dark matter-baryon segregation in the non-linear evolution of coupled dark energy models
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Dark Matter-Baryon segregation in the non-linear evolution of coupled Dark Energy models. Roberto Mainini Università di Milano Bicocca. Mainini 2005, Phys.Rev. D72, 083514. Post–linear evolution of density fluctuation: The spherical “ top-hat” collapse. Gravitational instability:. - PowerPoint PPT PresentationTRANSCRIPT
Dark Matter-Baryon segregation in the non-linear evolution of coupled Dark Energy models
Roberto MaininiUniversità di Milano Bicocca
Mainini 2005, Phys.Rev. D72, 083514
Post–linear evolution of density fluctuation:The spherical “top-hat” collapse
Perturbation evolution:
field)density (
eq.) (Jeans' 42 Ga
a
But…..for present structure >> 1
linear theory until << 1
Gravitational instability:
present strutures (galaxy, group, cluster) originated by small density perturbations
Simplest approach to non-linearity is to followan inhomogeneity with particularly simple form
Post–linear evolution of density fluctuation:The spherical “top-hat” collapse
Top-hat overdensity in SCDM:
13
4RGR mm
Assuming mass conservation ….
Initial expansion with Hubble flow, then separation from background universe and collapse
…as a closed FRW universe
Virial radius
05
322
2
R
MGTUT virvirvirta UTUU
2
1 tavir RR
2
1+
Virial theorem Energy conservation between turn-around and virialization
178cr
mvir
Density contrast
Post–linear evolution of density fluctuation:The spherical “top-hat” collapse
Top-hat overdensity in CDM and uncoupled DE models:
3113
4RwGR DEDEmm
Assuming an homogeneous DE field…..
Virial radius …again from virial theorem and energy conservation but…. tavir RR2
1
Density contrast no longer constant
Mainini, Macciò & Bonometto 2003, New Astron., 8, 173
Coupled Dark Energy (cDE)Basic equations
3
,2or )31(3 22
ccc
ccDEDEDE
Ca
a
aCVaa
aCw
a
a
Spatially flat FRW universe with:baryons, radiation, cold DM and DE (scalar field with potential V())
22
3
8aG
a
aDEcbr
Continuty equations:
Friedmann eq.
04
03
rr
bb
a
aa
a
Interaction DM-DE parametrized by
Usual eqs. for baryons and radiation
Cc ea 3
3/16 GC
Coupling effects: modified DM dynamics
Coupled Dark Energy
-Variable mass for DM particles CC
c emea 3
-Violation of equivalence principle 00 xm
mxp
-Newtonian interactions:
DM-DM particles: effective gravitational constant GGG
2*
3
41
DM-baryons or baryons-baryons: ordinary gravitational constant
2
2
*4
4
aGGCa
a
aGGa
a
bbcccc
bbccbb
Coupled Dark Energy (cDE)Coupling effects: DM-baryons bias
From linear theory:DM and baryons density fluctuations described by 2 coupled Jeans’ equations:
modified friction term modified source term
N-body simulations indicate that the bias persists also at non-linear levelMacciò, Quercellini, Mainini, Amendola & Bonometto2004, Phys.Rev.D 69, 123516
4
)(V
Linear bias
cb b
Spherical collapse in cDE models
-DM and baryons top-hat fluctuations of identical radius RTH,i expanding with Hubble flow
-Fluctuation amplitudes in DM and baryons set by linear theory: cb b
a set of n concentric shells with radii Rnc (DM) Rn
b (baryons) such that
Start with:
then, consider
a
a
R
R
R
Rbn
bn
cn
cn
bcniTH
bcbc RRRR ,,
,2
,1 ......
bn
cn RR and initial conditions:
Spherical collapse in cDE models:Time evolution of concentric shells
From T;= 0, using comoving radii / aRc c
nn / aRb bnn and
nbbccnn
nbbccnn
caGGcCa
ac
baGba
ab
2*
2
3
43
4
modified friction term modified source term
stronger gravitational push for DM layers, also strengthened by modified friction term
DEDE
bbb
ccc
)1(
)1(
Spherical collapse in cDE models:Time evolution of concentric shells
-DM fluctuation expands more slowly and reach turn-around earlier-Baryons contraction at different times for different layers-Baryons gradually leak out from the fluctuation bulk
As a consequence….. baryon component deviates from a top-hat geometry
Spherical collapse in cDE modelsDensity profiles
- Top-hat geometry kept for DM- Deviation from a top-hat geometry for baryons outside RTH
- Perturbation also in material outside the boundary of fluctuation:
outside RTH baryon recollapse fastened by increased density of DM
= 0 = 0.3
Spherical collapse in cDE models:Escaped baryon fraction
- Barion fraction fb outside RTH at virialization for :
RPfor %68%30
SUGRAfor %58%20
b
b
f
f
- Mildly dependence on the scale
3.01.0
Virialization in cDE models
How to define virialization in cDE models?
1 - Only materials within top-hat considered: escaped baryon fraction neglected2 - All materials inside original fluctuation plus intruder DM considered
- Slower gravitational infall for baryons: outer layers of halo rich of baryons
- Gradually recollapse of external baryons onto the DM-richer core: DM materials outside the original fluctuation carried with them
- Original DM / baryons ratio increased
but……..any intermediate choice also alloweded
No virialization with all the materials of original fluctuation – and only them
Virialization in cDE models
Our choice: 1 - Only materials within top-hat considered: escaped baryon fraction neglected
)()()()()()(~
)()()(
2
1
2
1)()()( 22
rrrdmrrrdmRURURU
rdmrdmRTRTRT
DEcbbDEbccTHb
THc
TH
bcTHb
THc
TH
Potential energy made of three terms: self-interaction, mutual interaction, interaction with DE
2
2
13
4~
0 ; ,, )1(3
4
rG
DEbcirG
ccc
DEiii
DM-DE energy exchange for fluctuation described by G*=G
dR
RdURRT TH
TH
)()(2 Virialization condition:
Kinetic and potential energies:
Virialization in cDE modelsPerforming integrals…
THbn
n n
bn
bn
bnbTH
b RRRMTrdmRT allfor )(2
1
2
1)( 22
…but different baryons layers have different growth rates R
R
r
r not valid for Tb(RTH)
22
2
2
5
3
2
1
2
1)(
5
4
5
3)()()()(
5
4
5
3)()()(
~ )(
THc
cTHc
THDEb
TH
cbb
DEcbbTHb
THDEc
TH
bccc
DEbccTHc
RMrdmRT
RGMR
MMMGrrrdmRU
RGMR
MMMMGrrrdmRU
used R
R
r
r
Density contrast
Conclusions
Ambiguity of definition of halo virialization:difficulty in comparing simulations outputs or data with PS or similar prediction
But…indipendently of the way how virialization is defined:1 - Only materials within top-hat considered: escaped baryon fraction neglected2 - All the materials inside the original fluctuation plus intruder DM considered (or any intermediate choice)
Final virialized system is richer of DM
Spherical top-hat collapse model in cDE theories:
DM-baryons segregation during spherical growth: a fresh approach in the treatment of a number of cosmological problems
large scale: baryon enrichment of large clusters?
intermediate scale: lost baryonic materials observed as intra-cluster light? (X-ray, EUV excess emission problem)
small scale: systems likely to loose their outer layers because of close encounters with heavier objects (missing satellite problem solved?)
-Simulations of DM-DE coupled cosmologies urgently required
Conclusions
bnDEDEbc
bn RwGR )31(
3
4
cnDEDEbcc
cn
cn
cn RwGR
a
aCRCR )31()1(
3
4
Eqs. in physical coordinatesUsual Friedmann-like equation for baryon shells
Modified equation for DM shells