New dissipation mechanisms from multilevel dark matter scattering

Multilevel dark matter with diagonal and off-diagonal interactions shows a rich phenomenology in its self-scattering. If the interactions are mediated by a particle that is less massive than the dark matter, the Sommerfeld effect can lead to resonant enhancement of the scattering. For mediators lighter than the level separation, dark matter particles can upscatter to excited states and deexcite by emitting these mediators. We compute these cross sections, both above and below the kinematic threshold, in a generic two-component dark matter model and identify the large inelastic cross section as a result of maximal mixing between the two states. A new route for cooling of large dark matter halos and a new drag force between two colliding halos are identified and shown to arise purely from the inelastic scattering.

Figure 1

Typical Feynman diagrams for elastic self-scattering of DM in the ground state (left) and for upscattering induced decay (right). The intermediate vertical lines represent multiple exchanges of scalar $\rho$ particles in the nonrelativistic limit of the incoming DM particles.

Figure 2

The ${\chi }_1{\chi }_1\to {\chi }_1{\chi }_1$ cross section in the regime ${\mu }_1{v}^2/2<2\mathrm{\Delta }$, i.e., below threshold for our two-level SIDM model. This is approximately the same as in a single-state SIDM model but with the potential given by Eq. (9).

Figure 3

Left: The eigenvalues ${\tilde{V}}_1$ (blue solid line) and ${\tilde{V}}_2$ (red dashed line) of the rotated potential matrix as in Eq. (9). The mixing angle $\theta (r)$ is shown as the green dotted line. The unit on the vertical axis is arbitrary. Note that the eigenvalues remain well separated and there is no level crossing, which explains why the evolution is adiabatic. The parameters chosen here correspond to an above-threshold scenario, but the behavior of the eigenvalues does not depend on that. Right: Real and imaginary parts of the off-diagonal component of the scattering matrix function, Re(${\mathit{S}}_{12}(r)$) (blue solid line) and Im(${\mathit{S}}_{12}(r)$) (red dashed line), as well as the instantaneous mixing angle $\theta (r)$ (green dotted line). Note that $\theta (r)$ reaches $\pi /4$ at $r\to 0$, shown as a grey dotted-dashed line. The real and imaginary parts of ${\mathit{S}}_{12}(r)$ are shown multiplied by factors of 100 and 10, respectively, for visual clarity. Note that the off-diagonal component ${\mathit{S}}_{12}(r)$ deviates from its value at large $r$ only at $r\lesssim 50$, where the eigenvalues are well separated but the mixing is maximal. This shows that any nonzero inelastic scattering, that comes from a nonzero ${\mathit{S}}_{12}(r)$, is a result of maximal mixing and not level mixing or lack of adiabaticity. The velocity was chosen to be $100\mathrm{km}/\mathrm{s}$ (above threshold).

Figure 4

Left: The velocity dependence of the elastic self-scattering cross section for different values of $m_{\rho }$ as indicated in the figure. Right: The elastic transfer and viscosity cross sections for a particular choice of the parameter values: $M=200\mathrm{GeV},\alpha =0.01,v=10\mathrm{km}/\mathrm{s}$. The grey dashed line shows the analytical estimate of the Born cross section for the two-level model, obtained using the one-level equivalent proposed in Ref. [45] with the substitution $\alpha \to 2\alpha$ explained in the text, and the numerical results are in good agreement with the analytical estimate of the Born cross section in the large $m_{\rho }$ limit. The resonant values of $m_{\rho }$, given in Eq. (17), similarly agree very well.

Figure 5

The ratio of the inelastic to the elastic cross sections in the purely off-diagonal interaction DM model, with parameters as indicated in the figure, showing that the inelastic cross section can be much smaller or much larger than the elastic cross section in strongly off-diagonal models.

Figure 6

The radial dependence of the cooling rate $dE/dt$ [see Eq. (22)] of a Virgo-cluster-size halo with a scale radius $r_s=560\mathrm{kpc}$ and density ${\rho }_s=3.2\times {10}^5{\mathrm{M}}_{\odot }/{\mathrm{kpc}}^3$. The chosen DM parameters are $M=10\mathrm{GeV}$, $\mathrm{\Delta }={10}^{-4}\mathrm{GeV}$, and ${\sigma }_{\mathrm{in}}/M=1{\mathrm{cm}}^2/\mathrm{g}$.