A fluctuation analysis of the Bolocam 1.1 mm Lockman Hole Survey

We perform a fluctuation analysis of the 1.1 mm Bolocam Lockman Hole Survey, which covers 324 arcmin(2) to a very uniform point-source-filtered rms noise level of sigma similar or equal to 1.4 mJy beam(-1). The fluctuation analysis has the significant advantage of using all of the available data, since no extraction of sources is performed: direct comparison is made between the observed pixel flux density distribution [P( D)] and the theoretical distributions for a broad range of power-law number count models, n(S) = n(0)S(-delta). We constrain the number counts in the 1 - 10 mJy range and derive significantly tighter constraints than in previous work: the power-law index delta = 2.7(-0.15)(+0.18), while the amplitude is n(0) 1595(-238)(+85) mJy(-1) deg(-2), or N(> 1 mJy) 940(-140)(+50) deg(-2) (95% confidence). At flux densities above 4 mJy, where a valid comparison can be made, our results agree extremely well with those derived from the extracted source number counts by Laurent et al.: the best-fitting differential slope is somewhat shallower (delta = 2.7 vs. 3.2), but well within the 68% confidence limit, and the amplitudes ( number of sources per square degree) agree to 10%. At 1 mJy, however [the limit of the P(D) analysis], the shallower slope derived here implies a substantially smaller amplitude for the integral number counts than extrapolation from above 4 mJy would predict. Our derived normalization is about 2.5 times smaller than that determined by the Max-Planck Millimeter Bolometer (MAMBO) at 1.2 mm ( Greve et al.). However, the uncertainty in the normalization for both data sets is dominated by the systematic (i.e., absolute flux calibration) rather than statistical errors; within these uncertainties, our results are in agreement. Our best-fit amplitude at 1 mJy is also about a factor of 3 below the prediction of Blain et al., but we are in agreement above a few millijanskys. We estimate that about 7% of the 1.1 mm background has been resolved at 1 mJy.