2000, ApJ, 542, 622 (CAV 2000) 2001, ApJ, 559, 516 (Avila-Reese et al. 2001)

1. Halos en una cosmología con materia oscura tibiaPedro Colín (CRyA, UNAM, Mexico)colaboradoresV. Avila-Reese y O. Valenzuela (IAUNAM) • 2000, ApJ, 542, 622 (CAV 2000) • 2001, ApJ, 559, 516 (Avila-Reese et al. 2001) P. Bode

2. The dark side of the universe The dark matter appears to be dissipationless, collisionless, and cold. Candidates cover a range of masses from 10-22 eV (fuzzy dm) to 103-4 M￮ ~ 1070-71 eV. The group leaders Axions: Non-thermal candidate: it is born cold. Proposed to explain the CP violation in the strong force. 1 meV < mα< 10-2 eV. SUSY: The lightest supersymetric particle. Mass ~ hundreds of GeV. Halos do not shine and are not round. Nevertheless, sidm can produce flat cores.

3. Hot, warm, and cold dark matter Textbook definition (Kolb & Turner 1990): dark matter is usually defined as hot or cold if at the moment of decoupling from the rest of the cosmic plasma it is relativistic or nonrelativistic, respectively. “Normal”, known, active neutrinos are an example of hot dark matter! They are fermions. Warm dark matter have a typical velocity of few km/s at the time of structure formation. They can be important at subgalactic scale. Two effects on the structure and distribution of matter:

4. Non-negligible primordial velocity dispersion • Filtering of the power spectrum (suppresion of small-scale • structure) • 2.- Phase space density is conserved (Liouville theorem) Q = ρ/<v2>3/2 for collisionless particles Q can not increase. <v2>= 3 P/nm,P and n depend on the distribution function f. For thermal, active, neutrinos f is given by f(p) = (ep/T+ 1)-1, where TD>> m. Q = qg m4(q= 0.0019625 and g=2) or in astronomical units Q= 5 10-4 (M￮/pc3)/(km/s)3 (m/1 keV)4(HD 2000)

5. Q Q goes as r-1.875 (Taylor & Navarro 2001) for CDM halos. rcore= 0.44 (Q G vasymp)-1/2 rthermal= 5.5 kpc (m/100 eV)-2 (vasymp/30 km s-1)-1/2 ( isothermal sphere model with β= 0, HD 2000). For m=0.5 keV rthermal= 85 pc. m= 0.5 keV Constraints on the core radius of Fornax as a function of central phase density (Strigari et al. 2006). From observations. The long-dashed, solid, and short-dashed lines use β=0.5, 0.0, and -0.5, respectively.

6. WDM simulations (ingredients) • ΛWDM flat cosmology: Ωm= 0.3 ΩΛ=0.7 • Random Gaussian distributed density field • Pν(k) (thermal$ and non-equilibrium production of sterile neutrino&) • σ8=1.0, 0.8 • vi= vi(Zeldovich) + vi(thermal)* * Speed comes from f(p) (FD thermal neutrino). On the other hand, velocities are randomly oriented. $Much earlier decoupling. &Come from active neutrino mixing. Both are much less abundant than normal neutrinos.

7. Power spectrum n= 1 Density fluctuations grow by gravitational instability. P(k) as kn n  -3 Garcia-Bellido (2002) wdm truncation k3P(k): the amount of power, ~ overdensity2, as a function of scale.

8. and the wdm mwdm= 0.5 keV Bode et al. (2001) BBKS Neutrino esteril ( Abazajian) Pwdm(k)= T2wdm(k) Pcdm(k)

9. Adaptive Refinement Tree code The ART code (KKK 1997) achieves high spatial resolution by refining the base uniform grid in all high density regions with an automated refinement algorithm. A slice through the refinement structure (base grid is not shown) in one of the CDM simulations with 323 particles and (b) the corresponding slice through the particle distribution. (b)

10. ART multiple mass scheme ART has the ability to handle particles with different masses (Klypin et al. 2001). We thus can select an arbitrary region to be resimulated with more resolution. Example: distribution of particles of different Masses in a thin slice through the center of a MW size halo at z = 10.

11. Mvir, Rvir, etc. Rvir is defined as the radius at which the average halo density is 337times the background density for our selected cosmology, according to the TH model. Mvir is then the mass within Rvir. Distribution of particles of different masses at z = 0.

12. BDM: halo finding algorithm The BDM algorithm finds the positions of local maxima in the density field smoothed at the scale of interest and applies physically motivated criteria* to test whether a group of particles is a gravitationally bound halo. Np= 2 105 particles Distribution of DM in a Virgo-like cluster. The cluster virial mass is 2.45 × 1014h-1M. The particles inside a sphere of the radius of 1.5 h-1 Mpc (solid circle) are shown. The size of the small box, shown to provide the comparison scale, is 100 h-1 kpc. Circles represent halos found by BDM. There are 121 halos in the plot (Colin et al. 1999).

13. CDM versus WDM mν= 0.5 keV 10 Mpc/h Particles are color coded according to the log of their density Np= 643 particles Mh= 3.0 1012 M￮ Mh= 2.7 1012 M￮ ( ~ 500,000 particles) vrms~ 4 km/s at z=40 for 0.5 keV neutrino

14. The evolution CDM WDM Ifrit (Ionization FRont Interactive Tool) Nick Gnedin.

15. The substructure problem Moore et al. (1999) 400 kpc/h Vmax= 240 km/s Old simulations.

16. and the wdm Rf = 0.2 (Ωwdmh2)1/3 (mw/1 keV)-4/3 Mpc Mf= (4π/3) ρm (λf/2)3 λf= 2π/kf = 13.6 Rf kf when Twdm = 0.5. For BBKS Twdm= exp ( -0.5 kRf – 0.5(kRf)2)

17. Concentration I mν = 0.6 keV CDM linear fit (isolated halos) Host halos have ~ 105 particles Lbox= 15 Mpc/h r1/5 = the radius within which 1/5 of the halo mass is contained. > 90 particles (pqueño) CDM linear fit (halos in groups and galaxy-size halos) WDM subhalos are twice less concentrated as their CDM counterparts

18. Concentration II Filtering mass for Rf= 0.2 and 1.7 Mpc. 1011 1014 mwdm= 0.6 keV Halos with mass below the filtering mass. HDM Mass (h-1 M￮) Halos below the filteringmass are well fit by a NFW profile but are less concentrated.

19. Density profiles (vrms= 0) Lbox= 15 Mpc/h Mhalo= (1.7,3.3) 1012 M￮/h Masses > Mf= 3 1011 M￮/h 0.6 keV 1.0 keV 1.7 keV Density profiles are well described by the NFW formula. Halo x for Rf= 0.2 is less concentrated than for CDM. 2 halos cdm 4 halos 3 halos X same halo (CAV 2000)

20. Density profiles with vth Density profiles of subhalos are well described by NFW fit.The halo x is also cuspy even with a thermal velocity = 2 vth (605 eV). The innermost bin is = 400 pc/h. Masses below Mf (Avila-Reese et al. 2001)

21. More and new art wdm simulations mwdm= 0.5 The halo K is taken from this simulation 10 Mpc/h

22. A flat core detected? Lbox= 10 Mpc/h mwdm= 0.5 keV res= 1.2 kpc/h Rvir = 285 kpc/h Np ~ 550,000 particles P(k) (Abazajian, sterile neutrino) Mf= 2.6 x 1012 Msun/h vth 4 res

23. Halos just below the exponential cutoff of P(k) Mf= 1.7 x 1014 Msun/h Forma del perfil. Avila-Reese et al. (2001)

24. A convergence study 32 k 4 res A 1.3 x 1012 Msun/h halo with 16 m particles inside Rvir. LowRes: 2 m, 255k, 32k.

25. Are they well fit by a NFW profile? ρ The good Δρ/ρ

26. The bad

27. The ugly Most halos present this kind of “two-regime density profile”.

28. Halo good with vth 4 res

29. Halo good with vth 4 res

30. Halo good with vth 4 res

31. Summary • The goal was to find the core predicted by theory using • the sterile neutrino P(K) and its non-thermal DF. • 2. A flat core was seen by us (Avila-Reese et al. 2001) • when vth was increased artificially. • 3. According to our results, the core appears to be close to • that predicted by, for example, HD (2000). • 4.-Density profiles of halos close or below the cut of the • power spectrum are not well fit by the NFW expression.

32. Summary continues 5.- Halos appear to show a “two-regime” density profile. The inner DP lies above its best NFW fit while the intermedium one lies below. 6.- Is the inner zone a reflect of the early monolithic collapse and the intermedium of secondary infall?