andreas Schruba
16
, and Fabian Walter
11
1
Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA; gallagher.674@osu.edu
2
Institute für theoretische Astrophysik, Zentrum für Astronomie der Universität Heidelberg, Albert-Ueberle Str. 2, D-69120 Heidelberg, Germany
3
Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, Irfu/Service d’Astrophysique, CEA Saclay, F-91191 Gif-sur-Yvette, France
4
Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
5
Observatorio Astronómico Nacional (IGN),C/Alfonso XII, 3, E-28014 Madrid, Spain
6
Department of Astronomy, Laboratory for Millimeter-wave Astronomy, and Joint Space Institute, University of Maryland, College Park, MD 20742, USA
7
CNRS, IRAP, 9 av. du Colonel Roche, BP 44346, F-31028 Toulouse cedex 4, France
8
Université de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex 4, France
9
National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
10
Research School of Astronomy & Astrophysics, Australian National University, Canberra, ACT 2611, Australia
11
Max Planck Institute für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany
12
Department of Physics, New Mexico Institute of Mining and Technology, 801 Leroy Place, Soccoro, NM 87801, USA
13
Institut de Radioastronomie Millimètrique (IRAM), 300 Rue de la Piscine, F-38406 Saint Martin d’Hères, France
14
Observatoire de Paris, 61 Avenue de l’Observatoire, F-75014 Paris, France
15
Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
16
Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße 1, D-85748 Garching, Germany
Received 2017 April 14; revised 2018 March 19; accepted 2018 March 20; published 2018 May 10
Abstract
We use new ALMA observations to investigate the connection between dense gas fraction, star formation rate (SFR),
and local environment across the inner region of four local galaxies showing a wide range of molecular gas depletion
times. We map HCN (1–0),HCO
+
(1–0),CS(2–1),
13
CO (1–0),andC
18
O (1–0) across the inner few kiloparsecs of
each target. We combine these data with short-spacing information from the IRAM large program EMPIRE, archival
CO maps, tracers of stellar structure and recent star formation, and recent HCN surveys by Bigiel et al. and Usero et al.
We test the degree to which changes in the dense gas fraction drive changes in the SFR.
I
I
HCN CO
(tracing the dense gas
fraction) correlates strongly with I
CO
(tracing molecular gas surface density), stellar surface density, and dynamical
equilibrium pressure, P
DE
. Therefore,
I
I
HCN CO
becomes very low and HCN becomes very faint at large galactocentric
radii, where ratios as low as
I
I 0.0
1
HCN CO
~
become common. The apparent ability of dense gas to form stars,
SFR dense
SS
(where Σ
dense
is traced by the HCN intensity and the star formation rate is traced by a combination of Hα
and 24 μm emission), also depends on environment.
SFR dense
SS
decreases in regions of high gas surface density, high
stellar surface density, and high P
DE
. Statistically, these correlations between environment and both
SFR dense
SS
and
I
I
HCN CO
are stronger than that between apparent dense gas fraction (
I
I
HCN CO
) and the apparent molecular gas star
formation efficiency
SFR mol
SS
. We show that these results are not specifictoHCN.
Key words: galaxies: ISM – galaxies: star formation – radio lines: ISM
Supporting material: tar.gz file
1. Introduction
Observations of star-forming regions in the Milky Way (e.g.,
Lada & Lada 2003; Kainulainen et al. 2009; Heiderman
et al. 2010; Lada et al. 2010; André et al. 2014) indicate that
stars form mainly in dense substructures. These studies have
inspired a large body of literature investigating how the amount
of dense gas relates to the star formation rate of a cloud or
galaxy. Lada et al. (2012) found the star formation rate ( SFR)
surface density (Σ
SFR
) in individual Milky Way clouds to be
proportional to the fraction of the gas that is dense (where
here “dense” is n3×10
4
cm
−3
). Similarly, both Evans
et al. (2014 ) and Lada et al. (2010) found that the SFR in
individual clouds relates linearly to the molecular gas mass
above an extinction threshold chosen to select only dense gas:
A
V
≈8mag and A
K
≈0.8mag, respectively (see also
Könyves et al. 2015). In a pioneering study, Gao & Solomon
(2004) showed that galaxy-integrated SFR, traced by IR
emission, relates linearly to the total mass of dense molecular
gas, traced by HCN emission. Based on this result, they argued
for a similar picture for whole galaxies, with the SFR set by the
amount of dense, HCN-emitting gas.
Spectroscopic studies of other galaxies indicate a more
complex relationship between dense gas and SFR. Usero et al.
(2015) surveyed ∼60 regions across 30 star-forming galaxies
with a ∼1–2 kpc sized beam. They found that the dense gas star
formation efficiency (SFE
dense
,defined as Σ
SFR
/Σ
dense
),
inferred from HCN, Hα, and 24 μm emission, anticorrelates
with both the stellar surface density (Σ
*
) and the fraction of gas
in the molecular phase (
f
mol
). Using one of the first whole-
galaxy HCN galaxy maps, Bigiel et al. (2016) found similar
trends across the disk of NGC5194 (consistent with Chen
et al. 2015): at roughly kiloparsec resolution, SFE
dense
drops
with increasing Σ
*
and increasing
f
mol
. The sense of these
results agrees with recent work studying the Milky Way, which
finds the rate of star formation per unit dense gas to be lower in
The Astrophysical Journal, 858:90 (29pp), 2018 May 10 https://doi.org/10.3847/1538-4357/aabad8
© 2018. The American Astronomical Society. All rights reserved.
1
the Galactic center than in solar neighborhood molecular
clouds (see Longmore et al. 2013).
The abundance of dense gas is also of interest and appears to
depend strongly on environment. Gao & Solomon (2004)
observed large variations in the dense gas fraction (
f
dense
º
dense mol
SS
),tracedbythe
I
I
HCN CO
ratio. Usero et al. (2015)
and Bigiel et al. (2016) found that f
dense
varies significantly ,
correlating with Σ
*
and f
mol
. Furthermore, the Milky Way center
appears far richer in dense gas (Longmore et al. 2013) than the
local clouds studied by Lada et al. (2010) and Evans et al. (2014).
Usero et al. (2015) and Bigiel et al. (2016) found that
SFE
dense
and f
dense
vary as a function of Σ
*
and f
mol
. Both Σ
*
and f
mol
relate closely to the interstellar pressure needed to
support a gas disk in vertical dynamic equilibrium, P
DE
(Elmegreen 1989). We know that P
DE
correlates closely with
f
mol
(Wong & Blitz 2002; Blitz & Rosolowsky 2006; Leroy
et al. 2008) and with the internal pressure of molecular clouds
(Hughes et al. 2013). We also expect a correlation between P
DE
and the density of the interstellar gas. Indeed, Helfer & Blitz
(1997) suggested this correlation to help explain the paucity of
HCN emission outside galaxy centers.
This central role of gas pressure and interstellar medium
(ISM) weight appears to be consistent with star formation self-
regulation theory (see e.g., Ostriker et al. 2010; Kim et al.
2011; Ostriker & Shetty 2011) and simulations (see e.g., Kim
et al. 2011, 2013; Kim & Ostriker 2015), which predict that
Σ
SFR
will be proportional to the total pressure. However, P
DE
should not be the only factor at play. The turbulent Mach
number (e.g., Krumholz & Thompson 2007; García-Burillo
et al. 2012; Usero et al. 2015), virial parameter (Kruijssen
et al. 2014), and large-scale kinematics (Meidt et al. 2018) may
also influence SFE
dense
.
Testing these ideas and advancing this field requires more
resolved multiline mapping of galaxies, in the style of Chen
et al. (2015), Usero et al. (2015), and Bigiel et al. (2016). In this
approach, one observes a suite of lines whose emissivity peaks
at different densities, n
eff
.
17
To first order, molecular line
emission will be proportional to the mass of gas above n
eff
,as
long as all other physical conditions remain fixed. Thus,
changes in the ratio of intensities between two emission lines
with different n
eff
can indicate a changing ratio of masses above
each density (though there are crucial subtleties; see, e.g.,
Krumholz & Thompson 2007; Leroy et al. 2017b). Because
this method gives access to changes in the density distribution
without the need to resolve molecular cloud substructure, it can
be deployed to study changing gas density distributions across
whole galaxies or large parts of galaxies. This, in turn, gives
access to a much wider range of physical conditions in which
we can study the origin and role of dense gas.
Until recently, interferometers have lacked the surface bright-
ness sensitivity to survey high-n
eff
lines like HCN(1–0) across the
disks of nearby normal galaxies (for an early attempt limited by
sensitivity, see Helfer & Blitz 1997).HCN(1–0),oftenthe
brightest dense gas tracer, can be ∼30 or more times fainter than
CO(1–0)(Usero et al. 2015). The Atacama Large Millimeter/
submillimeter Array (ALMA) changes this. ALMA makes it
practical to map entire nearby galaxies with multiline, density-
sensitive spectroscopy. The high sensitivity of ALMA allows us
to reach noise levels comparable to those of previous single-dish
maps (e.g., Bigiel et al. 2016) in less than an hour. The high
resolution of ALMA helps to bridge the gap in scale between the
individual molecular clouds and cores studied in the Milky Way
andgalaxyaveragesusedinpreviousseminalstudies(e.g., Gao &
Solomon 2004; García-Burillo et al. 2012).ALMA’s resolution
also makes it possible to distinguish distinct dynamical regions,
for example, disentangling the nuclear gas structures in galaxies
(analogs to the Milky Way’s “central molecular zone,” CMZ)
from extended emission associated with the disk and spiral arms.
Here, we employ ALMA multiline spectroscopy to study the
origin and role of dense molecular gas in nearby galaxies. Our
main goals are to measure any variations in the dense gas fraction
and the star formation efficiency of dense gas and to understand
the physical drivers of such variations. We present new ALMA
observations of NGC3351, NGC3627, NGC4254, and
NGC4321. These observations cover high-n
eff
transitions
(HCN(1–0),HCO
+
(1–0),andCS(2–1)) and two CO
isotopologues (
13
CO(1–0) and C
18
O(1–0)) across the inner
≈1′ (≈3–5 kpc) of each galaxy. We chose these four targets
because together they show a wide range of apparent SFR per unit
molecular gas (SFE
mol
) over their inner few kiloparsec (Leroy
et al. 2013b). By observing the dense gas and contrasting it with
SFR tracers and CO imaging, we aim to understand if these
apparent variations in the SFE
mol
within and among our targets
are driven by changes in the dense gas fraction. We also aim to
understand the physical drivers of the dense gas fraction.
In this paper, we combine these new observations with the
data from Usero et al. (2015) and Bigiel et al. (2016) to test the
hypotheses that (1) the dense gas fraction alone drives the SFR
and (2) the mean midplane pressure drives the density
distribution and the role of dense gas in star formation.
In Section 2, we describe our ALMA observations
(Section 2.1), previous CO observations (Section 2.2), and data
processing (Section 2.4). We also summarize the multiwave-
length data used in our analysis (Sections 2.5–2.8). Then, in
Section 3, we describe some qualitative properties of our data
(Section 3.1) and explore the quantitative relationship between
dense gas and SFR in our sample (Section 3.2). We discuss the
validity of using
I
I
HCN CO
as a tracer of gas density (Section 3.3
) and then explore what sets the star formation efficiency of
dense gas (Section 3.4) and the dense gas fraction (Section 3.5),
highlighting the possible role of ISM pressure (Section 3.6).In
Section 4 we discuss the implications of our results, including
theoretical implications for the link between gas density, star
formation, and galactic environment (Section 4.1). Finally, we
lay out key caveats and next steps (Section 4.2), and then we
summarize our findings in Section 5.
2. Data
We mapped tracers of dense gas over the inner regions of
NGC3351, NGC 3627, NGC4254, and NGC4321. We chose
these targets from the sample of nearby galaxies of Leroy et al.
(2013b), which had the best available supporting multi-
wavelength data (CO, H
I, infrared (IR),Hα, etc., mapping)
at the time of the proposal. Based on the measured IR surface
brightness of the targets in that study, we estimated the likely
HCN emission of each target (following Gao & Solomon 2004;
Usero et al. 2015). Out of the subset of Leroy et al. (2013b)
targets that could feasibly be detected by ALMA, we chose
these four because together they spanned a large range of CO-
to-24 μm ratios over their inner few kiloparsecs (see plots
17
n
eff
refers to the lowest density for which a line achieves 95% of its
maximum emissivity at a given T
kin
and τ. It is closely related, though not
identical, to the effective critical density; see Shirley (2015) and Leroy et al.
(2017b).
2
The Astrophysical Journal, 858:90 (29pp), 2018 May 10 Gallagher et al.
below). This implies variations in the efficiency with which the
total molecular gas reservoir forms stars, making this small
sample ideal to test the hypothesis that variations in the
molecular gas depletion time are driven by variations in the
dense gas fraction.
2.1. ALMA Molecular Line Observations
As part of ALMA’s Cycle 2 campaign, we observed
HCN(1–0), HCO
+
(1–0),CS(2–1),
13
CO(1–0), and
C
18
O(1–0) in four galaxies using ALMA’s main array of
12 m antennas. For the remainder of the paper, we will refer to
these lines as HCN, HCO
+
, CS,
13
CO, and C
18
O. HCN,
HCO
+
, and CS all have n
eff
∼10
4
–10
5
cm
−3
(see Table 1) and
so are expected to trace mainly dense gas (though in the
absence of such gas they can still emit; e.g., Shirley 2015;
Leroy et al. 2017b). The CO isotopologues,
13
CO and C
18
O,
trace lower-density gas, n
eff
∼10
3
cm
−3
. The contrast between
the optically thin isotopologues and the optically thick
12
CO
emission constrains the optical depth and physical conditions in
the bulk of the molecular gas. We make limited use of
13
CO
and C
18
O in this paper. These data are analyzed in detail by
Jiménez-Donaire et al. (2017a). Fainter lines in the bandpass
were analyzed by Jiménez-Donaire et al. (2017b).
Table 2 gives our adopted position, morphology, orientation,
distance, beam size, and field of view for each target. We
observed seven fields in a hexagonally packed mosaic pointed
toward the center of each galaxy. The mosaic pattern used the
default Nyquist spacing set by the ALMA observing tool.
We observed each galaxy with two spectral setups. The
first covered lines tracing the dense gas: HCN, HCO
+
,and
CS. The four spectral windows covered 85.4–87.2 GHz, 87.2–
89.0 GHz, 97.2–99.0 GHz, and 99.0–100.8 GHz. The second
spectral setup covered lines tracing the overall distribution of
molecular gas:
13
CO and C
18
O. Those four spectral windows
covered 98.2–100.0 GHz, 96.6–98.4 GHz, 108.5–110.3 GHz,
and 110.3–112.1 GHz. For both setups, we observed using a
channel width of 976.6 kHz (∼3kms
−1
at ν=100 GHz) and
bandwidth of 1.875GHz, sufficient to cover the full velocity
extent of each line in question.
We observed in a compact configuration in order to
emphasize flux recovery and surface brightness sensitivity,
reflecting the faint nature of the dense gas tracers. After
calibration, the HCN observations had 703 (NGC 3351), 630
(NGC 3627), 561 (NGC 4254), and 561 (NGC 4321) baselines,
with minimum and maximum unprojected lengths of 15 and
348 m, respectively, median baseline length of 90–100 m, and
20%–90% range of typically 50–195 m. For reference at the
ν∼89.5 GHz of the HCN and HCO
+
lines, 50, 100, and
200 m correspond to ∼13
8, 6 9, and 3 5.
We processed the data using the the CASA software package
(McMullin et al. 2007) and the observatory-provided calibra-
tion scripts. Most of the calibration occurred in CASA version
4.2.2, with one data set calibrated in CASA version 4.3.1. The
calibration scripts were a mixture of the observatory-produced
CASA scripts and calls to the formal ALMA pipeline. In all
cases they are available, along with the data, from the ALMA
archive. After inspecting the pipeline calibrated data, we
imaged each line separately. For the final version of the
imaging, we used CASA version 4.6.0.
We first subtracted continuum emission using the CASA
task uvcontsub and avoiding the frequencies of known
bright lines. We then imaged each cube using natural
weighting, averaging in frequency to produce 10 km s
−1
wide
channels, and applying a small u−v taper (2″–3″ depending
on the line and target). The taper further emphasizes surface
brightness sensitivity. The small loss of resolution is irrelevant
to the science in this paper because the comparison to tracers of
recent star formation already limits our work to 5″ resolution.
With the taper, but before any other processing, the
synthesized beams in the deconvolved HCN images were
4
2×3 6 (NGC 3351),4 4×3 7 (NGC 3627),6 0×3 5
(NGC 4254), and 4
6×3 2 ( NGC 4321). The pixel size
adopted during imaging was always chosen to heavily over-
sample the beam. After imaging, we convolved each cube
using the CASA task imsmooth to have a round 8″ × 8″
Gaussian beam. This allowed us to beam-match the poorer-
resolution CO and infrared data that are crucial to the analysis.
The final images used in this analysis all have 8″ (FWHM)
beams, 10 km s
−1
channel width, and 0 5 pixels that heavily
oversample the beam.
Given the u−v coverage mentioned above, we expect
structures larger than ∼14″ in a single channel to suffer from
spatial filtering in the ALMA main array data. To account for
this, we combined our 12 m HCN, HCO
+
,
13
CO, and C
18
O
data with single-dish maps obtained as part of the IRAM
EMPIRE Survey (Bigiel et al. 2016; Cormier et al. 2018,M.
Jimenez Donaire et al. 2018, in preparation). To do this, we
aligned the IRAM maps to the grid of the ALMA data, applied
the primary beam response of the ALMA images to the IRAM
data, and converted the IRAM data to have units of Jybeam
−1
.
Then we combined the two data sets using the CASA task
feather. After the combination, we verified that the
feathered cube indeed matched the spectral profile of the
IRAM 30 m cube when both were convolved to a common 30″
resolution. Short-spacing data were not available for the CS, so
those data are from ALMA’s main 12 m array only in this
paper.
Table 3 reports the total flux recovered for each line from
each galaxy both with and without the addition of the IRAM
30 m data. We calculate the total flux by summing the pixels in
the original data cubes. The table shows that ALMA recovers
95% of the flux for all lines in NGC 3351, which is
Table 1
Lines Observed
Line ν
rest
a
Fiducial τ
b
n
eff
c
(GHz)(cm
−3
)
12
CO (1–0) 115.27 10 1×10
2
13
CO (1–0) 110.20 0.1 8×10
2
C
18
O (1–0)
d
109.78 0.1 8×10
2
CS (2–1)
d
97.98 1 7×10
4
HCO
+
(1–0) 89.19 1 4×10
4
HCN (1–0) 88.63 1 2×10
5
Notes.
a
From Splatalogue (http://splatalogue.net/).
b
Typical optical depth. See Jiménez-Donaire et al. (2017a, 2017b) for more
details.
c
Density at which the emissivity reaches 95% of its maximum given our
fiducial τ and taking T
kin
=25 K. From Leroy et al. (2017b).
d
CS(2–1) was only observed by ALMA, not the IRAM 30 m, and so not
covered in NGC5194 and not short-spacing corrected in the other targets.
3
The Astrophysical Journal, 858:90 (29pp), 2018 May 10 Gallagher et al.
dominated by a bright, compact nuclear source. In fact, for
the two faintest lines, ALMA finds slightly more flux than the
IRAM 30 m, indicating modest (∼10%) discrepancies in the
flux calibration scale. ALMA recovers a lower fraction of
the flux for galaxies with more extended, low signal-to-noise
ratio (S/N) emission. On average, ALMA recovers ∼60%–
80% of the flux found by the IRAM 30 m. Our worst case is
NGC 4254, where the faint line emission appears extended and
ALMA recovers only ∼30%–50% of the flux seen by the
IRAM 30 m. This likely results from two factors: the large
extent of the CO emission in the galaxy and the lack of a
compact, bright nuclear source (in contrast to the other three
targets). This variable, sometimes poor flux recovery empha-
sizes the importance of including short-spacing data.
Throughout the paper, we work with intensity in units of
brightness temperature, T
B
. We convert our final data cubes
from their native units of Jy beam
–1
to T
B
via the standard
Rayleigh–Jeans formula:
T
c
k
IK
210
Jy beam , 1
B
B
2
23 2
n
=
´
n
[] [ ] ()
where ν is the frequency of the line, k
B
is Boltzmann’s
constant, and I
ν
is the original intensity in Jybeam
−1
.
Finally, we measure the rms noise from the signal-free
region of each cube. At 8″ resolution, the statistical noise in
each 10 km s
−1
channel is ∼5–10 mK for HCN, HCO
+
, and
CS and ∼10mK for
13
CO and C
18
O. These vary somewhat
from cube to cube, and we use the correct local value to
construct uncertainty maps for the integrated intensity. The
nominal flux calibration accuracy of ALMA in Band 3 during
Cycle 2 was 5% according to the ALMA Cycle 2 Technical
Handbook, though this may be somewhat optimistic. The
IRAM 30 m intensity calibration for EMPIRE observations is
internally consistent to ≈5% from night to night, but the
absolute calibrations scale is uncertain at the 10%–15% level
(M. Jimenez Donaire et al. 2018, in preparation).
2.2. CO Observations
We use
12
CO(1–0) emission, hereafter referred to as CO, to
trace the overall molecular gas reservoir. We draw these maps
from literature data. In each case, our CO data include both
interferometric and single-dish data, allowing us to reach our
working ∼8″ resolution, but also recover zero- and short-
spacing information. All of the CO data have a larger field of
view than our ALMA maps, bandwidth that covers the entire
CO line for the galaxy, and pixels that oversample the beam by
more than the Nyquist rate.
For NGC 3351 and NGC 3627, we use CO observations
from BIMA SONG (Helfer et al. 2003). These cubes include
data from both the BIMA interferometer and the NRAO 12 m
single-dish telescope on Kitt Peak. The combined BIMA+12 m
cubes have native resolutions of 7
4×5 2×10 km s
−1
(NGC 3351) and 7 3×5 8×10 km s
−1
(NGC 3627). Helfer
et al. (2003) quote a flux calibration uncertainty of 15%.
For NGC 4254, we use interferometric CO observations
from CARMA STING (Rahman et al. 2011) and single-dish
data from the CO extension to the IRAM EMPIRE survey
(Cormier et al. 2018, M. Jiménez-Donaire et al. in preparation).
Before convolution, the native resolution of the CARMA data
is 3
3×2 7 ×5kms
−1
. Rahman et al. (2011) do not quote
an amplitude calibration uncertainty but discuss ∼10% as a
typical value. We combine the CARMA and IRAM data using
Table 2
Targets Observed
Galaxy R.A. Decl. Morphology Inclination Position Angle Distance Linear Beam FOV
(J2000)(J2000)(degree)(degree)(Mpc)(pc)(kpc)
NGC 3351 160.990417 11.703806 SB(r)b 41.0 192.0 9.33 392 3.67
NGC 3627 170.0623508 12.9915378 SAB(s)b 62.0 173.0 9.38 380 3.56
NGC 4254 184.706682 14.416509 SA(s)c 32.0 55.0 14.4 605 5.67
NGC 4321 185.728463 15.821818 SAB(s)bc 30.0 153.0 14.3 636 5.96
NGC 5194
30m
202.4667 47.1947 SA(s)bc pec 22.0 7.5 7.6 295 9.22×12.55
Note. R.A., decl.: adopted center of the galaxy. Inclination: inclination used to construct the radial profi les and correct surface densities for projection. Position Angle:
position angle measured north through east used to construct the radial pro files. Distance: adopted distance to the galaxy in Mpc. Linear Beam: linear scale in pc of the
FWHM of the beam used in this analysis. This is 8″ at the distance of the galaxy for the first four targets and 30″=1.1 kpc for NGC 5194 (Bigiel et al. 2016). FOV:
field of view across the dense gas maps at the distance of the galaxy without accounting for inclination. References: centers and morphologies adopted from the NASA
Extragalactic Database, which draws key information from RC3 (de Vaucouleurs et al. 1991). Source for orientation parameters: NGC3351, Dicaire et al. (2008);
NGC3627, de Blok et al. (2008); NGC4254, Boissier et al. (2003); NGC4321, Muñoz-Mateos et al. (2009); NGC5194, Colombo et al. (2014). Distances adopted
from Kennicutt et al. (2011).
30m
Observed with the IRAM 30 m. Data from Bigiel et al. (2016); see that paper for more details. The other targets were all observed with ALMA with short- and
zero-spacing correction from the IRAM 30 m. See Section 2.
Table 3
Flux Recovery
Data Type
13
CO C
18
O HCO
+
HCN
(10
3
Kkms
−1
arcsec
2
)
NGC 3351
ALMA+IRAM30 m 3.32 0.41 1.21 2.24
ALMA only 3.20 0.45 1.24 2.14
Fraction recovered 0.96 1.11 1.02 0.96
NGC 3627
ALMA+IRAM30 m 16.98 1.55 4.96 6.47
ALMA only 11.98 1.40 3.77 4.39
Fraction recovered 0.71 0.91 0.76 0.68
NGC 4254
ALMA+IRAM30 m 15.98 3.31 3.98 4.34
ALMA only 6.84 0.67 1.11 1.42
Fraction recovered 0.43 0.20 0.28 0.33
NGC 4321
ALMA+IRAM30 m 14.52 2.61 3.86 5.10
ALMA only 8.79 1.81 2.20 3.55
Fraction recovered 0.61 0.70 0.57 0.70
4
The Astrophysical Journal, 858:90 (29pp), 2018 May 10 Gallagher et al.
the CASA task feather, which carries out a Fourier plane
combination of the two cubes.
For NGC 4321, we use CO data provided as part of the
ALMA science verification program. These include both main
12 m array and Atacama Compact Array short-spacing and
total power data. We use the feathered “reference image”
provided as part of the science verification release, which has
resolution 3
9×2 5 ×5kms
−1
. As above, the nominal
amplitude calibration accuracy for ALMA at Band 3 is ±5%,
though in practice this seems optimistic. We convert all CO
data to units of brightness temperature following Equation (1),
convolve them to our working 8″ resolution, and align them to
the astrometric and velocity grid of the ALMA dense gas data.
2.3. CO and Dense Gas Conversion Factors
Whenever possible, we report our results in terms of
observable quantities, e.g., I
CO
, I
HCN
, etc. We also express
our results in terms of physical quantities, e.g., molecular gas
mass and dense gas mass. The translation from observed to
physical quantities carries substantial uncertainty and remains a
topic of active research (e.g., Sandstrom et al. 2013; Usero
et al. 2015; Leroy et al. 2017b). However, these physical
quantities—e.g., Σ
H2
and Σ
dense
—are of considerable interest
and are central to our science goals. Therefore, following Usero
et al. (2015), we will also express our results as best-estimate
physical terms. Given a choice, we prefer the simplest possible
translation from observed to physical quantities and will plot
both axes whenever we can.
By default, we quote total molecular gas mass assuming a
CO(1–0) to molecular gas mass conversion factor of
M4.3 pc K km s
CO
211
a »
---
()
. In order to derive a fiducial
dense gas mass, we convert from HCN intensity to dense gas mass
surface density assuming
M10 pc K km s
HCN
211
a »
---
()
.
Both factors include helium.
Both of these conversion factors carry substantial
uncertainty, though for different reasons. Our
CO
a »
M
4
.3 pc K km s
211---
()
is often taken as the Milky Way
conversion factor and applied as a default to solar-metallicity
massive galaxies (see Bolatto et al. 2013). However, dust-based
studies that include our current targets suggest that the gas-rich
regions in the central parts of some galaxies have lower α
CO
(Sandstrom et al. 2013). This presumably reflects dynamical
broadening of the CO line width, leading to more CO emission
per unit mass.
Meanwhile, we consider α
HCN
uncertain because the
abundance and opacity of HCN as a function of density and
environment remain poorly known. Gao & Solomon (2004)
argue for
M10 pc K km s
HCN
211
a »
---
()
to convert from
HCN intensity to surface density of gas above
n
310
H2
4
~´
cm
−3
based on large velocity gradient modeling and invoking
the virial theorem. However, if the inputs to these calculations,
e.g., the abundance of HCN, the opacity of HCN, or the
dynamical state of dense gas, vary from their assumed values,
then the absolute value of α
HCN
also changes (see, e.g., Leroy
et al. 2017b). Constraints on these quantities in other galaxies
remain very weak (see Martín et al. 2006; Jiménez-Donaire
et al. 2017a), but observations of the Milky Way do
demonstrate important variations (e.g., Pety et al. 2017).
In this paper, we focus on the dense gas fraction. Many environ-
mental factors that affect CO might also affect HCN emission.
Because we lack a useful prescription for α
HCN
, it is unclear how
we should implement variations in α
CO
(for an in-depth discussion
of how these quantities may relate, see Usero et al. 2015).
Moreover, we aim to clearly present our results in terms of
observed line ratios, e.g.,
I
I
HCN CO
.Thisrequiresasimpleα
CO
and α
HCN
.
We do consider how our multiline observations support the
idea that HCN traces the dense gas. For a complete discussion
of the variation in α
CO
, α
HCN
, and their effects on f
dense
and
SFE
dense
, we refer the reader to Usero et al. (2015).
2.4. Creation of Integrated Intensity Maps
For each galaxy, we create a position – position–velocity
mask using the CO data. We first identify pixels with S/N>5
in at least two adjacent velocity channels. We then remove
contiguous S/N>5 regions that are small compared to the
size of the beam. Next, we grow these regions to include
adjoining pixels where S/N>2. The resulting mask does a
good job of capturing the region of bright CO emission that one
would identify by eye.
CO emission tends to be brighter and easier to excite than
emission from rarer isotopologues or dense gas tracers.
Therefore, we take this region of bright CO emission to also
represent the position–position–velocity region where we
might find these fainter lines. We verify by eye that no clear
dense gas tracer emission extends beyond this mask. Thus,
regions outside this mask are taken to be signal free and used to
estimate the rms noise in each cube.
We sum the masked line data cubes along each line of sight
to produce maps of integrated intensity, in K km s
−1
. In this
sum, masked pixels have a value of zero, and lines of sight with
no identi fied signal have an integrated intensity of zero. Thus,
we also produce a 2D mask indicating which lines of sight
include any bright signal in the CO cube.
We calculate the statistical uncertainty in the integrated
intensity from the rms noise in an individual channel map (in
K) times the channel width (in km s
−1
) times the square root of
unmasked voxels along a line of sight. Typical rms
uncertainties due to statistical errors in the integrated lines are
∼0.2Kkms
−1
for the CO isotopologues and ∼0.1Kkms
−1
for the dense gas tracers. The CO data tend to have poorer
sensitivity, with typical uncertainty ∼2Kkms
−1
in the
integrated intensity per line of sight. However, because the
CO is brighter, the CO data still have higher S/N.
2.5. Star Formation Rates
The deep multiwavelength data available for our sample
allow the prospect to estimate the surface density of recent star
formation, Σ
SFR
, in several ways. In our table of radial profiles,
we provide the measurements necessary to reconstruct most
popular monochromatic or “hybrid” tracers (see, e.g., review in
Kennicutt & Evans 2012).
In the plots accompanying the main text, we present Σ
SFR
estimated from a combination of Hα and 24 μm emission
following Calzetti et al. (2007) and Leroy et al. (2012).We
adopt this choice because for nearby nonstarburst galaxies it
has emerged as a widely accepted estimator of Σ
SFR
(see
Kennicutt & Evans 2012).
Although Hα+24 μm is widely accepted, its calibration
remains fundamentally empirical, with limited fundamental
work on resolved targets (Calzetti et al. 2007; Kennicutt et al.
2007; Murphy et al. 2011). Much of the literature surrounding
dense gas remains focused on infrared luminosity, considering
5
The Astrophysical Journal, 858:90 (29pp), 2018 May 10 Gallagher et al.
