SED Fits to ULIRG Galaxies In order to test these "multiple HII region" models for the SEDs of Starburst Galaxies, Reuland et al.  have collected data from the literature for 41 ultra-luminous infrared galaxies (ULIRGs) in the local universe. The data consist of UV/optical fluxes from the Third Reference Catalogue of Bright Galaxies v3.9, aperture-corrected JHK-band photometry from Spignolio  and 3-1500 µm data from Klaas et al. [56, 57] and from Spoon . The cosmological model used to derive luminosity distance is the concordance cosmology with M = 0.27, = 0.73 and Ho = 71 km s-1 Mpc-1 [79, 86].
The variables characterising the fit are:
The ISM pressure, P / k cm-3K. As described above, this determines the temperature distribution of the grains, and hence the position and shape of the far-IR dust re-emission peak. It serves the same role as the compactness parameter of Takagi et al [84, 85]
The attenuation of the foreground dust screen expressed in equivalent optical magnitudes of extinction, Av. The extinction computation is not fully self-consistent, because we do not compute the far-IR emission arising from this absorption. However, this will be unimportant provided that the covering factor of the molecular clouds around the star formation region is large. This should be a good approximation because, as discussed above, the dust obscuration is observed to increase both with galaxian mass , and with the absolute rate star formation [12, 1, 23, 88].
The molecular cloud destruction timescale, or, equivalently, the timescale taken for stars to escape from the dense region of star formation and molecular clouds, Myr. This effectively determines the fraction of UV / visible radiation which is intercepted by dust in dense clouds, and which is therefore re-emitted in the far-IR. This number effectively determined the intrinsic ration of UV to far-IR, while the previous factor determines the shape of the UV / visible SED.
The star formation rate (SFR, M yr-1). The model spectra are scaled to an absolute star formation rate of 1.0 M yr-1, so that the SFR is simply the inverse of the factor by which the observed SED has to be scaled to fit the theoretical models.
The result of this fitting exercise is shown in Fig 5 for four well-known ULIRGS. The remaining 37 objects give fits of comparable quality. The largest deviations are seen in the far-UV, but this is most likely due to the presence of a small number of relatively unobscured stars. These make a negligible contribution to the Bolometric flux, and hence to the estimated total SFR.
Figure 5. Here we show the fits to the SEDs of a few well-known ULIRGS in the local universe, scaled to a star formation rate of 1.0 M yr-1. The shape of the far-IR bump is used to fit the pressure; P/k. The visible and UV part of the spectrum is fitted by a combination of foreground screen attenuation with an effective Av, and a molecular cloud dissipation timescale, Myr. Finally, the overall scaling factor provides the estimate of the total star formation rate.
Implications for hi-z Starbursts All of the fits ULIRGS are characterized by high pressures, log P / k > 6 cm-3 K, and therefore have far-IR bumps which peak below 100 µm . This result is not unexpected, because the star formation region can only be as compact as it is in ULIRGS if the star formation is occuring in a very high pressure and high density environment. The pressure can be indirectly inferred from measurements of pressure in the HII regions though measurements of the density-sensitive [S II] 6717, 6731 Å doublet in warm IRAS galaxies. This has been done by Kewley [50, 51] and indeed, pressures log P / k > 6 cm-3 K are inferred for most objects.
In the local universe, the "dust temperature" inferred from the modified Black-Body fits to the long wavelength side of the far-IR peak in starburst galaxies is observed to correlate with the absolute luminosity, which for these galaxies can be interpreted as proportional to the rate of star formation . However, the same exercise applied to high-redshift submillimeter selected galaxies (SMGs) provides a similar correlation, but shifted to higher luminosity. At a given luminosity, the dust in SMGs is about 20K cooler than in ULIRGs in the local universe, and at a given dust temperature, the SMGs are typically 30 times as luminous as their ULIRG counterparts.
What does this mean? As reported above, Takagi et al [84, 85] had found that most ULIRGS have a constant surface brightness of order 1012 L kpc-2. Our results show that this corresponds to an ISM with a pressure of order log P / k ~ 7 cm-3 K . These parameters probably characterise "maximal" star formation, above which gas is blown out into the halo of the galaxy and star formation quenched. Only mergers, which provide an additional ram-pressure confinement of the star formation activity may exceed this surface brightness. Thus, in order to scale the star formation up to the rates inferred for SMGs (~ 1000 - 5000 M yr-1), we must involve a greater area of the galaxy in star formation, rather than trying to cram more star formation into the same volume. For a typical value of 1013 L kpc-2, we require "maximal" star formation over an area of ~ 10 kpc2, and the most luminous SMGs require star formation to be extended over an area of at least ~ 100 kpc2. We can therefore conclude:
SMGs are truly starbursts extended on a galaxy-wide scale, rather than the more confined or nuclear starbursts which characterise ULIRGs in the local or moderate-redshift universe.
Because of the greater physical extent inferred for the starburst region in the SMGs, the modelling parameters we have derived for local ULIRGS: pressure, molecular gas dissipation timescales, and line of sight attenuations can probably be directly applied to modelling SMGs in the distant universe. This is good news indeed!