On the Origin of the Halo
Universal Density Profile and
the Correlations of its Shape
Parameter
Alberto Manrique
Eduard Salvador-Solé
José María Solanes
September 14, 2004
JENAM 2004, Granada
Some “empirical“ facts…
1.
Dark halos show universal density profiles (NFW):
ρc rs3
ρ(r ) =
r(rs + r)2
2.
One scale parameter, rs (or c=R/ rs), when M is fixed
3.
Recent correlations involving rs
n
n
c – zf (Wechsler et al. 02)
Ms – rs (Zhao et al. 03)
seem to suggest rs depends on the halo MAH
September 14, 2004
JENAM 2004, Granada
Fit of empirical MAHs (Wechsler et al. 2002)
  a ( z0 )  
M ( z)
= exp− α 
− 1 
M0
a
z
(
)

 
α=
September 14, 2004
JENAM 2004, Granada
a( z f )
a ( z0 )
S
c – a(zf ) correlation (Wechsler et al. 2002)
c=
September 14, 2004
JENAM 2004, Granada
4.1
a( z f )
Masses and scales along halo evolutionary main branches
(Zhao et al. 2003)
September 14, 2004
JENAM 2004, Granada
Scaled Ms – rs correlation on both sides of ztp (Zhao et al. 2003)
September 14, 2004
JENAM 2004, Granada
Theoretical dependence of rs
Assume:
n
n
n
spherical, non-rotating, relaxed halos
inside-out growth during slow accretion
universal density profile à la NFW
Once M is given, the halo structure depends only on rs
Use the virial relation as an equation to determine its value:
R
GM (r )
2 E = − ∫ d M (r )
+ 4π R 3 P
r
0
rs only depends on the current values of M, E, dM/dt, dE/dt
As a consequence:
Ø Halo profile does not depend on aggregation history
September 14, 2004
JENAM 2004, Granada
The theoretical dependence of rs
and the “empirical” correlations
Is the dependence of rs on the current values of M, E, dM/dt,
dE/dt compatible with the c – zf and Ms – rs correlations
found in N-body simulations?
To check this:
n
n
September 14, 2004
Monte Carlo simulations of MAHs in the EPS framework
Physical model for the evolution of rs
Relies only on the current value of M
JENAM 2004, Granada
Monte Carlo simulations of halo evolutionary main branches
using our model for rs (with no memory) in the EPS framework
September 14, 2004
JENAM 2004, Granada
Scaled Ms – rs correlation on both sides of za and ztp
from our Monte Carlo simulations
September 14, 2004
JENAM 2004, Granada
rs – α & c – a(zf) correlations from our Monte Carlo simulations
September 14, 2004
JENAM 2004, Granada
Conclusions
n The structure of halos only depends on the current values
of M, E, dM/dt, dE/dt
Not on the halo aggregation history
n The correlations found in N-body simulations are
compatible with the above result
September 14, 2004
JENAM 2004, Granada
Discussion
S. Mieske: As I am not a theoretical cosmologist, I would like
to reassure myself that I understood you correctly. Is it
really the case that dark matter halos have the same
density profiles, no matter whether they have lived
silently all the time or undergone mergers?
A. Manrique: What we have proved is that dark matter halos
with the same mass at a given time have the same profile
if besides they have the same mass and energy accretion
rates. Two halos with the same M at t, one accreting at a
rate dM/dt, and the other not (e.g., an isolated halo), do
not have the same density profile.
September 14, 2004
JENAM 2004, Granada
Discussion
L. Secco: From the study of 23 S galaxies, Garrido told us
this morning that the dark halo density profile is not like
NFW, and that the logarithmic inner slop is less than -1.
What do you think about?
A. Manrique: The results presented here are independent of
the exact value of the inner slope of the halo density
profile, provided we stick to the assumptions of the
modeling : sphericity, inside-out growth, universal profile.
September 14, 2004
JENAM 2004, Granada