[Paper Review] Statistical constraints on the IR galaxy number counts and cosmic IR background from the Spitzer GOODS survey

Richard S. Savage, Seb Oliver|arXiv (Cornell University)|Nov 11, 2005

Galaxies: Formation, Evolution, Phenomena3 citations

TL;DR

This study uses Markov Chain Monte Carlo (MCMC)-based fluctuation analysis on Spitzer GOODS survey data to constrain near-IR galaxy number counts down to 10⁻⁸ Jy, revealing a significant excess over extrapolated counts from Fazio et al. (2004). It demonstrates that fluctuation analysis accounts for most of the 3.6 μm cosmic infrared background, resolving a substantial fraction of the background light and confirming consistency with prior background measurements while highlighting systematic discrepancies in flux calibration.

ABSTRACT

We perform fluctuation analyses on the data from the Spitzer GOODS survey (epoch one) in the Hubble Deep Field North (HDF-N). We fit a parameterised power-law number count model of the form dN/dS = N_o S^{-δ} to data from each of the four Spitzer IRAC bands, using Markov Chain Monte Carlo (MCMC) sampling to explore the posterior probability distribution in each case. We obtain best-fit reduced chi-squared values of (3.43 0.86 1.14 1.13) in the four IRAC bands. From this analysis we determine the likely differential faint source counts down to $10^{-8} Jy$, over two orders of magnitude in flux fainter than has been previously determined. From these constrained number count models, we estimate a lower bound on the contribution to the Infra-Red (IR) background light arising from faint galaxies. We estimate the total integrated background IR light in the Spitzer GOODS HDF-N field due to faint sources. By adding the estimates of integrated light given by Fazio et al (2004), we calculate the total integrated background light in the four IRAC bands. We compare our 3.6 micron results with previous background estimates in similar bands and conclude that, subject to our assumptions about the noise characteristics, our analyses are able to account for the vast majority of the 3.6 micron background. Our analyses are sensitive to a number of potential systematic effects; we discuss our assumptions with regards to noise characteristics, flux calibration and flat-fielding artifacts.

Motivation & Objective

• To constrain the differential number counts of faint infrared galaxies in the Spitzer GOODS survey down to flux levels below 10⁻⁸ Jy, where direct detection is limited by confusion noise.
• To determine the contribution of unresolved faint galaxies to the cosmic infrared background (CIRB) using statistical fluctuation analysis.
• To assess the consistency of the inferred number counts with previous direct measurements and background light estimates.
• To investigate potential systematic effects such as flux calibration errors, noise modeling, and flat-fielding artifacts that may affect the inferred number counts and background light.

Proposed method

• Applying a parameterized power-law number count model, dN/dS = N₀S⁻ᵟ, to Spitzer IRAC data across four bands (3.6, 4.5, 5.8, 8 μm).
• Using Markov Chain Monte Carlo (MCMC) sampling to explore the full posterior probability distribution of model parameters, enabling robust uncertainty estimation without assuming Gaussian error distributions.
• Performing fluctuation analysis on the spatial variance of the maps to extract statistical information from source confusion, treating the confusion noise as a probe of the underlying source population.
• Fitting the observed power spectrum of flux fluctuations to theoretical models of Poisson-distributed, point-like sources to infer number counts below the confusion limit.
• Comparing the inferred number counts with direct measurements from Fazio et al. (2004) to assess discrepancies and their implications.
• Estimating the total integrated background light by combining resolved contributions from Fazio et al. (2004) with the unresolved contribution from the fluctuation analysis.

Experimental results

Research questions

• RQ1 What are the statistical constraints on the number counts of infrared galaxies fainter than 10⁻⁸ Jy in the Spitzer GOODS survey?
• RQ2 To what extent can fluctuation analysis account for the observed cosmic infrared background at 3.6 μm, and how does this compare to direct measurements?
• RQ3 Why do the inferred number counts from fluctuation analysis differ systematically from the direct counts reported by Fazio et al. (2004), and what are the possible causes?
• RQ4 How sensitive are the results to systematic effects such as flux calibration, noise modeling, and flat-fielding artifacts?
• RQ5 Is the excess in the inferred number counts consistent with the recently reported excess in the cosmic infrared background by Kashlinsky et al. (2005)?

Key findings

• The study constrains near-IR galaxy number counts down to 10⁻⁸ Jy, extending the dynamic range of previous measurements by over two orders of magnitude in flux.
• The best-fit reduced chi-squared values for the power-law model are (3.43, 0.86, 1.14, 1.13) across the four IRAC bands, indicating a good fit for most bands.
• The fluctuation analysis reveals a systematic excess in faint number counts compared to the extrapolated Fazio et al. (2004) counts, suggesting a potential 50% flux calibration offset or intrinsic differences in the source population.
• The analysis accounts for the vast majority of the 3.6 μm cosmic infrared background, with results consistent with prior estimates by Dwek & Arendt (1998), Gorjian et al. (2000), Wright & Reese (2000), and Matsumoto et al. (2005).
• The total integrated background light in each IRAC band is estimated by combining resolved contributions from Fazio et al. (2004) with the unresolved contribution from the fluctuation analysis, confirming that over half the background is resolved.
• The results are consistent with the excess background detected by Kashlinsky et al. (2005), as both studies find a significant excess over extrapolated number counts, though the physical interpretation of the excess remains open.