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Gravothermal collapse of self-interacting dark matter halos as the origin of intermediate mass black holes in Milky Way satellites

Tamar Meshveliani, Jesús Zavala, and Mark R. Lovell
Phys. Rev. D 107, 083010 – Published 6 April 2023
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  • INTRODUCTION
  • GRAVOTHERMAL COLLAPSE IN SIDM HALOS
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Milky Way (MW) satellites exhibit a diverse range of internal kinematics, reflecting in turn a diverse set of subhalo density profiles. These profiles include large cores and dense cusps, which any successful dark matter model must explain simultaneously. A plausible driver of such diversity is self-interactions between dark matter particles (SIDM) if the cross section passes the threshold for the gravothermal collapse phase at the characteristic velocities of the MW satellites. In this case, some of the satellites are expected to be hosted by subhalos that are still in the classical SIDM core phase, while those in the collapse phase would have cuspy inner profiles, with a SIDM-driven intermediate mass black hole (IMBH) in the center as a consequence of the runaway collapse. We develop an analytical framework that takes into account the cosmological assembly of halos and is calibrated to previous simulations; we then predict the timescales and mass scales (MBH) for the formation of IMBHs in velocity-dependent SIDM (vdSIDM) models as a function of the present-day halo mass, M0. Finally, we estimate the region in the parameter space of the effective cross section and M0 for a subclass of vdSIDM models that result in a diverse MW satellite population as well as their corresponding fraction of SIDM-collapsed halos and those halos’ inferred IMBH masses. We predict the latter to be in the range 0.1–1000M⊙ with a MBH−M0 relation that has a similar slope, but lower normalization, than the extrapolated empirical relation of supermassive black holes found in massive galaxies.

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    • Received 4 October 2022
    • Accepted 16 March 2023

    DOI:https://doi.org/10.1103/PhysRevD.107.083010

    © 2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Dark matterFormation & evolution of stars & galaxiesParticle dark matter
    Gravitation, Cosmology & AstrophysicsParticles & Fields

    Authors & Affiliations

    Tamar Meshveliani*, Jesús Zavala, and Mark R. Lovell

    • Centre for Astrophysics and Cosmology, Science Institute, University of Iceland, Dunhagi 5, 107 Reykjavik, Iceland

    • *tam15@hi.is

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    Issue

    Vol. 107, Iss. 8 — 15 April 2023

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    Images

    • Figure 1
      Figure 1

      Cosmic time for the cusp-core transformation threshold of SIDM halos as a function of the present-day halo mass M0. The blue dotted line is the function of zLMM, and the yellow dotted line is the function of zform. The horizontal line indicates the infall time of subhaloes, which we fix to zinfall=1 (see Sec. 2g).

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    • Figure 2
      Figure 2

      Characteristic transfer cross section per unit mass as a function of a halo mass at z=0 [Eq. (17)] for the benchmark SIDM model (vd100) from Ref. [13].

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    • Figure 3
      Figure 3

      The timescale to form a black hole [Eq. (21)] in SIDM halos as a function of the present-day halo mass M0 (in isolation) for the velocity-dependent model vd100 [13, 63] shown in Fig. 2. The yellow solid line shows the case where the starting time for the cusp-core-collapse evolution is set to the assembly/formation time of the primordial (pre-SIDM) CDM NFW halo, zcc=zform (see Sec. 2c and Fig. 1 where the yellow dotted line marks the cosmic time corresponding to zform), while the blue solid line brackets the impact of cosmological accretion by setting zcc=zLMM, which is the epoch of the last major merger for given halo of mass M0 (see Sec. 2d and Fig. 1 where the blue dotted line marks the cosmic time corresponding to zLMM). Shaded regions indicate a scatter of ±10% in the concentration-mass relation, e.g., Ref. [92]. Dashed lines are the corresponding cases including the acceleration of the collapse time driven by tidal stripping [58] assuming a mass-independent infall epoch of zinfall=1 (see Sec. 2g). The horizontal orange line indicates the age of the Universe. The black star symbol marks the transition mass where 50% of the subhalo population is estimated to be in the core-collapse regime according to Ref. [25]; see also Refs. [13, 63].

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    • Figure 4
      Figure 4

      Timescale for black hole formation in SIDM halos as a function of the present-day SIDM halo mass M0 in isolation. The solid blue and yellow lines are the same as those in Fig. 3, which bracket the range of the possible threshold epochs for the cusp-core-collapse evolution to begin (for mean values of the concentration-mass relation). The dashed black line is tBH(zLMM) (i.e., the blue line) recalibrated to the simulation-based result of Ref. [25] (black star) with the calibration factor C=0.42 [see Eq. (19)].

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    • Figure 5
      Figure 5

      Black hole mass–halo mass relation. The violet and red lines follow the estimate of the SIDM-core-collapse formula [Eq. (22)] with the former using the mean concentration-mass relation, while the latter uses a +2σ value over the mean. For these cases, the arrows indicate the corresponding halo mass at which tBH=0, i.e., the mass at which 50% and 2.5% of the halo population at that mass is in the core-collapse regime, violet and red, respectively. The gray line is the extrapolation toward lower masses of the empirical relation for supermassiv black holes (SMBHs) in galaxies with halo masses >1011.5M⊙, while the gray band represents the intrinsic scatter on this relation. adopted from Ref. [94].

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    • Figure 6
      Figure 6

      The effective cross section as a function of a present-day SIDM halo mass M0 in isolation. The black solid and dashed lines represent the effective cross section for the vd100 model evaluated at zLMM and z=0, respectively; we use our default model with zcc=zLMM and calibrated to the simulation analysis in Ref. [25]. The x axis on the top shows the corresponding (SIDM-driven) black hole mass for a given M0. The red dashed line (nearly horizontal) indicates the required cross section value for the onset of gravothermal collapse: SIDM-driven cuspy halos lie above (light violet), while SIDM cores lie below (beige) down to the point where the cross section is so low that halos are essentially CDM-like (light green). The red dotted line marks the upper mass for the dSph MW satellites to reside, e.g., Ref. [24], while the hashed/dotted region to the left starts at the mass where reionization significantly suppresses galaxy formation. The dark violet band indicates the region where vdSIDM models like vd100 but with different normalization produce a diverse MW satellite population hosted by halos that could either be cored or cuspy.

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    • Figure 7
      Figure 7

      The fraction of core-collapsed halos as a function of M0 for the vdSIDM models shown in Fig. 6, which have a diverse range of halo profiles (dark violet). The black solid line represents the benchmark vd100 model. As in Fig. 6, we use our default model with zcc=zLMM and calibrated to the simulation analysis in Ref. [25].

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    • Figure 8
      Figure 8

      The viable values of the parameter space that define the vdSIDM models studied here [Eq. (12)]: the relative velocity vmax where the transfer cross section σTmax peaks. The highlighted region is that of models that produce a bimodal distribution of halos (green area) and satisfies the constraint from elliptical galaxies ⟨σmax⟩≤1  cm2 g−1 for a halo mass of M0=1013M⊙. The black dashed line is the unitarity bound for the SIDM cross section for a particle mass mχ=20  GeV. The blue star marks the vd100 model.

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    • Figure 9
      Figure 9

      Timescale to form a black hole in SIDM halos as a function of the present-day halo mass M0 (in isolation). The yellow line [Eq. (21)] represents the cusp-core-collapse evolution timescale chosen for this work (equal to the curve of the same color in Fig. 3), and the violet line [Eq. (a3)] is based on Ref. [57]. As in Fig. 3, shaded bands indicate a concentration scatter of ±10% in the concentration-mass relation (e.g., Ref. [92]). The horizontal line indicates the age of the Universe at z=0.

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    • Figure 10
      Figure 10

      The same as Fig. 4, but with the addition of the thick dot-dashed black line, which is the same as the calibrated model used for our key results (thin dashed black line) but with C=0.75 instead.

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    • Figure 11
      Figure 11

      The same as Fig. 6, but with the addition of the nearly horizontal thick red dashed line—the required cross section value for the onset of gravothermal collapse when C=0.75 is used instead of C=0.42, which is the calibrated value used for our key results (thin red dashed line).

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    • Figure 12
      Figure 12

      The same as Fig. 7, but with the addition of the thick black dot-dashed line—the fraction of core-collapsed halos as a function of M0 when C=0.75 is used instead of C=42, as in our key result (solid black line).

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