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

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3. The FIR to UV flux ratio of individual galaxies

3.1. The FIR to UV flux ratio as an indicator of dust extinction

The FIR to UV ratio in star forming galaxies is now well recognized as a powerful indicator of extinction. The basic idea is to perform an energetic budget: the amount of stellar emission lost due to the extinction is re-emitted by the dust in the FIR. Nevertheless the quantitative calibration relies on models. In galaxies with an active star formation activity the heating of the dust is mostly due to the emission of young and massive stars; therefore the FIR to UV flux ratio is expected to be tightly related to the extinction. Following this approach, Buat & Xu (1996) have estimated the extinction at 0.2 µm in star forming galaxies using a radiation transfer model. Meurer et al. (1999) have followed a more empirical way to relate the FIR to UV ratio to the extinction at 0.16 µm using a dust screen model and various extinction curves. They obtained a relation between the extinction and the FIR to UV flux ratio and then between the extinction and the UV slope [FORMULA].

The results of both studies are compared in Fig. 1. The FIR flux is taken in the range 40-120 µm as a combination of the emission at 60 and 100 µm (Helou et al. 1988) and the UV flux is defined as [FORMULA] where [FORMULA] is a flux per unit wavelength.

[FIGURE] Fig. 1. The extinction in the UV wavelength range as a function of the ratio of the FIR and UV emissions. The points are the results of Buat & Xu (1996) and the UV fluxes are taken at 0.2 µm, the dashed curve is the result of the polynomial fit to the points. The solid curve is obtained using the relation of Meurer et al. (1999) between the extinction and the FIR to UV ratio at 0.16 µm.

The extinction estimated by the model of Meurer et al. is calculated using their relation between the FIR to UV flux ratio and the extinction:

[EQUATION]

It is shown as the solid curve in Fig. 1.

The results found by Buat & Xu (1996) for their sample of nearby galaxies are also reported in Fig. 1. A polynomial fit on the individual points gives:

[EQUATION]

The fit is reported as the dotted curve in Fig. 1.

We must account for the difference in wavelengths used in the two studies. First, we discuss the difference between the UV flux of galaxies at 0.2 or 0.16 µm which affects the x-axis of the Fig. 1. Deharveng et al. (1994) have found the fluxes at 0.165 µm of a sample of nearby galaxies systematically higher by 29% than the fluxes at 0.2 µm. Adopting this result, the definition of the UV fluxes as [FORMULA] almost cancels the effect of wavelength and we can consider the fluxes at 0.16 and 0.2 µm as similar.

The extinctions at 0.16 µm and 0.2 µm ([FORMULA] and [FORMULA]) plotted along the y-axis of the Fig. 1 can also be considered as similar: their ratio is expected to vary from 0.9 to 1.1 using the extinction curve of the MW, LMC (Pei 1992) or that of Calzetti (1997). Therefore we will note both values as [FORMULA] without any correction.

The UV extinctions derived from the two methods when the FIR to UV flux ratio of a galaxy is known are tightly correlated (correlation coefficient 0.99) since both are directly related to this FIR to UV flux ratio: the calculations of Meurer et al. lead to an extinction systematically larger than ours, The difference is [FORMULA] mag for low FIR to UV flux ratio ([FORMULA]) and reaches [FORMULA] mag for [FORMULA]. This difference may arise from the different assumptions and calculations made in the two studies. Since they are interested by starburst galaxies Meurer et al. use a galaxy spectrum obtained from a constant star formation rate for at most [FORMULA] years whereas we use empirical broadband spectra: the contribution of the old evolved stars to dust heating is certainly larger in our approach leading to a lower UV extinction for the same amount of dust emission. Another major difference is the treatment of geometrical effects. Meurer et al. use a screen model and we calculate the extinction with a radiation transfer model in an infinite plane parallel geometry where dust and stars are uniformly distributed and which accounts for scattering effects and disk inclination (Xu & Buat 1995). Finally we assume a Milky Way extinction curve whereas Meurer et al. adopt a uniform UV extinction for the entire spectrum of the starburst. Therefore, our model is probably more appropriate for normal star-forming galaxies and the entire disk of starburst galaxies whereas the calculations of Meurer et al. are made for starburst regions. Given these fundamental differences and the rather large uncertainties on the corrections for extinction the two methods are in reasonable agreement. The FIR to UV flux ratio appears relatively insensitive to the dust characteristics (type, distribution) and the stars/dust geometry. This has been confirmed by the recent study of Witt & Gordon (1999) who explore various dust distributions (homogeneous or clumpy), extinction properties (Milky Way or Small Magellanic Cloud) and stars/dust distributions (uniform mixture or shells). Such a robustness makes the FIR to UV flux ratio a reliable quantitative tracer of the dust attenuation in star forming galaxies.

3.2. The variation of the FIR to UV ratio: the influence of the FIR selection

One basic difficulty of these studies based on individual galaxies is that the samples used are all biased and sometimes in a very complicated sense. The diagnostics on the UV slope of nearby galaxies all derive from the compilation of Kinney et al. (1993) of IUE observations of starburst galaxies which is not complete in any sense. Buat & Xu (1996) have used samples of star forming galaxies selected on their UV and FIR emissions leading to very complicated biases. Whereas the use of sample of galaxies which may be strongly biased is probably not a limitation to calibrate the physical link between the FIR to UV flux ratio and the extinction, the presence of these biases must be accounted for when generic properties of galaxies are deduced from these samples.

Our purpose is to use our FIR selected galaxy sample to test the influence of such a selection on the deduced value of the FIR to UV ratio. We will consider both fluxes at 60 µm and in the range 40-120 µm, the so-called FIR flux. Each one has its own advantages: on one hand more galaxies have a measured flux at 60 µm than at 100 µm and the luminosity function has been derived at 60 µm, on an other hand the FIR emission over the range 40-120 µm is more easily related to the total emission of the dust and hence to the amount of extinction than a single band flux.

In this section, we only discuss the observational biases and therefore use the data at 60 µm. In Fig. 2 is reported the ratio of fluxes at 60 µm and 0.2 µm, [FORMULA] as a function of the flux and luminosity of the galaxies at 60 µm. [FORMULA] and [FORMULA] are of the form [FORMULA] where [FORMULA] is a flux per unit wavelength. The Fig. 2a with the flux of the galaxies can be used to study the selection bias in limited flux samples. The Fig. 2b where are reported the luminosities of the galaxies is useful to discuss the intrinsic properties of the galaxies.

[FIGURE] Fig. 2a and b. The ratio of the emission at 60 and 0.2 µm as a function of a the flux at 60 [FORMULA] and b the luminosity at 60 µm. The ratio of the luminosity densities [FORMULA] is reported as a dotted horizontal line, the vertical line is the error bar

There is a clear trend in both figures in the sense of a larger [FORMULA] ratio for brighter galaxies at 60 µm. The tail found in Fig. 2a at large 60 µm flux toward low [FORMULA] ratios is due to very nearby galaxies. This effect of distance disappears when the luminosity is considered (Fig. 2b). In order to highlight the general trend we have calculated a moving median on the sample. The data are sorted according to the 60 µm luminosity, then a median is calculated for bins of 11 objects each time shifted by 5 objects. The result is shown in Fig. 3. As expected the moving median has reduced the dispersion of the data and flattened the dispersed trend of the Fig. 2b. A linear fit gives

[EQUATION]

These figures illustrate the bias introduced by a FIR selection. As we consider galaxies with an increasing 60 µm flux or luminosity, their [FORMULA] ratio also increases and is less and less representative of the mean properties of the local Universe as we will see below.

[FIGURE] Fig. 3. The ratio of the emission at 60 and 0.2 µm as a function of the luminosity at 60 µ m obtained with a moving median. The value reported on the X axis is the mean value of the 60 µm luminosity within each bin. The linear fit is represented by the full line. The ratio of the luminosity densities [FORMULA] is reported as a dotted horizontal line, the vertical line is the error bar

3.3. The galaxies detected at 60 µm and not at 0.2 µm

The case of these galaxies is especially interesting since they are good candidates for very obscured galaxies. Nevertheless their low number (5 cases, Sect. 2.2) makes them having no or little influence on the statistical properties discussed in this paper. Moreover, little information is known about these objects. Only one galaxy (F12242+0919) has a known redshift in the NED database.

The [FORMULA] ratio of each object is reported in Table 2 and plotted in Fig. 2a. The upper limits found for these galaxies are compatible with the values found for some galaxies of the IRAS/FOCA sample but their location in the figure is surprising since they do not follow the general (although dispersed) trend of a larger [FORMULA] flux for a larger [FORMULA] ratio. However, only the Fig. 2b where the luminosity of the galaxies are reported has a physical meaning and unfortunately only one object (F12242+0919) has a measured redshift. Since F12235+0914 and F12259+1141 are classified by Yuan et al. as members of the Virgo cluster we assign them a distance of 17 Mpc. These three galaxies are reported in Fig. 2b. For the most luminous (F12242+0919) the upper limit of [FORMULA] is compatible with the general trend, the two faint Virgo dwarfs clearly disagree. Due to their faintness not much information is available for them, F12259+1141 is classified as dE and F12235+0914 dE or Im. A large FIR to UV ratio is not expected for elliptical galaxies, therefore these objects are probably not dE. We will see in Sect. 6 that even the most FIR bright and extincted objects known in the Universe follow and extend the trend found in Fig. 2b so the behavior of these two objects is difficult to understand.

We can try to estimate an extinction for the objects listed in Table 2. Only two (F12041+6519, F13041+2907) have been detected at both 60 and 100 µm. For these two galaxies we have the FIR flux to estimate the UV extinction (a lower limit for F13041+2907) using the formula (polynomial fit) established in Sect. 3.1. For the galaxies not detected at 100 µm we estimate arbitrarily this flux such as [FORMULA] which is intermediate between the values for warm and cool dust (Lonsdale & Helou 1987), if this value is incompatible with the upper limit, we adopt the upper limit. The extinctions are listed in Table 2. Adopting the relation of Meurer et al. leads to extinctions larger by 0.4 mag.

Three galaxies have a UV extinction larger than 3.5 mag, they are the two objects without any optical identification and the faintest galaxy of the Table 2 detected in B. The three other cases (two non detections and the uncertain one) are less extreme ([FORMULA]).

Note that the upper limits found for these galaxies are compatible with the values found for some galaxies of the IRAS/FOCA sample (Figs. 2). For example the two most extincted galaxies of our sample, namely M82 and IC732, have a UV extinction larger than 5 mag and a [FORMULA] ratio larger than 2 in log unit.

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© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999
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