Optimal observing strategies for velocity-suppressed dark matter annihilation

Numerous particle models for the cosmological dark matter feature a pair-annihilation rate that scales with powers of the relative velocity between the annihilating particles. As a result, the annihilation rate in the central regions of a dark matter halo can be significantly lower than at the halo’s periphery for particular ambient gravitational potentials. While this might be offset by an increasing dark matter pair number density in the inner halo, it raises the question; what angular region for dark matter models with velocity-suppressed annihilation rates optimizes the signal to noise ratio? Here, we consider simplified background models for galactic and extragalactic targets and demonstrate that the optimal observing strategy varies greatly case by case. Generally, a bright central source warrants an annular region of interest, while a flatter background warrants as large as possible an angular region, possibly including the central regions.

Figure 1

Geometric parameters used in J-factor calculation. EG is a generic extragalactic body that hosts DM; $r_d$ is the displacement between our star, Sol, and the center of EG; $l$ is the displacment between Sol and a point in EG’s DM halo; $b$ is the angle made between $r_d$ and $l$; and $r$ is the radial distance from the center of EG.

Figure 2

The shaded annulus region is the area in which we evaluate the signal to noise ratio.

Figure 3

$\mathcal{J}$ per solid angle as a function of the angle $b$ for different annihilation channels, normalized to their respective values at $b={10}^{-3}$ degrees. The contribution to the J-factor from the velocity-dependent $p$- and $d$-wave channels extends to larger angles when compared to the velocity-independent $s$-wave case.

Figure 4

$\frac{\mathcal{J}}{N_{\mathrm{tot}}^{1/2}}$ for $s$-, $p$-, and $d$-wave annihilation for an extragalactic source using an NFW density profile with $\sigma =0.05°$ and $\eta =20$. The black dot is the field of view used in a Fermi-LAT survey of Milky Way (MW) satellites [18, 34], while the orange and yellow dots correspond to observations of M31 using Fermi-LAT [15, 16].

Figure 5

$\frac{\mathcal{J}}{N_{\mathrm{tot}}^{1/2}}$ for $s$- and $p$-wave annihilation for an extragalactic source using a Burkert profile with $\sigma =0.05°$ and $\eta =3$. The black dot is the field of view used in a Fermi-LAT survey of MW satellites [18, 34], while the orange and yellow dots correspond to observations of M31 using Fermi-LAT [15, 16].

Figure 6

$\frac{\mathcal{J}}{N_{\mathrm{tot}}^{1/2}}$ for $s$-, $p$-, and $d$-wave annihilation in the Galactic Center with Fermi-LAT background model ${{}^S\mathrm{S}}^Z{4}^R{20}^T{150}^{C}5$ in the $-5°\le b\le 5°$ Galactic longitudinal window [33] (Fig. 21, top-left panel). The green dot is the field of view used by a Fermi-LAT survey of the Galactic Center looking for $p$-wave annihilation [37, 38]. The red dot corresponds to a search for $s$-wave annihilation using Fermi-LAT with a two degree plane mask [36].

Figure 7

$\frac{\mathcal{J}}{N_{\mathrm{tot}}^{1/2}}$ for $s$-, $p$-, and $d$-wave annihilation in the Galactic Center with Fermi-LAT background model ${{}^S\mathrm{S}}^Z{4}^R{20}^T{150}^{C}5$ in the latitudinal window $-30°\le l\le 30°$ [33] (Fig. 20, middle panel). The green dot is the field of view used by a Fermi-LAT survey of the Galactic Center looking for $p$-wave annihilation [37, 38]. The red dot corresponds to a search for $s$-wave annihilation using Fermi-LAT with a two degree plane mask [36].