{"id":"145be2b8-4641-4792-a37c-f75e5922316f","arxiv_id":"astro-ph/0101481","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Realistic black-hole formation, with the seed born off-center and spiraling in by dynamical friction, weakens or destroys the steep dark-matter spike that Gondolo and Silk claimed at the Galactic center.","lead":"This paper re-examines the claim that the Milky Way's central black hole squeezed dark matter into a very steep density spike, and argues the spike needs implausibly fine-tuned initial conditions. If the authors are right, null results from dark-matter annihilation searches toward the Galactic center cannot be used to rule out neutralino dark matter.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The pivot is Fig. 3's Chandrasekhar inspiral time, quoted at 100 pc–1 kpc for a baryon-free halo. At the paper's own 50–60 pc scale, and with the Section VI baryon-contracted profile, a seed light enough to preserve the GS spike may still arrive within a Hubble time.","rationale":"The reader's weakest_assumption correctly identifies the dynamical-friction inspiral estimate of Section V A and Fig. 3 as the load-bearing pivot, and the CONDITIONAL verdict is the right level of confidence. I agree with that diagnosis and only sharpen it. The paper's central structural move is a two-branch exhaustion: massive seeds arrive but destroy the cusp, light seeds preserve the spike but cannot arrive. That argument is only as strong as the boundary between the branches, and the boundary is drawn from a Chandrasekhar estimate whose quoted numbers (100 pc for 10^4 M⊙, 1 kpc for 10^6 M⊙) are evaluated at radii larger than the 50–60 pc scale the paper itself identifies as the relevant one in Section II A. Because t_df falls steeply with radius for an NFW cusp, this is not a cosmetic mismatch; it can move a 10^4 M⊙ seed from marginal to comfortably within a Hubble time, and 10^4 M⊙ sits in the regime where the paper's own Fig. 4 shows a dramatic spike. The second tension is that Fig. 3 explicitly excludes baryons while Section VI computes a baryon-contracted profile that would shorten the inspiral; the two sections are not fed into each other. The paper is otherwise careful and honest: the factor-of-2 agreement between the circular-orbit and isotropic treatments in Fig. 1 is a genuine internal check, the reproduction of the GS A = 7/3 exponent is a real validation, and the caption's caveat about the Coulomb factor and orbital eccentricity is an acknowledged limitation I do not re-raise as a new finding. The Nakano–Makino import in Eq. 16 is a secondary modeling concern, not the load-bearing one. The unpublished reference [19] is a minor citation gap. None of this overturns the qualitative conclusion of abstract:s3, which is stated at a level of precision the modeling can support; it does mean the quantitative threshold in abstract:s4 should be bounded before being quoted as a number. Hence UNCHANGED relative to the reader's CONDITIONAL.","tokens_in":17348,"tokens_out":5025,"duration_ms":115272,"concrete_test":"Recompute Fig. 3 with two changes: (a) substitute the Section VI baryon-contracted inner density profile for the pure NFW/Moore profile, and (b) evaluate the inspiral time at r = 50 pc, the radius enclosing M_BH per Section II A, for M_SBH = 10^4, 10^5, and 10^6 M⊙. If t_spiral(50 pc, 10^4 M⊙) falls below the Hubble time, then a seed in the M_SBH ≲ M_BH/200 regime — where Fig. 4 already shows a dramatic spike — can reach the center, and abstract:s4 must be weakened to a statement about seeds forming beyond roughly 100 pc.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper closes the GS loophole by exhausting two branches: (i) a seed with M_SBH ≳ 0.1 M_BH arrives within a Hubble time but heats the cusp on the way in (Fig. 4/5, Eq. 16), and (ii) a seed with M_SBH ≲ M_BH/200 preserves the spike (Section V: 'a dramatic enhancement in the dark-matter density') but cannot arrive (Fig. 3). The union covers parameter space only if the Fig. 3 boundary is correct at the radius that actually matters, and two internal tensions suggest it is not stated at that radius. First, Fig. 3 is plotted against r, and the text quotes '100 pc' for a 10^4 M⊙ seed and '1 kpc' for 10^6 M⊙. But Section II A establishes that the spike draws on the halo mass within ~50–60 pc, the radius enclosing M_BH. For an NFW inner cusp, t_df ∝ v_c^3/(G^2 M_SBH ρ) with ρ ∝ r^-1 and v_c^2 ∝ r, so t_df ∝ r^{5/2}/M_SBH; moving from 100 pc to 50 pc shortens the 10^4 M⊙ inspiral by roughly 5×. A 10^4 M⊙ seed is M_BH/260, squarely inside the regime where Section V says adiabatic contraction yields a dramatic spike. Second, the Fig. 3 caption states the curves assume an 'initially pure NFW or pure Moore halo profile (no baryons),' yet Section VI computes baryon adiabatic contraction that enhances the dark-matter density from a few pc to a few kpc. That contracted profile is precisely what should enter the Chandrasekhar estimate; using the un-contracted profile overestimates t_df and biases the result toward the paper's conclusion. Neither point is acknowledged. The qualitative claim of abstract:s3 may survive, but abstract:s4 ('the seed mass must be at least a significant fraction of the present BH') is stated more firmly than Fig. 3 supports once the relevant radius and the baryon-contracted profile are used.","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The paper examines whether the very-dense dark-matter spike claimed by Gondolo & Silk (GS) at the Galactic center is a robust prediction of adiabatic black-hole growth. Sections II–IV review and re-derive the standard adiabatic-contraction machinery (Eddington inversion, Eq. 2; conservation of radial action and angular momentum, Eq. 1; final density from Eq. 3), reproducing the GS exponent A = 7/3 for an NFW profile in Fig. 1, and contrast it with instantaneous growth (Section IV, Eq. 11, giving r^-4/3). Section V is the paper's core: it argues that a seed black hole formed off-center must spiral in by dynamical friction, that a seed massive enough to arrive within a Hubble time (M_SBH > ~0.1 M_BH) heats and erases the inner cusp (Eq. 16, Figs. 4–5), and that a seed light enough to preserve the spike (M_SBH < ~M_BH/200) cannot arrive in time (Fig. 3). Section VI adds baryonic adiabatic contraction. The conclusion is that the GS spike requires the majority of the black-hole mass to grow adiabatically within ~50 pc of the dark-matter center from cold orbits, conditions the authors argue are unlikely in our Galaxy, so null annihilation searches should not be read as evidence against neutralino dark matter or cuspy halos.","tokens_in":17737,"tokens_out":5009,"duration_ms":100303,"significance":"The question is well posed and consequential: if the GS spike is generic, existing gamma-ray, neutrino, and synchrotron bounds exclude large regions of neutralino parameter space and possibly cuspy halos; if it is not generic, those bounds say much less. The paper's adiabatic calculation is textbook and correctly executed, Fig. 1 reproduces the published GS exponent, and the qualitative point that the spike draws on cold orbits within the radius enclosing M_BH (Section II A) is correct and well supported by Quinlan et al. (1995). The paper is a useful corrective to over-reading null searches. Its weakness is that the load-bearing quantitative boundary between the 'cusp destroyed' and 'spike preserved' branches is quoted at radii and for a halo model that do not match the scale the paper itself identifies as relevant.","major_comments":[{"comment":"The inspiral boundary that decides the paper's dichotomy is quoted at the wrong radius. Fig. 3 and the text state that a 10^4 M⊙ seed takes roughly a Hubble time to spiral in from 100 pc, and a 10^6 M⊙ seed from 1 kpc. But Section II A establishes that the spike draws on the halo mass within ~50–60 pc, the radius enclosing M_BH. For an NFW inner cusp, t_df ∝ v_c^3/(G^2 M_SBH ρ) with ρ ∝ r^-1 and v_c^2 ∝ r, so t_df ∝ r^{5/2}/M_SBH; moving from 100 pc to 50 pc shortens the 10^4 M⊙ inspiral by a factor of about 5–6, bringing it within a Hubble time. Since 10^4 M⊙ is roughly M_BH/260, squarely inside the regime where Section V states that adiabatic contraction produces 'a dramatic enhancement in the dark-matter density,' the two branches may not cover the parameter space as claimed. The paper should quote t_df explicitly at 50 pc and mark on Fig. 3 where the boundary actually falls at the radius that matters for spike formation.","section":"Section V A, Fig. 3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The Fig. 3 caption states that the curves assume an 'initially pure NFW or pure Moore halo profile (no baryons),' yet Section VI computes baryonic adiabatic contraction that enhances the dark-matter density from a few pc out to a few kpc. Since t_df scales inversely with the ambient density, the contracted profile is precisely what should enter the Chandrasekhar estimate, and using the uncontracted profile overestimates t_df and biases the result toward the paper's conclusion. The authors should either recompute Fig. 3 with the Section VI contracted profile or state explicitly the direction and approximate size of the bias, and note whether it changes the M_SBH threshold.","section":"Section V A, Fig. 3 caption; Section VI","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The heating model is a spliced profile with a break at r_s defined by M_h(r_s) = M_SBH, calibrated to the Nakano & Makino (1999) N-body result, and the transition between 'cusp destroyed' and 'spike preserved' is read off Figs. 4–5 rather than derived. The thresholds quoted in the text (M_SBH ~ M_BH/10 versus M_SBH ~ M_BH/200) should be stated together with the criterion used to define them (for example, the final central density relative to ρ_core or to the initial profile) and with an estimate of their sensitivity to the splicing prescription. As written, the reader cannot tell whether the intermediate window M_BH/200 < M_SBH < M_BH/10 is empty, narrow, or substantial, which is exactly the window the Fig. 3 concern above probes.","section":"Section V B, Eq. (16), Figs. 4–5","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim that it would be 'somewhat surprising' for the black hole to form within 50 pc of the dark-matter center is the load-bearing plausibility argument for the whole conclusion, but it is qualitative and unquantified. The paper should either flag it explicitly as a plausibility argument rather than a calculation, or support it with a reference or an order-of-magnitude estimate of the expected baryon–dark-matter center offset at the relevant epoch. As it stands, the abstract's claim that the spike 'disappears completely or is greatly weakened' rests on this step as much as on the dynamical calculations.","section":"Section II A, Section VII","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"Several typographical errors should be corrected: 'adiabaticly' in the abstract, 'contradict with' in the abstract, and 'hierarachical' in Section I.","section":"Abstract and Section I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Eq. (9) is derived for 1 ≤ α < 2 under the assumption c1 ≠ 0, and its limit as α → 2 gives A = 7/4, whereas the text states that at α = 2 the distribution function is non-singular (n = 0) and A = 3/2. The two statements are each internally consistent but do not connect continuously, and the text should say explicitly that Eq. (9) breaks down at α = 2 so the apparent discontinuity is not read as an error.","section":"Section III B, Eqs. (5) and (9)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The value of ρ_core (approximately 10^8 M⊙ pc^-3) is used throughout as a reference line but the annihilation cross section and WIMP mass assumed to derive it are not stated in the text or caption; a one-line statement would make the figures self-contained.","section":"Fig. 1 and Section III A","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The denominator of the second square-root factor in Eq. (14) is difficult to parse as typeset; the intermediate steps from Eq. (13) to the r^-4/3 result should be checked and the expression cleaned up.","section":"Section IV, Eq. (14)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Reference [19] (Zhao et al.) is listed as 'in preparation' and is cited in Section VII for the black-hole growth-rate estimate; either a published substitute should be given or the reliance on it should be made explicit in the text.","section":"References","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The replacement of the disk with a spherical mass distribution producing the same rotation curve is acknowledged as a simplification; it would help to state how much the inner few-pc dark-matter density in Fig. 6 changes if the disk is treated as flattened, since that is the region the paper's conclusion concerns.","section":"Section VI","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The qualitative conclusion is likely to survive, but the abstract's quantitative claim about the required seed mass is not established at the radius the paper itself identifies as relevant, and the no-baryon inspiral estimate is inconsistent with the paper's own Section VI. These are fixable within the manuscript's scope and should be addressed before publication."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Bottom line: the qualitative claim holds and is worth taking seriously, but the quantitative boundary behind abstract:s4 is stated more firmly than Fig. 3 supports. The stress-test note lands on both counts, and neither is acknowledged in the text. What is new is the off-center formation channel. GS assumed a zero-mass seed growing adiabatically at the exact center of a cuspy halo. Ullio, Zhao, and Kamionkowski point out that a seed formed off-center must spiral in by dynamical friction, and that the inspiral either heats the inner cusp (if the seed is massive) or takes longer than a Hubble time (if it is light). That is a genuine loophole in the GS picture, and it is not in GS or QHS. The adiabatic calculation in Section III is standard and correctly executed: Eddington inversion, radial-action conservation, and the reproduction of A = 7/3 for NFW in Fig. 1 is a real internal check. The instantaneous-growth result (r^-4/3) in Section IV is a nice addition, and the paper is honest about its approximations, including the factor-of-2 agreement between the circular-orbit and isotropic treatments. Where it is soft: the pivot is Fig. 3, and the boundary is quoted at the wrong radius. The spike draws on the halo mass within ~50-60 pc (Section II A), but the text quotes 100 pc for a 10^4 M_sun seed. For an NFW cusp, t_df scales as r^{5/2}/M, so at 50 pc the inspiral is roughly 5x faster; a 10^4 M_sun seed (M_BH/260) arrives in ~2 Gyr, squarely inside the regime where Section V says adiabatic contraction yields a dramatic spike. Second, Fig. 3 uses a baryon-free halo, but Section VI's contracted profile is denser by a factor of a few at 100 pc, which shortens t_df further. The result is a window of seed masses (~2x10^3 to ~10^4 M_sun) that both arrive in time and preserve the GS spike. The paper's own Fig. 4 and Fig. 5 show this branch exists; whether it is populated is not settled by Fig. 3 at the relevant radius. Minor: Ref. [19] is 'in preparation' and carries the AGN-era growth-rate claim in the conclusions, and the Nakano-Makino r^-0.5 profile is imported from one N-body study and applied generically without a bound. Who should read it: anyone working on indirect detection toward the Galactic center or on adiabatic growth of BHs in DM halos. The qualitative takeaway, that the GS spike is not a robust prediction, is correct and useful. The quantitative threshold in abstract:s4 needs tightening before it is quoted. Recommendation: send it out. The central argument is sound and the paper is honest; the referee should push on the Fig. 3 boundary and on the seed formation-radius distribution.","headline":"The off-center seed channel is a real loophole in Gondolo-Silk, but the Fig. 3 inspiral boundary that carries the quantitative claim is quoted at the wrong radius and with an un-contracted halo.","tokens_in":18528,"tokens_out":3329,"would_cite":true,"duration_ms":66237,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["95.35.+d","14.80.Ly","95.55.Vj"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The claimed dark-matter spike at the Galactic center is not a generic prediction: it requires the central black hole to have grown slowly, from a near-zero seed, exactly at the center of a cuspy halo made of very cold orbits, and realistic黑","keywords":["dark matter spike","Galactic center","black hole growth","adiabatic contraction","dynamical friction","neutralino annihilation","WIMP indirect detection","NFW profile"],"falsifier":"A numerical simulation, or a dynamical measurement, showing that a black-hole seed well below a tenth of the present mass can reach the Galactic center within a Hubble time while the surrounding dark-matter cusp stays intact would restore the steep spike and with it the annihilation bounds.","tokens_in":18622,"feed_emoji":"🌌","tokens_out":2293,"duration_ms":48812,"temperature":0.7,"pith_summary":"A widely quoted calculation holds that as the Milky Way's central black hole grew, it squeezed the surrounding dark matter into a very dense spike, with density rising so steeply toward the center that the annihilation rate of neutralino dark matter would diverge and exceed experimental upper bounds. That claim, if true, would let null gamma-ray and radio searches rule out either neutralino dark matter or a cuspy halo. This paper asks what initial conditions that spike actually requires and then redoes the calculation with the dynamical processes the original treatment left out: the black hole forming away from the halo's exact center, spiraling inward by dynamical friction, merging, and growing inside a galaxy that also contains stars. The authors conclude the very-dense spike either disappears entirely or is greatly weakened, so the annihilation bounds lose their force as arguments against WIMPs or against cuspy halos.","feed_headline":"Galactic dark-matter spike may be an artifact","feed_subtitle":"If the black hole spiraled in from off-center, it heats the inner cusp, so null annihilation searches prove nothing.","key_machinery":"The argument rests on adiabatic invariants in a spherical potential: the angular momentum $L$ and the radial action $J_r$ are conserved when the black hole grows slowly, so the distribution function is carried over unchanged, $f_f(E_f,L)=f_i(E_i,L)$. For an initial power-law cusp $rho_i propto r^{-gamma}$ this gives the spike slope $A=(9-2gamma)/(4-gamma)$, i.e. $2.25 < A < 2.5$ for $0<gamma<2$, and a circular-orbit toy model reproduces the same scaling from angular-momentum conservation alone. The competing piece of machinery is the dynamical-friction inspiral time, which sets whether a seed can reach the center at all and therefore decides which regime the Galaxy is in.","core_discovery":"The paper's central claim is that the Gondolo-Silk very-dense spike, with a dark-matter density profile steeper than $r^{-2}$, is an artifact of an idealized setup rather than a robust consequence of black-hole growth. Reproducing the standard adiabatic-contraction machinery, the authors confirm that a black hole grown slowly at the exact center of an NFW cusp does produce a spike with slope $A=7/3$, matching the earlier result. But they then show the spike is built entirely from particles that were initially on very cold orbits within roughly the inner 50 pc, the region enclosing about the black-hole mass. If the seed black hole forms off-center, it must sink by dynamical friction, and the Chandrasekhar inspiral time exceeds a Hubble time unless the seed is already at least a significant fraction of the present black-hole mass. A seed that heavy heats and evacuates the inner cusp as it sinks, leaving a shallow $r^{-0.5}$ profile instead of a spike; a seed light enough to preserve the spike cannot arrive in time. The subsequent at-the-center growth of the black hole squeezes the remaining halo only mildly, whether that growth is adiabatic or instantaneous.","pith_inferences":["The paper turns a dark-matter prediction into a black-hole-formation discriminator: the presence or absence of a spike measures where and how fast the seed formed, which is otherwise hard to observe.","The same reasoning should apply to other galaxies with measured black-hole masses: the spike, and hence the annihilation flux, should be suppressed wherever the black hole shows evidence of having merged or sunk into place rather than grown in situ.","If the inspiral threshold is really a factor-of-a-few boundary around the Hubble time, then a modest improvement in the inner potential from baryonic compression could flip individual galaxies between the spike and no-spike regimes, making the prediction environment-dependent rather than universal.","An independent handle would be a direct measurement of the central dark-matter profile slope on 10-100 pc scales, which would test whether the cusp survives to the radii where the spike would have to be built."],"forward_implications":["Null searches for neutralino annihilation radiation from the Galactic center cannot be used to exclude neutralino dark matter, because the predicted flux depends on a spike that need not be there.","Likewise, such null searches do not constrain whether the Milky Way's dark halo has a central cusp, since the cusp can be heated away by the black hole's own inspiral.","The existence of a dark-matter spike becomes a probe of black-hole formation history: a detected spike would favor slow growth from a tiny seed placed essentially at the halo center.","For a seed to sink to the center within a Hubble time it must be at least roughly a tenth of the present black-hole mass, which in turn means the cusp is destroyed rather than amplified.","Any annihilation signal predicted for the Galactic center should be computed with a shallow, inspiral-heated profile rather than the steep adiabatic spike."],"supporting_citations":[{"why":"Gondolo and Silk; the very-dense spike prediction this paper sets out to test and weaken.","marker":"[9]"},{"why":"Quinlan, Hernquist and Sigurdsson; supplies the scaling result $A=(9-2gamma)/(4-gamma)$ and the phase-space-singularity origin of the spike.","marker":"[8]"},{"why":"Young; the earlier adiabatic-growth calculation for a non-singular isothermal distribution, giving the shallower $r^{-1.5}$ spike.","marker":"[6]"},{"why":"Nakano and Makino; N-body result that inspiral of a black hole leaves an $r^{-0.5}$ cusp, the basis for the heated-profile branch.","marker":"[17]"},{"why":"Navarro, Frenk and White; the NFW profile used as the initial dark-matter distribution.","marker":"[10]"},{"why":"Moore et al.; the steeper alternative cusp profile used to check that the conclusion is not NFW-specific.","marker":"[11]"},{"why":"Binney and Tremaine; the textbook formalism for the radial action, Eddington inversion and adiabatic invariants.","marker":"[15]"},{"why":"Magorrian and Tremaine; the present-day stellar-consumption growth rate used to argue most black-hole mass formed early.","marker":"[14]"}],"fun_headline_variants":["Galactic center dark-matter spike hinges on an idealized black hole","Off-center black hole seeds erase the Galactic dark-matter spike","The Gondolo-Silk spike needs a seed black hole that can't arrive in time","Heavy seeds sink and heat the cusp, leaving no dark-matter spike","Spike survives only if the black hole grows at the exact center"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The verdict hinges on the dynamical-friction inspiral time computed with Chandrasekhar's formula, which the authors themselves note depends on the Coulomb factor and orbital eccentricity, and whose threshold falls only a factor of a few from the Hubble time at the relevant 100 pc scale.","fun_headline_variants_meta":{"raw":{"variants":["Galactic center dark-matter spike hinges on an idealized black hole","Off-center black hole seeds erase the Galactic dark-matter spike","The Gondolo-Silk spike needs a seed black hole that can't arrive in time","Heavy seeds sink and heat the cusp, leaving no dark-matter spike","Spike survives only if the black hole grows at the exact center"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1399,"prompt_tokens":989,"completion_tokens":410,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":326}},"tokens_in":989,"tokens_out":410,"duration_ms":7999,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":326,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T17:58:13.470441+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A numerical simulation, or a dynamical measurement, showing that a black-hole seed well below a tenth of the present mass can reach the Galactic center within a Hubble time while the surrounding dark-matter cusp stays intact would restore the steep spike and with it the annihilation bounds.","supporting_citations":[{"cited_title":"Phys. Rev. Lett. 83, 1719","cited_arxiv_id":null,"evidence_quote":"Gondolo and Silk; the very-dense spike prediction this paper sets out to test and weaken."},{"cited_title":"Astro- phys. J. 440, 554","cited_arxiv_id":null,"evidence_quote":"Quinlan, Hernquist and Sigurdsson; supplies the scaling result $A=(9-2gamma)/(4-gamma)$ and the phase-space-singularity origin of the spike."},{"cited_title":"Astrophys. J. 242, 1232","cited_arxiv_id":null,"evidence_quote":"Young; the earlier adiabatic-growth calculation for a non-singular isothermal distribution, giving the shallower $r^{-1.5}$ spike."},{"cited_title":"Astrophys. J. 525, L77","cited_arxiv_id":null,"evidence_quote":"Nakano and Makino; N-body result that inspiral of a black hole leaves an $r^{-0.5}$ cusp, the basis for the heated-profile branch."},{"cited_title":"The Structure of Cold Dark Matter Halos","cited_arxiv_id":"astro-ph/9508025","evidence_quote":"Navarro, Frenk and White; the NFW profile used as the initial dark-matter distribution."},{"cited_title":"Moore et al., Astrophys","cited_arxiv_id":null,"evidence_quote":"Moore et al.; the steeper alternative cusp profile used to check that the conclusion is not NFW-specific."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Binney and Tremaine; the textbook formalism for the radial action, Eddington inversion and adiabatic invariants."},{"cited_title":"Mon. Not. R. Astron. Soc. 309, 447","cited_arxiv_id":null,"evidence_quote":"Magorrian and Tremaine; the present-day stellar-consumption growth rate used to argue most black-hole mass formed early."}],"review_version":1}