A solution of the cusp problem in virialized DM halos in standard cosmology

Transcription

1 DSU6, Univesidad Autonoma de Madid, June A solution of the cusp poblem in viialized DM halos in standad cosmology A.G.Dooshkevich, V.N.Lukash, E.V.Mikheeva Asto Space Cente of Lebedev Physics Institute

2 Advanced study in cosmology Analysis of CMB and its polaization Investigation of Ly-α foest Popeties of ealie galaxies and quasas at lage edshifts Popeties of dwaf galaxies and the intenal stuctue of galaxies (black holes, otation cuves, etc) Lukash A solution of the cusp poblem, DSU6, Madid, June

3 Cusp poblem in galaxy halos (simulations) ρ~ -α α (1, 3/) Diemand et al. 4

4 The cusp poblem is being consideed as main poblem of the standad cosmology (DM non-inteacting to bayons) We ague : it is solved within the famewok of standad DM model Lukash A solution of the cusp poblem, DSU6, Madid, June

5 Intenal stuctue of elaxed halos (coes instead of cusps) Idea : take into account the small scale pat of initial cosmological petubations that tansfoms into the themal enegy of DM paticles duing violent elaxation Method : exta entopy of DM paticles elated to initial backgound petubations entopy pofiles elated to density pofiles of DM halos Lukash A solution of the cusp poblem, DSU6, Madid, June

6 Standad cosmological model H = 7 km/s/mpc, h=.7 Ω Λ =.7 Ω m =.3 ΛCDM powe spectum: P(k)=A κt (κ) exp(-r f κ ), κ=k/k k =. h/mpc, A=4σ 8 /k 3 Lukash A solution of the cusp poblem, DSU6, Madid, June

7 H (z) 3 3/ = 1+ Ω (z 3z 3z).5(1 z) m H, z > 1 ρ m = 3H 8 Ω πg m (1 + z) (1 + z) 3 g cm 3 n = ρ m m DM µ 1 (1+ z) 3 cm 3, µ m m DM p Rf - paticle fee path in the ealy Univese m 6 DM 1, Rf < 4 1 > stella halos Lukash A solution of the cusp poblem, DSU6, Madid, June

8 Obsevational and model specta Lukash A solution of the cusp poblem, DSU6, Madid, June

9 Equilibium DM halos Adiabatic and ievesible pocesses Entopy function: F = T/n /3 = p/n 5/3 Hydostatic equilibium: 1 ρ dp d = GM() Initial (backgound) entopy in small scale: F ~ M 1/3-/3 Hieachical and violent elaxation of compessed matte (lage scale): F ~ M 5/6, F ~ M 4/3 Lukash A solution of the cusp poblem, DSU6, Madid, June

10 Entopy of collisionless paticles fo isotopic velocity distibution p = ρ<v > = nt = Fn 5/3 one-dimensional peculia velocity Powe-law density pofiles: α (, ) ρ() - α, M 3- α, p= C 1 +C (1-α) α < 1 - finite pessue in the cente (coe) α 1 - infinite pessue at (cusp) M conseving both fo initial and elaxed matte fields Lukash A solution of the cusp poblem, DSU6, Madid, June

11 F(M) C M 1 + C M 1 β β M β β ( β 1, β ), β 1, = β 5 6 c = β1 = β = αc = α / α 3 ± α α 1 3 oe (β < 5/6): β 1 5, 6, β 3, 5 6 cusp (β 5/6): β 1 5 6, 4 3, β 5 6, 1 3 Lukash A solution of the cusp poblem, DSU6, Madid, June

12 48 low bightness galaxies (LBG, de Blok et al. 1)

13 15 low bighness galaxies (Swates et al. 3)

14 NB (in elation to A. Klypin talk): we call coes by coes and cusps by cusps Lukash A solution of the cusp poblem, DSU6, Madid, June

15 (z, x) Initial velocity field = (1 + z) [x g(z)s(x)] 1 V(z, x) & = H(z) [x 1+ z δ(x) δρ / ρ = H(z)[ + g (z)s(x)] g(z)s(x)], z > 1 div( S) cosmological backgound non-conditional peculia velocity δ( x) = S(x) =, x1 x = xe, q = x/ l v ξ ( x) δ(x1 ) δ(x ) = σ G (q), G() = 1 1 ξij( x) S i(x1)s j(x) = σs [eiejg1(q) + ( δij eiej)g 1(q)] 3 Lukash A solution of the cusp poblem, DSU6, Madid, June

16 small scale density coelations l < 1 kpc (G =.5) lage scale velocity coelations 1 l1 σs = 11 h Mpc (G1 =.5) 1 l v 31 h Mpc (G 1 =.5) Lukash A solution of the cusp poblem, DSU6, Madid, June

17 DM halo fomation (Zel dovich appoximation) (z, x) V(z, x) = (1 + z) 1 [x gs(x)], g 1/ H (1 + z) [x / S (x) = SR (x) + S* (x) 1.(1 + z) 1 g(z)s(x)] local backgound potohalo with scale/mass esolution R (tuns into elaxed halo via violent/hieachical elaxation) сonditional petubations (tansfom adiabatically to micoscopic motion of paticles inside the halo) halo fomation time S R (x) * = (1 + z )x /, S * (x) * =, σ * S S * * σ S Lukash A solution of the cusp poblem, DSU6, Madid, June

18 Vaiance of one-dimensional peculia velocities inside halo v x (z, x) H (1 + z) = e [v (z,x ) v 1/ v * * 1 1 x * = l v q 1 * S (x) (z,x )] e, e = 1 σ 1 v1 H σs(1+ z) (1 G1(q)) v * M 1 15 q 3 M S Lukash A solution of the cusp poblem, DSU6, Madid, June

19 Analytical appoximation 1 G 1 (q) =.5q 4 + q 1.5q + q (p / q) q p 1 3 1, q Dooshkevich, Demianski 5 Lukash A solution of the cusp poblem, DSU6, Madid, June

20 Backgound entopy at moment z F(M) { mdmσv(z,q) 3 = F /3 z5 n (z) 1 + z 5.33 M9, M9 >.56 M9, M9 < 5 M.66, M 1 5/ 3 F = µ kev cm, z 5, M n = Pobability distibution function f / df dw(f) = e F(M), f = πf F(M) f M(q) n 1 M = 3 f = 3 lage vaiations of F fom the mean value Lukash A solution of the cusp poblem, DSU6, Madid, June S

21 Violent elaxation entopy Isotemal shee (Fillmoe & Goldeich 1984) ρ ~, M ~, α ~ F ~ M Collapse of ellipsoide (Guevich, Zybin 1988) Geneated entopy in the cental egion is negligible in compaison with backgound one! 4/3 Lukash A solution of the cusp poblem, DSU6, Madid, June

22 Numeical simulation (N-body) Facilities and limitations Slopes of density and entopy in halo: ρ ~ - α, F ~ M β coe (α<1) o cusp (α >1)? Univesal NFW pofile: x=/ s, ρ ~ x -1 (1+x) -, α=1, β =5/6 Empiical Buket pofile: ρ~(1+x) -1 (1+x ) -1, α=, β= Lukash A solution of the cusp poblem, DSU6, Madid, June

23 Rotation cuves (Machesini )

24 Rotation cuves (Machesini )

25

26 Galaxy clustes pofiles (Pointecouteau et al., 5)

27 M(x) M Obsevational otation cuves M ρ = (x m 4 πρ ρ + x)(1 + x 3 s, x ) m, x m << 1, x max, vc vmax x m = 1.3, x max 3.5, vc vmax xm ln(1 + x / xm ) +.5 ln(1 = 1+ xm x (x) = (, (x) (x) (x) x s 1.3) ).5 M(x) xm M(x) 5. xm Lukash A solution of the cusp poblem, DSU6, Madid, June + x m actg(x)

28 Analytically modeled halos F b (M) ~ M β b, b < 5/ 6 F (M) ~ M, β 5/ 6 F(M) = 1M β + M b β κ = F (M) b F (M) g (, 1) Lukash A solution of the cusp poblem, DSU6, Madid, June

29 α β k ~ 1 α β k << 1 (M/M max ) 1/3 Lukash A solution of the cusp poblem, DSU6, Madid, June

30 =5/6 / max =4/3 κ~1 solid line, κ << 1 dashed line, NFW stas, Buket dots Lukash A solution of the cusp poblem, DSU6, Madid, June

31 Conclusions * The backgound entopy can pevent the cusp fomation fo halos with 1 6 M < M < 1 1 M * Fo smalle and lage galaxies and fo clustes of galaxies its impact is attenuated * The impact of the backgound entopy allows to epoduce the obseved otation cuves Lukash A solution of the cusp poblem, DSU6, Madid, June