We present a comparison of star formation rates ( SFR ) determined from mid-infrared 7.7 \mu m 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 \pm 0.2 , for SFR in M _ { \odot } yr ^ { -1 } and \nu L _ { \nu } ( 7.7 \mu m ) the luminosity at the peak of the 7.7 \mu m PAH feature in ergs s ^ { -1 } , is found to agree with SFR ( radio ) .
Comparing with SFR ( UV ) determined independently from ultraviolet observations of the same sources with the GALEX 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 form log [ SFR ( PAH ) /SFR ( UV ) ] = ( 0.53 \pm 0.05 ) log [ \nu L _ { \nu } ( 7.7 \mu m ) ] - 21.5 \pm 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 \pm 0.05 ) log L _ { ir } - 4.11 \pm 0.18 , for L _ { ir } in L _ { \odot } .
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 \sim 10 for typical local starbursts but this factor increases to > 700 for the most luminous starbursts at z \sim 2.5 .
Application of this factor explains why the most luminous starbursts discovered by Spitzer at z \sim 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 \sim 25.6 .