one contributes relic abundance Ω
α
h
2
to the total relic abundance Ω
DM
h
2
where Ω
DM
h
2
=
P
α
Ω
α
h
2
≈ 0.12 [13] and h is the Hubble constant. Theoretical models on the two-
component DM (2DM) scenario have been proposed recently [14–19]. Works regard the
2DM models on the direct and indirect searches can be also found in refs. [20–22] and
references therein. In addition, cosmological N -body simulation incorporates 2DM that
leads to the large scale structure which agrees the observation has been done recently [23].
In this work, we study the DM evolution in the Sun under the 2DM scenario with
particle species χ and ξ. Recent studies on solar captured 2DM are only a few, and, to our
understanding, such studies consider the evolution of two species that are independent in
the Sun. On the other hand, the collision between χ and ξ does not account for the DM
capture in the Sun. The collisions among DM particles are generally characterized as DM
self-interactions. In the 1DM scenario, DM self-interaction [24–29] is addressed to alleviate
the discrepancy between the collisionless N -body simulation and the observations. Such
inconsistency arises from small-scale structure [30–39] could be resolved by imposing the
constraint 0.1 < σ
DM
/m
DM
< 10 cm
2
g
−1
, where σ
DM
and m
DM
are DM self-interacting
cross section and mass respectively. In addition, by incorporating baryonic effect, that the
problem of diverse galactic rotation curves [40, 41] could be mitigated with the constraint
3 < σ
DM
/m
DM
< 6 cm
2
g
−1
[42–45].
The study of DM captured by the Sun has been investigated in refs. [46–51]. Updated
calculation including the non-zero momentum transfer and implication for DM-electron
capture are also indicated in ref. [52]. Our work is based on the earlier ones, and we further
extend the framework to the 2DM scenario. The contribution to the capture rate from DM
self-interaction denotes the self-capture in general. Furthermore, in the 2DM scenario, a
plausible situation is that aside from χχ and ξξ collisions, the self-interactions can also
happen between χ and ξ, the heterogeneous self-interaction. In this case, χξ collision plays
a role of heterogeneous self-capture. In the presence of heterogeneous self-interaction, extra
coupling terms should be incorporated in the evolution equations. The evolution processes
of χ and of ξ cannot be treated separately. In our analysis, we found that the number
of the sub-dominant DM specie is subject to a correction from the dominant DM specie.
Nevertheless, the heterogeneous self-interaction not only increases the capture rate, it also
responsible for the self-evaporation and self-ejection effects.
The general formalism to calculate the 2DM evolution in the Sun is given in this paper.
Full expressions for the rates of DM-nucleus capture, evaporation and contributions from
DM self-interaction including heterogeneous effects are presented. Although the framework
shown here focuses on the 2DM scenario, it can be easily generalized to any nDM scenario.
Unless subtle interaction is specified in the nDM case, e.g. 3-body scattering, the results
provided in this paper are generally applied to any 2-body scattering with different masses.
As a remark, when the 2DM scenario is invoked, co-annihilation could happen if the masses
are nearly degenerate between χ and ξ [53–55]. However, in the later analysis, we scan a
broad range of DM mass spectrum. In most of the situation, the masses are not degenerate.
Thus, the co-annihilation can be considered irrelevantly. Omitting it from our discussion
is reasonable. Works in regard to co-annihilation and its implication for the solar-captured
DM can be found in refs. [56, 57].
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