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A likelihood analysis for gamma-ray background models

Chance Hoskinson, Jason Kumar, Pearl Sandick

Abstract

Indirect searches for dark matter using dwarf spheroidal galaxies are limited by systematic uncertainties in modeling diffuse gamma-ray backgrounds. We present a likelihood-based comparison of locally constructed empirical background models and theoretically-motivated models that incorporate the Fermi-LAT diffuse background. The empirical models we study include both an independent-binning approach and a covariance-based approach that captures cross-energy correlations. Using ensembles of blank-sky regions and information criteria which account for model complexity, we find that empirical background descriptions provide a statistically competitive fit to gamma-ray data on degree scales in high-latitude regions.

A likelihood analysis for gamma-ray background models

Abstract

Indirect searches for dark matter using dwarf spheroidal galaxies are limited by systematic uncertainties in modeling diffuse gamma-ray backgrounds. We present a likelihood-based comparison of locally constructed empirical background models and theoretically-motivated models that incorporate the Fermi-LAT diffuse background. The empirical models we study include both an independent-binning approach and a covariance-based approach that captures cross-energy correlations. Using ensembles of blank-sky regions and information criteria which account for model complexity, we find that empirical background descriptions provide a statistically competitive fit to gamma-ray data on degree scales in high-latitude regions.
Paper Structure (10 sections, 10 equations, 3 figures, 2 tables)

This paper contains 10 sections, 10 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Purely Empirical Models
  3. Independent Energy Bins
  4. Including Covariance
  5. A Theoretically-Motivated Model
  6. Background Model Selection
  7. Results
  8. Comparison of models E1 and E2
  9. Comparison of models E1 and FT
  10. Conclusion

Figures (3)

  • Figure 1: Distribution of information-criterion differences for Set A blank-sky regions. Histograms show the distribution of $\Delta\mathrm{BIC}$ (top row) and $\Delta\mathrm{AIC}$ (bottom row) for the three pairwise model comparisons: $(\mathrm{E1},\mathrm{FT})$, $(\mathrm{E2},\mathrm{FT})$, and $(\mathrm{E1},\mathrm{E2})$. Vertical black lines denote $\Delta \mathrm{B/AIC} = 0$. Shaded regions correspond to conventional evidence-strength thresholds ($|\Delta\mathrm{IC}| = 0$--$2$: weak/no preference; $2$--$6$: positive; $6$--$10$: strong; $>10$: very strong evidence).
  • Figure 2: Distribution of information-criterion differences for Set B blank-sky regions. Histograms show the distribution of $\Delta\mathrm{BIC}$ (top row) and $\Delta\mathrm{AIC}$ (bottom row) for the three pairwise model comparisons: $(\mathrm{E1},\mathrm{FT})$, $(\mathrm{E2},\mathrm{FT})$, and $(\mathrm{E1},\mathrm{E2})$. Vertical black lines denote $\Delta \mathrm{B/AIC} = 0$. Shaded regions correspond to conventional evidence-strength thresholds ($|\Delta\mathrm{IC}| = 0$--$2$: weak/no preference; $2$--$6$: positive; $6$--$10$: strong; $>10$: very strong evidence).
  • Figure 3: Empirical photon count map for ROI center: RA = 57.2065$^\circ$, Dec = 26.4928$^\circ$. The map shows the spatial distribution of observed photon counts within the ROI. A coherent extended feature is visible in the upper-left quadrant, which is not captured by the independent empirical model (E1) but is recovered by the covariance and theoretical models. The color scale indicates pure photon counts in the $1-100~\, {\rm GeV}$ range.