The Baryon Induced Transformation of CDM Halos

Mario G. Abadi

Universidad Nacional de Córdoba, CONICETArgentina

In collaboration with Julio Navarro and the Canadian Computational

Cosmology Collaboration (C4), University of Victoria, Canada

LENAC Latin-american WorkshopOctober 29 to November 1

Guaruja Brazil

How dark matter halos are transformed by baryons?

Profile (Theory vs Simulations)

Shape (Sphericity vs Triaxiality)

Orientation (Halo vs Disk)

Introduction

Profile: Theory Blumenthal et al. (1986)

Contraction of a dark matter halo in response to condensation

of baryons in its center.

The cooling of gas in the centers of dark matter halos is

expected to lead to a more concentrated dark matter

distribution.

The response of dark matter to the condensation of baryons is

usually calculated using the standard model of adiabatic

contraction

Adiabatic contraction

Spherically simetric dark matter halo with circular orbits

Conservation of the adiabatic invariant M(r)r

I=Integral of q dp = Integral of p dq

If p is the circular velocity, then dq=r dtheta

I=Integral of v r dtheta using v^2=GM/r

I=Int(GM/r)^(1/2) r dtheta = (GM/r)^(1/2)

Int(dtheta)/2pi=(GM/r)^(1/2)

I=GMr=r^2 v^2

Profile: Simulations Gnedin et al (2004)

High-resolution cosmological simulations which include gas

dynamics, radiative cooling, and star formation

Particle orbits in the halos are highly eccentric

Dissipation of gas indeed increases the density of dark matter

and steepens its radial profile in the inner regions of halos

compared to the case without cooling Simple modification of the assumed invariant from M(r)r to

M(r_av)r, where r and r_av are the current and orbit-

averaged particle positions

Profile: Simulations Abadi et al. (2006)

The adiabatic contraction model

C4 Numerical simulations

Simulations of 13 galactic dark matter halos

With and without gas

High and low resolution

One halo also at super high and super low resolution

Profile: Simulations Abadi et al. (2006)

The abadiatic contraction model

C4 Numerical simulations

Simulations of 13 galactic dark matter halos

With and without gas

High and low resolution

One halo also at super high and super low resolution

Dark matter halo: with and without gas

Circular Velocity Profile

Circular velocity and density profiles are increased by the presence of the baryons

Different models give different dark matter profiles in the inner parts

Contracted dark matter halos

Polinomial fit to infer contracted dark matter profiles from non-contracted dark matter + gas profiles

Inverse model

● Total mass of the disk Mdisk

● Contribution of the exponential disk to the total velocity

● Vdisk^2(r)=2 G Mdisk/Rdisk x^2 (I0(x) K0(x)-I1(x) K1(x))

● where x=r/2/Rdisk

● Contribution of the (contracted) dark matter halo to the total velocity

Vdark^2=Vrot^2-Vdisk^2

● Invert the model in order to obtain the circular velocity of the non-

contracted (i.e. without gas) dark matter (only) halo at r=2.2Rdisk

● Assuming the shape of the dark matter halo (i.e. a concentration

parameter “c” for the NFW fit), you have the non-contracted dark

matter halo density profile and its Vvirial and Vmaximum

Application to the Milky Way

Mdisk=6.0x10^10 solar masses

Rdisk=3.5 kpc

Vrot(2.2Rdisk)=220 km/sec

Mvir=1.9, 1.0 and 0.3 10^12 solar masses

Mvir > Mdisk/f_b=0.4 10^12 solar masses

Ours: Vmax=188, Vvir=156 km/s

Gnedin: Vmax=155, Vvir=129 km/s

Standard: Vmax=107, Vvir= 89 km/s

Application Semianalytic models

Application to other galaxies

● Main observables for galaxies: x-band surface brightness

profile (photometry) and rotation curve (kinematic)● Obtain x-band scalelength Rdisk of and exponential disk,

rotational velocity Vrot(r=2.2Rdisk) and also x-band total

luminosity L● Assume a stellar mass-to-light ratio M/L (REM: depends on the

color index)● It is possible to obtain the disk total mass Mdisk ● Go back 3 slides: “Inverse model”● Compare Vrot vs Vmax

Luminosities and Scalelenghts

● Courteau (1996, 1997) 306 galaxies with luminosities and scalelengths in

Kent-Thuan-Gunn system r-band. Also luminosities in Johnson B-band

from RC3 taken from NED

● r=R+0.94 (Jorgensen 1994)

● Courteau et al (2000) only 36 galaxies with absolute magnitudes and

scalelenghts in "Landolt" (is interchangeable

with Johnson) I-band and SDSS colors (g-r)

and (g-i)

● i=I+0.62 and g=V+0.49 (Courteau et al 2006)

● M-Msun=-2.5Log(L/Lsun)

Mass-to-light ratio guesstimation from Bell & de Jong (2001)

● Compute R=r-0.354 (Jorgensen 1994), then compute B-R, thenM/LR=aR+bR(B-R)

● Compute i=I+0.62, then g=i+(g-i), then V=g-0.49, then (V-I), then M/LI=aI+bI (V-I)

Mass-to-light ratio guesstimation from Bell et al (2003)

● M/Li=ai+bi(g-r) and/or M/Li=ai+bi(g-i)

The baryonic Tully-Fisher relation

● B-R colors (white dots)● g-i colors (green dots)

The baryonic Tully-Fisher relation

● B-R colors (white dots)● g-r colors (green dots)

The baryonic Tully-Fisher relation

● B-R colors (white dots)● V-I colors (green dots)

Application to UGC 5794

Mdisk=7.4x10^9 solar masses

Rdisk=2.5 kpc

Vrot(2.2Rdisk)=128 km/sec

Mvir=1.9, 1.8 and 1.6 10^12 solar masses

Mvir > Mdisk/f_b=5.4 10^10 solar masses

Vrot vs Vmax: Galaxies “with” disk

● Vrot = Vmax corresponds to

semianalytic models that

simultaneously reproduce

both the Tully-Fisher and the

luminosity function● There are differences

between the 3 models

Vrot vs Vmax: Galaxies “without” disk

● Vrot = Vmax corresponds to

semianalytic models that

simultaneously reproduce

both the Tully-Fisher and the

luminosity function● There are no differences

between the 3 models

Conclusions

● A new model for the contraction of dark matter halos● Previous models (probably?) overestimate the amount of

contraction (Bower & Benson: reason for small disk in semianalytic models?)

● Nice rotation curve for the Milky Way● Agreement with semianalytic models● Pending: application to other galaxies with more or less

reliable M/L ratios