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Dark matter annihilation in the Galaxy
Veniamin Berezinsky Vyacheslav Dokuchaev Yury Eroshenko


Institute for Nuclear Research, RAS, Moscow


Laboratori Nazionali del Gran Sasso, Italy

14th Lomonosov Conference on Elementary Particle Physics


DM clumps

Standard cosmological scenario with an inflationary-produced primordial fluctuation sp ectrum Spike in the sp ectrum of p erturbations Clumps from isothermal fluctuations Clumps seeded by top ological defects Various DM models


Numerical simulations

3 kp c N = 62 106 , m = 1 .2 1 0
-10

60 p c M ,

0.024 pc

z = 350 26 (Diemand, Moore, Stadel, 2005)


Integral mass function and numb er density of clumps dM dM 0.02(n + 3) M M (r ) DM ncl (M , R )d ln Md ln R = (M , )d ln Md M
int

(Berezinsky, Dokuchaev, Eroshenko, 2003, 2006, 2008)
10 10 dn(M) / dlog M [(h Mpc) ]
-3
16

15

10 10 10 10 10 10 10

14

-1

13

12

M

-1

11

10

9

8

10

-6

10

-5

10

-4

10 10 10 -1 M [h Msolar]

-3

-2

-1

10

0

10

1

(Diemand, Moore, Stadel, 2005)


Remnants (cores) of clumps
gravitational shocks

(E )j E - rough criterium for destruction
j

Gradual mass loss remnants of clumps. Core size = ? Rc /R 10-5 (Gurevich, Zybin, 1995) Rc /R 0.01 (Diemand, Moore, Stadel, 2005)
r int

(r ) r

-

,

N
0

4 r 2 dr

2 int

(r )

There is no dep endence on r if

> 3/2 and Rc /R 1!


Survival probability

1 0.75 0.5 0.25 100 0 80 60

Pr

104 103
40 20

r, kpc

102

cl, Gev cm3
100

Fraction of survived clumps with M = 10 of clump density cl in GeV cm-3 .

-6

M



and

= 2 i n dep endence


50
250

40 30
ann
H

IH

200 150 100 50 0

20 10 0 0 25 50 75 100 125 150 175

Icl I

I

0

25

50

, degree

75 100 , degree

125

150

175

Left: The annihilation signal (upper curve) as a function of the angle between the line of observation and the direction to the Galactic center. Right: amplification of the signal (Icl - IH )/IH .


Transformation of the mass function
1014

dlog M , Mpc

3

1012

3 kpc

1010

dn M

8.5 kpc
108 10 8 10 6 10 4

MM

Numerically calculated modified mass function of clump remnants for galactocentric distances 3 and 8.5 kpc. The solid curve shows the initial mass function.


Despite the small survival probability of clumps during early stage of hierarchial clustering, they provide the major contribution to the annihilation signal (in comparison with the unclumpy DM). The amplification (b oost-factor) can reach 102 or even 103 dep ending on the initial p erturbation sp ectrum and minimum mass of clumps. This b oost-factor must b e included in calculations of the annihilation signals. These remnants of DM clumps form the low-mass tail in the standard mass distribution of small-scale clumps extended much b elow Mmin of the standard distribution. The numerical estimate of the b oost-factor for DM particle annihilation inside clumps is very model-dep endent. It dep ends on nature of DM particles and on their interaction with ambient plasma. The sp ectral index of density p erturbation np affects strongly the b oost-factor.


Lo ops length distribution

Cosmological phase transitions network of cosmic strings interconnections transient stage scaling regime closed loops with l ct , where 0.1. dn
loop

=

Ndl c
3/2 t 3/2 l 5/2

,

where N 2
(Olum, Vilenkin, 2006)

The loops distribution is translated to DM clumps distribution.


Formation of DM clumps at RD stage
Initial sp eed of the loops and rocket effect. vi2 1/2 0.15c (Allen, Shellard,1990) Probability of low velocity loop formation: Plv 2 в 10-7 . Formation of DM clumps at RD stage
x (x + 1) (Kolb, Tkachev, 1994) 3 db 1 1 + d 2b + 1+ x - b = 0, + 2 dx 2 dx 2 b2 is the comoving coordinate.

where x = a( )/aeq , r = a( )b ( ) ,

Continuous evap oration and fast decay approximations. dM l G =- dt c
2

,

lc /(G )

Adiabatic expansion of clumps M

tot

R = const


log eq

10 0 -10 -8 -1

1

0

log

8

-6

-2

log xi

-4 -3

Clump density in the units of density at matter-radiation equality eq in dependence on the loop birth moment xi = a(ti )/aeq and parameter -8 2 = 140 eq -8 = G /(10 c ). The break of the surface down to value corresponds to the proximity of turnaround and loop decay moments.


Ml /l , for the grand-unification-scale G /c 2 10-6 Restrictions: G /c 2 2 в 10-7 ­ CMB 10-7 ­ pulsar timing and nucleosynthesis 3 в 10-8 ­ stars in the first DM haloes seeded by the loops Search for gravitational wave bursts from strings by LIGO


0

2

log I



4

EGRET

6

8

1.5

1.0

0.5

0.0

0.5

1.0

log

8

The annihilation signal (in units cm-2 s-1 dependence on string parameter -8 = G line. The horizontal dashed line shows the I 2 в 10-5 cm-2 s-1 sr-1 . Dotted line approximation.

sr-1 ) from clumps in /(10-8 c 2 ) is shown by solid EGRET data continuous evaporation

100 GeV neutralino DM is incompatible with range of strings parameters 1 в 10-9 < G /c 2 < 5 в 10-9