|Annu. Rev. Astron. Astrophys. 2014. 52:
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Measuring dust masses to study their scalings with other galaxy properties requires submm detections that in the past were typically available only for modest size samples, pre-selected either by the IRAS far-infrared emission or in the optical. This is now changing with unbiased large surveys and large local samples.
Cortese et al. (2012) use SPIRE data to study dust scaling relations for a magnitude- and volume limited sample of about 300 nearby galaxies, including star forming as well as passive objects. The ratio of dust mass to stellar mass decreases with stellar mass, stellar mass surface density, and NUV-r colour, and is significantly lower for early type galaxies. Such scalings are reminiscent of the equivalent scalings for the HI component (Catinella et al. 2010) and molecular component (Saintonge et al. 2011) of the interstellar medium in local galaxies. Dust stripping by environmental effects is indicated, but at a lower level than for HI, consistent with the fact that dust is tracing both extended atomic and more compact molecular material. Bourne et al. (2012) stack SPIRE data for a large z < 0.35 optically selected spectroscopic sample. Again, dust masses increase with stellar mass while the Mdust / M* ratio decreases, and there are clear indications for an increase of dust masses with redshift in the redshift range studied. Evolution of the dust mass function is very prominent in the z < 0.5 study of Dunne et al. (2011). Dust masses increase by a factor ~ 5 from local to z ~ 0.5, and a similar increase is reported for the ratio of dust mass and stellar mass. Santini et al. (2013) bin the redshift - stellar mass - star formation rate space out to z = 2.5 and investigate scalings between dust mass, stellar mass, and star formation rate from stacked Herschel data. Dust masses increase with stellar mass and with redshift and strongly correlate with SFR. There is less of a trend with redshift for dust mass at given SFR and stellar mass.
These observed dust scalings plausibly fit the context in which SFR and stellar mass are linked via the evolving star forming sequence, and the increase of gas fraction of normal galaxies with redshift (e.g. Daddi et al. 2010, Tacconi et al. 2010). Given rather short gas depletion times for high redshift galaxies, models of the cosmic evolution of dust will have to increasingly move from closed box assumptions to considering gas inflow, as well as outflow to and recycling from the intergalactic medium, all related to current equilibrium attempts to represent the interplay of gas flows and stellar mass buildup in galaxy evolution (e.g. Lilly et al. 2013). Another interesting question is to what extent it is observationally possible in this context to quantify the cold interstellar medium of high redshift galaxies via the dust mass rather than direct tracers of the gas.
6.1. Dust as a tracer of cold gas
The cold gas content of evolving high redshift galaxies is a key measurable for characterising the interplay of gas inflow, gas consumption by star formation, metal enrichment, and outflows or feedback, during steady evolution and while influenced by merging and other external effects. Traditionally, low lying rotational CO transitions are used to measure the molecular gas content. Even at the beginning of the ALMA era, z > 1 CO detections remain hard to obtain, though, with of order 200 total detections (Carilli & Walter 2013) of which only about 60 refer to galaxies near the star-forming main sequence (Tacconi et al. 2013). In addition, use of CO as a molecular gas tracer relies on the CO (1-0) luminosity to molecular gas mass `conversion factor' which depends on physical conditions of the source and on metallicity (see Bolatto, Wolfire & Leroy 2013 for a recent review). Often, a step is involved of applying excitation corrections to measurements of CO lines originating in higher rotational states, rather than measuring the CO (1-0) for which the conversion to gas mass is calibrated.
Herschel has obtained a large number of dust continuum detections of high redshift galaxies, to which ALMA starts adding longer wavelength submm detections of unprecedented depth (e.g. Scoville et al. 2014). These resources have spawned great interest in using dust as a proxy for cold gas content, applying locally calibrated conversions from observed rest frame far-infrared and submillimeter fluxes to dust mass, and a metallicity-dependent conversion from dust to cold gas mass. Several assumptions and steps enter such methods.
Conversions from dust emission SEDs to dust mass are calibrated in the Milky Way or nearby galaxies and implicitly assume dust properties similar to the ISM of these galaxies. ISM dust has a variety of sources including AGB star mass loss and supernova explosions. The relative weight of these can vary especially towards highest redshift, depending on the histories of star formation and outflow from the galaxy. In addition, dust destruction and re-formation in the ISM proper may play a significant role (e.g. Jones, Tielens & Hollenbach 1996), depending on physical conditions. Observational evidence against homogeneous dust properties includes long-known variations in the optical/UV extinction curves, variations of the submm emissivity index with dust temperature (e.g. Paradis et al. 2010, note discussion in the literature on influence of fitting techniques), presence of crystalline silicate dust in some local ULIRGs but not normal galaxies (Spoon et al. 2006), unusual silicate properties in some AGN spectra (Sturm et al. 2005, Markwick-Kemper et al. 2007), and the rest frame ≳ 500 μm submillimeter excess often appearing in the SEDs of low metallicity galaxies (e.g., Rémy-Ruyer et al. 2013b and references therein).
Dust masses are most easily measured on the Rayleigh-Jeans tail of the SED where the dependence on dust temperature is only linear and there is almost no concern of optically thick emission. This wavelength condition is often not met for pure Herschel data, with the 500 μm end of the SPIRE range and in particular source confusion severely limiting the accessible rest wavelength range for high redshift galaxies, except for extremely luminous objects. High S/N color information is then needed instead to constrain either the dust temperature, or equivalent parameters such as radiation field intensity in physical dust emission models. In addition, such measurements will be insensitive to any very cold dust. Draine et al. (2007) demonstrate that for a local disk galaxy sample and the physical dust model of Draine & Li (2007), coverage out to rest wavelength 160 μm is sufficient to obtain dust masses with an extra error due to this wavelength constraint of less than a factor 2.2, and often less than a factor 1.5, for appropriately constrained model parameters. Similarly, (Dale et al. 2012) compare dust masses of 61 local KINGFISH galaxies from fitting (Draine & Li 2007) models to either the Spitzer only data out to 160 μm, or combined Spitzer and Herschel data out to 500 μm. Masses from these two approaches agree well on average with only 0.2 dex dispersion, but the ratio has trends with both dust temperature and metallicity. Such use of λrest ≤ 160 μm fits to derive dust masses may be transferable to high redshift galaxies, as long as the ISM conditions are similar to the local calibration sample and dust emission is not optically thick near the far-infrared peak.
Conversion from dust mass to (atomic plus molecular) gas mass δGDR Mdust = MH2 + MHI has to assume a metallicity dependence of the gas-to-dust ratio δGDR. This is typically assumed to be close to inverse linear (e.g. Leroy et al. 2011), but steeper relations have also been argued for Muñoz-Mateos et al. (2009) or constancy assumed (Scoville 2012). For a z ~ 2 lensed sample with measured metallicities, Herschel dust masses and CO measurements, Saintonge et al. (2013) deduce a relation of gas-to-dust ratio to metallicity that is larger by a factor 1.7 with respect to the local one of Leroy et al. (2011). Irrespective of an origin in changed dust properties or changed CO conversion, this offset cautions about the transfer of local calibrations. Scatter around such relations is significant (Draine & Li 2007, Rémy-Ruyer et al. 2013a), and a number of high redshift SMGs have been reported with apparently much smaller gas-to-dust ratio than expected from their nebular metallicity (Santini et al. 2010). Typically, individual metallicities are however unavailable for high-z galaxies, requiring to adopt scalings such as redshift dependent mass-metallicity relations (e.g. Zahid et al. 2013) or the fundamental metallicity relation of Mannucci et al. (2010) which links metallicity to stellar mass and star formation rate in a redshift-independent way. Differences between such scalings, and the largely unconstrained scatter of high redshift galaxies around the scaling can lead to uncertainties of a factor of a few in metallicity alone.
These data practicalities and systematic effects suggest that dust based methods provide a largely independent second view on the cold gas content of high-z galaxies in addition to CO, but with significant uncertainty.
For a sample of ten normal spiral galaxies in the local universe with spatially resolved high quality PACS and SPIRE photometry as well as CO and HI data, Eales et al. (2012) assumed homogeneous dust and gas properties and solved for minimal dispersion between dust based and CO+HI based estimates of the interstellar medium mass. They verified that this leads to a consistent picture with a CO conversion factor and dust emissivity close to commonly adopted values for the Milky Way.
At higher redshift, Magdis et al. (2011a) and Magdis et al. (2012a) study small samples of galaxies with Herschel and (sub)mm detections and low-J CO data, applying the Draine & Li (2007) dust model. Like Magnelli et al. (2012b), they also find dust-based ISM masses in support of a decrease of the CO conversion factor α when moving from main sequence z ~ 1-2 galaxies to (merger) starbursts. Resorting to stacking because of the requirements that even the Draine & Li (2007) model puts on photometric S/N and rest wavelength coverage, Magdis et al. (2012a) then study the properties of larger z ≲ 2.3 samples near the main sequence. They find that SSFR trends across and along the main sequence are related mostly to varying gas fractions. Detected variations with redshift are a significant increase in gas fraction and a mild decrease in gas depletion times MGas / SFR, in agreement with CO based results (e.g. Tacconi et al. 2013). Santini et al. (2013) use similar stacking methods for mostly near-main sequence bins in the redshift - stellar mass - star formation rate space out to z = 2.5, finding a steeper decrease of gas depletion time and suggesting a fit by a redshift-independent fundamental relation between gas fraction, stellar mass, and star formation rate.
Following a different approach, Nordon et al. (2013) derive a method for estimating the molecular gas content of near main sequence galaxies solely from more readily available integrated far-infrared luminosities and rest UV obscuration properties. Based on a study of the UV properties of Herschel galaxies and comparison to CO, they derive a quantity that encodes the attenuation contributed by the molecular gas mass per young star. These estimates thus include a next order correction, compared to the average gas depletion time of the calibration sample with CO data. Berta et al. (2013a) use this method as well as gas depletion time scalings from Tacconi et al. (2013) to derive the molecular gas mass function since z ~ 3.
Dust emission has been successfully applied as an ISM tracer for high redshift galaxies, with results in satisfactory agreement with and partly calibrated on CO based studies. Moving from current samples to higher redshifts, lower stellar masses and lower metallicities will require more sensitive (and difficult) observations with ALMA, as well as larger extrapolation from the ISM conditions at which current dust based methods are calibrated.