Astron. Astrophys. 352, 371-382 (1999)

4. Comparison with the luminosity functions and densities in the local universe

4.1. The ratio of the luminosity densities

The luminosity functions and luminosity densities of the local universe are available at both wavelengths (0.2 and 60 µm). Therefore we can compare some of their properties to the characteristics of individual galaxies. The 60 µm local luminosity function and density at z=0 have been calculated by Saunders et al. (1990). The 0.2 µm luminosity function and density have been derived by Treyer et al. (1998) at a mean z=0.15. From these studies we can calculate the ratio of the local luminosity densities at z=0. To this aim we correct the UV density for the redshift evolution. From Madau et al. (1998) we estimate that the luminosity density increases by a factor from z=0 to z=0.15 which is consistent with the estimates of Lilly et al. (1996) and Cowie et al. (1999). Applying this factor to the estimate of Treyer et al. we obtain . With we find at z=0. In the same way, from (Saunders et al. 1990), we calculate .

is reported in Figs. 2 and 3. The ratio appears lower than almost all the ratios found for individual galaxies and is systematically lower than all the median values calculated for increasing 60 µm luminosity (Fig. 3). Therefore the study of individual galaxies of our sample does not lead to a reliable estimate of the mean FIR to UV ratio of the local Universe .

Our sample is FIR selected since we have searched for FIR galaxies detected in UV, therefore a bias toward large FIR to UV flux ratio is expected and this bias increases as we select brighter galaxies (Fig. 2). For comparison, we can also re-consider the sample used by Buat & Xu (1996): the galaxies were primarily selected to have a UV measurement and then searched in the IRAS database. Only galaxies detected both in UV and FIR are considered. Whereas the selection biases of this sample are very complicated since the primary selection is on the UV the bias toward the FIR is certainly less strong than for the IRAS/FOCA sample.

In Fig. 4 the histograms of ratio are reported for three samples: the IRAS/FOCA sample (solid line), the IUE/IRAS templates of Meurer et al. (1999) (dotted line) and the sample of Buat & Xu (dashed line). We can see that almost all the IRAS/FOCA galaxies and the local IUE/IRAS templates exhibit a larger ratio than the ratio of the local luminosity densities . The situation is less extreme for the Buat & Xu sample for which the median of the flux ratio is 1.66, translating to (0.94 mag with the formula of Meurer et al.). This difference in the FIR and UV properties of the samples explains the rather low extinction found by Buat & Xu for this sample as compared with those obtained by Meurer et al.

Fig. 4. The ratio of the FIR and UV fluxes for different samples of galaxies:the IRAS/FOCA sample (solid line) and the sample of Buat & Xu (1996) (dashed line) with UV fluxes are taken at 0.2 µm), the IUE/IRAS templates of Meurer et al. (1999) (dotted line) with UV fluxes taken at 0.16 µm. The vertical dot-dashed line is the location of , the horizontal line is the error bar

The mean property of the local Universe in terms FIR to UV luminosity density ratio is not well represented by the samples of galaxies considered here. Therefore much caution must be taken to estimate global correction for extinction to be applied to the luminosity function.

4.2. The local luminosity functions

An explanation for the discrepancy between the ratio of individual galaxies and the ratio of the local luminosity densities is that it is not the same galaxies which form the bulk of the UV emission on one hand and the FIR emission on the other hand. Indeed, the large difference found in the shape of the two luminosity functions is consistent with this explanation as already discussed in Buat & Burgarella (1998). The adopted value of depends on the reliability of the luminosity functions and is subject to some uncertainties. Nevertheless very large modifications must be invoked to make consistent the ratios in our IRAS/FOCA sample and the mean value of the local universe. Moreover it would not explain the trend found of an increase of the ratio with the FIR luminosity of the galaxies.

We have evaluated the contribution to the luminosity function and the luminosity density at 0.2 µm (resp. 60 µm) of the galaxies as a function of their intrinsic luminosity (per decade of luminosity). These values are reported in Table 3 (resp 4) together with the number of galaxies of our IRAS/FOCA sample in each bin of luminosity (in log unit). The luminosity functions are truncated at .

Table 3. Contribution of the galaxies to the UV luminosity function and to the UV luminosity density in the local Universe per decade of luminosity. The luminosity function is truncated at ().

Table 4. Same as Table 3 at 60 µm

As expected for a magnitude limited sample, our individual galaxies do not truly sample the luminosity functions. This effect is dramatic in UV: the steepness of the faint end slope of the UV luminosity function (Treyer et al. 1998) implies a large number of faint galaxies. These objects largely contribute to the UV luminosity density. The relative numbers of galaxies in each bin of UV luminosity are similar to those used by Treyer et al. to calculate the UV luminosity function.

Conversely, the FIR luminosity function is better sampled in the sense that the deficiency of low luminosity galaxies has less implications than in UV. Indeed, the FIR luminosity function is extremely flat at low luminosities (Saunders et al. 1990) and the contribution of the faint FIR galaxies to the local luminosity density is very low. As a consequence the number of galaxies in each bin of luminosity is more representative of its contribution to the FIR luminosity density than in UV. The bright end of both luminosity functions is not represented in the IRAS/FOCA sample because of the scarcity of these objects and the small statistics. In terms of global (cumulated) luminosity of our sample of individual galaxies we are entirely dominated by the galaxies between and at both wavelengths (0.2 and 60 µm) but this does not influence our results since each galaxy is considered individually whatever its luminosity is, without any summation on individual objects.

Hence our sample IRAS/FOCA sample of individual galaxies is more representative of the FIR properties of the universe. If the faint UV galaxies are dwarf galaxies they probably have a low extinction and therefore a low FIR to UV ratio. Our sample being FIR selected, it is probably biased against these objects.

A consequence of these effects is that when a correction for extinction is calculated from individual galaxies using such a correction to correct the entire luminosity function can lead to some mistakes as we will discuss in the next subsection.

4.3. Consequences on the estimate of the UV extinction for large samples of galaxies and statistical studies

Most of the time neither the FIR flux nor the UV continuum ( slope) are available for large and/or deep surveys of galaxies and one cannot use these dust extinction calibrators. The situation is better at high z due to the redshifting of the UV continuum. For instance Meurer et al. (1999) have performed individual corrections on the Lyman break U-dropouts galaxies at in the HDF by estimating the slope from the V and I measurements. Nevertheless they sampled only bright galaxies ( i.e. whose UV luminosity is larger than ) since only such bright objects are reachable at high z.

The problem of the correction for extinction arises when one has to derive an intrinsic UV luminosity distribution (Treyer et al. 1998, Steidel et al. 1999). At low redshift the UV slope is not available for the moment on a large sample of galaxies and cannot be used to correct the UV luminosity function for dust extinction. The extinction has been found to vary as a function of the absolute bolometric magnitude of the galaxies (e.g. Wang 1991, Heckman et al. 1998, Buat & Burgarella 1998). Unfortunately, the UV luminosity is not a good tracer of the bolometric luminosity of a galaxy since it is expected to be very influenced by the current star formation activity. Moreover the extinction (larger for brighter galaxies) adds an anti correlation between the observed UV luminosity and the bolometric one. Therefore, relating the extinction to the UV luminosity is not possible. Indeed no correlation exists between the UV luminosity and the FIR/UV ratio in the IRAS/FOCA sample or that previously used by Buat & Xu (1996). In the same way Heckman et al. (1998) have used the sum of the FIR and UV luminosities as a tracer of the bolometric luminosity.

The use of the absolute B magnitude is also far from ideal since it suffers from the same caveats as the UV luminosity (star formation history and extinction), although in a less extreme way. Actually a trend has been found between the ratio of the dust to UV emission and for a sample of nearby starburst galaxies (Buat & Burgarella 1998) but the relation is too dispersed to be used as a quantitative calibrator of the extinction. More promising is the use of data at longer wavelengths like the R or I band: the effects of extinction will be largely reduced and we can hope to better trace the mass of the galaxies. Such investigations are devoted to a subsequent paper.

We have also compared the extinction deduced from the FIR/UV flux ratio (, Sect. 3.1) to the UV-B color since this color is often available for large samples (e.g. Treyer et al. 1998). The extinction is plotted against the UV-B color for our IRAS/FOCA sample in Fig. 5.

Fig. 5. The UV extinction at 0.2 µm calculated with the FIR to UV flux ratio of galaxies as a function of the UV-B color for the IRAS/FOCA sample. The solid line is the result of a linear regression:

A correlation is found between these two quantities (R=0.70). Indeed, a clear correlation has already been found between the FIR/UV flux ratio and the UV-B color (Deharveng et al. 1994) which has been interpreted to be due at least in part to the influence of the dust extinction (Buat et al. 1997). The UV-B color is also sensitive to the star formation history on timescales of the order of some years: it is likely to be at the origin of the dispersion found in Fig. 5 and only rough tendencies can be securely deduced. Nevertheless, it appears necessary to account for the variation of the extinction among galaxies which can vary by three magnitudes. In particular galaxies with a UV-B color lower than are very little affected by the extinction and it would seem reasonable to apply no correction of extinction to them.

© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999
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