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 μm 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 [νL ν(7.7 μm)] - 42.57 ± 0.2, for SFR in Msun yr-1 and νL ν(7.7 μm) the luminosity at the peak of the 7.7 μm 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 [νLν(7.7 μm)] - 21.5 ± 0.18, indicating that more luminous starbursts are also dustier. Using our adopted relation between νLν(7.7 μm) and L ir, this becomes log [SFR(PAH)/SFR(UV)]= (0.53 ± 0.05)log Lir - 4.11 ± 0.18, for Lir in Lsun. 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 ∼10 for typical local starbursts but this factor increases to >700 for the most luminous starbursts at z ∼ 2.5. Application of this factor explains why the most luminous starbursts discovered by Spitzer at z ∼ 2.5 are optically faint; with this amount of extinction, the optical magnitude of a starburst having fν(7.7 μm) of 1 mJy should be V∼ 25.6.