Escalating core formation with dark matter self-heating

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Escalating core formation with dark matter self-heating

Ayuki Kamada and Hee Jung Kim

Phys. Rev. D 102, 043009 – Published 12 August 2020

Abstract

Exothermic scatterings of dark matter (DM) produce DM particles with significant kick velocities inside DM halos. In collaboration with DM self-interaction, the excess kinetic energy of the produced DM particles is distributed to the others, which self-heats the DM particles as a whole. The DM self-heating is efficient towards the halo center, and the heat injection is used to enhance the formation of a uniform density core inside halos. The effect of DM self-heating is expected to be more significant in smaller halos for two reasons: 1) the exothermic cross section times the relative velocity, $⟨ σ_{exo} v_{rel} ⟩$ , is constant; 2) and the ratio of the injected heat to the velocity dispersion squared gets larger toward smaller-size halos. For the first time, we quantitatively investigate the core formation from DM self-heating for halos in a wide mass range ( $10^{9} - 10^{15} M_{⊙}$ ) using the gravothermal fluid formalism. Notably, we demonstrate that the core formation is sharply escalating toward smaller-size halos by taking the self-heating DM (i.e., DM that semiannihilates and self-interacts) as an example. We show that the sharp escalation of the core formation may cause a tension in simultaneously explaining the observed central mass deficit of Milky Way satellites and field dwarf/low surface brightness spiral galaxies. We expect DM self-heating to be present also in other models that exhibit exothermic scatterings and self-interaction of DM, which can appreciably contribute to the core formation of DM halos.

Received 6 December 2019
Revised 28 February 2020
Accepted 28 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.043009

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Formation & evolution of stars & galaxies Particle dark matter

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Ayuki Kamada ^1,* and Hee Jung Kim ^2,†

¹Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon 34126, Korea
²Department of Physics, KAIST, Daejeon 34141, Korea

^*akamada@ibs.re.kr
^†hyzer333@kaist.ac.kr

Article Text

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Vol. 102, Iss. 4 — 15 August 2020

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Images

Figure 1
Left panel—Present density profiles of SHDM halos. Colored lines represent different masses of halos; a galaxy cluster (green), a field dwarf/LSB galaxy (blue), and a MW satellite galaxy (red). The NFW profile (dotted black) is used as initial condition; we use the concentration-mass relation from Ref. [59] to determine $ρ_{s}$ and $r_{s}$ . We take the fudge factor to be $b = 1$ . Solid lines represent the SHDM mass ( $m = 0.3 MeV$ ) that reproduce a similar core size as the inferred pure SIDM cross section for field dwarf/LSB galaxies, $σ_{self} / m = 1. 9_{- 0.4}^{+ 0.6} {cm}^{2} / g$ [25]. Note that for given cross sections, rescaling $b$ is equivalent to rescaling the SHDM mass $m$ [see Eq. (10)]; e.g., if we take $b = 10$ , the solid curves represent the result for $m = 3 MeV$ . The core formation is efficient toward smaller-size halos. For galaxy clusters, the resultant profiles for $m = 0.3 MeV$ and $m = 3 MeV$ are almost identical; this is because the effect of DM self-heating is negligible, and the core formation is predominantly determined by the effect of DM self-scattering. In the case of $m = 3 MeV$ , the core density of the galaxy cluster is lower than that of the field dwarf/LSB galaxy. This is because the core formation is still dominated by the self-scattering effect, and the self-scattering time scale [Eq. (6)] is longer toward smaller-size halos, $t_{self} \propto M_{200}^{- 0.08}$ . Right panel—Same as the left panel but for the one-dimensional velocity dispersion. $t_{G} (r_{s}) = 1 / \sqrt{4 π G ρ_{NFW} (r_{s})}$ is the gravitational time scale with $ρ_{NFW} (r_{s}) = ρ_{s} / 4$ .
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Figure 2
Left panel—Halo-mass dependence of resultant core densities of SHDM halos (in orange). We took the evolution time that is determined by the virial mass of a halo [see Appendix pp1]. Gray curves represent the case of pure SIDM; the gray curves can be understood by noting that $t_{self}$ [Eq. (6)] is shorter for larger-size halos, while $(t_{age} - t_{*})$ is also shorter for larger-size halos. The data points are the core densities predicted from the inferred values of pure $σ_{self} / m$ from the observations on field dwarf (red)/LSB (blue) galaxies, and galaxy clusters (green) [25]. The core formation is sharply escalating toward smaller-size halos, which appears to disfavor SHDM as a solution to small-scale issues; while the SHDM mass $m = 0.3 MeV$ (solid orange) is preferred to explain the core size of field dwarf/LSB galaxies, the central densities of MW satellites [54] (black circle) require the SHDM mass to be heavier than 3 MeV (dashed orange). This is in contrast to the pure SIDM; there is a lower limit on the core density since the SIDM halos undergo the gravothermal collapse at present for $σ_{self} / m ≳ 10 {cm}^{2} / g$ . The red line represents the analytic estimation given in Eq. (11). Note that for given cross sections, rescaling $b$ would be equivalent to rescaling the SHDM mass $m$ [see Eq. (10)]; e.g., if we take $b = 10$ , the solid orange curve would represent the result for $m = 3 MeV$ . Right panel—Same as the left panel but for the resultant core radius.
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Figure 3
The halo-mass dependence of the halo formation time $t_{*}$ . The assignment of the formation time is based on the spherical collapse model, and the observed CDM density fluctuations. The solid curve corresponds to the condition $2 σ_{M} (t_{*}) = δ_{c}$ . The dashed curve is the one that we use in this work, which is determined by the condition $3 σ_{M} (t_{*}) = δ_{c}$ .
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Figure 4
Left panel—Time evolution of DM density $ρ$ of a MW satellite galaxy ( $M_{200} = 10^{9} M_{⊙}$ ). NFW profile ( $ρ_{s} = 0.02 M_{⊙} / {pc}^{3}$ , $r_{s} = 1.26 kpc$ ) is used as the initial condition. Heat conduction effect through self-interaction of DM is not taken into account. Numerical solutions from the Lagrangian formulation [Eqs. (3)] and the Eulerian formulation [Eqs. (b2)] are in blue and red, respectively. The reference time scale is $t_{0} = 1 Gyr$ . We set the fudge factor $b = 1$ , and the cross sections are $⟨ σ_{semi} v_{rel} ⟩ / m = 6 \times 10^{- 26} {cm}^{3} / s$ and $σ_{self} / m = 0.1 {cm}^{2} / g$ with SHDM mass $m = 0.3 MeV$ . We find that two formalisms result in consistent profiles for $ρ$ . The agreement between two formalisms validates the quasistatic equilibrium assumption in the Lagrangian formulation. Right panel—Same as the left panel but for the velocity dispersion $ν$ . $t_{G} (r_{s}) = 1 / \sqrt{4 π G ρ_{NFW} (r_{s})}$ is the gravitational time scale with $ρ_{NFW} (r_{s}) = ρ_{s} / 4$ .
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Figure 5
Left panel—Present core sizes of a MW satellite galaxy (red) and a field dwarf/LSB galaxy (blue) from initial halos of the CNFW profile with $r_{c}$ . We took the benchmark cross sections, $⟨ σ_{semi} v_{rel} ⟩ = 6 \times 10^{- 26} {cm}^{3} / s$ and $σ_{self} ≃ 0.1 {cm}^{2} / g$ , and set the fudge factor to be $b = 1$ . We show the results for the benchmark SHDM mass $m = 0.3 MeV$ (solid), and the largest SHDM mass allowed from the observed central densities of MW satellites [Eq. (12)], $m = 3 MeV$ (dashed). For $r_{c} ≲ 10^{- 3}$ , the present core sizes are identical to the ones from the initial halo of the NFW profile. Right panel—Time evolution of core size of a MW satellite galaxy (red) and a field dwarf/LSB galaxy (blue) for $r_{c} / r_{s} = 0.01$ (solid) and $r_{c} / r_{s} = 0.1$ (dashed). We fix the SHDM mass to be the benchmark value, $m = 0.3 MeV$ . The other parameters took are the same as the left panel.
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