Self-Heating Dark Matter via Semiannihilation

The freeze-out of dark matter (DM) depends on the evolution of the DM temperature. The DM temperature does not have to follow the standard model one, when the elastic scattering is not sufficient to maintain the kinetic equilibrium. We study the temperature evolution of the semiannihilating DM, where a pair of the DM particles annihilate into one DM particle and another particle coupled to the standard model sector. We find that the kinetic equilibrium is maintained solely via semiannihilation until the last stage of the freeze-out. After the freeze-out, semiannihilation converts the mass deficit to the kinetic energy of DM, which leads to nontrivial evolution of the DM temperature. We argue that the DM temperature redshifts like radiation as long as the DM self-interaction is efficient. We dub this novel temperature evolution as self-heating. Notably, the structure formation is suppressed at subgalactic scales like keV-scale warm DM but with GeV-scale self-heating DM if the self-heating lasts roughly until the matter-radiation equality. The long duration of the self-heating requires the large self-scattering cross section, which in turn flattens the DM density profile in inner halos. Consequently, self-heating DM can be a unified solution to apparent failures of cold DM to reproduce the observed subgalactic scale structure of the Universe.

Figure 1

A schematic figure showing the DM interactions under consideration and their relative strength. We assume that the self-interaction is the strongest interaction, while the pair annihilation is the weakest and irrelevant.

Figure 2

Evolution of the DM yield. The black solid line is $Y_{\chi }$, while the black dotted line is $Y_{\chi }^{\mathrm{eq}}(x_{\chi })\mathcal{J}(x_{\chi },x)$. The blue lines are the same except that $T_{\chi }=T_{\varphi }$ is kept by hand, whose asymptotic value is indicated by the horizontal gray line.

Figure 3

Evolution of the DM temperature normalized by the SM one. Different colors represent different values of $m_{\varphi }/m_{\chi }$, while the invariant amplitude is fixed to reproduce $({\sigma }_{\mathrm{semi}}{v}_{\mathrm{rel}})=6\times {10}^{-26}{\mathrm{cm}}^3/\mathrm{s}$ for $m_{\varphi }/m_{\chi }=0$ (Fig. 2). The solid lines are the numerical results, while the dashed lines are the analytic estimations of the asymptotic value, Eq. (15). The thin red line shows the adiabatic cooling: $T_{\chi }/T=x_{\mathrm{fo}}/x$ (for the definition of $x_{\mathrm{fo}}$, see Ref. [30]).

Figure 4

Asymptotic value of the temperature ratio ${(T_{\chi }/T)}_{\mathrm{asy}}$ as a function of the semiannihilation cross section in the nonrelativistic limit. The dots are the numerical results ($T_{\chi }/T$ at $x={10}^5$), while the solid line is the analytic estimation given in Eq. (15). Since ${(T_{\chi }/T)}_{\mathrm{asy}}$ is inversely proportional to the freeze-out temperature, it increases logarithmically as the cross section increases.