We perform a combined fit to angular power spectra of unresolved infrared ( IR ) point sources from the Planck satellite ( at 217 , 353 , 545 and 857 GHz , over angular scales 100 \lesssim \ell \lesssim 2200 ) , the Balloon-borne Large-Aperture Submillimeter Telescope ( BLAST ; 250 , 350 and 500 \mu m ; 1000 \lesssim \ell \lesssim 9000 ) , and from correlating BLAST and Atacama Cosmology Telescope ( ACT ; 148 and 218 GHz ) maps .
We find that the clustered power over the range of angular scales and frequencies considered is well fit by a simple power law of the form C _ { \ell } ^ { \textrm { clust } } \propto \ell ^ { - n } with n = 1.25 \pm 0.06 .
While the IR sources are understood to lie at a range of redshifts , with a variety of dust properties , we find that the frequency dependence of the clustering power can be described by the square of a modified blackbody , \nu ^ { \beta } B ( \nu,T _ { \textrm { eff } } ) , with a single emissivity index \beta = 2.20 \pm 0.07 and effective temperature T _ { \textrm { eff } } = 9.7 K .
Our predictions for the clustering amplitude are consistent with existing ACT and South Pole Telescope results at around 150 and 220 GHz , as is our prediction for the effective dust spectral index , which we find to be \alpha _ { 150 - 220 } = 3.68 \pm 0.07 between 150 and 220 GHz .
Our constraints on the clustering shape and frequency dependence can be used to model the IR clustering as a contaminant in Cosmic Microwave Background anisotropy measurements .
The combined Planck and BLAST data also rule out a linear bias clustering model .