Extreme CO Isotopologue Line Ratios in ULIRGS: Evidence for a top-heavy IMF

TL;DR

This study uses high-resolution ALMA observations to analyze isotopologue line ratios in ULIRGs, providing evidence that these galaxies may have a top-heavy initial mass function due to unusual chemical abundance ratios.

Contribution

It presents new measurements of CO isotopologue line ratios in ULIRGs, supporting the hypothesis of a top-heavy IMF in these galaxies based on chemical abundance evidence.

Findings

High $^{12}$CO/C$^{18}$O and $^{12}$CO/$^{13}$CO ratios observed

Low $^{13}$CO/C$^{18}$O ratios suggest C$^{18}$O is more abundant

Evidence supports a top-heavy stellar initial mass function in ULIRGs

Abstract

We present high-resolution ALMA observations of the C$^{18}$O, $^{13}$CO and $^{12}$CO $J$=1-0 isotopologues in 3 nearby ultra-luminous infrared galaxies (ULIRGS; Arp 220, IRAS 13120-5453, IRAS 17208-0014) and 1 nearby post-merger galaxy (NGC 2623). In all 4 systems, we measure high $^{12}$CO/C$^{18}$O and $^{12}$CO/$^{13}$CO integrated line ratios while the $^{13}$CO/C$^{18}$O ratio is observed to be extremely low in comparison to typical star-forming disks, supporting previous work. We investigate whether these unusual line ratios are due to dynamical effects, astrochemistry within the gas, or nucleosynthesis in stars. Assuming both lines are optically thin, low $^{13}$CO/C$^{18}$O values suggest that C$^{18}$O is more abundant than $^{13}$CO in the interstellar medium of these systems. A plausible explanation is that local ULIRGs and their progeny have an excess in massive star formation; in other words, they are producing a top-heavy stellar initial mass function.

Tables

Table 1. Table 1: List of target galaxies and their C 18 O J 𝐽 J =1-0, 13 CO J 𝐽 J =1-0 and 12 CO J 𝐽 J =1-0 line and ratio properties. The associated measurement errors are quoted (no brackets) and ALMA band 6 calibration uncertainties are provided in brackets where

Galaxy	Arp 220	IRAS 13120-5453	IRAS 17208-0014	NGC 2623
DL [Mpc]	79	135	189	80
log $L_{IR}$ [$L_{\odot }$]	12.2	12.3	12.4	11.4
Resolution [”]	0.86 $\times$ 0.51	0.73 $\times$ 0.52	0.47 $\times$ 0.40	1.37 $\times$ 1.04
C18O $J$=1-0 flux [Jy km s-1]	10 $\pm$ 0.4 [$\pm$ 0.7]	1 $\pm$ 0.2 [$\pm$ 0.1]	0.5 $\pm$ 0.1 [$\pm$ 0.04]	2 $\pm$ 0.2 [$\pm$ 0.1]
13CO $J$=1-0 flux [Jy km s-1]	8 $\pm$ 0.3 [$\pm$ 0.5]	2 $\pm$ 0.2 [$\pm$ 0.2]	1 $\pm$ 0.2 [$\pm$ 0.1]	0.6 $\pm$ 0.1 [$\pm$ 0.04]
12CO $J$=1-0 flux [Jy km s-1]	294 $\pm$ 3 [$\pm$ 21]	156 $\pm$ 0.8 [$\pm$ 11]	70 $\pm$ 1 [$\pm$ 5]	109 $\pm$ 1 [$\pm$ 8]
C18O $J$=1-0 rms [mJy beam-1] (35 km s-1)	0.7	0.3	0.3	0.4
13CO $J$=1-0 rms [mJy beam-1] (35 km s-1)	0.7	0.3	0.3	0.4
12CO $J$=1-0 rms [mJy beam-1] (20 km s-1)	4.2	1.1	1.4	1.9
C18O Vmin:Vmax [km s-1]	5130:5550	8840:9300	12040:12320	4090:4510
13CO Vmin:Vmax [km s-1]	4010:4320	7760:8140	10990:11510	5240:5590
12CO Vmin:Vmax [km s-1]	5060:5660	8790:9240	1970:12650	5240:5660
Mean 12CO/C18O $J$=1-0	39 $\pm$ 2 [$\pm$ 0.1]	63 $\pm$ 4 [$\pm$ 0.2]	81 $\pm$ 6 [$\pm$ 0.2]	40 $\pm$ 2 [$\pm$ 0.1]
Mean 12CO/13CO $J$=1-0	48 $\pm$ 2 [$\pm$ 0.1]	36 $\pm$ 0.8 [$\pm$ 0.1]	45 $\pm$ 2 [$\pm$ 0.1]	92 $\pm$ 10 [$\pm$ 0.5]
Mean 13CO/C18O $J$=1-0	0.9 $\pm$ 0.05	2 $\pm$ 0.2	2 $\pm$ 0.2	0.5 $\pm$ 0.1
Median 12CO/C18O $J$=1-0	26 $\pm$ 3 [$\pm$ 3]	48 $\pm$ 5 [$\pm$ 3]	70 $\pm$ 8 [$\pm$ 7]	31 $\pm$ 2 [$\pm$ 3]
Median 12CO/13CO $J$=1-0	37 $\pm$ 2 [$\pm$ 4]	30 $\pm$ 1 [$\pm$ 2]	38 $\pm$ 2 [$\pm$ 4]	81 $\pm$ 13 [$\pm$ 6]
Median 13CO/C18O $J$=1-0	0.7 $\pm$ 0.06	2 $\pm$ 0.2	2 $\pm$ 0.2	0.4 $\pm$ 0.2

Full text

galaxies: ISM – galaxies: starburst – ISM: abundances – stars: luminosity function, mass function – submillimeter: galaxies

1 Introduction

It is well established that the merging of two galaxies has a significant effect on the system’s interstellar medium (ISM) and star formation properties. Radial atomic and molecular gas flows towards the merger’s center dissipate energy and angular momentum (Barnes & Hernquist, 1991). Once there, increased densities and dust contents aid the conversion of atomic gas into its molecular, star-forming phase, and strong tidal forces combine with frequent molecular cloud collisions to elevate star formation rates (SFRs; Mirabel & Sanders, 1989; Sanders & Mirabel, 1996; Genzel et al., 1998). In extreme cases, where the merging pair is both massive and gas-rich, SFRs can reach hundreds or even thousands of solar masses per year, heating the interstellar dust such that infrared luminosities exceed 1012 L⊙ (e.g., Armus et al., 1989; Barnes & Hernquist, 1992; Murphy et al., 1999). In the local Universe, these objects are often known as ultra-luminous infrared galaxies (ULIRGs).

While ULIRGs are relatively rare in comparison to typical nearby galaxies, extreme star-forming systems become many hundreds of times more common at high redshift, where the bulk of galaxy formation took place (see review by Lonsdale et al., 2006, and references therein). Indeed, these so-called starburst galaxies are often cited as a major driver of the peak in the cosmic SFR density at $z\sim 2-3$ (Madau & Dickinson, 2014). The proximity and luminosity of nearby ULIRGs enable highly detailed, resolved observations and their extreme SFRs make them compelling analogues of high-$z$ galaxies, ideal for testing current theories of star formation and galaxy evolution.

Regardless of the galaxy and its redshift, the determination of many intrinsic galaxy properties (including SFR and stellar mass) must assume an initial distribution of birth masses for stars, the so-called stellar initial mass function (IMF). The precise form of the stellar IMF plays a leading role in current star formation theories; however, the past three decades have seen considerable debate within the literature on the shape and variable nature of the IMF (see reviews by Chabrier, 2003; Bastian et al., 2010). Historically, IMF estimates have relied on infrared, optical, and ultraviolet observations of either individual stars or integrated stellar populations. However, the large quantities of interstellar dust present in ULIRGs heavily obscure light at these wavelengths; thus, traditional techniques for measuring the IMF are not possible for starburst galaxies at any redshift.

Less traditional methods using submillimeter observations of the molecular gas content that are immune to dust attenuation hold much promise as sensitive probes of the IMF. In particular, there is a considerable body of work that has had some success using the measurement of isotopologue (isotope bearing molecule) line ratios in the ISM (e.g., Sage et al., 1991; Henkel & Mauersberger, 1993; Papadopoulos et al., 1996; Meier & Turner, 2004; Danielson et al., 2013; Sliwa et al., 2017; Zhang et al., 2018). This approach relies upon differences in stellar evolutionary paths which mean the production of carbon, oxygen, and their isotopes varies with individual star mass. High-mass stars ($\gtrsim 8\,{\rm M}_{\odot}$) are the predominant source of the oxygen-18 isotope (18O) while the carbon-13 isotope (13C), a by-product of the CNO-cycle, is primarily synthesized in low- to intermediate-mass stars ($<8\,{\rm M}_{\odot}$; Iben, 1975; Wilson & Matteucci, 1992; Meynet & Maeder, 2002; Matteucci, 2012). Assuming that the isotopologue line ratio 13CO/C18O traces the abundance ratio of 13C/18O in the high-pressure ISM of ULIRGs, 13CO/C18O can be used as chemical tracer of the stellar IMF and the star formation history (for an extensive discussion of this approach see Section 2.3 of Romano et al., 2017).

In the Milky Way and nearby normal star-forming galaxies, 13CO is typically 7-10 times brighter than C18O (Langer & Penzias, 1993; Jiménez-Donaire et al., 2017). However, much lower 13CO/C18O values have been observed in ULIRGs and starbursting systems. Both Greve et al. (2009) and Matsushita et al. (2009) find 13CO/C18O to be around unity or below in the ULIRG Arp 220, with the latter suggesting that either optical depth effects or Arp 220’s ongoing star formation activity are responsible for the observed strength of C18O with respect to 13CO. More recently, Sliwa et al. (2017) observed similarly low 13CO/C18O values in another ULIRG, IRAS 13120-5453, along with an unusually high 12CO/13CO ratio of $>60$. The authors find these unusual line ratios to be consistent with a very recent star formation episode ($<7$ Myr) and/or a top-heavy IMF. An IMF biased in favor of massive stars has been suggested previously by Sage et al. (1991), Henkel & Mauersberger (1993), and Papadopoulos et al. (1996) to explain an observed overabundance of 18O in the starburst nuclei of 4 nearby active galaxies. Meier & Turner (2004) also attribute observed enhancements in 12CO and C18O relative to the 13CO in the nucleus of the nearby barred spiral galaxy NGC 6946 to the same effect. At redshift $z\sim 2-3$, the top-heavy IMF scenario has been invoked to explain low 13CO/C18O ratios found in a small number of gravitationally lensed starbursts (Danielson et al., 2013; Zhang et al., 2018).

The challenge now is to understand whether the unusual CO isotopologue line ratios observed in extreme star-forming galaxies can be attributed primarily to their recent star formation activity or to a more fundamental difference in the IMF of these systems, or, as is possible, neither.

Building on previous work, this paper aims to investigate the prevalence, robustness, and physical cause of unusual CO isotopologue intensity ratios in systems that span the merger sequence. To do so, we combine new and archival Atacama Large Millimeter/submillimeter Array (ALMA) spatially resolved observations of 12CO, 13CO and C18O in dense molecular gas for a sample of 3 nearby ULIRGs and 1 post-merger galaxy. In Section 2, we describe the ALMA data reduction and present our observations. Section 3 discusses several possible explanations for our results, including optical depth effects, selective photodissociation, a recent burst of star formation, and an excess in massive star formation. Section 4 presents our conclusions. All distant dependent quantities are derived assuming a $\Lambda$CDM cosmology with $\Omega=0.3$, $\Lambda=0.7$, and a Hubble constant $\text{H}_{0}=70\;\text{km s}^{-1}\;\text{Mpc}^{-1}$.

2 Observations

This paper combines new and archival ALMA 12m-array observations of C18O, 13CO and 12CO $J$=1-0 lines in 4 nearby ($<$200 Mpc) advanced mergers: Arp 220, IRAS 13120-5453, IRAS 17208-0014, and NGC 2623. With infrared luminosities, LIR, exceeding 1012 L*⊙, Arp 220, IRAS 13120-5453, and IRAS 17208-0014 are all ULIRGs, while NGC 2623 is a post-merger galaxy with LIR = 1011.6* L*⊙* (Armus et al., 2009). The targets, their distances, infrared (IR) luminosities, and individual isotopologue line properties are listed in Table 1. The combination of new and archival data means that our targets were observed across ALMA cycles 2-5. Each calibrated measurement set was reduced using the appropriate Common Astronomy Software Applications (CASA; McMullin et al., 2007) version recommended by ALMA’s science pipeline documentation. The calibrated measurement sets are continuum subtracted and reduced using CASA v5.1.1. We image all data using CASA’s TCLEAN command with a Briggs weighting (Briggs, 1995), robust parameter of 0.5, and rms threshold of 2$\sigma$. We set the image channel width to 20 km s*-1* for 12CO and 35 km s*-1* for C18O and 13CO.

\startlongtable

For each galaxy, we match the pixel size, beam resolution and length of the minimum baseline for all 3 emission lines using TCLEAN’s CELL, UVTAPER and UVRANGE parameters, with the final beam matching achieved using IMSMOOTH.

Figure 1 shows 12CO, C18O and 13CO $J$=1-0 integrated intensity maps for the 4 galaxies in our sample. All moment maps have a 3$\sigma$ threshold and are primary beam corrected using the CASA routine IMPBCOR. The beam sizes are illustrated by the ellipse in the lower left corner and a 500pc scale bar is provided for reference. We note that IRAS 13120-5453’s distribution of 13CO emission in panel (Fig. 1e) differs from that previously reported by Sliwa et al. (2017), who found a central hole in the emission. We do not recover the central depression in emission found by Sliwa et al. (2017) in either their data (resolution = 0.55” $\times$ 0.41”) or the more recent higher resolution data (0.4” $\times$ 0.26”) with which it is combined in this work. We suggest that this may be due to the manual calibration conducted by those authors but cannot confirm this. The C18O distribution for IRAS 13120-5453 and IRAS 17208-0014 is less extended than 13CO which is in turn more compact than 12CO. Interestingly, this is not the case for Arp 200 and NGC 2623. In the former, C18O and 13CO are distributed over the same area while in the latter, C18O is more extended throughout the disk than 13CO.

The double nuclei of the merger system, Arp 220, are visible in all 3 emission lines while, despite having undergone a major merger at some point in their past, IRAS 13120-5453, IRAS 17208-0014, and NGC 2623 all distribute their molecular gas over a single nucleus. Combined with their different infrared luminosities, these morphological differences suggest our sample can be considered snapshots of different stages of the merger sequence, evolving from the bright ongoing merger (Arp 220), through the late stages of merging (IRAS 13120-5453, IRAS 17208-0014) and, finally, resulting in the fainter post-merger system (NGC 2623).

Figure 2 shows the intensity ratio maps of three line ratios for each target. The ratios shown are $\frac{\rm{}^{12}CO}{\rm C^{18}O}\,J=1-0$, $\frac{\rm{}^{12}CO}{\rm{}^{13}CO}\,J=1-0$, and $\frac{\rm{}^{13}CO}{\rm C^{18}O}\,J=1-0$. To make these ratio maps, we convert each moment map in Figure 1 from Jy beam*-1* km s*-1* to K km s*-1* before computing the ratio using CASA’s IMMATH routine. In all 4 targets, the values of 12CO/C18O $J$=1-0 are consistent with those reported previously for Mrk 231, IRAS 13120-5453, and Arp 220 ($\sim$20-140; González & Koenigsberger, 2014; Falstad et al., 2015; Sliwa et al., 2017). Similarly, the 12CO/13CO $J$=1-0 line ratios exhibit a large range of values, from $\sim 20-30$ in central regions of Arp 220 and IRAS 13120-5453 to $\sim 50-150$ across the disks of IRAS 17208-0014 and NGC 2623.

Excluding potentially unreliable measurements in the outer regions where signal-to-noise is low and emission regions are smaller than the beam, we observe 12CO/13CO ratios over $\sim 100$ in IRAS 17208-0014 and NGC 2623. In the case of IRAS 13120-5453, we do not recover a robust 12CO/13CO measurement that agrees with the very high values ($>100$) reported by Sliwa et al. (2017). This is due to the reduced central 13CO intensities recovered by those authors which we do not find in our analysis.

Most intriguingly, each system has C18O emission that is relatively strong compared to 13CO, particularly across the central regions where mismatches in UV coverage and differences between the intrinsic size of emission regions are not likely to be influencing the ratios. The 13CO/C18O $J$=1-0 line ratio dips well below the typical values found in normal star-forming galaxies ($\sim$7-10; e.g., Jiménez-Donaire et al., 2017). Indeed, there are large areas in each system where the line ratio is actually inverted and C18O line emission is stronger than 13CO.

3 The Origins of Extreme Isotopologue Line Ratios

We now discuss six potential explanations for the unusual isotopologue ratios presented in the previous section. The first scenario is dynamically driven changes in the molecular gas properties, the second is the optical depth of the lines, the next two are astro-chemical effects occurring within the gas, and the last two are the result of nucleosynthesis in stars.

3.1 Radial Flows of Molecular Gas

Dilution of abundances can occur as pristine gas flows from the outer regions of the merging system towards the center. The main problem with this scenario is that the 13CO/C18O ratio is expected to increase with galactic radius (Wouterloot et al., 2008; Jiménez-Donaire et al., 2017). In addition, Herschel studies of OH and H2O have found 16O/18O $>$500 for mergers where gas inflow is still strongly ongoing (young mergers; e.g., Falstad et al., 2015; König et al., 2016) and 16O/18O $<$150 for mergers with no strong evidence of inflowing gas (advanced mergers; e.g., González & Koenigsberger, 2014; Falstad et al., 2015). Thus, we do not expect the C18O abundance to increase relative to 13CO with gas inflow, yet we observe C18O emission to be strong relative to 13CO in all 4 targets.

3.2 Optical Depth Effects

One possibility is that self-absorption due to high molecular gas column densities, rather than changes in isotopologue abundance, is the root cause of the low 13CO/C18O ratio. A scenario where either one or both of the 13CO and C18O lines is optically thick is of particular concern in Arp 220 where high density gas tracers (e.g., HCN, HCO+) have been observed and, in the core of the Western nucleus, dust is known to be optically thick at $\lambda=2.6\,{\rm mm}$ with molecular hydrogen (H2) column densities exceeding N${}_{\rm H_{2}}\sim 10^{26}\,{\rm cm}^{-2}$ (Greve et al., 2009; Scoville et al., 2017).

When analyzing 13CO and C18O lines in a sample of high-$z$ starburst galaxies, Zhang et al. (2018) find that H2 column densities of N${}_{\rm H_{2}}\sim 10^{25}\,{\rm cm}^{-2}\,{\rm or}\,\sim 10^{26}\,{\rm cm}^{-2}$ are required for 13CO/C18O to approach unity in local thermodynamic equilibrium (LTE) or non-LTE conditions, respectively. While this is consistent with the highest column densities found in the center of Arp 220’s Western nucleus, it remains an order of magnitude or more greater than the H2 column densities of Arp 220’s larger disk structures, as well as the molecular gas in IRAS 13120-5453, IRAS 17208-0014, and NGC 2623 (N${}_{\rm H_{2}}\sim 10^{21}-10^{24}\,{\rm cm}^{-2}$; Casoli et al., 1988; Aalto et al., 2015; Privon et al., 2017; Scoville et al., 2017). Zhang et al. (2018) also find that even moderate 13CO optical depths ($\tau_{{}^{13}{\rm CO}}\sim 0.2-0.5$) do not cause the 13CO/C18O line ratio to deviate significantly from more typical values (13CO/C18O $\sim 7$). We note that the lowest average 13CO/C18O value occurs in NGC 2623, a system where 13CO is unlikely to be optically thick.

Thus, although we cannot completely exclude optical depth effects, especially in Arp 220, we find it unlikely that this is the primary cause of the unusual ratios seen across the disks of every galaxy in our sample. This conclusion is supported by Martín et al. (2019) who account for optical depths in their analysis of CO isotopologues across the central regions of the nearby starburst galaxy NGC 253. However, to properly test this assumption, observations of multiple line transitions are required to measure excitation conditions and derive the optical depths. This will be the focus of future work.

3.3 Preferential Photodissociation

The low 13CO/C18O ratios also rule out preferential photodissociation of 13CO molecules compared to C18O, especially in the inner regions. This is because C18O would also undergo preferential photodissociation and at a faster rate than 13CO (van Dishoeck & Black, 1988; Casoli et al., 1992); thus, preferential photodissociation would not skew the 13CO/C18O ratios towards lower values.

We see higher 12CO/13CO, 12CO/C18O, and

${}^{13}{\rm CO/C}^{18}{\rm O}$ in the outermost, less dense regions of our targets. Although it is difficult to completely exclude preferential photodissociation in these regions, Romano et al. (2017) find the fraction of gas that resides in so-called photodissociation regions to be minimal, confirming that this mechanism is unlikely to play a key role in determining the abundance ratios in these galaxies.

3.4 Chemical Fractionation

The process of chemical fractionation can also drive increases in 13CO with respect to both 12CO and C18O via the forward direction of the exchange reaction, 13C${}^{+}\,+\,^{12}$CO $\rightleftharpoons\,^{13}$CO$\,+\,^{12}$C+ (Watson et al., 1976). This enhancement is sensitive to temperature with the forward direction dominating where gas temperatures are $\lesssim$ 20-30 K while, at higher temperatures, both directions are equally likely (Smith & Adams, 1980; Romano et al., 2017). Theoretical modeling of the dense molecular gas in Arp 220 and IRAS 13120-5453 suggests temperatures in local ULIRGs comfortably exceed this threshold (Sakamoto et al., 1999; Sliwa et al., 2017). In any case, increasing 13CO abundance would lead to larger, not smaller 13CO/C18O ratios. It is therefore an unlikely pathway for producing the observed line ratios.

3.5 Very Recent Star Formation

Sliwa et al. (2017) are able to reproduce enhanced 12C/13C ratios in IRAS 13120-5453 using a Kroupa IMF (Kroupa, 2001) if the system has undergone a very recent ($\lesssim$7 Myr) burst of star formation. A scenario whereby the extreme ratios are driven by significant, recent star formation is also invoked by Matsushita et al. (2009) in the case of Arp 220. In both cases, the recent nature of the starburst is critical. If star formation is responsible for the observed deficiency in 13CO with respect to C18O across all our targets, one would expect that 13C produced in the intermediate mass stars would begin to be ejected into the ISM on timescales of $\sim$30 Myrs (Schaller et al., 1992). Mixing between the newly produced and ejected 13C and the metals already present in the optically thin ISM would therefore drive the 13CO/C18O line ratio from around unity and below toward the values found in more typical star-forming galaxies ($\sim$7-10).

While we cannot entirely exclude recent star formation as the driving factor, the low ratios in NGC 2623, a galaxy that finished the merging process 80 Myrs ago (Privon et al., 2013), do not fit well with this mechanism. Indeed, a study of the star formation history of NGC 2623 by Cortijo-Ferrero et al. (2017) found that stars younger than 30 Myrs contribute only $\sim 20\%$ of the total light density in this galaxy. Thus, we suggest it is unlikely that the observed extreme ratios in NGC 2623 are caused by a very recent ($\lesssim$7 Myr) burst of star formation.

3.6 A Top-Heavy Initial Mass Function

Short-lived massive stars ($\leq$30 Myr, $\gtrsim 8{\rm M}_{\odot}$) are the predominant source of 18O in the ISM. In contrast, the 13C atom is dredged-up via convection into the envelopes of long-lived, low-mass stars ($\lesssim 8{\rm M}_{\odot}$) that are entering the red-giant phase. These stars replenish the ISM over a longer timescale than their more massive counterparts ($\sim 10^{9}$ years; Vigroux et al., 1976; Schaller et al., 1992). Furthermore, the fact that the low 13CO/C18O ratios are observed in all 3 ULIRGs and the post-merger system is tentative evidence that the extreme line ratios are insensitive to evolution in the merger stage. Therefore, a stellar IMF biased toward such massive stars in our targets is a plausible explanation for the observed 13CO/C18O ratios.

4 Conclusions

In this paper, we use state-of-the-art ALMA observations of molecular gas in a sample of 4 nearby merger systems to probe isotopologue emission line ratios. In doing so we find unusual ratios compared to typical star-forming galaxies and test physical mechanisms for driving this trend. Our main conclusions are as follows:

1. i)

We confirm and expand upon the results of Greve et al. (2009); Matsushita et al. (2009) and Sliwa et al. (2017), reporting unusually low values of the isotopologue line intensity ratio 13CO/C18O $J$=1-0 ($\lesssim 1$) across the spatially resolved central regions of 3 nearby ULIRGs (Arp 220, IRAS 13120-5453, IRAS 17208-0014) and 1 nearby post-merger galaxy (NGC 2623) with respect to normal star-forming disks. 2. ii)

We also find the isotopologue line ratios 12CO/C18O and 12CO/13CO $J$=1-0 are unusually large, supporting results by previous work (e.g., Aalto et al., 1991; Casoli et al., 1992; Paglione et al., 2001; Sliwa et al., 2013). 3. iii)

We suggest that the presence of very low 13CO/C18O line ratios in our sample and their persistence across systems at different stages of the merger process suggests C18O is more abundant than 13CO in the molecular gas of these systems. We find this to be consistent with a scenario in which an excess in the C18O isotopologue is driven by excess formation of massive stars ($>8\,{\rm M}_{\odot}$) in these extreme environments i.e., a top-heavy stellar IMF.

These results contribute to a growing body of evidence that the prevailing stellar IMF in nearby ULIRGs is top-heavy, and highlights the potential of submillimeter observations as probes of the IMF in galaxies that are inaccessible via traditional techniques. The stellar IMF is central to our understanding galaxy formation and, although beyond the scope of this paper, further work must conduct a full abundance analysis of local ULIRGs using state-of-the-art theoretical models that account for optical depth effects. Such a study would make a considerable contribution to our knowledge of starburst galaxies, both locally and at high redshift.

We would like to thank the referee for their detailed and constructive comments. T. Brown also thanks A. Leroy for helpful discussions that certainly improved this paper. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00379.S, ADS/JAO.ALMA#2015.1.00167.S, ADS/JAO.ALMA#

2015.1.00287.S, ADS/JAO.ALMA#2015.1.01191.S,

ADS/JAO.ALMA#2016.1.00140.S, ADS/JAO.ALMA

#2017.1.01306.S.

ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. CDW acknowledges financial support from the Canada Council for the Arts through a Killam Research Fellowship. The research of CDW is supported by grants from the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chairs program.