Among the most viable mechanisms of cusp-core transformation that require changes to the assumed cosmogony is one that was proposed specifically as a possible solution to the cusp-core problem. It proposes that the DM is in fact not collisionless but self-interacting (SIDM; Spergel & Steinhardt 2000; Yoshida et al. 2000; Davé et al. 2001; Colín et al. 2002; Vogelsberger, Zavala & Loeb 2012; Rocha et al. 2013; see Tulin & Yu 2018 for a review). In SIDM, particles can exchange energy and momentum through elastic scattering, causing an outside-in energy redistribution within the centre of DM haloes, resulting in the formation of an isothermal core. The time-scale on which an initially cuspy SIDM halo forms a flat and isothermal core is roughly given by the time it takes for each DM particle in the inner halo to scatter at least once (Vogelsberger et al. 2012; Rocha et al. 2013). The strength of the self-interaction in SIDM models is parametrized in terms of the momentum transfer cross-section per unit mass, σT/mχ. Depending on the specific SIDM model, σT/mχ can either be constant or dependent on the relative velocity between the two scattering DM particles. SIDM is an efficient mechanism of cusp-core transformation in dwarf-size haloes for $\sigma _T/m_\chi \gtrsim 1\, {\rm cm^2g^{-1}}$, whereas SIDM haloes are virtually indistinguishable from CDM haloes if $\sigma _T/m_\chi \lesssim 0.1\, {\rm cm^2g^{-1}}$ (Zavala, Vogelsberger & Walker 2013). The most stringent and precise constraints on the self-interaction cross-section have been put on the scales of galaxy clusters (e.g. Robertson, Massey & Eke 2017; Robertson et al. 2019) and large elliptical galaxies (Peter et al. 2013), where observations require that $\sigma _T/m_chi \lesssim 1\, {\rm cm^2g^{-1}}$. On smaller scales, Read, Walker & Steger (2018) concluded that $\sigma _T/m_\chi \lesssim 0.6\, {\rm cm^2g^{-1}}$, based on their findings that the central density profile of the MW dwarf spheroidal galaxy Draco is cuspy (see also the SIDM results of Valli & Yu 2018). Moreover, based on a DM only analysis of the updated too-big-to-fail problem, Zavala et al. (2019) concluded that SIDM models with a constant cross-section of $\sigma _T/m_\chi \sim 1\, {\rm cm^2g^{-1}}$ fail to explain the apparently large central densities of the host haloes of the ultra-faint satellites of the MW (Errani, Peñarrubia & Walker 2018). It should be pointed out that the constraints on σT/mχ on the scale of dwarf galaxies are affected by significantly larger systematic uncertainties than on the scales of galaxy clusters or elliptical galaxies. Moreover, Zavala et al. (2019) demonstrate that SIDM with a strongly velocity-dependent self-interaction cross-section may provide a natural explanation for the observed diversity in the rotation curves of the MW dwarf spheroidals (see also Correa 2021). The strong dependence of the self-interaction cross-section on the typical DM velocities would create a bimodal distribution of rotation curves in the MW satellites in which the heavier haloes have constant density cores while the lighter haloes have undergone gravothermal collapse and have very steep central cusps as a consequence. The same mechanism of gravothermal collapse might be accelerated by tidal interactions in the environment of the MW leading to an agreement between constant cross-section SIDM models with $\sigma _T/m_\chi \sim 3\, {\rm cm^2g^{-1}}$ and the internal kinematics of MW satellites (e.g. Kahlhoefer et al. 2019; Sameie et al. 2020).
Citation: Robertson, Massey & Eke 2017
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Citation: Robertson et al. 2019
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