CUSP or CORECUSP or CORE

Antonino Del PopoloAntonino Del Popolo AiFa Bonn, GermanyAiFa Bonn, Germany

OutlineOutline

• The cusp/core problem in CDM haloesThe cusp/core problem in CDM haloes

• Proposed solutionsProposed solutions

• Semi-Analytical Models and the cusp/core Semi-Analytical Models and the cusp/core problemproblem

1.02 0.02

0.73 0.04

0.27 0.04

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71 4 / /

13.7 0.2

H km s Mpc

t Gyr

0.044 0.04B

Structure formation

Main problems of the Main problems of the -CDM -CDM paradigmparadigm

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 1994Flores & Primack 1994: pointed out that at small radii, the halos are not : pointed out that at small radii, the halos are not going to be singular (the density would not increase monotonically with going to be singular (the density would not increase monotonically with radius): from analysis of the flat rotation curves of the low surface radius): from analysis of the flat rotation curves of the low surface brightness (LSB) galaxies. brightness (LSB) galaxies. LSBsLSBs are used because there is not much baryonic matter inside LSB are used because there is not much baryonic matter inside LSB systems, therefore, there is not much baryonic infall that could have systems, therefore, there is not much baryonic infall that could have modified the dark matter halo profile. modified the dark matter halo profile. Other studiesOther studies (Moore 1994; Burkert 1995; Kravtsov et al. 1998; Borriello (Moore 1994; Burkert 1995; Kravtsov et al. 1998; Borriello & Salucci 2001; de Blok et al. 2001; de Blok & Bosma 2003, etc.) indicates & 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 that the shape of the density profile is shallower than what is found in numerical simulations numerical simulations ( = 0.2 ± 0.2 (de Blok, Bosma, & McGaugh 2003))( = 0.2 ± 0.2 (de Blok, Bosma, & McGaugh 2003))

cusp

core

Navarro, Frenk Navarro, Frenk & White (1997)& White (1997)Navarro, Frenk Navarro, Frenk & White (1997)& White (1997)

log(

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sity

log(

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log(radius)log(radius)

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ccc

cM

Mr

MrMc

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virc

s

virvir

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inner slope in higher-resolution simulations inner slope in higher-resolution simulations is steeper (~ –1.5) than the NFW value (–is steeper (~ –1.5) than the NFW value (–1.0)1.0)

Moore et al. (1998)

mass resolution

•Asymptotic outer slope -3; inner -1Asymptotic outer slope -3; inner -1

Navarro et al. 2004

ln( / 2) ( 2 /)[(r /r 2) 1]

d log /d log r2

rr-2-2 radius at radius at whichwhich

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

Fitting Formula, Stadel-Moore

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/rs)(1+(r/rs)2)

NFW = s/(r/rs)(1+r/rs)2

Moore = s/(r/rs)1.5(1+(r/rs)1.5)

HI-scaling, with a cst factorMOND, without DM

Gentile et al 04

CL0024+1654CL0024+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, & Falco1993) for the mass density versus projected radius

Proposed solutionsProposed solutions• Observational problemsObservational problems

– Beam smearing; non-circular motion etc.Beam smearing; non-circular motion etc.• Failure of the CDM model or problems with simulationsFailure of the CDM model or problems with simulations (del Blok (del Blok

et al et al 2001, 2003; Borriello & Salucci 2001) (resolution; relaxation; 2001, 2003; Borriello & Salucci 2001) (resolution; relaxation; overmergingovermerging))

• New physicsNew physics– WDM (Colin et al. 2000; Sommer-Larsen & Dolgov 2001)WDM (Colin et al. 2000; Sommer-Larsen & Dolgov 2001)– Self-interacting DM (Spergel & Steinhardt 2000; Yoshida et al. Self-interacting DM (Spergel & Steinhardt 2000; Yoshida et al.

2000; Dave et al. 2001)2000; Dave et al. 2001)– RRepulsive DM (Goodman 2000)epulsive DM (Goodman 2000)– Fluid DM (Peebles 2000),Fluid DM (Peebles 2000),– Fuzzy DM (Hu et al. 2000),Fuzzy DM (Hu et al. 2000),– Decaying DM (Cen 2001),Decaying DM (Cen 2001),– Self-Self-Annihilating DM (Kaplinghat et al. 2000),Annihilating DM (Kaplinghat et al. 2000),– Modified gravityModified gravity

• Solutions within standard Solutions within standard ΛΛCDMCDM (requires “heating” of dark matter)(requires “heating” of dark matter)

– Rotating barRotating bar– Passive evolution of cold lumps (e.g., El Zant et al., 2001)Passive evolution of cold lumps (e.g., El Zant et al., 2001)– AGNAGN

ALTERNATIVE APPROACH TO N-BODY ALTERNATIVE APPROACH TO N-BODY SIMULATIONSSIMULATIONS

• The controversy regarding central slope and universality of the The controversy regarding central slope and universality of the density profile has stimulated a great deal of analytical work, often density profile has stimulated a great deal of analytical work, often connected to Gunn & Gott’s SIM connected to Gunn & Gott’s SIM (Ryden & Gunn 1987; Avila-Reese (Ryden & Gunn 1987; Avila-Reese 1998; DP2000; Lokas 2000; Nusser 2001; Hiotelis 2002; Le Delliou 1998; DP2000; Lokas 2000; Nusser 2001; Hiotelis 2002; Le Delliou Henriksen 2003; Ascasibar et al. 2003; Williams et al. 2004).Henriksen 2003; Ascasibar et al. 2003; Williams et al. 2004).

• DP2000, Lokas 2000DP2000, Lokas 2000 reproduced the NFW profile considering radial reproduced the NFW profile considering radial collapse. SIM is improved by calculating the initial overdensity collapse. SIM is improved by calculating the initial overdensity from the perturbation spectrum and eliminating limits of previous from the perturbation spectrum and eliminating limits of previous SIM’s implementations.SIM’s implementations.

• The The other authorsother authors in the above list studied the effect of angular in the above list studied the effect of angular momentum, L, and non-radial motions in SIM showing a flattening momentum, L, and non-radial motions in SIM showing a flattening of the inner profile with increasing L.of the inner profile with increasing L.

• El-Zant et al. (2001)El-Zant et al. (2001) proposed a semianalytial model: dynamical proposed a semianalytial model: dynamical friction dissipate orbital energy of gas distributed in clumps friction dissipate orbital energy of gas distributed in clumps depositing it in dark matter with the result of erasing the cusp.depositing it in dark matter with the result of erasing the cusp.

• We assume as Hoffman & Shaham (1985) that objects forms around We assume as Hoffman & Shaham (1985) that objects forms around maxima of the (Gaussian) smoothed density field.maxima of the (Gaussian) smoothed density field.

• The simplest version of SIM considers an initial point mass, which acts as a The simplest version of SIM considers an initial point mass, which acts as a nonlinear seed, surrounded by a homogeneous uniformly expanding nonlinear seed, surrounded by a homogeneous uniformly expanding universe. universe.

• In our approach, the density profile of each protostructure is approximated In our approach, the density profile of each protostructure is approximated by the superposition of a spherical profile, δ(r), and a random CDM by the superposition of a spherical profile, δ(r), and a random CDM distribution, ε(r), which provides the quadrupole moment of the distribution, ε(r), which provides the quadrupole moment of the protostructure. protostructure.

• We study the collapse in presence of ordered and random angular We study the collapse in presence of ordered and random angular momentum, dynamical friction, and baryons adiabatic contraction (AC).momentum, dynamical friction, and baryons adiabatic contraction (AC).

• The dynamical evolution of matter at the distance xThe dynamical evolution of matter at the distance x ii from the peak is from the peak is determined by the mean cumulative density perturbation within xdetermined by the mean cumulative density perturbation within x ii and the and the maximum radius of expansion can be obtained knowing xmaximum radius of expansion can be obtained knowing x ii and the mean and the mean cumulative density of the perturbation. cumulative density of the perturbation.

• After reaching maximum radius, a shell collapses and will start oscillating 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 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 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 obtained by assuming that the potential well near the center varies adiabatically (Gunn 1977; FG84; Ryden & Gunn 1987). adiabatically (Gunn 1977; FG84; Ryden & Gunn 1987).

The Model: SA +L+DF+BDC*

• Initial density peak are smooth, but contain many smaller Initial density peak are smooth, but contain many smaller scale positive and negative perturbations that originate in scale positive and negative perturbations that originate in the same Gaussian random field producing the main peak. the same Gaussian random field producing the main peak. These secondary perturbations will perturb the motion of These secondary perturbations will perturb the motion of the dark matter particles from their otherwise purely radial the dark matter particles from their otherwise purely radial orbits.orbits.

• Ordered angular momentum was calculated by means of Ordered angular momentum was calculated by means of the standard theory of acquisition of angular momentum the standard theory of acquisition of angular momentum through tidal torques, while the random part of angular through tidal torques, while the random part of angular momentum was assigned to protostructures according to momentum was assigned to protostructures according to Avila-Reese et al. (1998) scheme.Avila-Reese et al. (1998) scheme.

• Dynamical friction was calculated dividing the gravitational Dynamical friction was calculated dividing the gravitational field into an average and a random component generated field into an average and a random component generated by the clumps constituting hierarchical universes. by the clumps constituting hierarchical universes.

• The baryonic dissipative collapse (adiabatic contraction) The baryonic dissipative collapse (adiabatic contraction) was taken into account by means of Gnedin et al. (2004) was taken into account by means of Gnedin et al. (2004) model and Klypin et al. (2002) model taking also account of model and Klypin et al. (2002) model taking also account of exchange of angular momentum between baryons and DM.exchange of angular momentum between baryons and DM.

RResultsesults

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.

910 M

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.

1110 M1210 M

a ba

c d

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

810 M1010 M

810 M

Distribution of the total specific angular momentum, JTot. 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.

1210 M

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 fitWith a NFW model.

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.

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.

1410 M1410 M

*

– CDM struggles to answer questions of galaxy formation, including missing CDM struggles to answer questions of galaxy formation, including missing satellites, cusps vs. cores, and structure in voids.satellites, cusps vs. cores, and structure in voids.

– Numerical simulations for collisionless dark matter consistently suggest the Numerical simulations for collisionless dark matter consistently suggest the formation of a central cusp rather than a core while galactic rotation curves formation of a central cusp rather than a core while galactic rotation curves indicate a relatively flat core rather than a cusp.indicate a relatively flat core rather than a cusp.

– SIM has proven to predict correctly density profiles. It agrees with SIM has proven to predict correctly density profiles. It agrees with simulations over all radial ranges if the collapse is purely spherical.simulations over all radial ranges if the collapse is purely spherical.

– SIM with LSIM with Linin , L , Loutout , DF, Baryons AC agrees with simulations except in the , DF, Baryons AC agrees with simulations except in the inner part of the density profile where predicts core-like profiles (different inner part of the density profile where predicts core-like profiles (different slopes for galaxies and clusters).slopes for galaxies and clusters).

– On galactic scales, where DM dynamics and baryons dynamics are On galactic scales, where DM dynamics and baryons dynamics are entangled, the cusp/core problem seems to be a “genuine” one, in the entangled, the cusp/core problem seems to be a “genuine” one, in the sense that the disagreement between observations and N-body simulations sense that the disagreement between observations and N-body simulations is not due to numerical artifacts or problems with simulations. is not due to numerical artifacts or problems with simulations.

– At the same time it is an apparent problem, since the disagreement At the same time it is an apparent problem, since the disagreement between observations and dissipationless simulations is related to the fact between observations and dissipationless simulations is related to the fact that the latter are not taking account of baryons physics. This means that 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 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 the other dissipational (i.e., inner part of structures), and we cannot expect them to have the same behavior.them to have the same behavior.

Summary & Conclusions

Del Popolo A., 2009, ApJ 698:2093-2113Del Popolo A., 2009, ApJ 698:2093-2113

Del Popolo A., Kroupa P., 2009, A&A 502, 733-747Del Popolo A., Kroupa P., 2009, A&A 502, 733-747