1. CUSP or CORE Antonino Del Popolo Antonino Del Popolo AiFa Bonn, Germany AiFa Bonn, Germany

2. Outline The cusp/core problem in CDM haloes The cusp/core problem in CDM haloes Proposed solutions Proposed solutions Semi-Analytical Models and the cusp/core problem Semi-Analytical Models and the cusp/core problem

3. Structure formation

4. Main problems of the  -CDM paradigm  Despite successes of ΛCDM on large and intermediate scales, serious issues remain on smaller, galactic and sub-galactic, scales.  Dark matter cusps in galaxy centers, in particular absent LSBs and in dwarf Irr, dominated by dark matter Flores & Primack 1994: pointed out that at small radii, the halos are not going to be singular (the density would not increase monotonically with radius): from analysis of the flat rotation curves of the low surface brightness (LSB) galaxies. LSBs are used because there is not much baryonic matter inside LSB systems, therefore, there is not much baryonic infall that could have modified the dark matter halo profile. Other studies (Moore 1994; Burkert 1995; Kravtsov et al. 1998; Borriello & Salucci 2001; de Blok et al. 2001; de Blok & Bosma 2003, etc.) indicates that the shape of the density profile is shallower than what is found in numerical simulations ( = 0.2 ± 0.2 (de Blok, Bosma, & McGaugh 2003)) cusp core

5. Navarro, Frenk & White (1997) log(density) log(radius) inner slope in higher-resolution simulations is steeper (~ –1.5) than the NFW value (–1.0) Moore et al. (1998) mass resolution Asymptotic outer slope -3; inner -1 Asymptotic outer slope -3; inner -1 Navarro et al. 2004 r -2 radius at which

6. Stadel et al. (2008) (mass resolution 1000 Solar masses.Slope at 0.05% R_vir is -0.8) Fitting Formula, Stadel-Moore

7. Gentile et al. 2004 (and similarly Gentile et al. 2007) have decomposed the rotational curves for 5 spiral galaxies into their stellar, gaseous and dark matter components and fit the inferred density distribution with various models and found that models with a constant density core is preferred. Burkert: with a DM core  =  s /(1+r/r s )(1+(r/r s ) 2 ) NFW  =  s /(r/r s )(1+r/r s ) 2 Moore  =  s /(r/r s ) 1.5 (1+(r/r s ) 1.5 ) HI-scaling, with a cst factor MOND, without DM Gentile et al 04

8. CL0024+1654 Tyson, Kochanski & Dell’Antonio (1998) Gravitational lensing yield conflicting estimates, as well, sometime in agreement with Numerical simulations (Dahle et al 2003; Gavazzi et al. 2003) or finding much shallower Slopes (-0.5) (Sand et al. 2002; Sand et al. 2004) On cluster scales X-ray analyses have led to wide ranging of value of the slope from: -0.6 (Ettori et al. 2002) to -1.2 (Lewis et al. 2003) till -1.9 (Arabadjis et al. 2002) InnerSlope= 0.57 0.02 Elliptical potentials can be unphysical (Schramm 1994), so the mass distribution is parameterized as a cluster of mass concentrations (“mascons”). Each mascon is based on a power-law (PL) model (Schneider, Ehlers, & Falco 1993) for the mass density versus projected radius

9. Proposed solutions Observational problems Observational problems –Beam smearing; non-circular motion etc. Failure of the CDM model or problems with simulations (del Blok et al 2001, 2003; Borriello & Salucci 2001) (resolution; relaxation; overmerging) Failure of the CDM model or problems with simulations (del Blok et al 2001, 2003; Borriello & Salucci 2001) (resolution; relaxation; overmerging) New physics New physics –WDM (Colin et al. 2000; Sommer-Larsen & Dolgov 2001) –Self-interacting DM (Spergel & Steinhardt 2000; Yoshida et al. 2000; Dave et al. 2001) –Repulsive DM (Goodman 2000) –Fluid DM (Peebles 2000), –Fuzzy DM (Hu et al. 2000), –Decaying DM (Cen 2001), –Self-Annihilating DM (Kaplinghat et al. 2000), –Modified gravity Solutions within standard ΛCDM Solutions within standard ΛCDM (requires “heating” of dark matter) (requires “heating” of dark matter) –Rotating bar –Passive evolution of cold lumps (e.g., El Zant et al., 2001) –AGN

10. ALTERNATIVE APPROACH TO N-BODY SIMULATIONS The controversy regarding central slope and universality of the density profile has stimulated a great deal of analytical work, often connected to Gunn & Gott’s SIM (Ryden & Gunn 1987; Avila-Reese 1998; DP2000; Lokas 2000; Nusser 2001; Hiotelis 2002; Le Delliou Henriksen 2003; Ascasibar et al. 2003; Williams et al. 2004). The controversy regarding central slope and universality of the density profile has stimulated a great deal of analytical work, often connected to Gunn & Gott’s SIM (Ryden & Gunn 1987; Avila-Reese 1998; DP2000; Lokas 2000; Nusser 2001; Hiotelis 2002; Le Delliou Henriksen 2003; Ascasibar et al. 2003; Williams et al. 2004). DP2000, Lokas 2000 reproduced the NFW profile considering radial collapse. SIM is improved by calculating the initial overdensity from the perturbation spectrum and eliminating limits of previous SIM’s implementations. DP2000, Lokas 2000 reproduced the NFW profile considering radial collapse. SIM is improved by calculating the initial overdensity from the perturbation spectrum and eliminating limits of previous SIM’s implementations. The other authors in the above list studied the effect of angular momentum, L, and non-radial motions in SIM showing a flattening of the inner profile with increasing L. The other authors in the above list studied the effect of angular momentum, L, and non-radial motions in SIM showing a flattening of the inner profile with increasing L. El-Zant et al. (2001) proposed a semianalytial model: dynamical friction dissipate orbital energy of gas distributed in clumps depositing it in dark matter with the result of erasing the cusp. El-Zant et al. (2001) proposed a semianalytial model: dynamical friction dissipate orbital energy of gas distributed in clumps depositing it in dark matter with the result of erasing the cusp.

11. We assume as Hoffman & Shaham (1985) that objects forms around maxima of the (Gaussian) smoothed density field. We assume as Hoffman & Shaham (1985) that objects forms around maxima of the (Gaussian) smoothed density field. The simplest version of SIM considers an initial point mass, which acts as a nonlinear seed, surrounded by a homogeneous uniformly expanding universe. The simplest version of SIM considers an initial point mass, which acts as a nonlinear seed, surrounded by a homogeneous uniformly expanding universe. In our approach, the density profile of each protostructure is approximated by the superposition of a spherical profile, δ(r), and a random CDM distribution, ε(r), which provides the quadrupole moment of the protostructure. In our approach, the density profile of each protostructure is approximated by the superposition of a spherical profile, δ(r), and a random CDM distribution, ε(r), which provides the quadrupole moment of the protostructure. We study the collapse in presence of ordered and random angular momentum, dynamical friction, and baryons adiabatic contraction (AC). We study the collapse in presence of ordered and random angular momentum, dynamical friction, and baryons adiabatic contraction (AC). The dynamical evolution of matter at the distance x i from the peak is determined by the mean cumulative density perturbation within x i and the maximum radius of expansion can be obtained knowing x i and the mean cumulative density of the perturbation. The dynamical evolution of matter at the distance x i from the peak is determined by the mean cumulative density perturbation within x i and the maximum radius of expansion can be obtained knowing x i and the mean cumulative density of the perturbation. After reaching maximum radius, a shell collapses and will start oscillating and it will contribute to the inner shells with the result that energy will not be an integral of motion any longer. The dynamics of the infalling shells is obtained by assuming that the potential well near the center varies adiabatically (Gunn 1977; FG84; Ryden & Gunn 1987). After reaching maximum radius, a shell collapses and will start oscillating and it will contribute to the inner shells with the result that energy will not be an integral of motion any longer. The dynamics of the infalling shells is obtained by assuming that the potential well near the center varies adiabatically (Gunn 1977; FG84; Ryden & Gunn 1987). The Model: SA +L+DF+BDC *

12. Initial density peak are smooth, but contain many smaller scale positive and negative perturbations that originate in the same Gaussian random field producing the main peak. These secondary perturbations will perturb the motion of the dark matter particles from their otherwise purely radial orbits. Initial density peak are smooth, but contain many smaller scale positive and negative perturbations that originate in the same Gaussian random field producing the main peak. These secondary perturbations will perturb the motion of the dark matter particles from their otherwise purely radial orbits. Ordered angular momentum was calculated by means of the standard theory of acquisition of angular momentum through tidal torques, while the random part of angular momentum was assigned to protostructures according to Avila-Reese et al. (1998) scheme. Ordered angular momentum was calculated by means of the standard theory of acquisition of angular momentum through tidal torques, while the random part of angular momentum was assigned to protostructures according to Avila-Reese et al. (1998) scheme. Dynamical friction was calculated dividing the gravitational field into an average and a random component generated by the clumps constituting hierarchical universes. Dynamical friction was calculated dividing the gravitational field into an average and a random component generated by the clumps constituting hierarchical universes. The baryonic dissipative collapse (adiabatic contraction) was taken into account by means of Gnedin et al. (2004) model and Klypin et al. (2002) model taking also account of exchange of angular momentum between baryons and DM. The baryonic dissipative collapse (adiabatic contraction) was taken into account by means of Gnedin et al. (2004) model and Klypin et al. (2002) model taking also account of exchange of angular momentum between baryons and DM.

13. Results Results

14. Density profile evolution of a halo. The solid line represents the profile at z=10. The profile at z=5, z=3, z=2, z=1, z=0 is represented by the uppermost dashed line, long-dashed line, short-dashed line, dot-dashed line, dotted line, respectively.

15. Dark matter haloes generated with the model described. In panels (a)-(d) the solid line represents the NFW model while the dotted line the density profile obtained with the model of the present paper for masses (panel a), (panel b). The dashed line in panel (b) represents the density profile obtained reducing the magnitude of h, j and mu. a ba

16. c d (panel c), (panel d),. The dashed line in panel (c) represents the Burkert fit to the halo.

17. Distribution of the total specific angular momentum, J Tot. The dotted-dashed and dashed line represents the quoted distribution for the halo n. 170 and n. 081, respectively, of van den Bosch et al. (2002). The dashed histogram is the distribution obtained from our model for the halo and the solid one the angular momentum distribution for the density profile reproducing the NFW halo.

18. Comparison of the rotation curves obtained our model (solid lines) with rotation curves Of four LSB galaxies studied by Gentile et al. (2004). The dotted line represents the fit With a NFW model.

19. Comparison of the rotation curves obtained with the model of the present paper (solid lines) with the rotation curves of four LSB galaxies studied by de Blok & Bosma (2002). The dashed line represents the fit with NFW model.

20. The density profile evolution of a halo. The (uppermost) dot-dashed line represents the total density profile of a halo at z=0. The profile at z=3, z=1.5, z=1 and z=0 is represented by the solid line, dotted-line, short-dashed-line, long-dashed-line, respectively. *

21. –CDM struggles to answer questions of galaxy formation, including missing satellites, cusps vs. cores, and structure in voids. –Numerical simulations for collisionless dark matter consistently suggest the formation of a central cusp rather than a core while galactic rotation curves indicate a relatively flat core rather than a cusp. –SIM has proven to predict correctly density profiles. It agrees with simulations over all radial ranges if the collapse is purely spherical. –SIM with L in, L out, DF, Baryons AC agrees with simulations except in the inner part of the density profile where predicts core-like profiles (different slopes for galaxies and clusters). –On galactic scales, where DM dynamics and baryons dynamics are entangled, the cusp/core problem seems to be a “genuine” one, in the sense that the disagreement between observations and N-body simulations is not due to numerical artifacts or problems with simulations. –At the same time it is an apparent problem, since the disagreement between observations and dissipationless simulations is related to the fact that the latter are not taking account of baryons physics. This means that we are comparing two different systems, one dissipationless (i.e., DM) and the other dissipational (i.e., inner part of structures), and we cannot expect them to have the same behavior. Summary & Conclusions

22. Del Popolo A., 2009, ApJ 698:2093-2113 Del Popolo A., Kroupa P., 2009, A&A 502, 733-747