ANGULAR MOMENTUMAND THE STRUCTURE OF DM HALOS

Chiara Tonini

Special guest: Andrea LapiDirector: Paolo Salucci

C.T., A. Lapi & P. Salucci (astro-ph/0603051, 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 vdvrfr 3),()(

Function of the integrals of motion

vfdvOfdO 33Macroscopic observables:

In case of isotropic systems: f(E)

d

d

d

d

df

08

1)(

20 2

1vE 0

Eddington’s inversion:

Binney & Tremaine 1987

Halos in phase-space: NFW

Standard theory of hierarchical clustering:

density profile: 2

2

3 )1(

)(

4)(

cxx

cgc

R

Mx

v

v

x

cxcgvx v

)1ln()()( 2

gravitational potential

2

2

1)(r

r anisotropy profile

MACROSCOPIC

Navarro, Frenk & White 1997

If the anisotropy profile is nontrivial, the symmetry of the halo is not described by a one-variable DF

)(2

22

2

0 Lr

Lff

a

TvrL 2-D tangential component of the internal, randomly-oriented motions of the DM

22 2 arL particle orbital energy

22 2 arLQ the particles are less bound, due to the increase of tangential motions

ar anisotropy radius

Halos in phase-space: NFW

01ar

Lokas & Mamon 2001

dr

r

dQ

dQf

Q

a

)(12

1)(

0 2

2

2

2

22/50

Cudderford 1991

Halos in phase-space: NFW

reconstructed

NFW

Halos in phase-space: NFW

22

22

)(a

a

rr

rrr

Halos in phase-space: a.m. perturbation

)(2

22

2

0 Lr

Lff

a

2L 22 LL E EE ar

new equilibrium state

dQdLLQfGdr

d

rdr

d arrQr

)/1/()(2

0

2

02

2 222

),(42

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

dQQQfrr

rr

a

2/1

0 0122

22/3

))(()2/3(

)1(

)/1(

2)2()(

density, integrated over

L^2:I

for small radii:

0 Q

dr

r

dQ

dQf

Q

a

)(12

1)(

0 2

2

2

2

22/50 energy part of the

DFII

PoissonIII

)2/()1(20 )( rr

)2/()21(2)( rr

0 1 r

2/1 const

NFW

Halos in phase-space: a.m. perturbation

2)/1/()(2

0 2222

2

0 02

222

)/1)(/()(2

)()(

2)( dL

rrrLQ

LLdQQf

rrL

arrQr

a

angular momentum transferred to the halo:

)2/()21(2)( rr

22

22

)(a

a

rr

rrr

)(r

)2/(32/10 ))(()( rrrrL

DF

)1,0( ar NFW

)21,21( ar CORELIKE

0 1 r

2/1 const

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

CM222 )/( rLvv r

)0(r )0(e )1/()1( eerr

r

r r

r

r Cfr

dvdr

MFvdvdr

dt

dE

)/(

/)/(

r

r r

r

r Cfr

dvdr

vMFLdvdr

dt

dL

)/(

)/()/(

22 /1/1

)]()([2)0(

rr

rrL

2)()0(

2vrE

20

3

22')'(

ln4v

vdvfMGF

v

Cf

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 22 2/1)( xx vr 0xv

Monte Carlo

Angular momentum transfer: a toy-model

power-law CC MM )( ]1010[: 25 CM]20[:

collapse time from 0 to 2 Gyr

El-Zant et al. 2004

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

)(fTotally isotropic systems: 222TyTxR vvv

),( 2Lf Tangentially-anisotropic systems:

222TyTxR vvv

),,( 2ZLLf 222

TyTxR vvv Spinning systems:

),()(),,( 210

2ZZ LLfQfLLQf odd in Lz vvT

DiscussionBaryons piling up in the center of the halo deepen the well: negligible1) 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, theycollapse early in the very center of the halo feeding the spheroidal componentsmall clouds are slow in setting down, they retain a larger fraction of theirangular 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. 2005

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/0603051, ApJ in press)