CUSP or CORE CUSP or CORE Antonino Del Popolo Antonino Del Popolo - PowerPoint PPT Presentation

* CUSP or CORE CUSP or CORE Antonino Del Popolo Antonino Del Popolo Vulcano Workshop 2010 Workshop 2010 Vulcano May 23-29, Vulcano, Italy

* Outline Outline • The cusp/core problem in CDM haloes • The cusp/core problem in CDM haloes • Proposed solutions • Proposed solutions • Secondary • Secondary Infall Infall Model (SIM) and the cusp/core Model (SIM) and the cusp/core problem problem

* Structure formation 1.02 0.02 � = ± H 71 4 km s Mpc / / = ± tot 0 0.73 0.04 � = ± t 13.7 0.2 Gyr = ± � 0 0.27 0.04 � = ± m 0.044 0.04 � = ± B

Main problems problems of of the the Λ -CDM Main Λ -CDM * paradigm paradigm  Despite successes of Λ CDM on large and cusp 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 core Flores & Primack Primack 1994 1994: at small radii halos are not going to be singular (analysis of : at small radii halos are not going to be singular (analysis of Flores & the flat rotation curves of the low surface brightness (LSB) galaxies). the flat rotation curves of the low surface brightness (LSB) galaxies). Other studies Other studies (Moore 1994; (Moore 1994; Burkert Burkert 1995; 1995; Kravtsov Kravtsov et al. 1998; et al. 1998; Borriello Borriello & & Salucci Salucci 2001; de Blok Blok et al. 2001; de et al. 2001; de Blok Blok & & Bosma Bosma 2003, etc.) indicates that the shape of 2003, etc.) indicates that the shape of 2001; de the density profile is shallower than what is found in numerical simulations the density profile is shallower than what is found in numerical simulations ( = 0.2 ± 0.2 (de Blok ( = 0.2 ± 0.2 (de � Blok, , Bosma Bosma, & , & McGaugh McGaugh 2003)) 2003))

Moore et al. (1998) * Navarro, Frenk Frenk & & Navarro, inner slope in higher-resolution simulations is inner slope in higher-resolution simulations is White (1997) • Asymptotic outer slope -3; • White (1997) Asymptotic outer slope -3; steeper (~ – –1.5) than the NFW value ( 1.5) than the NFW value (– –1.0) 1.0) steeper (~ inner -1 inner -1 mass log(density) ) log(density resolution � 2 ) � � 1] ln( � � / � � 2 ) = ( � 2/ � )[( r / r r -2 r -2 radius at radius at which which � = � d log � / d log r = 2 log(radius) ) log(radius � � ( r ) c crit � = 2 ( r / r )( 1 r / r ) + s s r ( M ) c ( M ) vir � vir r ( M ) s 3 c � � vir 0 ( M ) � � c 3 [ln( 1 c ) c /( 1 c )] + � + Navarro et al. 2004

* Stadel et et al. al. (2009) (2009) Stadel (mass resolution (mass resolution 1000 1000 Solar masses.Slope masses.Slope Solar at 0.05% R_vir R_vir is is -0 -0.8 .8) ) at 0.05% Fitting Formula, Stadel-Moore

* Gentile et al. 2004 (and similarly Gentile et al. 2007): models with a constant density core are preferred. Burkert: with a DM core ρ = ρ s /(1+r/r s )(1+(r/r s ) 2 ) NFW ρ = ρ s /(r/r s )(1+r/r s ) 2 Moore ρ = ρ s /(r/r s ) 1.5 (1+(r/r s ) 1.5 ) HI-scaling, with a cst factor MOND, without DM

* CL0024+1654 CL0024+1654 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) Tyson, Kochanski & Dell’Antonio (1998) model (Schneider, Ehlers, & Falco 1993) for the mass density versus projected radius • 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)

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

* ALTERNATIVE APPROACH TO N-BODY ALTERNATIVE APPROACH TO N-BODY SIMULATIONS SIMULATIONS • • Gunn & & Gott Gott’ ’s SIM s SIM ( (Ryden Ryden & & Gunn Gunn 1987; 1987; Avila-Reese Avila-Reese 1998; 1998; Gunn DP2000; Lokas Lokas 2000; 2000; Nusser Nusser 2001; 2001; Hiotelis Hiotelis 2002; Le 2002; Le Delliou Delliou DP2000; Henriksen 2003; 2003; Ascasibar Ascasibar et et al. 2003; Williams al. 2003; Williams et et al. 2004). al. 2004). Henriksen • • DP2000, Lokas Lokas 2000 2000 reproduced reproduced the NFW the NFW profile profile considering considering radial radial DP2000, collapse. . collapse • • The other other authors authors in the in the above above list list studied studied the the effect effect of of angular angular The momentum, L, and , L, and non-radial non-radial motions motions in SIM in SIM showing showing a a flattening flattening momentum of the inner inner profile profile with with increasing increasing L. L. of the • • El-Zant El-Zant et et al. (2001) al. (2001) proposed proposed a a semianalytial semianalytial model: model: dynamical dynamical friction dissipate friction dissipate orbital orbital energy energy of gas of gas distributed distributed in in clumps clumps depositing depositing it it in dark in dark matter matter with with the the result result of of erasing erasing the the cusp cusp. .

Why SIM (or SIM (or semi-analytical semi-analytical models models) ) ? ? Why • advantages: • advantages: – computationally efficient (it takes about 10 s to compute the computationally efficient (it takes about 10 s to compute the – density profile of a given object at a given epoch on a density profile of a given object at a given epoch on a desktop PC) desktop PC) – flexible – flexible (one can (one can study study the the effects effects of of physical physical processes processes one one at a time) at a time) – can incorporate many physical effects in at least a schematic – can incorporate many physical effects in at least a schematic manner manner • disadvantages: • disadvantages: – treatment of physical processes is only approximate – treatment of physical processes is only approximate (but (but SIM provides a viable dynamical model for predicting the SIM provides a viable dynamical model for predicting the structure and evolution of the density profile of dark matter structure and evolution of the density profile of dark matter haloes (Toth Toth & & Ostriker Ostriker 1992; 1992; Huss Huss et al. 1999; et al. 1999; Ascasibar Ascasibar et et haloes ( al. 2006, etc.). al. 2006, etc.).