STAR FORMATION RATES FOR STARBURST GALAXIES FROM ULTRAVIOLET, INFRARED, AND RADIO LUMINOSITIES

We present a comparison of star formation rates ( SFR) determined from mid-infrared 7.7 mu m polycyclic aromatic hydrocarbon (PAH) luminosity [SFR(PAH)], from 1.4 GHz radio luminosity [ SFR( radio)], and from far-ultraviolet luminosity [SFR(UV)] for a sample of 287 starburst galaxies with z < 0.5 having Spitzer IRS observations. The previously adopted relation log[SFR(PAH)] = log[nu L-nu( 7.7 mu m)] - 42.57 +/- 0.2, for SFR in M circle dot yr(-1) and nu L-nu(7.7 mu m) the luminosity at the peak of the 7.7 mu m PAH feature in erg s(-1), is found to agree with SFR(radio). Comparing with SFR( UV) determined independently from ultraviolet observations of the same sources with the Galaxy Evolution Explorer mission ( not corrected for dust extinction), the median log [SFR(PAH)/SFR(UV)] = 1.67, indicating that only 2% of the ultraviolet continuum typically escapes extinction by dust within a starburst. This ratio SFR(PAH)/SFR(UV) depends on infrared luminosity, with the form log [SFR(PAH)/SFR(UV)] = (0.53 +/- 0.05) log [nu L-nu(7.7 mu m)] - 21.5 +/- 0.18, indicating that more luminous starbursts are also dustier. Using our adopted relation between nu L-nu(7.7 mu m) and L-ir, this becomes log [SFR(PAH)/SFR(UV)]= (0.53 +/- 0.05) log L-ir -4.11 +/- 0.18, for L-ir in L circle dot. Only blue compact dwarf galaxies show comparable or greater SFR(UV) compared to SFR(PAH). We also find that the ratio SFR(PAH)/SFR(UV) is similar to that in infrared-selected starbursts for a sample of Markarian starburst galaxies originally selected using optical classification, which implies that there is no significant selection effect in SFR(PAH)/SFR(UV) using starburst galaxies discovered by Spitzer. These results indicate that SFRs determined with ultraviolet luminosities require dust corrections by a factor of similar to 10 for typical local starbursts but this factor increases to > 700 for the most luminous starbursts at z similar to 2.5. Application of this factor explains why the most luminous starbursts discovered by Spitzer at z similar to 2.5 are optically faint; with this amount of extinction, the optical magnitude of a starburst having f(nu)(7.7 mu m) of 1 mJy should be V similar to 25.6.