Transcript Numerical simulations of galaxy formation in non

Impact of Early Dark Energy
on non-linear
structure formation
Margherita Grossi
MPA, Garching
Advisor :
Volker Springel
3rd Biennial Leopoldina Conference on Dark Energy
LMU Munich, 10 October 2008
Early dark energy models
Parametrization in terms of three
parameters (Wetterich 2004) :
Flat universe :
Fitting formula :
Effective contribution during structure
formation :
(see Bartelmann’s Talk)
Current predictions for EDE
Bartelmann, Doran, Wetterich (2006)
Geometry of the universe: distance, time reduced
Cosmic time relative to LCDM
Dcom
da
 2
a E (a)
1
da
t
H 0  aE (a)
redshift z
Current predictions for EDE
Bartelmann, Doran, Wetterich (2006)
Geometry of the universe: distance, time reduced
Spherical collapse model: virial overdensity moderately changed,
linear overdensity significantly reduced
The ‘Top Hat Model’ : uniform, spherical perturbation di
o Overdensity within virialized halos
 vir
o Overdensity linearly extrapolated to
collapse density
 vir
d c  D( z )d ini
collapse redshift zc
Current predictions for EDE
Bartelmann, Doran, Wetterich (2006)
Geometry of the universe: distance, time reduced
Spherical collapse model: virial overdensity moderately changed,
linear overdensity significantly reduced
Mass function: increase in the abundance of dark matter
halos at high-z
dn/dM (M, z)
At any given redshift, we can compute the probability of living in a place
with
(PS)
2
2 dc
 dc 
f ( , PS ) 
exp   2 
 
 2 
Current predictions for EDE
Bartelmann, Doran, Wetterich (2006)
Geometry of the universe: distance, time reduced
Spherical collapse model: virial overdensity moderately changed,
linear overdensity significantly reduced
Mass function: increase in the abundance of dark matter
halos at high-z
Halo properties: concentration increased
Rvir
Concentration parameter :
cvir 
Rs
Halos density profile have roughly self similar form
(NFW)
dc
 (r )

 crit (r / Rs )(1  r / Rs ) 2
Current predictions for EDE
Bartelmann, Doran, Wetterich (2006)
Geometry of the universe: distance, time reduced
Spherical collapse model: virial overdensity moderately changed,
linear overdensity significantly reduced
Mass function: increase in the abundance of dark matter
halos at high-z
Halo properties: concentration increased
Simulations are necessary to interpret
observational results and compare them with
theoretical models
N-Body Simulations
Models :
•
•
•
•
ΛCDM
DECDM
EDE1
EDE2
Resolution requirements:
• 5123 particles, mp  5 *10 9 solar masses
• L=1003 (Mpc/h)3 , softening length of 4.2 kpc/h
Codes:
• N-GenIC (IC) + P-Gadget3 (simulation) ( C + MPI)
Computation requests :
• 128 processors on OPA at RZG (Garching)
Expansion function
From the Friedmann equations:
Growth factor
Structures need to grow
earlier in EDE models in
order to reach the same
level today
The mass function of DM haloes
FoF
b=0.2
The mass function of DM haloes
z = 0.
Constant initial
density contrast
The mass function of DM haloes
z = 0.25
The mass function of DM haloes
z = 0.5
The mass function of DM haloes
z = 0.75
The mass function of DM haloes
z = 1.
The mass function of DM haloes
z = 1.5
The mass function of DM haloes
z = 2.
The mass function of DM haloes
z = 3.
Theoretical MFs
~ 5-15% errors
(0<z<5)
Do we need a modified virial
overdensity for EDE ?
Friends-of-friends (FOF) b=0.2
Spherical overdensity (SO)
The virial mass is :
M
4
3
 vir  crit rlim
3
Introduction of the linear density contrast predicted by BDW
for EDE models worsens the fit!
The concentration-mass relation
Halo selections: >3000 particles
• Substructure mass fraction
f sub  0.1
• Centre of mass displacement s  rc  rcm / rvir  0.07
• Virial ratio 2T / U  1.35
Profile fitting
• Uniform radial range for density
profile 0  log (r / r )  2.5
10
vir
• More robust fit from maximum in
2
the r  profile
Eke
al. (2001)
works
EDEethalos
always
more
forconcentrated
EDE without
modifications
Substructures in CDM haloes
N(>DM2) [h-1Mpc]3
 SH  300km / sec
DM2[km/sec]2
Robust quantity against
richness threshold.
Cumulative velocity
dispersion function
from sub-halos
dynamics
Conclusions
 Higher cluster populations at high z for EDE models:
linear growth behaviour and power spectrum analysis
 Halo-formation time: trend in concentration for EDE
halos
 Possibility of putting cosmological constraints on
equation of state parameter: cumulative velocity
distribution function
 Connection between mass and galaxy velocity
dispersion: virial relation for massive dark matter halos
 Constant density contrast (spherical collapse theory for
EDE models): mass function
Probing Dark Energy is one of the major
challenge for the computational cosmology