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Core mass -- halo mass relation of bosonic and fermionic dark matter halos harbouring a supermassive black hole
General Relativity and Quantum Cosmology · Submitted 5 Nov 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For noninteracting bosons and for bosons with a repulsive self-interaction, we find that the core mass $M_c$ increases with the halo mass $M_h$ and achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing.
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The abstract, sentence by sentence
We study the core mass -- halo mass relation of bosonic dark matter halos, in the form of self-gravitating Bose-Einstein condensates, harbouring a supermassive black hole. We use the ``velocity dispersion tracing'' relation according to which the velocity dispersion in the core $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_h^2\sim GM_h/r_h$ (this relation can be justified from thermodynamical arguments) and the approximate analytical mass-radius relation of the quantum core in the presence of a central black hole obtained in our previous paper [P.H. Chavanis, Eur. Phys. J. Plus 134, 352 (2019)]. For a given minimum halo mass $(M_h)_{\rm min}\sim 10^8\, M_{\odot}$ determined by the observations, the only free parameter of our model is the scattering length $a_s$ of the bosons (their mass $m$ is then determined by the characteristics of the minimum halo). For noninteracting bosons and for bosons with a repulsive self-interaction, we find that the core mass $M_c$ increases with the halo mass $M_h$ and achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. The whole series of equilibria is stable. For bosons with an attractive self-interaction, we find that the core mass achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. The series of equilibria becomes unstable above a maximum halo mass $(M_h)_{\rm max}\ge (M_h)_{*}$. In the absence of black hole $(M_h)_{\rm max}=(M_h)_{*}$. At that point, the quantum core (similar to a dilute axion star) collapses. We perform a similar study for fermionic dark matter halos. We find that they behave similarly to bosonic dark matter halos with a repulsive self-interaction, the Pauli principle for fermions playing the role of the repulsive self-interaction for bosons.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the core mass -- halo mass relation of bosonic dark matter halos, in the form of self-gravitating Bose-Einstein condensates, harbouring a supermassive black hole. | contribution 0.99 | 0.87 | 0.05 | asserted 0.75 |
| s1 | We use the ``velocity dispersion tracing'' relation according to which the velocity dispersion in the core $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_h^2\sim GM_h/r_h$ (this relation can be justified from thermodynamical arguments) and the approximate analytical mass-radius relation of the quantum core in the presence of a central black hole obtained in our previous paper [P.H. Chavanis, Eur. | method 1.00 | 0.44 | 0.04 | asserted 0.86 |
| s2 | Phys. J. Plus 134, 352 (2019)]. | method 0.73 | 0.10 | 0.02 | unclear 0.75 |
| s3 | For a given minimum halo mass $(M_h)_{\rm min}\sim 10^8\, M_{\odot}$ determined by the observations, the only free parameter of our model is the scattering length $a_s$ of the bosons (their mass $m$ is then determined by the characteristics of the minimum halo). | method 0.90 | 0.48 | 0.05 | asserted 1.00 |
| s4 | For noninteracting bosons and for bosons with a repulsive self-interaction, we find that the core mass $M_c$ increases with the halo mass $M_h$ and achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. | result 1.00 | 0.96 | 0.30 | asserted 1.00 |
| s5 | The whole series of equilibria is stable. | result 1.00 | 0.88 | 0.11 | asserted 1.00 |
| s6 | For bosons with an attractive self-interaction, we find that the core mass achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. | result 1.00 | 0.96 | 0.15 | asserted 1.00 |
| s7 | The series of equilibria becomes unstable above a maximum halo mass $(M_h)_{\rm max}\ge (M_h)_{*}$. | result 1.00 | 0.93 | 0.15 | asserted 1.00 |
| s8 | In the absence of black hole $(M_h)_{\rm max}=(M_h)_{*}$. | result 0.98 | 0.76 | 0.07 | asserted 1.00 |
| s9 | At that point, the quantum core (similar to a dilute axion star) collapses. | result 0.62 | 0.70 | 0.10 | asserted 1.00 |
| s10 | We perform a similar study for fermionic dark matter halos. | contribution 0.99 | 0.88 | 0.03 | asserted 0.63 |
| s11 | We find that they behave similarly to bosonic dark matter halos with a repulsive self-interaction, the Pauli principle for fermions playing the role of the repulsive self-interaction for bosons. | result 0.93 | 0.93 | 0.18 | asserted 1.00 |
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Original abstract
We study the core mass -- halo mass relation of bosonic dark matter halos, in the form of self-gravitating Bose-Einstein condensates, harbouring a supermassive black hole. We use the ``velocity dispersion tracing'' relation according to which the velocity dispersion in the core $v_c^2\sim GM_c/R_c$ is of the same order as the velocity dispersion in the halo $v_h^2\sim GM_h/r_h$ (this relation can be justified from thermodynamical arguments) and the approximate analytical mass-radius relation of the quantum core in the presence of a central black hole obtained in our previous paper [P.H. Chavanis, Eur. Phys. J. Plus 134, 352 (2019)]. For a given minimum halo mass $(M_h)_{\rm min}\sim 10^8\, M_{\odot}$ determined by the observations, the only free parameter of our model is the scattering length $a_s$ of the bosons (their mass $m$ is then determined by the characteristics of the minimum halo). For noninteracting bosons and for bosons with a repulsive self-interaction, we find that the core mass $M_c$ increases with the halo mass $M_h$ and achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. The whole series of equilibria is stable. For bosons with an attractive self-interaction, we find that the core mass achieves a maximum value $(M_c)_{\rm max}$ at some halo mass $(M_h)_{*}$ before decreasing. The series of equilibria becomes unstable above a maximum halo mass $(M_h)_{\rm max}\ge (M_h)_{*}$. In the absence of black hole $(M_h)_{\rm max}=(M_h)_{*}$. At that point, the quantum core (similar to a dilute axion star) collapses. We perform a similar study for fermionic dark matter halos. We find that they behave similarly to bosonic dark matter halos with a repulsive self-interaction, the Pauli principle for fermions playing the role of the repulsive self-interaction for bosons.
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How the literature uses it
8 arXiv papers cite this in 14 sentences
Papers citing it · 8 sentences without a confident label
Compares with it 1 paper
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On the other hand, when $Λ̂>0$ and $Λ̂(1.16×10^-7M_h,12^2/3)≫1$, we arrive at the TF regime for the central soliton profile, resulting in a core-halo mass relation in the form: [equation] This core-halo mass relation in the TF regime is in agreement with the one obtained in [ref] .
Core-Halo Mass Relation in Scalar Field Dark Matter Models and its Consequences for the Formation of Supermassive Black Holes · Core-halo structure in the self-interacting scenario · 0.99
Cites it as background 4 papers
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The case of boson stars with an attractive self-interaction ($a_s<0$), possibly representing axion stars, has been considered only recently [ref] (see a review in [ref] ).
Quantum tunneling rate of dilute axion stars close to the maximum mass · Introduction · 0.97
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For instance, Brax et al. [ref] employed an analytical relativistic treatment to study the infall of the SF onto the central Schwarzschild BH (see also Ref. [ref] for the case of charged BHs), while Chavanis et al. used a Gaussian ansatz [ref] and velocity dispersion tracing [ref] as part of their analytical approach.
Constraining Self-interacting Scalar Field Dark Matter From the Black Hole Shadow of the Event Horizon Telescope · Introduction · 0.83
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Following these efforts, the attention has been directed to the possible role of BSs in astrophysics whether as a DM candidate [ref] or as black hole mimickers [ref] .
Bosonic Dark Matter in Light of the NICER Precise Mass-Radius Measurements · Introduction · 0.95
What it cites · 30 sentences without a confident label
Builds on 1 paper
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Finally, using the “velocity dispersion tracing” relation, we could generalize the core mass – halo mass relation obtained by Schive et al. [ref] to the case of DM halos made of bosons with attractive or repulsive interaction and to the case of DM halos made of fermions [ref] .
Derivation of the core mass -- halo mass relation of fermionic and bosonic dark matter halos from an effective thermodynamical model · Introduction · 1.00
Uses data or values from 1 paper
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In order to match the characteristics of the smallest halos like dwarf spheroidals (dSphs) that are interpreted as purely quantum objects (see below), the mass of the fermion should be of the order of $m∼170 eV/c^2$ while the mass of the boson should be of the order of $m∼2.92×10^-22 eV/c^2$ if it has a vanishing self-interaction, or lie in the range $2.19×10^-22 eV/c^2<m<2.92×10^-22 eV/c^2$ if it has an attractive self-interaction, and in the range $2.92×10^-22 eV/c^2<m<1.10×10^-3 eV/c^2$ if it has a repulsive self-interaction (see Appendix D of [ref] and Ref. [ref] ).[These values are indicative.
Derivation of the core mass -- halo mass relation of fermionic and bosonic dark matter halos from an effective thermodynamical model · Introduction · 0.97
Compares with 2 papers
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For a DM halo of mass $M_h=10^12 M_⊙$ similar to the one that surrounds our Galaxy, we obtain a core mass $M_c=10^10 M_⊙$, the same value as the one found in [ref] in the absence of a central BH (we have taken $(M_h)_min=10^8 M_⊙$).
Derivation of the core mass -- halo mass relation of fermionic and bosonic dark matter halos from an effective thermodynamical model · Bosons with a repulsive self-interaction · 0.96
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Accordingly, for the DM halos considered by Davies and Mocz [ref] , with mass $M_v=10^12 M_⊙$ (Milky Way) and $M_v=2×10^14 M_⊙$ (elliptical galaxy in the Virgo cluster), the presence of the SMBH is expected to change the value of the core mass (especially in the second case), except if it forms after the quantum core as assumed by these authors.[As discussed by Davies and Mocz [ref] at the end of their Sec. 4, their conclusions are robust and should not significantly change if we properly account for the modification of the quantum core mass due to the presence of the SMBH as suggested above.
Fuzzy Dark Matter Soliton Cores around Supermassive Black Holes · Comparison with other works · 0.86
Cites as background 2 papers
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In order to solve these problems, some authors have proposed to take the quantum nature of the DM particle into account (see an exhausive list of references in Refs. [ref] and in the reviews [ref] ).
Axion Stars · Introduction · 0.92
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The effects of a SMBH on BECDM halos have also been studied recently by Avilez et al. [ref] , Eby et al. [ref] , Bar et al. [ref] , Chavanis [ref] and Brax et al. [ref] .
Fate of scalar dark matter solitons around supermassive galactic black holes · Introduction · 0.99
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