REVIEW
Dark matter annihilation at the galactic center
Astrophysics · Submitted 24 Jun 1999 · 14 references
Pith's verdict: The paper that made the galactic-center dark matter spike a calculable target; the γ_max ≈ 1.5 bound is the part people use, and it holds up, with one real gap.
T0 · AI review
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Referee report
The paper
The paper claims
If the galaxy's dark halo is cusped, the black hole at its center should sit inside a dense spike of dark matter whose annihilations light it up in neutrinos — and the absence of such a signal already caps how steep the inner halo can be.
The reading
What carries the argument
The load-bearing device is the adiabatic spike: assuming the black hole grew slowly compared with the orbital times of the dark matter, the final phase-space distribution is fixed by conservation of angular momentum and of the radial action, $f'(E',L')=f(E,L)$ with $L'=L$ and $I'(E',L')=I(E,L)$. Integrating that distribution over the orbits that survive capture (those with $L>2cR_S$) gives the spike profile $ρ'(r)=ρ_R g_γ(r)(R_{sp}/r)^{γ_{sp}}$ with $g_γ≃(1-4R_S/r)^3$. A second ingredient caps the density: annihilations themselves deplete the innermost region, imposing a core density $ρ_{core}=m/(σv t_{bh})$ with $t_{bh}$ taken conservatively as $10^{10}$ yr, so that the final profile is $ρ_{sp}=ρ'ρ_{core}/(ρ'+ρ_{core})$. Together these two pieces set both the slope and the inner cutoff $R_{in}$ that the neutrino flux integral needs.
Extended reading notes
Core claim
The central claim is that the luminosity of the black-hole-induced dark matter spike is controlled almost entirely by the inner slope $0<γ<2$ of the halo profile, and that this dependence is extreme enough to be read backwards from a neutrino non-detection. For a halo with a finite core the phase-space density near the center tends to a constant and the spike slope is $γ_{sp}=3/2$; the resulting flux is about $10^{-9}$ of the smooth-halo emission, i.e. invisible. For a cusped halo the spike slope is $γ_{sp}=(9-2γ)/(4-γ)$, which runs only between 2.25 and 2.5 as $γ$ varies over its full range, yet the flux, scaling as $(R_{sp}/R_{in})^{2γ_{sp}-3}$, rises by roughly five orders of magnitude or more above the smooth halo. Imposing that the predicted neutrino-induced muon flux not exceed the existing limit of about $2×10^{4}$ muons km$^{-2}$ yr$^{-1}$ above 1 GeV yields an upper bound $γ_{max}∼1.5$ on the inner halo slope, and a future northern-hemisphere telescope with a 25 GeV threshold could push the reach down to $γ∼0.05$.
Load-bearing premise
The whole calculation assumes the central black hole grew slowly and adiabatically, so that each dark matter orbit conserves its angular momentum and radial action; if the black hole instead grew by mergers, or if the spike were later heated or scattered by stars and gas, the predicted flux and the resulting bound on the halo slope would move.
Editorial extensions
If this is right
- A halo with a finite core produces no observable spike, so a neutrino detection from the galactic center would itself argue that the inner halo is cusped.
- For cusped halos the current null result translates into a bound on the inner slope of order $γ_{max}∼1.5$, competitive with or tighter than other inferences about halo cusps.
- A future northern-hemisphere neutrino telescope with a 25 GeV muon threshold could probe slopes as shallow as $γ∼0.05$, and the surviving flux could still exceed the atmospheric background by more than three orders of magnitude.
- The same spike enhances photon, electron, positron, proton, and antiproton yields, so the argument generalises beyond neutrinos to any annihilation channel that escapes or can be modelled.
- Because the spike flux depends on $σv$ and $m$, a measured flux (or a tightened limit) constrains the dark matter particle's mass and annihilation cross section as well as the halo.
Reading between the lines
- The bound on $γ$ is only as good as the assumption that the spike survived: heating by the central star cluster, infalling baryonic clumps, or a black hole grown by mergers rather than slow accretion would flatten the spike and weaken the bound without changing the halo's original cusp.
- Because the spike slope $γ_{sp}$ is nearly pinned between 2.25 and 2.5 while the flux varies by orders of magnitude, the observable is far more sensitive to the inner cutoff $R_{in}$ (set by $σv$ and $m$) than to the halo slope — an inversion that makes the neutrino channel a particle-physics probe as much as a halo-shape probe.
- The same adiabatic argument applied to the Milky Way's central black hole should also apply to the black holes of nearby galaxies, so stacked neutrino limits on nearby galactic nuclei could test the cusp hypothesis independently of the galactic center's uncertain baryonic history.
- The paper's own conservative density normalisation, $ρ_D/(1-γ/3)≃0.24$ GeV cm$^{-3}$, is derived by deliberately underestimating the central density; a direct measurement of the local halo normalisation would therefore tighten the $γ$ bound proportionally to the square of the density.
Original abstract
If cold dark matter is present at the galactic center, as in current models of the dark halo, it is accreted by the central black hole into a dense spike. Particle dark matter then annihilates strongly inside the spike, making it a compact source of photons, electrons, positrons, protons, antiprotons, and neutrinos. The spike luminosity depends on the density profile of the inner halo: halos with finite cores have unnoticeable spikes, while halos with inner cusps may have spikes so bright that the absence of a detected neutrino signal from the galactic center already places interesting upper limits on the density slope of the inner halo. Future neutrino telescopes observing the galactic center could probe the inner structure of the dark halo, or indirectly find the nature of dark matter.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
If cold dark matter is present at the galactic center, as in current models of the dark halo, it is accreted by the central black hole into a dense spike. Particle dark matter then annihilates strongly inside the spike, making it a compact source of photons, electrons, positrons, protons, antiprotons, and neutrinos. The spike luminosity depends on the density profile of the inner halo: halos with finite cores have unnoticeable spikes, while halos with inner cusps may have spikes so bright that the absence of a detected neutrino signal from the galactic center already places interesting upper limits on the density slope of the inner halo. Future neutrino telescopes observing the galactic center could probe the inner structure of the dark halo, or indirectly find the nature of dark matter.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | If cold dark matter is present at the galactic center, as in current models of the dark halo, it is accreted by the central black hole into a dense spike. | background 0.86 | 0.08 | 0.07 | asserted 0.57 |
| s1 | Particle dark matter then annihilates strongly inside the spike, making it a compact source of photons, electrons, positrons, protons, antiprotons, and neutrinos. | result 0.38 | 0.12 | 0.12 | asserted 1.00 |
| s2 | The spike luminosity depends on the density profile of the inner halo: halos with finite cores have unnoticeable spikes, while halos with inner cusps may have spikes so bright that the absence of a detected neutrino signal from the galactic center already places interesting upper limits on the density slope of the inner halo. | result 0.60 | 0.29 | 0.57 | hedged possibility 0.73 |
| s3 | Future neutrino telescopes observing the galactic center could probe the inner structure of the dark halo, or indirectly find the nature of dark matter. | future work 0.89 | 0.06 | 0.28 | hedged possibility 1.00 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:astro-ph/9906391 by the authors.
References
How later papers used it
327 later papers cite it
2 later papers by other authors are listed below: 2 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.
Uses its method or tool 3 of 14 papers with this label · 1 by the same authors
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We define the accumulated DM column density following [ref] as [equation] where $ρ_DM$ is the spike density profile of DM and is given by $ρ_DM (r) = ρ^core ρ̃(r)/ρ^core + ρ̃(r)$.
Probing chiral and flavored $Z^\prime$ from cosmic bursts through neutrino interactions (2023) · Cosmic blazar TXS0506 + 056 · 0.91
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For the spiky density profile, $n_p, sp(r)$, we follow [ref] and take the form [equation] where $4 R_s(M_SBH) ≤r ≤R_sp$ and $γ_sp=(9-2γ)/(4-γ)$ with $R_sp= α_γR_0(M_SBH/ρ_DM,⊙R_0^3)^1/(3-γ)$ and $0≤γ≤2$, respectively.
Rescuing The Primordial Black Holes all-Dark Matter Hypothesis from The Fast Radio Bursts Tension (2023) · Enhanced DM density at Galactic centers · 0.81
By the same authors
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Considered the dark matter spike profile derived by the authors of this paper for a spike growing from an initial profile.
Ruling out thermal dark matter with a black hole induced spiky profile in the M87 galaxy (2015) (same authors) · 0.81 · paraphrased: the licence does not allow quoting
How the literature uses it
272 arXiv papers cite this in 548 sentences
Papers citing it · 421 sentences without a confident label
Contests it 1 paper
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From a DM annihilation standpoint, the original Adiabatic Spike [ref] has also been ruled out by comparing the expected DM flux with the observed HESS data in the GC [ref] , which further motivates using this approach.
The potential of diffuse Galactic Ridge neutrino measurements to constrain dark matter · Galactic DM density profile · contest 0.73
Builds on it 3 papers
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The picture sketched in [ref] and [ref] has been further refined in [ref] , where a time-evolution analysis of the cusp formation is performed, including the effects of self annihilations, scattering of dark matter particles by stars, and capture in the black hole.
Multi-wavelength signals of dark matter annihilations at the Galactic center · A few benchmark scenarios · 0.85
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Gondolo and Silk [ref] applied the results obtained by Quinlan, Hernquist, and Sigurdsson [ref] to the dark matter cusps that several groups of authors had put forward in the 1990s [ref] .
Dark matter, black holes, and gravitational waves · Matter around Black Holes · 0.81
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The expression in rhofit is a generalization of Eq. (9) in [ref] to allow for a $θ$-dependent end point for the spike.
Dark matter spikes in the vicinity of Kerr black holes · Discussion · 0.97
Uses its method or tool 11 papers
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We consider the profile derived by the authors of Ref. [ref] for a DM spike growing from an initial profile $∝ρ_0 ( r/r_0 )^-γ$: [equation] where the saturation density determined by DM annihilations reads [equation] with $m_DM$ and $⟨σv ⟩$ respectively the mass and annihilation cross-section of the DM particle, and $t_BH$ the age of the BH.
Ruling out thermal dark matter with a black hole induced spiky profile in the M87 galaxy · Appendix A: DM spike model · 0.81
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In this work, we adopt the framework developed in Ref. [ref] , in which the dark matter distribution around stellar-mass black holes is modeled under the assumption of adiabatic growth [ref] .
Probing the Inert Doublet Dark Matter with Stellar-Mass Black Hole Mini-Spikes · Indirect Detection · 0.96
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We adopt the standard approach from [ref] , assuming the geodesics of DM particles are governed solely by the Schwarzschild metric of the central BH.
Black hole spacetimes with dark matter spikes: Energy-momentum tensor and backreaction effects · DM spike around a BH · 0.98
Uses its data or values 5 papers
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Generally the spike radius is taken to be $R_sp=10^5 R_s$ [ref] , where $R_s=2 GM_BH/c^2 (c=1$ in natural unit) is the Schwarzschild radius [ref] .
Blazar Boosted ALP and vector portal Dark matter confronting light mediator searches · DM density profile · 0.91
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[equation] where the constant $α_γ$ must be evaluated numerically, and is $α_γ≈0.1$ for $γ=0.7-1.4$ [ref] .
Dark matter spikes with strongly self-interacting particles · DM density profile · 0.98
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Here, we adopt the power-law index $γ$ from Refs. [ref] and mainly focus on the case of $γ∈[1/2,3/2]$ and then $γ_sp ∈[16/7,12/5]$.
Probing black holes in a dark matter spike of M87 using quasinormal modes · Density profile of a dark matter spike near the black hole · 0.97
Compares with it 7 papers
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We see that the density after SMS formation is significantly lower than the spike profile of Refs. [ref] , in the region where the gravitational wave signal is expected to peak.
Dark Matter Mounds: towards a realistic description of dark matter overdensities around black holes · Introduction · 0.86
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Our benchmark DM profiles are shown in Fig. [ref], together, for comparison, with the NFW profile and the "spiky" profile obtained implementing the original procedure outlined in [ref] .
Multi-wavelength signals of dark matter annihilations at the Galactic center · A few benchmark scenarios · 0.96
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In the previous section we saw that for several plausible scenarios for the initial black hole mass seed and DM and stellar initial density profiles, steep overdensities can be formed, in some scenarios even resembling the Gondolo and Silk expectation from Ref. [ref] , see Appendix [ref].
Formation and Redshift Evolution of Dark Matter Spikes · Cosmic Evolution of DM overdensities in a star cluster: The steady-state solutions · 0.86
Cites it as support 3 papers
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In fact, prior work has confirmed this: if dark matter is present around an IMBH in sufficiently large amounts, the density of a spherically symmetric DM overdensity (referred to as a DM “spike” [ref] ) could be inferred from a GW measurement with LISA [ref] .
Probing dark-matter effects with gravitational waves using the parameterized post-Einsteinian framework · Introduction · 0.97
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Such conjecture is reinforced, as several papers are agreeing on the fact that the density close to the galactic center is of the order of, or even much larger ($10^4$ times larger) than, that indicated by DC14 [ref] .
On the change of old neutron star masses with galactocentric distance · Mass Change of Neutron Stars · 0.98
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Our choice is physically well motivated by the scenario of adiabatic contraction of dark matter around the central super-massive black hole Sgr A$^*$ [ref] .
Fitting the Gamma-Ray Spectrum from Dark Matter with DMFIT: GLAST and the Galactic Center Region · Dark Matter Models · 1.00
Cites it as background 80 papers
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If the center of a galaxy hosts a supermassive black hole (SMBH), then the region just outside the black hole may exhibit a large density of dark matter, known as a dark matter spike [ref] .
Constraining $p$-wave Dark Matter Annihilation with Gamma-ray Observations of M87 · Introduction · 0.97
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The formation of a DM spike is contingent on several conditions, detailed for example in [ref] and [ref] .
Black Holes, Dark Matter Spikes, and Constraints on Simplified Models with $t$-Channel Mediators · Dark Matter Spike Near the Supermassive Black Hole · 0.91
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The traditional framework for the formation of dark-matter (DM) overdensities around a supermassive black hole (SMBH) is the adiabatic growth model from [ref] .
Formation and Redshift Evolution of Dark Matter Spikes · Canonical spike formation · 0.90
Discussion
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