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 arcmin² to a very uniform point-source-filtered rms noise level of σ ≃ 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) = n₀S^-δ. We constrain the number counts in the 1-10 mJy range and derive significantly tighter constraints than in previous work: the power-law index δ = 2.7_-0.15 ^+0.18, while the amplitude is n₀ = 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 (δ = 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.