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