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A solution of the cusp problem in relaxed halos

A solution of the cusp problem in relaxed halos. E.V. Mikheeva in collaboration with A.G.Doroshkevich and V.N.Lukash Astro Space Centre of P.N.Lebedev Physics Institute. Cusp problem: density profiles.  ( r )  r -  at r →0. observations.  < 1 - core.   1 - cusp.

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A solution of the cusp problem in relaxed halos

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  1. A solution of the cusp problem in relaxed halos E.V. Mikheeva in collaboration withA.G.Doroshkevich andV.N.Lukash Astro Space Centre of P.N.Lebedev Physics Institute

  2. Cusp problem: density profiles (r) r- at r→0 observations  <1 - core   1 - cusp N-body simulations Diemand et al. 2004

  3. The problem of cusp can be solved in the framework of standard CDM

  4. Idea and method Idea:to take into accountthe small scalepart of initial background perturbations that transforms into random velocities of DM particles in the process of relaxation Method:total entropy = initial (given) + generated (gained during relaxation)

  5. Entropy function Entropy profiles related to density profiles in DM halos for DM particles with isotropic velocity distribution in relaxed halos: p = <v2> =nT = Fn5/3 entropy function one-dimensional peculiar velocity

  6. (r) r-, Power-law density profiles:(0,2) + Hydrostaticequilibrium: p= C1 + C2 r2(1-)  =1is a critical value 0<  <1 - core (finite pressure in the centre) 1  < 2 - cusp (infinite pressure in the centre)

  7. Entropy mass function сore : cusp:

  8. Initial entropy Linear field of density perturbations • Displacement • Velocity • Density perturbation • Coordinates:Euler Lagrange

  9. DM halo formation(Zel’dovich approximation) local background – protohalo with linear scale R[collapsing into virialized halo byz0withcompression factor ~5(1+z0)] сonditionalperturbations[transform (adiabatically at least) into microscopic particles’ motion in halo]

  10. M Critical value for 

  11. Generated entropy Violent relaxation entropy (special analytical models) Isotermalshere (Fillmore & Goldreich 1984) Collapse of ellipsoide (Gurevich, Zybin 1988, 1995)

  12. Analytically modeled halos

  13. Generated rotation curves Fb<<F b=0.333 b=0.333 Fb~F NFW b=0.567 b=0.567 Burkert b=0.667 b=0.667 r/rmax g =4/3 (isothermal sphere) g=5/6 (NFW)

  14. Conclusions *The background entropy canpreventthe cusp formation for halos with 106M< M < 1012 M *For smallerand larger galaxies and for clusters of galaxies the impact of background entropy isattenuated *The impact of the background entropy allows to reproduce the observed rotation curves *N-body simulations: underestimation of initial perturbations at small scale?

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