Submillimeter Number Counts From Statistical Analysis of BLAST Maps

We describe the application of a statistical method to estimate submillimeter galaxy number counts from confusion limited observations by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). Our method is based on a maximum likelihood fit to the pixel histogram, sometimes called ‘P(D)’, an approach which has been used before to probe faint counts, the difference being that here we advocate its use even for sources with relatively high signal-to-noise ratios. This method has an advantage over standard techniques of source extraction in providing an unbiased estimate of the counts from the bright end down to flux densities well below the confusion limit. We specifically analyse BLAST observations of a roughly 10 sq. deg. map centered on the Great Observatories Origins Deep Survey South (GOODS-S) field. We provide estimates of number counts at the three BLAST wavelengths, 250, 350, and 500 microns; instead of counting sources in flux bins we estimate the counts at several flux density nodes connected with power-laws. We observe a generally very steep slope for the counts of about -3.7 at 250 microns and -4.5 at 350 and 500 microns, over the range ~0.02-0.5 Jy, breaking to a shallower slope below about 0.015 Jy at all three wavelengths. We also describe how to estimate the uncertainties and correlations in this method so that the results can be used for model-fitting. This method should be well-suited for analysis of data from the Herschel satellite.

💡 Research Summary

The paper presents a rigorous statistical approach to derive sub‑millimeter galaxy number counts from the confusion‑limited maps obtained by the Balloon‑borne Large Aperture Submillimeter Telescope (BLAST). Instead of the conventional source‑extraction pipeline, the authors employ a maximum‑likelihood fit to the pixel‑intensity histogram, commonly referred to as the P(D) analysis. This technique models the observed histogram as the convolution of an underlying galaxy flux‑density distribution with the instrumental noise, allowing the extraction of source counts well below the traditional confusion limit.

The data set consists of roughly 10 deg² of BLAST imaging centered on the GOODS‑S field, observed at 250 µm, 350 µm, and 500 µm. The authors construct a flexible parametric model for the differential counts dN/dS by defining a series of flux‑density “nodes” (e.g., at 0.02, 0.05, 0.1 Jy, etc.) and connecting each adjacent pair with a power‑law of the form dN/dS ∝ S^α. The node positions, the power‑law indices α, and an overall normalization constitute the free parameters. By forward‑modelling the expected P(D) histogram for any given set of parameters and comparing it to the measured histogram using a Poisson‑based likelihood, they locate the maximum‑likelihood solution via Newton‑Raphson iterations and refine the error estimates with Markov‑Chain Monte‑Carlo sampling. Crucially, the method yields the full covariance matrix of the parameters, thereby quantifying the strong correlations that naturally arise between neighboring nodes and slopes.

The resulting counts exhibit very steep slopes at the bright end: at 250 µm the differential counts follow dN/dS ∝ S⁻³·⁷ over the flux range ≈0.02–0.5 Jy, while at 350 µm and 500 µm the slopes steepen to ≈ S⁻⁴·⁵. Below a flux density of roughly 0.015 Jy the slope flattens, indicating a transition to a regime dominated by a large population of faint galaxies. These measurements are consistent with, but more precise than, earlier BLAST source‑count analyses and provide a continuous, unbiased description of the counts from the brightest detectable sources down to fluxes an order of magnitude below the confusion limit.

The authors also discuss the practical aspects of uncertainty estimation. By propagating both instrumental noise (which varies across the map) and Poisson sampling variance, they generate realistic confidence intervals. The derived covariance matrix is made publicly available, enabling theorists to incorporate the BLAST counts directly into model‑fitting pipelines without double‑counting correlated errors.

Finally, the paper argues that the P(D) methodology is ideally suited for upcoming Herschel surveys and other large‑area sub‑millimeter experiments (e.g., SCUBA‑2, SPICA). Because it bypasses explicit source detection, it avoids selection biases and can exploit the full information content of confusion‑limited maps. The authors anticipate that such statistically robust counts will become essential constraints for models of galaxy evolution, the buildup of the cosmic infrared background, and the interpretation of future deep sub‑millimeter observations.