ANGULAR MOMENTUM AND THE STRUCTURE OF DM HALOS Chiara Tonini Special guest: Andrea Lapi Director: Paolo Salucci C.T., A. Lapi & P. Salucci (astro-ph/ , ApJ in press)

Plan of the talk I - Halos in phase-space (microscopic) NFW halo and its dynamical properties Perturbing the halo with angular momentum A new equilibrium configuration II – Angular momentum transfer: a toy-model (macroscopic) Dynamical friction and galaxy formation (El-Zant et al. 2001, 2004) III – Discussion

Halos in phase-space The microscopic state of the system is determined by the 6-D phase-space distribution function: probability density in space and velocity Function of the integrals of motion Macroscopic observables: In case of isotropic systems: f(E) Eddington’s inversion: Binney & Tremaine 1987

Halos in phase-space: NFW Standard theory of hierarchical clustering: density profile: gravitational potential anisotropy profile MACROSCOPICMACROSCOPIC Navarro, Frenk & White 1997

If the anisotropy profile is nontrivial, the symmetry of the halo is not described by a one-variable DF 2-D tangential component of the internal, randomly-oriented motions of the DM particle orbital energy the particles are less bound, due to the increase of tangential motions anisotropy radius Halos in phase-space: NFW

Lokas & Mamon 2001 Cudderford 1991 Halos in phase-space: NFW

reconstructed NFW Halos in phase-space: NFW

Halos in phase-space: a.m. perturbation new equilibrium state rearrangement of the halo particles in phase-space: new density, anisotropy and potential the halo must conserve energy and angular momentum after the perturbation

Halos in phase-space: a.m. perturbation density, integrated over L^2: I for small radii: energy part of the DF II Poisson III NFW

Halos in phase-space: a.m. perturbation angular momentum transferred to the halo:

DF NFW CORELIKE NFW Halos in phase-space: a.m. perturbation

Angular momentum transfer: a toy-model Is there any physical mechanism that can account for an angular momentum transfer to the halo? modifying the angular momentum profile down to the inner regions compatible with spiral galaxies (no mergings?) involving baryons, where the discrepancy is present affecting the microscopic state of the system galaxy formation is the most promising scenario: the baryonic collapse and the dynamical friction

Angular momentum transfer: a toy-model

Recipe for galaxy formation: 0.16 fractional mass of baryons, in self-gravitating clouds uniformly distributed between 0 and the virial radius Maxwellian velocity distribution Monte Carlo Angular momentum transfer: a toy-model power-law collapse time from 0 to 2 Gyr El-Zant et al. 2004

Angular momentum transfer: a toy-model a fraction of the clouds collapses to the halo center in 2 Gyr along their trajectories, the clouds undergo dynamical friction and transfer angular momentum to the DM baryonic mass piles up in the center of the halo, and the protogalaxy is assembled

Angular momentum transfer: a toy-model the angular momentum profile produced by dynamical friction is compatible with that needed to perturb the halo DF and transform the halo equilibrium configuration from NFW to whatever… the tangential motions are enhanced, the symmetry between the velocity components is broken Is this a general property of DM halos?

Discussion Totally isotropic systems: Tangentially-anisotropic systems: Spinning systems: odd in Lz

Discussion Baryons piling up in the center of the halo deepen the well: negligible 1) feedback processes expel most of the baryons 2) energy transfer enhances halo expansion 3) after symmetry breaking, the isotropic enhancement of the sigma-components does not interfere Cloud mass function can affect the galactic morphology through dynamical friction timescales: DF efficiently deprives big clouds of all their angular momentum, they collapse early in the very center of the halo feeding the spheroidal component small clouds are slow in setting down, they retain a larger fraction of their angular momentum and are more likely to end up in a rotating disk (gradual assembly, inside-out?) Star formation in clouds could possibly disrupt them and offset the DF effect, but the timescales of SF are in general longer than that of the collapse (consistent with starburst regimes in the center of galaxies, cold flows of gas collapsing to the center) Mo & Mao 2004

Simulations? Dynamical friction with gas clumps is sub-grid, at least in galactic halos Chung-Pei Ma & Michael Boylan-Kolchin 2004 Robertson et al DM – DM gravitational scattering disks and bulges can indeed be originated from the merging of gaseous progenitors in hydrodynamical simulations

Conclusions An angular momentum perturbation in a NFW Dark Matter halo transforms the halo equilibrium configuration, leading to new density and anisotropy profiles: injection of angular momentum flattening of the cusp Dynamical friction in the early stages of galaxy formation can provide the halo with the necessary amount of angular momentum (not a unique plausible mechanism) C.T., A. Lapi & P. Salucci (astro-ph/ , ApJ in press)