Limits on dark matter annihilation in prompt cusps from the isotropic gamma-ray background

Recent studies indicate that thermally produced dark matter will form highly concentrated, low-mass cusps in the early universe that often survive until the present. While these cusps contain a small fraction of the dark matter, their high density significantly increases the expected $\gamma$-ray flux from dark matter annihilation, particularly in searches of large angular regions. We utilize 14 years of Fermi-LAT data to set strong constraints on dark matter annihilation through a detailed study of the isotropic $\gamma$-ray background, excluding with 95% confidence dark matter annihilation to $b\overline{b}$ final states for dark matter masses below 120 GeV.

Figure 1

Upper limits on the WIMP annihilation cross section, accounting for prompt cusps that form at early times and persist throughout the bulk of both the Milky Way and extragalactic halos. The dotted line shows the expected thermal WIMP annihilation cross section [24]. For dark matter with the thermal cross section, constraints from the isotropic $\gamma$-ray background obtained from our analysis exclude at 95% confidence masses below 120 GeV annihilating to $b\overline{b}$ and masses around 90 GeV annihilating to ${\mathrm{W}}^{+}{\mathrm{W}}^{-}$. Constraints lie near the thermal cross section for ${\tau }^{+}{\tau }^{-}$.

Figure 2

Power spectra of dark matter density variations, evaluated in linear theory at $z=31$ and shown in the dimensionless form, $\mathcal{P}(k)\equiv [k^3/(2{\pi }^2)]P(k)$. The black curve shows the prediction for idealized cold dark matter. Density variations in WIMP models are smoothed by thermal motion in the dark matter, imposing a small-scale cutoff in $\mathcal{P}(k)$ that depends on the particle mass $m_{\mathrm{DM}}$ and the temperature $T_{\mathrm{d}}$ at which it decoupled from the Standard Model plasma. The colored curves show $\mathcal{P}(k)$ for such scenarios; different colors correspond to different $m_{\mathrm{DM}}$ while different line styles correspond to different values of $T_{\mathrm{d}}$.

Figure 3

The effective dark matter density ${\rho }_{\mathrm{eff}}$ contributed by prompt cusps, relevant to the dark matter annihilation rate [see Eq. (7)], as a function of the particle mass $m_{\mathrm{DM}}$. ${\rho }_{\mathrm{eff}}$ is the annihilation $J$ factor (proportional to the annihilation rate) per mass of dark matter, or equivalently, the mass-weighted average dark matter density. Different colors correspond to different kinetic decoupling temperatures.

Figure 4

Integrated energy flux from annihilation in prompt cusps, as a function of angle from the Galactic Center. We adopt here a 100 GeV WIMP that decouples at 30 MeV and annihilates into $b\overline{b}$ with a cross section of $⟨\sigma v⟩={10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$.

Figure 5

Sensitivity of the annihilation signal from Galactic cusps to the mass $M_{200c}$ and initial NFW concentration $c$ of the Milky Way halo. We consider a 100 GeV WIMP that decouples at 30 MeV. The color scale (with contour lines every 10 percent) indicates the fractional change in the sky-averaged gamma-ray flux from Galactic cusps, compared to the fiducial parameters $c=8.7$ and $M_{200c}={10}^{12}{M}_{\odot }$. For comparison, the dashed and dotted curves mark the 68 and 95 percent confidence ranges, respectively, of the observational inference in Ref. [51]. Although the annihilation signal is stronger for higher $M_{200c}$ and higher $c$, its variation remains at the 10 percent level across the range of likely parameters.

Figure 6

Differential energy flux from annihilation in prompt cusps, averaged over latitudes $|b|>20\mathrm{deg}$. and longitudes $|l|>80\mathrm{deg}$. As in Fig. 4, we assume a 100 GeV WIMP that decouples at a temperature of 30 MeV and annihilates into $b\overline{b}$ with a cross section of $⟨\sigma v⟩={10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$.

Figure 7

Correlation coefficients for the 15 energy bins of the isotropic component. The diagonal is valued unity by definition. Otherwise nearby energy bins typically have strong positive correlations.

Figure 8

The diffuse isotropic emission (black points) and the results of our fit to it (black curve). This emission includes contributions from cosmic rays that have been misidentified as $\gamma$ rays by the Fermi-LAT instrument, $\gamma$-ray contributions from extragalactic star-forming activity, blazar and nonblazar AGN source classes, as well as potential contributions from dark matter annihilation. We find that our combined model, including astrophysical $\gamma$-ray emission (blue and orange curves) and misidentified cosmic rays (green curve), fits the observed data without any evidence for an excess from dark matter annihilation. Here we show the 95 percent confidence limit on the emission from dark matter with a mass of 100 GeV annihilating into $b$ quarks (dashed curve).

Figure 9

The three panels on the left display the marginalized posterior distribution for the fit parameters of the astrophysical model. Dashed black lines show the fit without dark matter while the solid blue lines show the result of the fit for a fixed dark matter mass of 100 GeV and annihilation into $b$ quarks. The rightmost panel displays the marginalized ${\chi }^2$ as a function of the dark matter annihilation cross section. The blue (yellow) line corresponds to a dark matter mass of 100 (300) GeV. The vertical dotted lines indicate the 95% upper limit on the dark matter annihilation cross section.

Figure 10

Posterior distribution of the three parameters of the astrophysical model and the dark matter annihilation cross section, for a dark matter mass of 100 GeV. The inner and outer contours enclose 68 and 95 percent of the distribution, respectively.

Figure 11

Upper limits on dark matter annihilation into $b$ quarks. The solid curve is our fiducial result, while the other blue curves test the sensitivity of the result to different assumptions (see the text for more detail). The dotted black line shows the annihilation cross section expected for a thermal WIMP [24].

Figure 12

Comparison with other results. This figure plots the upper limit on $⟨\sigma v⟩$ as a function of the dark matter particle mass $m_{\mathrm{DM}}$ for the case of annihilation into $b$ quarks. The solid curve shows our constraint using prompt cusps, while the dashed curve shows the Fermi Collaboration’s constraint using a halo model [33]; both of these constraints are based on measurements of the IGRB. The dot-dashed curve shows the Fermi Collaboration’s limit from dwarf spheroidal galaxies [61]. The shaded region is compatible with an annihilation origin for the Galactic Center $\gamma$-ray excess [62].