Sommerfeld-enhanced dark matter (DM) annihilation through s-wave has been widely considered as a consistent explanation for both the observed cosmic-ray (CR) positron excess and the DM thermal relic density. However, as the s-wave Sommerfeld-enhanced annihilation cross section increases monotonically with decreasing DM velocity, severe constraints appear from the data of gamma rays from dwarf spheroidal satellite galaxies (dSphs) and the cosmic microwave background (CMB), as the relevant typical DM velocities are even lower than that in the Galactic halo. In this work, we consider Sommerfeld-enhanced p-wave DM annihilation where the DM annihilation cross section can be enhanced at certain velocities but eventually be highly suppressed when the DM velocities become extremely low. We calculate the velocity-dependent astrophysics factors (J-factors) for the Sommerfeld-enhanced p-wave DM annihilation for fifteen nearby dSphs. Taking the channel of DM annihilating into 4μ through two light mediators as an example, we show that there are parameter regions where this mechanism can account for the CR positron excess and the DM relic density, while being compatible with the constraints from dSphs gamma rays measured by Fermi-LAT and that from the CMB measured by PLANCK.

Dark matter (DM) annihilation in the galactic halo can be enhanced relative to that in the early Universe due to the Breit–Wigner enhancement, if the DM particles annihilate through a narrow resonance. Although the s-wave Breit–Wigner enhancement can provide a consistent explanation for both the observed cosmic-ray (CR) positron excess and the DM thermal relic density, it is severely constrained by the observations of gamma rays from dwarf spheroidal satellite galaxies (dSphs) and the cosmic microwave background (CMB), which have relatively lower allowed DM annihilation cross section and typical DM velocities than that in the galactic halo. Furthermore, in the s-wave Breit–Wigner enhancement, the case where the resonance mass is below a threshold (twice the DM mass) is ruled out due to the monotonically increasing annihilation cross section with decreasing DM velocity. In this work, we consider Breit–Wigner enhanced p-wave DM annihilation. We explore the parameter regions which can simultaneously account for the CR positron excess and DM thermal relic density without violating the constraints from dSphs gamma rays and CMB. We show that the velocity-dependent cross section in this scenario can peak around the typical DM velocity in the galactic halo for the resonance mass both above and below the threshold. Moreover, the highly suppressed annihilation cross section at extremely low DM velocity can evade the constraints from dSphs gamma rays and CMB easily, which results in larger allowed parameter regions than that in the s-wave case.