MOST SUBMILLIMETER GALAXIES ARE MAJOR MERGERS

Our analyses generally follow the procedures of Tacconi et al. (2006, 2008); for the computation of cold gas masses, we use the approach of Tacconi et al. (2010). Flux maps were produced by integrating the line emission, determining the line extent via visual inspection of spatially integrated spectra. Fluxes are extracted from the line cubes by integrating over the area with significant emission. Given that the compact galaxies comprising a significant fraction of our sample here are in most cases only marginally resolved with the ∼05–1'' spatial resolution available, we determine source sizes by fitting circular Gaussians to the systems in the uv-plane using the task UVFIT in the IRAM data reduction package GILDAS, and taking the Gaussian FWHM_uv to be the best estimate of the source's diameter. In the two individual galaxies of the four new systems where a Gaussian fit was not possible (most likely due to insufficient signal to noise), the beam FWHM was used as an upper limit to the source diameter. We note that these size measurements may slightly underestimate the actual size of the galaxies, since there may be faint extended flux below our sensitivity limit. We do not assign a formal uncertainty to this, since, if such a putative faint emission region exists, we do not know anything about its size or morphology. However, the uncertainties due to this are unlikely to be significant.

Where possible, velocity and velocity dispersion maps were derived by fitting Gaussians to the line profiles. If the spectral signal to noise did not permit this, we produced moment maps of different velocity ranges, which were then overlaid as RGB images.

Since the dispersions of our galaxies are comparable to or larger than the rotational velocities, dynamical masses have been derived using the "isotropic virial estimator" (e.g., Spitzer 1987; Tacconi et al. 2008; Förster-Schreiber et al. 2009) given in M_☉ by

$$\begin{eqnarray} &&M_{\rm dyn,vir} = 2.8\times 10^5\Delta v^2_{\rm FWHM} R_{1/2}, \end{eqnarray} \tag{ 1 }$$

where Δv_FWHM (km s⁻¹) is the integrated line FWHM and R_1/2 (kpc) is the half-light radius (the radius within which half the total flux is emitted, here assumed to be equivalent to the Gaussian HWHM measured in the uv-plane). We note that the scaling factor appropriate for a rotating disk at an average inclination is a factor of ∼1.5 smaller (Bothwell et al. 2010), i.e., if the above formula were applied to a disk galaxy, it would somewhat overestimate the dynamical mass. However, Cappellari et al. (2009) find that this estimator agrees well with masses derived from more detailed Jeans modeling for a sample of massive z ∼ 2 early-type galaxies.

In order to derive molecular gas masses, we convert the measured line fluxes to CO(1–0) fluxes (in Jy km s⁻¹) using the results of SMG spectral energy distribution (SED) modeling (Figure 3 of Weiss 2007; yielding S_CO(6–5)/S_CO(1–0) = 13, S_{CO(4–3)/CO(1–0)} = 10, S_CO(3–2)/S_CO(1–0) = 7, S_CO(2–1)/S_CO(1–0) = 3; the same numbers were also used by Bothwell et al. 2010 and Casey et al. 2009b). We assign an uncertainty of 30% to these conversions based on the differences between the individual SED models of Weiss (2007); in the four cases where we have flux measurements from two different transitions (Table 1), we find the flux ratios to be consistent with these conversion factors. We do not calculate gas masses based on CO(7–6) fluxes, since the conversion factor is uncertain for this transition. We then calculate the CO(1–0) line luminosities (in K km s⁻¹ pc²) using Equation (3) of Solomon et al. (1997):

$${\selectfont\fontsize{9}{10}{\begin{eqnarray} &&\hspace{-6pt}L^{\prime }_{\rm CO(1\hbox{--}0)}=3.25\times 10^7 S_{\rm CO(1\hbox{--}0)}\Delta V \nu _{\rm CO(1\hbox{--}0),\rm rest}^{-2}D^2_L(1+z)^{-1}, \end{eqnarray}}} \tag{ 2 }$$

with S_COΔV in Jy km s⁻¹, ν_{CO(1–0),rest} in GHz, and D_L in Mpc. The CO(1–0) luminosities are then used to estimate the total gas mass via their Equation (19):

$$\begin{eqnarray} &&M_{\rm H_2}=\alpha L^{\prime }_{\rm CO (1\hbox{--}0)} \end{eqnarray} \tag{ 3 }$$

using α = 1 M_☉ /K km s⁻¹ pc² as measured for ULIRGs (Downes & Solomon 1998, for a discussion see also Genzel et al. 2010). For an in-depth discussion, we refer the reader to Appendix A of Tacconi et al. (2008); we would like to stress that our choice of α is motivated by the surface densities of SMGs (cf. Table 10 of Tacconi et al. 2008) rather than any a priori assumption about a similarity between local ULIRGs and SMGs. Our choice of conversion factor is here further supported by the fact that if for our SMGs the Milky Way conversion factor was adopted, in all but one case would the gas mass, rather implausibly, be equal to or larger than the dynamical mass. Finally, we apply a factor 1.36 correction to account for interstellar helium. We note that since the fluxes were measured in fixed apertures, and also that some flux may be resolved out or be below our detection limit, the gas mass is likely to be somewhat larger than our estimates.

The detailed analyses of the molecular CO line emission in this section reveal morphological and kinematic evidence that at least 8 of the 12 SMGs studied in this paper are ongoing mergers, and the remaining 4 are either disk galaxies or coalesced, late-stage mergers.

3.2.1. New Observations

3.2.2. Re-analysis of Existing Observations and Published Results

Ivison et al. (2002) first noted a preponderance of radio doubles among SMGs. With a larger sample, Ivison et al. (2007) were able to demonstrate that the likelihood of SMGs having companions within a few arcseconds is significantly larger than would be expected by chance. This overdensity suggests that at least a significant fraction of SMGs may currently be undergoing mergers. We are able to refine this picture substantially by investigating the mass ratios of the merging components. Five of the twelve SMGs in our sample consist of spatially separated interacting galaxies, and we are able to measure mass ratios for four of them (Table 2; SMM J09431, SMM J105141, HDF 242, N2850.4; no mass estimates for the individual components of SMM J02399 are published). In all cases, the mass ratios are consistent with being major (mass ratios of 1:3 or closer to unity) mergers. It must be kept in mind that if these are mergers between disk galaxies, the dynamical masses may be over- or under-estimated due to the dependence on viewing angle, and hence the uncertainties on these mass ratios are somewhat larger than the propagated errors stated in Table 2. All measured spatial separations (≲30 kpc) are well within the range where they would be deemed gravitationally interacting, and the masses of individual components are ≳10¹⁰ M_☉, much larger than clumps in a single galaxy (Förster-Schreiber et al. 2009).

We furthermore note that, as Bothwell et al. (2010) outline, one can also make a strong case for Lockman 38 and HDF 132 being mergers; they show clear indication of two kinematically distinct components, which are however not individually spatially resolved. Bothwell et al. (2010) calculate the mass ratios of the two subcomponents to be 0.24 ± 0.18 and 0.68 ± 0.14, respectively. However, since these two systems cannot unambiguously be classified as mergers, we do not include them in Table 2.

Size measurements of SMGs based on CO interferometric and mm-continuum data have indicated that these galaxies are comparatively compact, with median diameter ⩽4 kpc (FWHM of Gaussian fitted to source in uv-plane; Tacconi et al. 2006). On the other hand, based on the diameter at the 3σ detection level of MERLIN and Very Large Array (VLA) radio observations, Chapman et al. (2004) find the star formation to be "occurring on ∼10 kpc scales." However, Tacconi et al. (2006) and Biggs & Ivison (2008) point out that the size measurements from the MERLIN and VLA data are consistent with the CO size, when a comparable method (deconvolved major axes of Gaussians fitted to the emission) is applied. They find a median diameter of ∼5 kpc for their sample. We can compare radio and CO size measurements individually for two sources in our sample. For SMM J105141, Biggs & Ivison (2008) measure an overall radio size of 061 × 044, or 5.1 kpc × 3.7 kpc; we measure a CO(4–3) FWHM of 3.5 kpc for the main component of this two-galaxy system. For HDF 169, we find a CO(4–3) FWHM of 4.3 kpc and measure 4.5 kpc from an unpublished MERLIN radio map. Thus, there appears to be good agreement between CO(4–3) and radio extents in these two cases. Younger et al. (2008, 2010) measure the scale of far-infrared emission of four SMGs to be ∼5–8 kpc. This is somewhat larger than what we find for the sample discussed here (although Younger et al. 2008 say that their results are "qualitatively consistent with the results of Tacconi et al. 2006"). The most plausible explanation for the difference—besides the possibility that CO lines and far-IR continuum trace slightly different things—lies in the fact that the Younger et al. (2008, 2010) SMGs probe the brightest end of the luminosity distribution, with S_870 μm ≳ 15 mJy.

For our augmented sample, which contains all SMGs for which subarcsecond resolution interferometric CO observations are available (which are not strongly lensed), we have measured FWHM sizes for 11 galaxies (measuring each galaxy individually in the case of wide binaries). We find average and median FWHMs of 4.5 and 4.3 kpc, with a 1σ distribution of 2.8 kpc, slightly larger than the results of Tacconi et al. (2006). We are unable to identify a plausible explanation for this, other than small number statistics (Tacconi et al. 2006 measure sizes for five systems, and upper limits for a further four; here, we have size measurements for 12 systems). We also obtain upper limits of 3.4, 6.5, and 2.8 kpc for three other sources (Table 1).

We note that here we are collating measurements from a range of CO transitions, from (7–6) to (1–0), which may trace physically different environments. As Tacconi et al. (2008) elaborate, transitions up to J ≈ 5–6 should all provide reasonable tracers of the overall molecular gas. However, the extent to which, say, CO(2–1) and CO(6–5) trace the same gas is still ongoing (see also Weiss 2007; Narayanan et al. 2010b). That the CO(7–6) may trace denser gas might explain the comparatively small source sizes for N2850.2 and N2850.4, and hence be at least partially responsible for the small dynamical masses we derive for these two galaxies (see also the discussion in Danielson et al. 2010). In the one case, where we have a size measurement from two different transitions (SMM J09431 SW; J = 4 & J = 6), the two numbers are consistent within the uncertainties. Restricting to size measurements from J ⩽ 6 observations yields average and median FWHMs of 5.2 and 5.0 kpc, with a 1σ distribution of 2.6 kpc.

Thus, both radio and CO measurements are consistent with SMGs having FWHM sizes of ∼5 kpc.

In this section, we use our dynamical and gas masses to test stellar mass estimates. This is motivated by the large systematic uncertainties associated with stellar mass measurements, and the implications that a reliable determination of the stellar mass has both for a critical assessment of competing cosmological models of SMGs, as well as for the co-evolution of central black holes and their hosts (e.g., Hainline et al. 2010).

4.2.1. Stellar Mass Measurements

Hainline (2008; see also Hainline et al. 2010) derived the stellar masses of a large sample of SMGs, employing Spitzer observations to cover a significantly larger spectral range than earlier attempts (e.g., Smail et al. 2004). The Hainline (2008) data set was also used by Michałowski et al. (2010) to derive stellar masses. But despite using an identical observational data base, their results are very different: Hainline (2008) find a median stellar mass of (6.3–6.9) × 10¹⁰ M_☉, whereas Michałowski et al. (2010) arrive at a median of 3.5 × 10¹¹ M_☉. Therefore, testing these results is essential and the next key step toward deriving the stellar mass content of SMGs reliably.

Table 3 brings our dynamical and gas masses together with the stellar masses from Hainline (2008) and Michałowski et al. (2010) for the seven systems in common, and includes gas masses for two more galaxies based on flux measurements of Greve et al. (2005). We also show the stellar masses derived by Tacconi et al. (2008). As noted in Section 3.1, our dynamical masses may be underestimated due to undetected faint extended flux leading to somewhat smaller HWHM_uv. However, since this effect would be small and the gas masses also correspondingly larger, this is very unlikely to qualitatively impact our conclusions here. We furthermore note that we have neglected both dust and dark matter in our mass budget. Dust is unlikely to contribute more than a few percent, and Genzel et al. (2008) find the dark matter content in the central few kpc of high-z galaxies to be 10%–20%. Thus, whilst not negligible, these will not have a significant impact on the mass budget, and we have opted not to include it here for the sake of simplicity. We have converted the stellar mass estimates from a Salpeter (1955) to a Chabrier (2003) initial mass function (IMF) by reducing them by a factor of 1.7 (Hainline 2008). This is supported by Bastian et al. (2010), who find no conclusive evidence that an IMF different from the locally applicable Chabrier (2003) or Kroupa (2001) forms should be in place at high redshifts. Cappellari et al. (2009) also find that a Chabrier (2003) instead of a Salpeter (1955) IMF is required to bring the stellar masses derived for a sample of z ∼ 2 early-type galaxies via SED modeling in agreement with their dynamical masses calculated from Jeans models.

We find that (M_gas + M_⋆)/M_dyn for the seven galaxies for which all three mass estimates are available has an average (median) of 0.8 (0.9) for the adjusted Hainline (2008) stellar masses (with a 1σ distribution of 0.5), whereas for the adjusted Michałowski et al. (2010) masses, the average (median) is 2.1 (2.1), with a 1σ distribution of 1.2. We conclude that the Hainline (2008) stellar masses, adjusted to a Chabrier (2003) IMF, are consistent with our independent mass measurements (Figure 5).

Zoom In Zoom Out Reset image size

4.2.2. Implications for Cosmological Models

It has previously been conjectured, based primarily on radio and rest-frame UV morphologies, that the high luminosities of SMGs are triggered by merger activity. Our analysis in Section 3 of the CO emission shows convincing evidence that at least a majority of our 12 SMGs are indeed mergers. In particular, we have found that in all binary SMGs for which we could derive mass ratios, the merger partners are near-equal in mass, i.e., they are major mergers. While it is thus beyond doubt that some SMGs are triggered by major mergers, the question of the nature of the compact, non-binary SMGs comprising a significant fraction of the overall SMG sample is yet to be settled conclusively—are they end-stage major mergers, or isolated disk galaxies?

In the following, we will develop the argument that they mostly are end-stage major mergers, since a major merger will be detectable as an SMG for a significant amount of time spent in the "final coalescence" phase—and thus that the large fraction of observed binary SMGs implies a correspondingly large number of single SMGs, which are coalesced major mergers.

An illustrative comparison can be made with local ULIRGs, known to be exclusively major mergers. As Figure 5 of Veilleux et al. (2002) shows, ∼64% of local ULIRGs are either coalesced, or have projected nuclear separations ⩽2 kpc. This is what is expected from merger simulations (Mihos & Hernquist 1996; Springel et al. 2005), which show that a first, minor starburst is triggered upon the first encounter, and the most prodigious star formation rates are only achieved during the final coalescence of the two galaxies, when tidal torquing compresses gas into the center and leads to a ∼kpc-scale central starburst. Could it be that the SMG selection criterion selects a similar class of galaxies, at high redshift, and thus that the large fraction of compact SMGs in our sample is naturally explained as being those end-stage, coalesced major merger products? Indeed, as Figure 6 shows, local ULIRGs and our SMG sample show a strikingly similar distribution of projected separations (here, we have chosen to adopt a coarser bin size than Veilleux et al. 2002 adopted, due to the comparatively small SMG sample size and the relatively large upper limits on some SMG sizes—we note that most of the local ULIRGs in the ⩽6 kpc bin have projected separations ⩽2 kpc). However, a direct comparison of the two samples is difficult. This is because L_IR and S_850 μm may not always be correlated during a major merger, due to the way the IR SED changes with dust temperature at these redshifts—for a given L_IR, S_850 μm decreases with increasing dust temperature. This results in a cool dust bias in the SMG sample, illustrated by Figure 4 of Casey et al. (2009a), and borne out by observations (Magnelli et al. 2010). This is important, since it may affect which merger stages are sampled by L_IR and S_850 μm selection, respectively. Both observations and simulations indicate that dust temperatures increase toward the final stages of a merger, suggesting that SMGs should sample earlier merger stages than ULIRGs. Does this imply that the observed ratio of binary and single SMGs is reconcilable with the single SMGs being isolated disk galaxies, rather than end-stage major merger products as suggested by the comparison with local ULIRGs? In order to answer this, we need to quantify the impact of the SMG cool dust bias on the merger stage sampling function.

Zoom In Zoom Out Reset image size

Veilleux et al. (2002) use the ratio of IRAS 25 μm and 60 μm flux as a proxy for dust temperature, and find that local ULIRGs with f₂₅/f₆₀⩾ 0.2 ("warm ULIRGs") are only found among system with nuclear separations below 10 kpc (no trend is evident for smaller f₂₅/f₆₀, i.e., cooler systems; their Figure 6). However, the percentage of systems with f₂₅/f₆₀⩾ 0.2 is constant for all nuclear separations ⩽10 kpc. More importantly, only 14 out of 118 systems in their sample have f₂₅/f₆₀⩾ 0.2—i.e., less than 10% of ULIRGs are affected by this bias!

Turning to simulations, Figures 3 and 4 of Narayanan et al. (2010b) and Figure 1 of Narayanan et al. (2010a) show the evolution of the star formation rate, bolometric luminosity, and S_850 μm during simulated gas-rich major mergers. These show that after the peak in star formation rate during final coalescence, S_850 μm appears to drop off more sharply than L_bol, most likely due to an increasing AGN contribution effecting an increase in the dust temperature. However, variations between different simulations make it quite difficult to quantify the time a merger has both high bolometric luminosity and low S_850 μm (D. Narayanan 2010, private communication).

Another way to tackle this question may be to compare the AGN luminosity contributions in local ULIRGs and SMGs, since from the above we would expect SMGs to be biased against the merger phases with strong AGN contributions. Veilleux et al. (2009) find local ULIRG luminosities to have ≈39% AGN contribution; estimates for SMGs are more uncertain, but span a range of 8%–35% (Swinbank et al. 2004; Alexander et al. 2005, 2008; Lutz et al. 2005; Valiante et al. 2007; Pope et al. 2008; Menéndez-Delmestre et al. 2009). This seems to confirm a significant bias—however, one must bear in mind the differences between high-z and local galaxies; their absolute AGN luminosities should be comparable (similar black hole masses), but the stellar luminosities are factors of several larger in high-z galaxies (due to the larger gas fractions; Tacconi et al. 2010; Daddi et al. 2010), and we therefore expect significantly smaller relative AGN contributions in high-z galaxies. Lower relative AGN contributions in SMGs compared to local ULIRGs are therefore not necessarily a result of a merger stage bias.

The cool dust bias of the S_850 μm criterion implies that there should be a population of hot dust, ultra-/hyperluminous high-z galaxies which are not detected as SMGs. And indeed, Casey et al. (2009a) through 70 μm selection find a population of z > 1 galaxies with an average dust temperature of 52 K, which are not detected at 850 μm. These systems have a mean far-infrared luminosity of 1.9 × 10¹² L_☉, only slightly lower than that of SMGs, and thus it is plausible that they constitute the hot dust extension of the SMG sample. Although uncertain, the number density of these galaxies is estimated to be approximately five times lower than that of SMGs—implying that, if indeed all these systems are major mergers, a high-z major merger may be undetectable as an SMG for approximately 1/6th of its lifetime; or ≈25% of the time spent in the "final coalescence" phase, if all these hot dust systems are in that stage (as one would expect, based on the arguments above). This is larger than, but consistent with, the ∼10% of local ULIRGs showing a dust temperature–merger stage correlation.

It is clear that the merger stage sampling bias of S_850 μm versus L_IR selection is difficult to quantify. We can only say with confidence that an S_850 μm sampling of a major merger will likely result in a somewhat smaller fraction of coalesced systems, but it certainly will not exclude all of them. Local major mergers, selected via L_IR, consist ∼64% of systems with projected nuclear separations ⩽2 kpc (Veilleux et al. 2002); our sample of 12 SMGs contains 7 sources which are either poorly resolved or clearly single galaxies (Table 2). If we conservatively assume that a major merger is undetectable as an SMG for 50% (30%) of the time spent in the "final coalescence" stage, this implies that we would expect the fraction of coalesced systems in the sample to decrease from ∼64% to about 32% (45%). Thus, at most three (one) out of the seven compact/coalesced sources in our sample could plausibly be isolated disk galaxies, rather than end-stage major mergers.

This corroborates the argument made by Tacconi et al. (2006) that the extreme surface densities of compact SMGs can plausibly only be achieved during a major merger, and is further supported by our results of Section 4.2.2, where we show that our confirmation of the Hainline (2008) stellar mass estimates agrees with cosmological models in which SMGs result from major mergers.

These three independent arguments all point in one direction, namely that most, if not all, SMGs are major mergers.