3. STARBURST REDDENING AND THE SUB-MM BACKGROUND

Here I summarize the status of a recent debate within the field over the last four or five years: which population of galaxies contributes the most to the total star formation rate density at high redshift? The two top contenders are the optically selected LBG population and the "SCUBA" sub-mm and mm galaxies. Table 2 summarizes some properties of these contenders and their estimated contribution to the sub-mm background S_850µm = 44 Jy deg^-2 (Fixsen et al. 1998).

Table 2. What dominates the SFR at z ~ 3?

Property	LBGs	SCUBA galaxies
Detectability	"easy" & numerous	difficult & rare
	~ 6000 deg2 to R ~ 25.5	~ 300 deg2 to ~ 6.5 mJy
		confusion limited
	(Steidel et al. 2003)	(e.g. Hughes et al. 1998)
Luminosity	LUV ~ 1010-11 L	LFIR ~ 1012-13.5 L
	(without dust correction)
LFIR / LUV	100 (average 5 - 8)	30 - 3000 a
local analog	UV-bright starbursts	ULIRGs (Goldader
	(MHC99)	et al. 2002; AS00)
Contribution to S850	93%	100% (by definition...)
after corrections	~ 1.3 completeness	~ 5 completeness
	~ 6 dust absortion
	(AS00)	Chapman et al. (2000)
a One deviant sub-mm galaxy is SMMJ16358+4057 with LFIR / LUV ~ 10 (Smail et al. 2003).

As noted above, LBGs strongly resemble UV bright starbursts. One of the strongest correlations seen in local UV bright starbursts is the so-called IRX- relationship, shown in Fig. 1 (Meurer et al. 1995; MHC99). This relationship shows that the ratio of dust emission in the FIR to (residual) UV emission (infra-red excess or IRX) correlates with the UV spectral slope (defined by the spectrum f ). Since IRX is basically a measure of dust extinction this means that starburst redden as they become more extincted. The simplest explanation for this correlation is that the dust has a strong diffuse foreground contribution to its distribution, i.e. it behaves like a foreground screen (e.g. Witt & Gordon 2000; MHC99; Calzetti et al. 1994; Witt et al. 1992). Indeed, correcting survey data for dust absorption using simple reddening models greatly improves the consistency of multi-wavelength SFRD(z) plots (Calzetti 1999).

Figure 1. The IRX- correlation (from MMC99). The UV spectral slope is plotted on the abscissa. On the ordinate is plotted IRX, the ratio of fluxes in the FIR and and UV (at 1600Å). At right IRX is converted to the effective UV extinction A1600. The data points represent the UV-bright starburst sample of MMC99, derived from the IUE atlas of star forming galaxy (Kinney et al. 1993). The curve is a simple linear fit of A1600 as a function of .

It should be noted that not all local star forming galaxies obey this relationship. While it works well for the UV-bright calibrating sample whose members have L_bol 10^11.5 it does not work well for ULIRGs which typically have log(F_FIR / F₁₆₀₀) > 2 and fall well above the IRX- relationship (Goldader et al. 2002). A significant fraction (~ 30%) of normal (i.e. non starburst) galaxies fall below the IRX- relationship, presumably due to strong contamination from intermediate age populations in the near UV (Seibert, 2003).

Be that as it may, the IRX- correlation seems to work well for strongly star forming galaxies with modest amounts of dust absorption. While there is some distaste for the foreground screen geometry in the literature (e.g. Charlot & Fall 2000), we need not fixate on the interpretation to use the correlation. We have seen the myriad ways that LBGs resemble local starbursts, so it seems reasonable to suppose that they obey the same IRX- correlation. If so, then we can estimate the total extinction correction UV flux (and integrated cosmic UV flux density), and hence star formation rate of LBGs from just their rest-frame UV-flux and colors. This was done by MHC99. An even better job, using similar and other methods, was done by AS00. Both papers find that only 12% - 20% of the UV flux emitted at rest 1600Å reaches the earth (cf. Vijh et al. 2003, and references therein).

It is hard to test whether the IRX- relation holds for LBGs, since the predicted sub-mm fluxes are below the SCUBA confusion limit (MHC99). AS00 show that there are a few individual LBGs that have been directly detected with SCUBA and these largely obey the IRX- relation. One lensed LBG, MS1512+36-cB58, falls somewhat below the IRX- relationship, albeit with large error bars (Baker et al. 2001). If a large fraction of LBGs have similar properties, then the IRX- relationship would over predict their contribution to the total SFRD at z ~ 3.

Fortunately, while LBGs in general are not individually visible at other dust-insensitive wavelengths, stacked measurements of fluxes in the radio and X-ray can be used to test whether LBGs have similar dust extinction properties as nearby UV-bright starbursts.

The radio result is given as a note in proof to MHC99 and repeated in Table 3. Radio fluxes of the the ten U-dropout galaxies in the Hubble Deep Field North (HDF-N) with the highest predicted 850 µm SCUBA fluxes were computed by assuming that the galaxies obey the local FIR to radio correlation, have a radio spectral slope = - 0.7 (f ) and that the FIR flux is the reprocessed UV flux. The stacked radio fluxes, kindly provided by E. Richards, agree remarkably well with the predictions for these ten sources. AS00 also do an analysis of the stacked LBG fluxes at 20cm using the Richards et al. radio map. Their total observed and predicted fluxes are 105 ± 81 µJy and 114 ± 36 µJy respectively, similar to what is reported in MHC99 but with larger errors. The difference is in part due to AS00 stacking all their 46 HDF LBGs for the analysis. This includes many with very little predicted flux which contribute the majority of the error budget. In addition, AS00 derive a higher error per beam by integrating over the beam, which overestimates the error per source. Hence the stacked radio flux estimate is probably more significant than implied by AS00.

X-rays can also be used to probe high-z star formation. The Chandra soft X-ray band corresponds to 2-8 Kev at z = 3, "hard" enough to pass through the ISM of galaxies virtually unattenuated. Seibert, Heckman & Meurer (2002) compared the stacked soft X-ray flux of HDF-N AGN free U-dropouts given by Brandt et al. (2001) with predictions from dust reddening models. The results are consistent with a variety of plausible dust reddening laws including the IRX- correlation from MHC99, the Calzetti et al. (2000) starburst "obscuration curve", and the homogeneous and clumpy foreground dust screen models from Witt & Gordon (2000). The results are not consistent with the rest-frame UV flux from LBGs being like that of ULIRGs which have IRX values on the order of 10² to 10^3.5 (Goldader et al. 2002). In fact, if LBGs had similar values they would be easily observable individually in X-rays, the sub-mm, and radio (and they are not). Similarly the scenario that LBGs are not extincted at all under-predicts the stacked X-ray flux by a factor of six. Nandra et al. (2002) do an independent analysis of stacked X-ray results in the HDF-N from Chandra and reach similar conclusions.

The stacked radio and X-ray analyses are both consistent with the local starburst reddening relation applying to high-z LBGs. If so, then they would dominate total SFR density at z 3 (AS00). However, there may be a fly in the ointment. As earlier mentioned, in the MHC99 and AS00 picture we would expect the LBGs to have 850 µm fluxes up to ~ 1 mJy. While such fluxes are at or below the confusion limit of blank field SCUBA observations it may be possible to detect such sources through gravitational lensing. Smail et al. (2002b) constrain the faint counts at 850 µm using SCUBA observations towards lensing clusters. A little over half of their sample are undetected in their HST I images, with the non-detections preferentially being at the (sub-mm) faint end. These faint end sources have magnification corrected 850 µm micron fluxes like the predictions for LBGs. The implication is that the LBGs are not showing up in SCUBA observations presumably because the local IRX- relationship overpredicts their 850 µm flux as it does for MS1512+36-cB58. Instead the 850 µm background is actually dominated by star forming galaxies like local ULIRGs (Goldader et al. 2002) - totally hidden by dust, as is also the case with the brightest SCUBA sources.

While this scenario may be correct, a careful examination of Smail et al. (2002b) suggests that it is built on a shaky foundation. Their claim to having resolved the 850 µm background rests on four faint (S/N = 3 to 5) 850 µm detections. These have only have lower limits to their magnifications (presumably because their positions are uncertain, since they have no optical, NIR, or radio counterparts). Their Monte-Carlo simulations indicate that at least one of these sources should have a source plane 850 µm flux in the 0.5 to 1 Jy range, the only sources in their survey that could be that faint (or fainter). However, using the lower limit magnifications shows that none of the source plane fluxes need actually be fainter than 1.6 Jy, while the brightest predicted 850 µm flux for the LBGs in the HDF-N is 1.8 mJy (MHC99). Smail et al. are not convincingly dipping deep into the expected realm of LBGs with their SCUBA observations. The lack of optical counterparts at the faint end also does not thoroughly rule out the presence of LBGs. They state a detection limit of I ~ 26 in their HST images which corresponds to a typical brightness seen in LBGs. However, this is the detection limit at S/N = 2 for a point source. To do this well the detection limit should be stated at a higher S/N (at least 3) and be calculated for typical LBG sizes (corrected for lensing in their case). I expect this would lower the limiting mag to I ~ 25 or brighter. Figure 15 of AS00 implies that the optical counterparts of the ~ 1 - 2 Jy sources have magnitudes over a wide range I ~ 24 to 27 ABmag in the source plane. Smail et al. have not convincingly ruled this out yet.

I conclude that the nature of the sources dominating the sub-mm background is not yet well determined. It is clear that the leading contenders are galaxies at z 2 whose bolometric output is dominated by dust, and that these galaxies dominate the star formation rate density at these redshifts. It is not yet settled whether these galaxies are detectable in the rest-frame UV. Additional observations of lensing clusters in the mm and sub-mm would improve the statistics on the 850 µm counts at and below 2 mJy, while deeper optical observations of the faintest SCUBA sources (e.g. with ACS on HST) are needed to make a fair and convincing test of the LBG scenario.