Dark matter constraints from observations of 25 Milky Way satellite galaxies with the Fermi Large Area Telescope

The dwarf spheroidal satellite galaxies of the Milky Way are some of the most dark-matter-dominated objects known. Due to their proximity, high dark matter content, and lack of astrophysical backgrounds, dwarf spheroidal galaxies are widely considered to be among the most promising targets for the indirect detection of dark matter via $\gamma$ rays. Here we report on $\gamma$-ray observations of 25 Milky Way dwarf spheroidal satellite galaxies based on 4 years of Fermi Large Area Telescope (LAT) data. None of the dwarf galaxies are significantly detected in $\gamma$ rays, and we present $\gamma$-ray flux upper limits between 500 MeV and 500 GeV. We determine the dark matter content of 18 dwarf spheroidal galaxies from stellar kinematic data and combine LAT observations of 15 dwarf galaxies to constrain the dark matter annihilation cross section. We set some of the tightest constraints to date on the annihilation of dark matter particles with masses between 2 GeV and 10 TeV into prototypical standard model channels. We find these results to be robust against systematic uncertainties in the LAT instrument performance, diffuse $\gamma$-ray background modeling, and assumed dark matter density profile.

Figure 1

Known dwarf spheroidal satellite galaxies of the Milky Way overlaid on a Hammer-Aitoff projection of a 4-year LAT counts map ($E>1\text{GeV}$). The 15 dwarf galaxies included in the combined analysis are shown as filled circles, while additional dwarf galaxies are shown as open circles.

Figure 2

Histogram of the bin-by-bin LAT likelihood function used to test for a putative $\gamma$-ray source at the position of the Draco dwarf spheroidal galaxy. The bin-by-bin likelihood is calculated by scanning the integrated energy flux of the putative source within each energy bin (equivalent to scanning in the spectral normalization of the source). When performing this scan, the flux normalizations of the background sources are fixed to their optimal values as derived from a maximum likelihood fit over the full energy range. Within each bin, the color scale denotes the variation of the logarithm of the likelihood with respect to the best fit value of the putative source flux (truncated at $-\mathrm{\Delta }\log \mathcal{L}>10$). Upper limits on the integrated energy flux are set at 95% CL within each bin using the delta-log-likelihood technique and are largely independent of the putative source spectrum.

Figure 3

Bin-by-bin integrated energy-flux upper limits and expected sensitivities at 95% CL for each dwarf spheroidal galaxy. The expected sensitivities are calculated from 2000 realistic Monte Carlo simulations of the null hypothesis. The median sensitivity is shown by the dashed black line while the 68% and 95% containment regions are indicated by the shaded bands.

Figure 4

Distribution of TS values from individual fits of a 25 GeV $b\overline{b}$ annihilation spectrum to the null hypothesis generated from 50000 realistic Monte Carlo simulations and 7500 random blank-sky locations at high latitude in the LAT data. The distribution of TS values derived from simulations of individual ROIs is well matched to the expectations from the asymptotic theorem of Chernoff [70], while the distribution derived from random sky positions shows an excess at large TS values.

Figure 5

Constraints on the dark matter annihilation cross section at 95% CL derived from a combined analysis of 15 dwarf spheroidal galaxies assuming an NFW dark matter distribution (solid line). In each panel bands represent the expected sensitivity as calculated by repeating the combined analysis on 300 randomly selected sets of blank fields at high Galactic latitudes in the LAT data. The dashed line shows the median expected sensitivity while the bands represent the 68% and 95% quantiles. For each set of random locations, nominal J-factors are randomized in accord with their measurement uncertainties. Thus, the positions and widths of the expected sensitivity bands reflect the range of statistical fluctuations expected both from the LAT data and from the stellar kinematics of the dwarf galaxies. The most significant excess in the observed limits occurs for the $b\overline{b}$, channel between 10 and 25 GeV with $\mathrm{TS}=8.7$ (global $p$-value of $p\approx 0.08$).

Figure 6

Comparison of constraints on the dark matter annihilation cross section (${\tau }^{+}{\tau }^{-}$ channel) at 95% CL derived from a combined analysis excluding three ultrafaint dwarf galaxies: Segue 1, Ursa Major II, and Willman 1 (solid line). The expected sensitivity is also calculated excluding these three ultrafaint dwarf galaxies and is represented in the same manner as in Fig. 5.

Figure 7

Comparison of constraints on the dark matter annihilation cross section (${\tau }^{+}{\tau }^{-}$ channel) derived from the combined maximum likelihood and the combined Bayesian analyses of 15 dwarf spheroidal galaxies. The expected sensitivity for the maximum likelihood analysis is represented similarly to Fig. 5. The observed Bayesian limits are consistent with the expected Bayesian sensitivity bands (not shown), which are likewise higher than those of the maximum likelihood analysis.

Figure 8

Comparison of constraints on the dark matter annihilation cross section ($b\overline{b}$ channel) derived from the LAT combined analysis of 15 dwarf galaxies (assuming a NFW profile), 48-hour observations of Segue 1 by VERITAS (assuming an Einasto profile) [85], and 112-hour observations of the Galactic center by H.E.S.S. (assuming an Einasto profile) [86]. In the interest of a direct comparison, we also show the LAT constraints derived for Segue 1 alone assuming an Einasto dark matter profile consistent with that used by VERITAS [85]. For this rescaling, the J-factor of Segue 1 is calculated over the LAT solid angle of $\mathrm{\Delta }\mathrm{\Omega }\sim 2.4\times 10^{-4}\mathrm{sr}$ and yields a rescaled value of $1.7\times 10^{19}{\mathrm{GeV}}^2{\mathrm{cm}}^{-5}\text{sr}$ (uncertainties on the J-factor are neglected for comparison with VERITAS).