Kiloparsec-scale Variations in the Star Formation Efficiency of Dense Gas: the Antennae Galaxies (NGC 4038/39)

TL;DR

This study investigates how star formation efficiency varies across different regions of the Antennae galaxies by analyzing dense gas tracers and infrared data, revealing significant regional differences in star formation activity.

Contribution

It provides new ALMA observations of dense gas tracers in the Antennae galaxies and demonstrates regional variations in star formation efficiency and dense gas fractions.

Findings

The $ ext{L}_{ ext{TIR}}$-$ ext{L}_{ ext{HCN}}$ relation extends to the Antennae.

Star formation efficiency of dense gas varies by up to a factor of 10.

Nuclei show the lowest SFE$_ ext{dense}$ and highest dense gas fractions.

Abstract

We study the relationship between dense gas and star formation in the Antennae galaxies by comparing ALMA observations of dense gas tracers (HCN, HCO$^+$, and HNC $\mathrm{J}=1-0$) to the total infrared luminosity ($\mathrm{L_{TIR}}$) calculated using data from the \textit{Herschel} Space Observatory and the \textit{Spitzer} Space Telescope. We compare the luminosities of our SFR and gas tracers using aperture photometry and employing two methods for defining apertures. We taper the ALMA dataset to match the resolution of our $\mathrm{L_{TIR}}$ maps and present new detections of dense gas emission from complexes in the overlap and western arm regions. Using OVRO CO $\mathrm{J}=1-0$ data, we compare with the total molecular gas content, $\mathrm{M(H_2)_{tot}}$, and calculate star formation efficiencies and dense gas mass fractions for these different regions. We derive HCN, HCO$^+$ and HNC upper limits for apertures where emission was not significantly detected, as we expect emission from dense gas should be present in most star-forming regions. The Antennae extends the linear $\mathrm{L_{TIR}-L_{HCN}}$ relationship found in previous studies. The $\mathrm{L_{TIR}-L_{HCN}}$ ratio varies by up to a factor of $\sim$10 across different regions of the Antennae implying variations in the star formation efficiency of dense gas, with the nuclei, NGC 4038 and NGC 4039, showing the lowest SFE$_\mathrm{dense}$ (0.44 and 0.70 $\times10^{-8}$ yr$^{-1}$). The nuclei also exhibit the highest dense gas fractions ($\sim 9.1\%$ and $\sim7.9\%$).

Tables

Table 1. Table 1 Elliptical Apertures

Source	RA	Dec	EW	NS	Area
	(J2000)	(J2000)	(′′)	(′′)	(kpc2)
NGC4038	$12:01:52.895$	$-18:52:04.46$	24.1	24.3	5.23
NGC4039	$12:01:53.22$	$-18:53:12.29$	24.6	23.7	5.22
NGC4038-2	$12:01:52.332$	$-18:51:57.2$	9.8	9.5	0.84
WArm-1	$12:01:51.779$	$-18:51:40.27$	11.4	14.9	1.52
WArm-2	$12:01:51.156$	$-18:51:55.04$	9.5	16.3	1.39
WArm-3	$12:01:50.664$	$-18:52:11.98$	13.0	19.3	2.26
WArm-4	$12:01:51.97$	$-18:52:22.86$	13.6	14.4	1.76
SGMC1	$12:01:55.583$	$-18:52:49.02$	12.0	12.9	1.38
SGMC2	$12:01:54.862$	$-18:52:52.8$	13.1	13.7	1.60
SGMC345	$12:01:54.862$	$-18:53:04.6$	13.8	14.0	1.73
Schirm-C6	$12:01:54.351$	$-18:52:44.13$	12.6	12.7	1.44
Schirm-C7	$12:01:55.094$	$-18:52:39.71$	12.0	10.5	1.12
Overlap-8	$12:01:54.781$	$-18:52:29.88$	10.6	11.2	1.05
Overlap-9	$12:01:54.246$	$-18:53:08.14$	10.2	9.5	0.86

Equations

$$\frac{{\mathrm{L}}_{\mathrm{mol}}^{\prime }}{{\text{K km s}}^{-1}{\text{pc}}^2}$$

$${\left(\frac{{\mathrm{D}}_{\mathrm{L}}}{\text{Mpc}}\right)}^2{\left(\frac{{\nu }_0}{\text{GHz}}\right)}^{-2}(1+\mathrm{z}{)}^{-1}$$

$${\mathrm{L}}_{\mathrm{TIR}}={\int }_{3\mu \mathrm{m}}^{1100\mu \mathrm{m}}{\mathrm{L}}_{\nu }\mathrm{d}\nu .$$

$$\frac{\nu {\mathrm{L}}_{\nu }}{{\mathrm{L}}_{\odot }}=3.1256\times 10^2{\left(\frac{{\mathrm{d}}_{\mathrm{L}}}{\mathrm{Mpc}}\right)}^2\left(\frac{\nu }{\mathrm{GHz}}\right)\left(\frac{{\mathrm{S}}_{\nu }}{\mathrm{Jy}}\right).$$

$${\sigma }_{\mathrm{Gauss}}^{\mathrm{ap}}\approx 0.025\times \frac{2\sigma }{{ϵ}_{\mathrm{pb}}}\times \mathrm{\Delta v}\times {\mathrm{n}}_{\mathrm{pix}}\times {\mathrm{n}}_{\mathrm{chan}}÷\mathrm{ppb}$$

$${\sigma }_{\lim }^{\mathrm{ap}}$$

$$\log ({\mathrm{L}}_{\mathrm{TIR}})$$

$$\log \mathrm{SFR}({{\mathrm{M}}_{\odot }\mathrm{yr}}^{-1})$$

$${\sigma }_{{\mathrm{L}}^{\prime }}$$

$${\sigma }_{{\mathrm{S}}_{\nu }}(\mathrm{x},\mathrm{y})$$

$${\sigma }_{\nu {\mathrm{L}}_{\nu }}(\mathrm{x},\mathrm{y})=\nu {\mathrm{L}}_{\nu }(\mathrm{x},\mathrm{y})\sqrt{2{\left(\frac{{\sigma }_{{\mathrm{d}}_{\mathrm{L}}}}{{\mathrm{d}}_{\mathrm{L}}}\right)}^2+{\left(\frac{{\sigma }_{{\mathrm{S}}_{\nu }}(\mathrm{x},\mathrm{y})}{{\mathrm{S}}_{\nu }(\mathrm{x},\mathrm{y})}\right)}^2}$$

$${\sigma }_{\log ({\mathrm{L}}_{\mathrm{TIR}})}$$

$${\sigma }_{L_{\mathrm{TIR}}}=L_{\mathrm{TIR}}\ln 10{\sigma }_{\log L_{\mathrm{TIR}}}$$

$${\sigma }_{{\mathrm{L}}_{\mathrm{TIR}}}$$

Full text

1. Introduction

The Antennae galaxies are the nearest pair of merging galaxies (22 Mpc, Schweizer et al. 2008) and are rich in star formation (e.g. Whitmore et al. 1999), gas (e.g. Wilson et al. 2000, 2003), and dust (e.g. Klaas et al. 2010). The rarity of wet, major mergers (gas-rich galaxies with a mass ratio $\leq$ 3) makes the Antennae a particularly unique environment for studying star formation in interactions. Recent simulations suggest the Antennae is $\sim 40$ Myr after its second pass (Karl et al., 2010), placing it at an intermediate stage in the Toomre sequence. Thus, the Antennae contains multiple generations of stars from merger-induced starburst behavior. The two nuclei exhibit post-starburst populations $\sim$65 Myr old (Mengel et al., 2005), and even younger starburst populations ($\sim 3-10$ Myr) are concentrated in the overlap region and western arm (e.g. Mengel et al. 2001, 2005; Whitmore et al. 2010, 2014). Furthermore, different regions within the Antennae exhibit varying degrees of current ($\leq 100$ Myr, Brandl et al. 2009) star formation, with the overlap region of the Antennae (see Fig. 1) experiencing a particularly violent episode ( Star Formation Rate, SFR $>4$ M⊙ yr*-1*, Brandl et al. 2009; Klaas et al. 2010; this work).

Major mergers are a testbed for the extreme star formation ongoing at high-z, and show fundamental differences in their star formation properties compared with normal star-forming disk galaxies (e.g. Daddi et al. 2010; Tacconi et al. 2018). Futhermore, star formation occurs primarily in the densest regions within Giant Molecular Clouds (GMCs, $\mathrm{n(H_{2})}>10^{4}$ cm*-3* , Lada et al. 1991a, b). The HCN $\mathrm{J}=1-0$ transition has a critical density of $\mathrm{n_{crit}}\sim 10^{5}$ cm*-3*, while the CO $\mathrm{J}=1-0$ has $\mathrm{n_{crit}}\sim 10^{2}$ cm*-3*. Thus, it is essential to observe molecules such as HCN to constrain the properties of the directly star-forming gas.

Extragalactic studies often use observations of the total infrared luminosity ($\mathrm{L_{IR}}$) and HCN J$=1-0$ molecular luminosity ($\mathrm{L_{HCN}}$) in galaxies to study star formation and dense gas. This has largely been motivated by the seminal work of Gao & Solomon (2004a, b), who found a tight and linear relationship between the global values of $\mathrm{L_{IR}}$ and $\mathrm{L_{HCN}}$ in a sample of 65 galaxies. Their observations were of unresolved systems, thus comparing the Total Infrared (TIR) and HCN luminosities spanning $\mathrm{L_{IR}}\sim 10^{9}-10^{12}$ L⊙. This sample included normal star-forming galaxies as well as more extreme Luminous and Ultraluminous Infrared Galaxies (LIRGs/ULIRGs), suggesting a direct scaling between the SFR and dense molecular gas content across galaxy types. Other recent studies show that this linear relationship also extends to the scales of individual, massive clumps in the Milky Way and nearby galaxies (e.g. Wu et al. 2005, 2010; Bigiel et al. 2015; Chen et al. 2015), spanning nearly 10 orders of magnitude in luminosity. These observations have motivated density-threshold models of star formation (Lada et al., 2012), which assume that star formation begins once the gas reaches a threshold density ($\mathrm{n(H_{2})}=10^{4}$ cm*-3*). These models predict a constant Star Formation Efficiency of dense gas (SFEdense) that should span all regimes of star formation.

A number of recent studies target the $\mathrm{L_{TIR}-L_{\mathrm{HCN}}}$ relationship on a variety of scales, down to several hundred parsecs (Kepley et al., 2014; Bigiel et al., 2016; Gallagher et al., 2018). These studies fit well within the scatter of the original Gao & Solomon (2004a, b) relationship, extending it down to lower luminosities. Some have also revealed variations in the $\mathrm{L_{IR}}$ and $\mathrm{L_{HCN}}$ relationship at $\sim$kpc scales (e.g. M51 from Chen et al. 2015; Usero et al. 2015). Usero et al. (2015) study $\sim$kpc scales across the disks of normal star-forming galaxies and find a sublinear power-law index ($\sim 0.5$) for their sample of galaxies. Furthermore, evidence exists that (U)LIRGs may turn off the linear portion of the $\mathrm{L_{IR}-L_{HCN}}$ sequence (Graciá-Carpio et al., 2008), suggesting variations at the high luminosity end as well.

A separate class of star formation models that can, to some degree, better explain the variations of the $\mathrm{L_{IR}-L_{HCN}}$ relationship are turbulence-regulated density threshold models (Krumholz & McKee, 2005; Padoan & Nordlund, 2011). These models predict the variation of probability density profiles (PDFs) as a function of turbulence, and show that turbulence acts as a star formation inhibitor and subsequently increases the threshold density of gas required for star formation. Observational evidence of a correlation between stellar mass density and lower $\mathrm{L}_{\mathrm{TIR}}/\mathrm{L}_{\mathrm{HCN}}$ in disk galaxies supports the idea that stellar feedback, in the form of turbulence, etc., can inhibit star formation per unit dense gas mass (Bigiel et al., 2016). Interestingly, there have been observations of increases in the dense gas fraction (often traced by $\mathrm{L}^{{}^{\prime}}_{\mathrm{HCN}}/\mathrm{L}^{{}^{\prime}}_{\mathrm{CO}}$) in the central regions of disk galaxies, where the star formation efficiency of dense gas (traced by $\mathrm{L}_{\mathrm{TIR}}/\mathrm{L}^{{}^{\prime}}_{\mathrm{HCN}}$) appears lowest and stellar density appears highest. The Central Molecular Zone (CMZ) of the Milky Way is the closest example of an environment with low SFEdense and high dense gas fractions (e.g. Kauffmann et al. 2017b, c) compared to the solar neighborhood. There are a number of possible mechanisms that can explain this, with turbulence being the favored mechanism so far (Federrath & Klessen, 2012; Kruijssen et al., 2014; Rathborne et al., 2014). Federrath & Klessen (2012) compare the expectations of six different star formation with Magnetohydrodynamic (MHD) simulations that vary four fundamental parameters: virial parameter, sonic mach number, turbulent forcing parameter, and Alfven mach number. They find turbulence is the primary regulator of the SFR, and produce star formation efficiencies of the total gas (SFE) that agree well with observations ($1-10\%$).

High-resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations have revealed HCN, HCO+, and HNC $\mathrm{J}=1-0$ emission throughout star-forming regions in the Antennae (Schirm et al., 2016). Assuming these transitions trace $\mathrm{n(H_{2})}>10^{4}$ cm*-3*, this suggests there is an abundance of dense gas throughout this system. Futhermore, there are interesting variations in the molecular luminosities of these dense gas tracers, suggesting differences in dense gas properties across the system. Schirm et al. (2016) found evidence for variations of the dense gas fraction across the Antennae, evidenced by higher HCN-to-CO luminosity ratios in the two nuclei when compared to the overlap region (see Fig. 1). Bigiel et al. (2015) find that the $\mathrm{L_{IR}-L_{HCN}}$ relationship in the brightest regions of the Antennae galaxies is consistent with the linear relationship revealed by Gao & Solomon (2004a, b), but their sensitivity limits miss a large portion of the star-forming regions in the system (e.g. the western arm and fainter regions in the overlap region). In this paper, we attempt to understand the variations of this relationship in the context of the Antennae galaxies by assessing the variations of the physical properties with $\mathrm{L}_{\mathrm{TIR}}-\mathrm{L}^{{}^{\prime}}_{\mathrm{HCN(1-0)}}$ at subgalactic scales.

In §2, we present the ALMA, Herschel, and Spitzer data used in our study along with the total infrared luminosity calibrations. In §3, we describe our aperture photometry analyses. In §4, we present the luminosity fit results and compare to previous work. In §5, we discuss the variation we see in $\mathrm{SFE_{dense}}$ across the Antennae and explore potential explanations for these variations. The analysis and results of this study are summarized in §6. Molecular and infrared luminosity uncertainties are discussed in more detail in Appendix A. A comparison between total infrared luminosity calbrations from Galametz et al. (2013) is presented in Appendix B.

2. Data

We use Herschel, Spitzer, and ALMA data in our study to compare star formation traced by infrared emission to dense gas traced by high critical-density molecular transitions, HCN, HCO+, and HNC $\mathrm{J}=1-0$ (see Figure 1). We also use CO $\mathrm{J}=1-0$ data from the Owens Valley Radio Observatory (OVRO, Wilson et al. 2003) as our bulk molecular gas tracer, and we note that the OVRO data may be missing $\sim 20\%$ of the CO $\mathrm{J}=1-0$ flux (Schirm et al., 2016), likely a diffuse component of the gas, due to the limited range of $u-v$ coverage. Our resolution is limited by the Herschel data ($5.5^{\prime\prime}$ at 70 $\mu$m, and $6.8^{\prime\prime}$ at 100 $\mu$m), and thus our analysis is performed at these resolutions.

2.1. ALMA Data

Details on the observations of the ALMA data are available in Schirm et al. (2016). The original reduction scripts were used to apply calibrations to the raw data using the appropriate Common Astronomy Software Applications (CASA) version (CASA 4.2.0, McMullin et al. 2007). The ALMA data were then cleaned and imaged in in CASA 4.7.2. We cleaned using a velocity resolution of $\Delta\mathrm{v_{opt}}=5.2\ \mathrm{km\ s}^{-1}$ at the rest frequency of each transition over an optical velocity range of 1000-2000 km s*-1*. We tapered the data to the Full-Width Half-Maximum (FWHM) of the Herschel 70 $\mu$m Point Spread Function using a Briggs weighting of $0.5$ while cleaning. The largest angular scale of the ALMA observations is $\sim 17^{\prime\prime}$111ALMA Cycle 1 Proposer’s Guide ($\sim 1.8$ kpc). The tapered data reach a root mean square noise level (rms) of $\sigma=1.2\ \mathrm{mJy\ beam}^{-1}$. When working at the $100\ \mu$m resolution, we further smooth the tapered cube to $6.8^{\prime\prime}$.

We create moment zero maps of the molecular lines using CASA’s immoments command. This produces a two-dimensional image of the integrated intensity with units of Jy beam*-1* km s*-1*. We require that all pixels going into the final moment map be greater than $2\sigma$, where $\sigma=1.2$ mJy beam*-1* in the $5.5^{\prime\prime}$ maps and $\sigma=1.4$ mJy beam*-1* in the smoothed 6.8*′′* maps. We then convert to molecular luminosities ($\mathrm{L^{\prime}_{mol}}$) using the following equation (Wilson et al., 2008)

[TABLE]

where $\mathrm{S_{ap}}$ is the flux measured in an aperture in $\textrm{Jy km s}^{-1}$. This gives molecular luminosity in units of $\textrm{K km s}^{-1}\textrm{ pc}^{2}$. We use a redshift of $\mathrm{z}=0.005477$. Details on the uncertainty estimates are given in §3 and Appendix A.I.

2.2. Infrared Data and Total Infrared Luminosities

We obtain user-provided data products of the 70, 100, 160, and 250 $\mu$m maps from the Herschel (Pilbratt et al., 2010) Science Archive. Details on the observations and reduction of the 70, 100, and 160 $\mu$m (Photodetector Array Camera and Spectrometer) PACS (Poglitsch et al., 2010) data are available in Klaas et al. (2010) and reach resolutions of $5.5^{\prime\prime}$, $6.8^{\prime\prime}$, and $11.3^{\prime\prime}$, respectively. The Spectral and Photometric Imaging Receiver (SPIRE) 250 $\mu$m map ($18.1^{\prime\prime}$ resolution, Griffin et al. 2010) was obtained as part of the Very Nearby Galaxies Survey and details on the observations and calibrations can be found in Bendo et al. (2012b). We also retrieve user-provided Spitzer (Werner et al., 2004) 24 $\mu$m Multiband Imaging Photometer (MIPS) data (Rieke et al. 2004, $6.0^{\prime\prime}$ resolution) from the Spitzer Heritage Archive. These data were reprocessed by Bendo et al. (2012a) to provide ancillary data for the Herschel-SPIRE Local Galaxies Guaranteed Time Programs.

We use several calibrations from Galametz et al. (2013) to estimate LTIR, which is defined in that paper to be:

[TABLE]

Galametz et al. (2013) derive calibrations of LTIR using a combination of Herschel and Spitzer data from $8-250\ \mu\mathrm{m}$ as an alternative to fitting the dust spectral energy distribution (SED). They have provided monochromatic calibrations (e.g. 70 $\mu$m), as well as multi-band calibrations (e.g. 24+70+100 $\mu$m). We compare several of these calibrations for the Antennae in Appendix B and show the ratio maps for these calibrations in Figure 6 at the 250 $\mu$m resolution ($18.1^{\prime\prime}$).

In this paper, we use the monochromatic 70 $\mu$m (5.5” $\sim$ 590 pc) and the multi-band $24+70+100\ \mu$m (6.8” $\sim$ 725 pc) calibrations to estimate LTIR across the Antennae. The 70 $\mu$m calibration is the highest-resolution Herschel band and brackets the warm-dust (30-60 K) Spectral Energy Distribution (SED) peak ($\sim 100\ \mu$m). For multi-band calibrations, Galametz et al. (2013) recommend that any LTIR estimate using less than 4-5 bands should include the 100 $\mu$m flux or a combination of the $70+160$ bands, which should lead to LTIR predictions reliable within 25% ($\leq 50\%$ for monochromatic calibrations). Additionally, Galametz et al. (2013) note that including the 24 $\mu$m flux improves calibrations of LTIR for galaxies with higher 70/100 color, i.e. strongly star-forming environments. The overlap region is known to be vigorously star-forming, which could cause the 70 $\mu$m flux to underestimate LTIR. Therefore, we include the $24+70+100\ \mu$m calibration as a check for this. Overall, we find our L${}_{\mathrm{TIR}}(70)$ estimates agree well with the L${}_{\mathrm{TIR}}(24+70+100)$ estimates. The L${}_{\mathrm{TIR}}(70)$ estimate for SGMC345 (the combination of SGMCs 3, 4, and 5 from Wilson et al. 2000) is only $\sim 3\%$ lower than the L${}_{\mathrm{TIR}}(24+70+100)$ estimate and agrees within uncertainties.

To estimate LTIR using multiple IR bands, we converted the Herschel and Spitzer maps to the same units and resolution (i.e. to the FWHM of the beam size of the band with the lowest resolution). The Spitzer MIPS and Herschel SPIRE data were converted to units of Jy pixel*-1* from MJy sr*-1* and Jy beam*-1*, respectively (the Herschel PACS data were already in units of Jy pixel*-1*). Each dataset was then convolved to a common resolution using the Aniano et al. (2011) kernels. The Galametz et al. (2013) calibrations require infrared measurements be in solar luminosity units ($\text{L}_{\odot}$). We convert the Herschel infrared maps from Jansky units to solar luminosities using the following equation

[TABLE]

The background is then estimated and subtracted from each map. Once the data are formatted properly, we apply the corresponding Galametz et al. (2013) calibrations to create LTIR maps. We calculate absolute uncertainties on the LTIR calibrations (see Appendix A.II for details) and find they are much lower than the calibration uncertainties quoted above (25$\%$ uncertainties on the L${}_{\mathrm{TIR}}(24+70+100)$ measurements and $\sim 50\%$ uncertainties on the LTIR(70) measurements).

3. Aperture Analysis

We compare the emission of our SFR and gas tracers across different regions of the Antennae using aperture photometry. We use two approaches to defining apertures. In our first method, we identify clumps of emission using cprops (Rosolowsky & Leroy, 2006) in each of the dense gas data-cubes; we then manually define elliptical apertures (Table 3) to encompass infrared and integrated intensity dense-gas emission of individual “clumps” or complexes222There are multiple clumps of dense gas emission along most lines-of-sight, but in an aperture-photometry analysis we sum over all of this emission.. We vary the radii and position angles of the apertures to encompass potentially-associated emission of the IR and dense-gas tracers. In our second method, we perform a “pixel-by-pixel” analysis by dividing the maps into hexagonal grids that are sampled by the FWHM of the beam (i.e. the incircle diameter of each hexagon is $6.8^{\prime\prime}$). The hexagons are fixed in size across the map (edge = $3.9^{\prime\prime}$; inspired by a similar method employed by Leroy et al. 2016). The elliptical aperture method allows us to contrast the behavior of individual regions, while the hexagonal method eliminates selection bias that can be introduced in the manual-aperture method. Therefore, the hexagonal aperture method provides more robust data for trend-fitting, and the emphasis of the elliptical aperture analysis is region-by-region comparisons.