Spiked Dark Matter Profile

• Spiked dark matter profiles are centrally concentrated enhancements formed when an SMBH steepens a cusp, yielding power-law densities that vary with the halo's initial properties.
• Formation mechanisms include canonical adiabatic growth as well as noncanonical channels like PBH mini-spikes, relativistic effects, and dark matter self-interactions that alter the inner slope.
• Observational diagnostics—from gamma-ray and neutrino signals to gravitational-wave effects—critically depend on the spike model, initial halo profile, and annihilation or depletion processes.

Searching arXiv for recent and foundational papers on dark matter spikes around black holes. A spiked dark matter profile is a centrally concentrated dark-matter overdensity that develops around a black hole, most often a supermassive black hole (SMBH), when the hole reshapes the phase-space distribution of the surrounding halo. In the canonical adiabatic-growth picture, an initial inner halo cusp is transformed into a much steeper inner density law inside a characteristic spike radius, but subsequent work has shown that this idealized description is not universal: relativistic dynamics, stellar heating, annihilation saturation, self-interactions, primordial-black-hole formation channels, and the microscopic nature of dark matter can all alter the spike or even turn enhancement into depletion (Sandick et al., 2016, Crespi et al., 2024).

1. Canonical definition and analytic form

The standard starting point is an initial cuspy halo, often written as

$$\rho_{\rm cusp}(r)=\rho_0\Bigl(\frac{r}{r_0}\Bigr)^{-\gamma_c},$$

with inner slope $\gamma_c\sim1.0\!-\!1.5$. If an SMBH grows adiabatically at the halo center, the density inside the spike radius $R_{\rm sp}$ steepens to

$$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$

which gives $\gamma_{sp}\approx2.3\!-\!2.4$ for $\gamma_c=1.0\!-\!1.5$. For an NFW seed with $\gamma_c=1$, this reduces to the familiar $\gamma_{sp}=7/3$ result (Sandick et al., 2016).

A widely used phenomenological representation is a single power law inside the spike radius,

$$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$

valid for $r<r_{\rm sp}$, with $\gamma_c\sim1.0\!-\!1.5$0 defined at $\gamma_c\sim1.0\!-\!1.5$1. In some gravitational-wave applications, the normalization is traded for $\gamma_c\sim1.0\!-\!1.5$2, since $\gamma_c\sim1.0\!-\!1.5$3 sets the overall normalization of the inner potential (Tiwari et al., 5 Aug 2025).

The canonical adiabatic result is not unique. For an initially finite-central-density or cored halo, the classic Gondolo–Silk-type construction gives a shallower spike, $\gamma_c\sim1.0\!-\!1.5$4, rather than $\gamma_c\sim1.0\!-\!1.5$5. Fully relativistic treatments of constant-density initial configurations recover precisely this $\gamma_c\sim1.0\!-\!1.5$6 behavior just outside the innermost bound region (Crespi et al., 2024, Yu et al., 12 Mar 2025).

The definition of “spike” is therefore structural rather than tied to a single slope: it denotes the black-hole-induced inner rearrangement of the halo, usually expressed as a broken profile that matches onto the outer halo at $\gamma_c\sim1.0\!-\!1.5$7, but whose interior behavior depends on both dynamics and microphysics.

2. Characteristic scales, inner cutoffs, and saturation structure

For the Galactic Center, representative parameters used in spike studies are $\gamma_c\sim1.0\!-\!1.5$8, Schwarzschild radius $\gamma_c\sim1.0\!-\!1.5$9, stellar-velocity dispersion $R_{\rm sp}$0, and influence radius $R_{\rm sp}$1. In idealized adiabatic models this implies

$R_{\rm sp}$2

while a related Galactic-center parametrization gives $R_{\rm sp}$3 pc and $R_{\rm sp}$4 pc for $R_{\rm sp}$5 and $R_{\rm sp}$6 km/s (Sandick et al., 2016, Luque et al., 2024).

Practical spike profiles are almost always piecewise. One standard three-zone form consists of an inner annihilation plateau, an intermediate spike, and an outer cusp: $R_{\rm sp}$7 The core radius is set by equating the annihilation time to the spike age,

$R_{\rm sp}$8

Closely related constructions define an annihilation-saturation density

$R_{\rm sp}$9

and a saturation radius $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$0 via $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$1 (Sandick et al., 2016, Luque et al., 2024).

In relativistic and orbit-based treatments, the innermost spike does not necessarily terminate in a flat plateau. Several Galactic-center analyses use a softened inner law

$$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$2

for $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$3, combined with a relativistic suppression factor such as $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$4 or $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$5, and set $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$6 below $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$7 (Chattopadhyay et al., 26 Feb 2026, Luque et al., 2024).

These inner prescriptions matter because all indirect-detection observables scale with $$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$8. In gamma-ray analyses the line-of-sight integral is

$$\rho_{\rm sp}(r)\propto r^{-\gamma_{sp}},\qquad \gamma_{sp}=\frac{9-2\gamma_c}{4-\gamma_c},$$9

and for a Majorana WIMP with $\gamma_{sp}\approx2.3\!-\!2.4$0, the velocity-suppressed term is enhanced near the black hole through the local virial relation $\gamma_{sp}\approx2.3\!-\!2.4$1 (Sandick et al., 2016).

3. Formation channels and noncanonical spike classes

The literature now contains several distinct spike classes whose inner slopes and even qualitative behavior differ from the canonical adiabatic cusp.

Scenario	Inner behavior	Defining feature
Adiabatic SMBH growth in cuspy halo	$\gamma_{sp}\approx2.3\!-\!2.4$2, $\gamma_{sp}\approx2.3\!-\!2.4$3	Classical Gondolo–Silk construction
Adiabatic growth in cored/finite-density halo	$\gamma_{sp}\approx2.3\!-\!2.4$4	Finite central density
PBH mini-spike	$\gamma_{sp}\approx2.3\!-\!2.4$5 between $\gamma_{sp}\approx2.3\!-\!2.4$6 and $\gamma_{sp}\approx2.3\!-\!2.4$7	Early-universe turnaround/infall
Relativistic Bondi scalar spike	$\gamma_{sp}\approx2.3\!-\!2.4$8 piecewise	Self-interacting dark scalar accretion

For primordial black holes (PBHs), the mini-spike arises from early-universe infall rather than galactic adiabatic compression. In the cold-DM limit, the profile takes the form

$\gamma_{sp}\approx2.3\!-\!2.4$9

with $\gamma_c=1.0\!-\!1.5$0 and $\gamma_c=1.0\!-\!1.5$1. This $\gamma_c=1.0\!-\!1.5$2 law is traced to adiabatic compression of an initially uniform medium and to self-similar secondary infall after matter–radiation equality (Ireland, 2024).

When the orbital distribution and annihilation are treated self-consistently in PBH spikes, the central annihilation-modified region is not a flat plateau. For an initial exponential angular-momentum distribution of nearly radial orbits, orbit-averaged depletion produces a weak central cusp,

$\gamma_c=1.0\!-\!1.5$3

rather than $\gamma_c=1.0\!-\!1.5$4. The associated change in annihilation luminosity is an $\gamma_c=1.0\!-\!1.5$5 correction rather than a qualitative breakdown of the spike picture (Eroshenko, 2024).

Fermionic dark matter introduces a different departure from the standard power-law template. In the finite-temperature RAR model, dilute Boltzmannian fermions reproduce the classical $\gamma_c=1.0\!-\!1.5$6 spike, but semi-degenerate fermions with a dense core plus halo do not. The numerical profile has $\gamma_c=1.0\!-\!1.5$7 immediately outside the capture region, then decreases to values $\gamma_c=1.0\!-\!1.5$8 over $\gamma_c=1.0\!-\!1.5$9. In this class, the SMBH does not always enhance the density; for sufficiently large black-hole mass and sufficiently heavy fermions it can instead deplete it (Crespi et al., 2024).

A further noncanonical class appears in self-interacting dark scalar models treated through relativistic Bondi accretion. There the density cannot be fit by a single power law, but admits a three-segment form: $\gamma_c=1$0 which is much shallower than the $\gamma_c=1$1 profile associated with Coulomb-like self-interactions (Feng et al., 2021).

These alternatives make clear that “spike” is not synonymous with “$\gamma_c=1$2”. Inference based on a universal broken power law is therefore model dependent.

4. Relaxation, heating, depletion, and the possibility of density reduction

The main astrophysical mechanism that degrades a canonical spike is gravitational scattering by stars in the nuclear cluster. A widely used phenomenological model writes

$\gamma_c=1$3

so that the spike radius evolves as

$\gamma_c=1$4

For $\gamma_c=1$5, the depletion factor is $\gamma_c=1$6, suppressing the normalization and shrinking the spike radius (Sandick et al., 2016).

More broadly, violent processes such as galactic mergers, dynamical heating by stars, or self-interactions can flatten the spike to $\gamma_c=1$7. This places the classic adiabatic prediction $\gamma_c=1$8 at one end of a much wider physical range (Tiwari et al., 5 Aug 2025).

Annihilation itself also regulates the innermost density. In Galactic-center orbit analyses, steep Gondolo–Silk spikes are eroded into a weak $\gamma_c=1$9 cusp inside the saturation radius, with

$\gamma_{sp}=7/3$0

For S2-based fits, the surviving NFW-seed spike is compatible with the stellar-orbit constraints only if

$\gamma_{sp}=7/3$1

at $\gamma_{sp}=7/3$2 confidence, so that annihilation has already reduced the density enough to evade the dynamical bounds (Shen et al., 2023).

The possibility of depletion rather than enhancement is particularly explicit in fermionic models. For semi-degenerate RAR halos, the spike peak density first rises and then falls as $\gamma_{sp}=7/3$3 increases; there is a threshold $\gamma_{sp}=7/3$4 above which $\gamma_{sp}=7/3$5. Moreover, there is a critical fermion mass $\gamma_{sp}=7/3$6 keV such that for $\gamma_{sp}=7/3$7 no adiabatic spike exceeds the original central density (Crespi et al., 2024).

A common misconception is therefore that a central black hole necessarily creates a larger annihilation signal. The contemporary literature does not support that as a generic statement: the sign and magnitude of the effect depend on heating history, annihilation saturation, initial halo structure, and dark-matter phase-space properties.

5. Observational diagnostics and empirical constraints

Indirect searches remain the most developed probe because annihilation rates scale as $\gamma_{sp}=7/3$8. For the Galactic Center, a benchmark Fermi-LAT comparison integrates the flux over $\gamma_{sp}=7/3$9 GeV and a small angle $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$0, using the point source Sgr A$$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$1 with observed flux $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$2. In such analyses, the relative enhancement over a pure NFW profile can exceed $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$3, especially when the $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$4 term dominates. Yet the allowed dark-matter parameter space depends strongly on the spike assumptions: for a depleted spike with $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$5, even a thermal relic with $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$6 produces flux several orders of magnitude below $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$7, whereas idealized adiabatic spikes exclude $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$8 GeV for $$\rho(r)=\rho_{\rm sp}\Bigl(\frac{r}{r_{\rm sp}}\Bigr)^{-\gamma_{\rm sp}},$$9 (Sandick et al., 2016).

More recent line-search recasts sharpen this conclusion for thermal WIMPs. Photon-line constraints from Fermi-LAT and MAGIC exclude the entire Gondolo–Silk range $r<r_{\rm sp}$0 for $r<r_{\rm sp}$1, even when the $r<r_{\rm sp}$2 branching fraction is only $r<r_{\rm sp}$3. Neutrino-line searches with IceCube give a complementary bound, with the strongest limit $r<r_{\rm sp}$4 around $r<r_{\rm sp}$5 TeV (Chattopadhyay et al., 26 Feb 2026).

Radio and microwave emission provide a second $r<r_{\rm sp}$6-weighted channel. For a spike with $r<r_{\rm sp}$7, the small-angle surface-brightness scaling is $r<r_{\rm sp}$8, much steeper than the NFW expectation $r<r_{\rm sp}$9. In the specific Galactic-center synchrotron calculations with direct $\gamma_c\sim1.0\!-\!1.5$00 annihilation, a $\gamma_c\sim1.0\!-\!1.5$01 GeV WIMP plus spike yields $\gamma_c\sim1.0\!-\!1.5$02 Jy sr$\gamma_c\sim1.0\!-\!1.5$03 at $\gamma_c\sim1.0\!-\!1.5$04 GHz, compared with $\gamma_c\sim1.0\!-\!1.5$05 Jy sr$\gamma_c\sim1.0\!-\!1.5$06 for NFW. Planck and future SKA-like observations were proposed as probes of $\gamma_c\sim1.0\!-\!1.5$07, $\gamma_c\sim1.0\!-\!1.5$08, and $\gamma_c\sim1.0\!-\!1.5$09 (Lacroix et al., 2013).

The $\gamma_c\sim1.0\!-\!1.5$10 keV bulge line has also been modeled with a Galactic-center spike. Using a four-zone piecewise profile with either a Gondolo–Silk spike or a stellar-heated spike softened to $\gamma_c\sim1.0\!-\!1.5$11, dark matter with mass up to approximately $\gamma_c\sim1.0\!-\!1.5$12 MeV can reproduce most of the observed bulge intensity while remaining compatible with disk-emission and in-flight-annihilation constraints, provided the disk component is dominated by an astrophysical low-energy positron source (Luque et al., 2024).

Dynamical probes constrain the spike independently of annihilation physics. Fits to Keck and VLT S-star data rule out an initial slope $\gamma_c\sim1.0\!-\!1.5$13 for the generalized NFW spike at $\gamma_c\sim1.0\!-\!1.5$14 confidence. For $\gamma_c\sim1.0\!-\!1.5$15, the analyses find $\gamma_c\sim1.0\!-\!1.5$16 pc at $\gamma_c\sim1.0\!-\!1.5$17, excluding the corresponding Gondolo–Silk prediction $\gamma_c\sim1.0\!-\!1.5$18 pc, and also obtain $\gamma_c\sim1.0\!-\!1.5$19 at $\gamma_c\sim1.0\!-\!1.5$20, excluding $\gamma_c\sim1.0\!-\!1.5$21 (Shen et al., 2023).

Gravitational-wave observables are emerging as a particularly clean spike diagnostic. For binaries orbiting inside an SMBH spike, the dark-matter-induced center-of-mass acceleration produces a secular Doppler modulation of the waveform. Fisher plus Bayesian forecasts for LISA and DECIGO indicate that $\gamma_c\sim1.0\!-\!1.5$22 can be measured to a few-percent precision when $\gamma_c\sim1.0\!-\!1.5$23, improving to $\gamma_c\sim1.0\!-\!1.5$24 for $\gamma_c\sim1.0\!-\!1.5$25, while even $\gamma_c\sim1.0\!-\!1.5$26 can be constrained at the $\gamma_c\sim1.0\!-\!1.5$27 level. In that setup, dynamical friction and tidal effects are negligible compared with the conservative dark-matter potential (Tiwari et al., 5 Aug 2025).

A distinct extragalactic dynamical route is reverberation mapping. In a sample of fourteen AGN, five objects show $\gamma_c\sim1.0\!-\!1.5$28 evidence for an enclosed mass that grows with radius across multiple emission lines. A joint fit gives a preferred universal dark-matter profile

$\gamma_c\sim1.0\!-\!1.5$29

consistent with a mildly relaxed spike (Sharma et al., 11 Jun 2025).

6. Relativistic, numerical, and geometric refinements

Relativistic phase-space treatments do not simply reproduce the Newtonian broken-power-law profile. In Schwarzschild geometry, a numerical fit to the spike density over $\gamma_c\sim1.0\!-\!1.5$30 is

$\gamma_c\sim1.0\!-\!1.5$31

with best-fit parameters that are nearly universal across several halo and black-hole configurations: $\gamma_c\sim1.0\!-\!1.5$32 and $\gamma_c\sim1.0\!-\!1.5$33. This corresponds to a quasi-isothermal $\gamma_c\sim1.0\!-\!1.5$34 cusp over $\gamma_c\sim1.0\!-\!1.5$35 together with a relativistic cutoff at $\gamma_c\sim1.0\!-\!1.5$36 (Zhang et al., 2024).

Spin modifies the spike further. In the exact Kerr geometry, black-hole rotation increases the dark-matter density close to the hole despite angular-momentum transfer to the halo. For $\gamma_c\sim1.0\!-\!1.5$37, the nonrotating relativistic value is $\gamma_c\sim1.0\!-\!1.5$38, while an empirical fit gives

$\gamma_c\sim1.0\!-\!1.5$39

with $\gamma_c\sim1.0\!-\!1.5$40; at $\gamma_c\sim1.0\!-\!1.5$41, one finds $\gamma_c\sim1.0\!-\!1.5$42 and a normalization increase of about $\gamma_c\sim1.0\!-\!1.5$43 at the influence radius for $\gamma_c\sim1.0\!-\!1.5$44 (Ferrer et al., 2017).

The most significant numerical revision to the classical picture comes from fully simulated cold-dark-matter spikes in Hernquist halos. Using 218 SWIFT N-body runs, an empirical one-parameter “spike + Hernquist” profile was proposed: $\gamma_c\sim1.0\!-\!1.5$45 where $\gamma_c\sim1.0\!-\!1.5$46, $\gamma_c\sim1.0\!-\!1.5$47, and

$\gamma_c\sim1.0\!-\!1.5$48

This differs sharply from the classic $\gamma_c\sim1.0\!-\!1.5$49 scaling: the simulations give $\gamma_c\sim1.0\!-\!1.5$50 at low $\gamma_c\sim1.0\!-\!1.5$51 and saturation at $\gamma_c\sim1.0\!-\!1.5$52 for $\gamma_c\sim1.0\!-\!1.5$53, together with $\gamma_c\sim1.0\!-\!1.5$54 outer-halo depletion for $\gamma_c\sim1.0\!-\!1.5$55 (Kamermans et al., 2024).

Halo modeling can dominate observational inference. In M87, the assumption of an NFW host plus $\gamma_c\sim1.0\!-\!1.5$56 spike yields extremely strong annihilation limits, excluding thermal $\gamma_c\sim1.0\!-\!1.5$57-wave dark matter up to $\gamma_c\sim1.0\!-\!1.5$58 TeV. But adopting a cored Burkert halo changes the normalization at the spike radius by about five orders of magnitude; in that case the smooth halo overwhelmingly dominates the annihilation signal, with $\gamma_c\sim1.0\!-\!1.5$59, and the spike contribution becomes negligible (Lacroix et al., 2015, Phoroutan-Mehr et al., 2024).

At the level of spacetime backreaction, the spike is not accurately represented by rest-mass density alone. In an Einstein-cluster treatment of a Hernquist-seeded Milky-Way spike, the kinetic term contributes about $\gamma_c\sim1.0\!-\!1.5$60 of the peak energy density, the stress tensor is mildly anisotropic, all standard energy conditions are satisfied, and the resulting metric deviations from Schwarzschild reach fractional levels $\gamma_c\sim1.0\!-\!1.5$61, approximately $\gamma_c\sim1.0\!-\!1.5$62 larger than when only the mass density is used as the source (Xiong et al., 16 Nov 2025).

The present status is therefore mixed. Classical power-law spikes remain a useful organizing approximation, but current work shows that their slope, normalization, radial extent, and observational impact are all highly contingent on the underlying halo model, the black-hole growth history, the relativistic orbital structure, and the nature of the dark matter itself. This suggests that robust use of spiked profiles in indirect detection, stellar dynamics, or gravitational-wave inference requires system-specific modeling rather than a universal Gondolo–Silk template.