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Lebedev Physical Institute, Moscow, Russia
The evolution of dark matter in central areas of galaxies is considered (Milky Way is taken as an example). It is driven by scattering off of dark matter particlesby bulge stars and their absorption by the supermassive black hole, and is described by diffusion equation in phase space of energy and angular momentum.
It is shown that by now the density of dark matter inside central parsec is greatly diminished: approximately 10% of initial dark matter mass is captured byblack hole, about a half is evaporated. The annihilation of particles may explain observed gamma-ray flux from Galactic center.
dimensional diffusion equation – for energy and angu-lar momentum. However, even one-dimensional ap-
Dark matter is known to be the dominant compo-
proximations give qualitative predictions, being solv-
nent in outer parts of galaxies and in galactic clusters.
However, its behavior in central parts of galaxies isalso worth investigating.
• The diffusion along angular momentum axis L
creates flux of DM particles into black hole and
First of all, in the process of galaxy formation, bary-
drives the distribution function towards character-
onic matter (gas) cools and settles down in the grav-
istic logarithmic profile: f (L) ∝ ln L + const.
itational potential well created by dark matter, thus
• The diffusion along energy E leads to dark mat-
increasing the depth of the well and causing adiabatic
ter heating. The system “stars + DM particles”
contraction of dark matter (Blumenthal et al., 1986;
tends towards thermodynamical equilibrium and
Gnedin et al., 2004; Sellwood & McGaugh, 2005;
equipartition of energy, but due to enormous dif-
Vasiliev, 2006). Similar effect happens in the very
ference in masses this simply causes transfer of en-
centre of the galaxy, where a supermassive black hole
ergy to DM particles. Therefore, a stationary
dominates gravitational potential inside so-called re-
solution cannot exist, contrary to the case of
gion of influence (r < rh = GMbh/σ2), where σ2 is
star distribution around a black hole.
stellar velocity dispersion outside rh. (in our Galaxyrh = 2 pc). The adiabatic contraction should lead to
very steep dark matter density spike near a black hole
So the dark matter distribution is essentially time-
region of influence after 1010 yr of evolution (for
(Gondolo & Silk, 1999), which should be decreased
dependent, the timescales for diffusion along L and
Milky Way halo, initial DM density profile ρ(r) =
by self-annihilation of dark matter particles to form a
E being similar. Hence, a full two-dimensional equa-
density plateau or, more likely, a weak cusp (Vasiliev,
tion should be integrated numerically. This was done
σv = 3 · 10−26 cm3/s, particle mass M
for a dozen of variants, which differ in initial mod-
els of dark matter halo and in inclusion or neglection
The numbers are somewhat different for various ini-tial dark matter halo models, but the proportion re-
The more important process, however, is the gravita-
of some processes (e.g. dark matter annihilation or
mains approximately the same: after 1010 years al-
tional relaxation of dark matter on stars of galactic
most a half of DM mass is removed from the central
nucleus and their capture by the black hole, which is
region of black hole influence, mostly due to heat-
ing by stars. The amount of DM captured by blackhole is of order 10% of initial mass, and even less is
The quantitative results essentially depend on the
chosen initial model of dark matter halo, but the
The evolution of dark matter distribution function
The difference between initial models is reduced in
f is investigated by means of orbit-averaged Fokker-
result of the processes discussed. The knowledge of
density profile is crucial for predictions of annihila-tion flux from Galactic centre. The flux is a product
of astrophysical factor, dependent on spatial distri-
bution of dark matter, and a factor dependent on
particle mass and cross-section. Recently γ-radiation
Here ξα are the phase-space variables (e.g. energy E
from Galactic centre was detected by H.E.S.S. Aha-
and angular momentum L per unit mass), which are
ronian et al. (2006), which can be attributed to dark
integrals of motion in absence of scattering; G is the
matter annihilation. The observed flux is compatible
jacobian. The r.h.s consists of collision term, which
with the results of our calculation for rather typical
is determined by gravitational scattering of DM par-
ticles by bulge stars, and self-annihilation term. Thediffusion coefficients Dαβ are related to the relaxation
The conclusion is that dark matter distribution in
galactic centres significantly changes during the life-time of the galaxy, mainly because of gravitational
Additionally, the presense of supermassive black
interaction with stars of galactic nucleus and super-
hole in the centre of a galaxy imposes a boundary
massive black hole in its centre. Detailed calculation
condition at low angular momenta: particles with
of evolution is needed for making predictions of an-
L < Lg = 2GMbh/c2 are captured by the black
hole on passage of orbital pericentre. The form ofboundary condition depends on particle energy: low-
Figure 1: Evolution of dark matter density profile
energy particles with short periods “feel” an absorb-
ing boundary, while high-energy particles can diffuse
Initial profile is taken in the form ρ(r) ∝ r−γ, γ = 1
in and out the area L < Lg during their long orbital
for inner part of NFW profile (red dashed line).
period (the “loss cone” is full).
F. Aharonian et al., Phys.Rev.Lett. 97, 221102 (2006).
During formation of bulge (green dashed line for stardensity profile) and black hole in its centre (region
G. Bertone, D. Merritt, Phys.Rev.D 72, 103502 (2005).
We consider the problem both inside and outside the
r < rh ≈ 2 pc is dominated by black hole gravi-
G. Blumenthal, S. Faber, R. Flores, J. Primack, ApJ 301, 27
black hole region of influence consistently. The re-
tation) the dark matter is compressed adiabatically
laxation time is roughly constant inside rh, and is
(solid red line is DM density after contraction).
O. Gnedin, A. Kravtsov, A.Klypin, D. Nagai, ApJ 616, 16
less than Hubble time for the case of Milky Way
Subsequent DM evolution is governed by gravita-
(rh = 2 pc, Tr ∼ 2 · 109 yr); outside rh the relax-
tional scattering on stars which leads to DM heat-
P. Gondolo, J. Silk, Phys.Rev.Lett. 83, 1719 (1999).
ation time increases, so that evolution is significant
ing, and by capture by black hole. The density after
A. Ilyin, K. Zybin, A. Gurevich; JETP 98, 1 (2004).
only within roughly 10 pc. The diffusion coefficients
1010 years of evolution (solid blue line) is reduced
D. Merritt, Phys.Rev.Lett. 92, 201304 (2004).
αβ are different in these two regions.
several orders of magnitude inside rh. Additionally,if the self-annihilation cross-section is large enough,
J. Sellwood, S. McGaugh, ApJ 634, 70 (2005).
Unlike previous studies (Ilyin et al., 2004; Merritt,
then density in the very centre is depleted even more
2004; Bertone & Merritt, 2005), we consider full two-
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