Joint anisotropy and source count constraints on the contribution of blazars to the diffuse gamma-ray background

We place new constraints on the contribution of blazars to the large-scale isotropic gamma-ray background (IGRB) by jointly analyzing the measured source count distribution ($\log N$-$\log S$) of blazars and the measured intensity and anisotropy of the IGRB. We find that these measurements point to a consistent scenario in which unresolved blazars make $\lesssim 20\%$ of the IGRB intensity at 1–10 GeV while accounting for the majority of the measured anisotropy in that energy band. These results indicate that the remaining fraction of the IGRB intensity is made by a component with a low level of intrinsic anisotropy. We determine upper limits on the anisotropy from nonblazar sources, adopting the best-fit parameters of the measured source count distribution to calculate the unresolved blazar anisotropy. In addition, we show that the anisotropy measurement excludes some recently proposed models of the unresolved blazar population.

Figure 1

Left: Spectral index vs integrated flux above 100 MeV for the sources in the 1FGL catalog [11] located at Galactic latitudes $|b|>10°$. Right: The same for an integrated flux above 1 GeV. The bold lines denote an analytical calculation of the detection threshold (see text for more details).

Figure 2

Anisotropy measurements with $1\sigma$ uncertainties (light gray crosses) from Ref. 5 and $2\sigma$ upper limits (black bars) from this work on the anisotropy from nonblazar components in different energy bands. The points have been divided by the square of the energy bin width $(\Delta E{)}_i^2$ and multiplied by $E_i^4$, with $E_i$ the logarithmic center of the energy bin. The upper limits are slightly displaced in energy for clarity.

Figure 3

Left: Constraints on blazar $\log N$-$\log S$ parameters (break flux, $S_{\mathrm{b}}$, and faint-end slope, $\alpha$) from the intensity and anisotropy of the IGRB. Regions in which blazars provide 100% of the observed IGRB anisotropy and mean intensity in the 1–10 GeV energy band are shown; the widths of the regions indicate the 68% confidence intervals. Below these regions blazars overproduce the anisotropy and mean intensity. Labeled contours show the fraction of the blazar contribution to the IGRB intensity. The best-fit $1\sigma$ parameter region from the Fermi source count analysis [4] is marked, along with the best-fit $S_{\mathrm{b}}$ [4] (dot-dashed line). Right: Expanded view around the region of parameter space in the left panel where blazars contribute 100% of both the measured IGRB anisotropy and intensity.

Figure 4

Cumulative contribution of blazars in linear (top) and log (bottom) scale to the IGRB anisotropy (dashed) and intensity (solid) for the Fermi best-fit $\log N$-$\log S$ ($E>100\mathrm{MeV}$) as a function of source intensity.