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

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5. Estimating star formation rates

Both FIR and UV emissions are powerful star formation tracers. To derive reliable star formation rates (SFRs) one must account for the repartition of the emission of young stars in both wavelength ranges since the stellar emission lost by dust extinction is re-emitted in the FIR.

As already proposed by Heckman et al. (1998), perhaps the best way is to consider both UV and FIR emissions: each emission can be related to the star formation rate and the sum of the two SFRs deduced from the FIR and the UV should account for the total emission of young stars.

In such an approach the uncertainty resides in the translation of the UV and FIR emissions into quantitative star formation rate. The UV flux is directly proportional to the star formation rate provided that the star formation has been constant for some [FORMULA] years and assuming a universal initial mass function (IMF). We have used the models of Leitherer et al. (1999) for different IMFs (Salpeter IMF (-2.35) or -2.5, upper mass limit 100 or 125 M[FORMULA] for a lower mass limit equal to 0.1 M[FORMULA]). The metallicity is taken solar. After 5 [FORMULA] years of constant star formation the production of the UV luminosity reaches stationarity: [FORMULA] at 0.2 µm for a Salpeter IMF and an upper mass limit of 125 M[FORMULA]. Nevertheless after 5 [FORMULA] years the UV luminosity reaches more than 80[FORMULA] of this stationary value. For the same IMF, using Madau estimations (1998) based on the models of Bruzual & Charlot Treyer et al. (1998) have adopted a conversion factor [FORMULA] equal to [FORMULA] i.e. a difference of [FORMULA]. The uncertainty due to the IMF is around [FORMULA]. Therefore we can conservatively estimate that the uncertainty on the conversion of the UV luminosity in star formation rate is [FORMULA] provided that the galaxy has formed stars continuously for some [FORMULA] years.

The link between the SFR and the FIR luminosity is more indirect than for the UV luminosity since it depends of the dust heating which involves all types of stars. Nevertheless, in starbusting galaxies the situation is expected to be less complex since the dust heating is dominated by the young stars. Under such conditions Kennicutt (1998) has related the FIR luminosity to the star formation rate [FORMULA] where [FORMULA] is the total FIR luminosity. This conversion factor [FORMULA] is obtained using synthesis population models and is also subject to uncertainties on the stellar tracks, the IMF or the star formation history. From a comparison with the calculations of Lehnert & Heckman (1996), Meurer et al. (1997) and Buat & Xu (1996) we estimate the uncertainty of the order of 50[FORMULA] for [FORMULA].

Therefore we can reasonably estimate that the SFR deduced from the observed UV luminosity added to that deduced from the FIR one is also uncertain by a factor [FORMULA]. Nevertheless it must be noticed that the conversion formulae only apply to galaxies which have experimented a continuous star formation for at least [FORMULA] years and will not be valid for galaxies with more episodic star formation, especially post starbursting galaxies.

5.1. The IRAS/FOCA sample

The IRAS/FOCA sample is FIR selected, thus it is biased against very blue dwarf galaxies which may exhibit episodic bursts of star formation as suggested by Fioc & Rocca-Volmerange (1999). Therefore we can expect that the derivation of a SFR from the FIR and UV emissions is valid for this sample of galaxies. The comparison of the star formation rates obtained by adding the FIR and UV (observed) emissions to those deduced from the UV fluxes after a correction for extinction can be useful to test the consistency of both methods. Therefore we have calculated the star formation rates for the IRAS/FOCA sample of galaxies adding the contribution of the FIR and UV (not corrected for extinction) emissions and using the conversion formula of Treyer et al. (1998) for the UV and Kennicutt (1998) for the FIR. Total FIR fluxes have been estimated using the relation found by Buat & Burgarella (1998) between the ratio of the total dust flux to the FIR (40-120 µm) flux and [FORMULA]. The estimated SFRs can be compared to the ones obtained after correction of the UV fluxes from extinction. The correlation between the two estimates is very good but the SFRs deduced from the ([FORMULA]) emissions are higher than the SFRs deduced from the UV corrected emission by a factor 1.4. Another interesting comparison is that of the relative contribution of the UV (not corrected for extinction) and FIR emissions to the total ([FORMULA]) SFR. For our sample of IRAS/FOCA galaxies the relative contribution of the UV and FIR emissions to the total SFR are 0.3 and 0.7 respectively. However, these calculations assume that the FIR flux is exclusively due to the heating by young stars. Since all our galaxies are certainly not starbursting objects the contribution of the emission of dust heated by old evolved stars must be deduced from the FIR flux before translating it into star formation rate reducing the contribution of the FIR emission to the SFR. Let us assume that old stars contribute for 30 [FORMULA] of the dust heating (Xu 1990, Buat & Xu 1996), then the ratio of the SFR deduced from the ([FORMULA]) emissions and the SFR deduced from the UV corrected emission is reduced from 1.4 to 1.1 and the relative contributions of the UV and FIR emissions to the total SFR are now 0.4 and 0.6.

Given all the uncertainties inherent to these calculations we must be cautious in our conclusions. We can say that the corrections for dust extinction deduced from the FIR/UV flux ratio and applied to the UV observed emissions lead to a SFR consistent with that obtained by adding the SFRs deduced from both the FIR and observed UV emissions. This makes us confident in our estimate of the extinction.

5.2. The local volume-average star formation rate

Under the hypothesis of an average star formation of the local universe continuous over [FORMULA] years, we can derive global star formation rates from the local FIR and UV luminosity densities:

[EQUATION]

[FORMULA] is calculated using the value of [FORMULA] (Sect. 4.1) multiplied by 1.5 to account for the total dust luminosity density (e.g. Xu & Buat 1995, Meurer et al. 1999); [FORMULA] is calculated from [FORMULA]. We find:

[EQUATION]

This time the contributions of the FIR and UV are very similar, this is due to the lower value of the FIR to UV density ratio as compared to the FIR to UV flux ratio of individual galaxies. Then the volume-average star formation rate deduced from the UV luminosity density not corrected for dust extinction must be multiplied by a factor [FORMULA] to account for the global extinction, this corresponds to a mean extinction of 0.75 mag at 0.2 µm. As discussed before this rather low value is due to the contribution of faint blue galaxies to the UV luminosity density.

Actually, using the [FORMULA] ratio gives an extinction of 0.77 mag using the model of Meurer et al. and 0.55 mag for our polynomial fit (Sect. 3.1) As already underlined, the difference is likely to come from the contribution of the old stars to the dust heating: let us assume that 30[FORMULA] of the FIR emission comes from these old stars and is not related to the recent star formation then we find that [FORMULA] of the star formation is locked in FIR and [FORMULA] in UV. The resulting UV extinction is 0.58 mag and [FORMULA].

Therefore we can conclude that the derivation of the global star formation rate is in agreement with our estimate of the global extinction in UV and that the same amount of star formation rate is traced by the global FIR and UV (not corrected for extinction) luminosity densities.

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© European Southern Observatory (ESO) 1999

Online publication: December 2, 1999
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