We present the analysis of Herschel SPIRE far-infrared ( FIR ) observations of the z = 2.515 lensed galaxy SMM J163554.2+661225 .
Combining new 250 , 350 , and 500 \mu m observations with existing data , we make an improved fit to the FIR spectral energy distribution ( SED ) of this galaxy .
We find a total infrared ( IR ) luminosity of L ( 8–1000 \mu m ) = 6.9 \pm 0.6 \times 10 ^ { 11 } L _ { \odot } ; a factor of 3 more precise over previous L _ { IR } estimates for this galaxy , and one of the most accurate measurements for any galaxy at these redshifts .
This FIR luminosity implies an unlensed star formation rate ( SFR ) for this galaxy of 119 \pm 10 M _ { \odot } yr ^ { -1 } , which is a factor of 1.9 \pm 0.35 lower than the SFR derived from the nebular Pa \alpha emission line ( a 2.5 \sigma discrepancy ) .
Both SFR indicators assume identical Salpeter initial mass functions ( IMF ) with slope \Gamma = 2.35 over a mass range of 0.1 – 100 M _ { \odot } , thus this discrepancy suggests that more ionizing photons may be necessary to account for the higher Pa \alpha -derived SFR .
We examine a number of scenarios and find that the observations can be explained with a varying star formation history ( SFH ) due to an increasing star formation rate ( SFR ) , paired with a slight flattening of the IMF .
If the SFR is constant in time , then larger changes need to be made to the IMF by either increasing the upper-mass cutoff to \sim 200 M _ { \odot } , or a flattening of the IMF slope to 1.9 \pm 0.15 , or a combination of the two .
These scenarios result in up to double the number of stars with masses above 20 M _ { \odot } , which produce the requisite increase in ionizing photons over a Salpeter IMF with a constant SFH .