1. 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

2. Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Perturbation evolution: 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 follow an inhomogeneity with particularly simple form

3. Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Top-hat overdensity in SCDM: Assuming mass conservation …. Initial expansion with Hubble flow, then separation from background universe and collapse …as a closed FRW universe Virial radius + Virial theorem Energy conservation between turn-around and virialization Density contrast

4. Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Top-hat overdensity in  CDM and uncoupled DE models: Assuming an homogeneous DE field….. Virial radius …again from virial theorem and energy conservation but…. Density contrast no longer constant Mainini, Macciò & Bonometto 2003, New Astron., 8, 173

5. Coupled Dark Energy (cDE) Basic equations Spatially flat FRW universe with: baryons, radiation, cold DM and DE (scalar field  with potential V(  )) Continuty equations: Friedmann eq. Interaction DM-DE parametrized by Usual eqs. for baryons and radiation

6. Coupling effects: modified DM dynamics Coupled Dark Energy -Variable mass for DM particles -Violation of equivalence principle -Newtonian interactions: DM-DM particles: effective gravitational constant DM-baryons or baryons-baryons: ordinary gravitational constant

7. 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 level Macciò, Quercellini, Mainini, Amendola & Bonometto 2004, Phys.Rev.D 69, 123516 Linear bias

8. Spherical collapse in cDE models -DM and baryons top-hat fluctuations of identical radius R TH,i expanding with Hubble flow -Fluctuation amplitudes in DM and baryons set by linear theory: a set of n concentric shells with radii R n c (DM) R n b (baryons) such that Start with: then, consider and initial conditions:

9. Spherical collapse in cDE models: Time evolution of concentric shells From T  ;  = 0,using comoving radiiand modified friction term modified source term stronger gravitational push for DM layers, also strengthened by modified friction term

10. 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

11. Spherical collapse in cDE models Density profiles - Top-hat geometry kept for DM - Deviation from a top-hat geometry for baryons outside R TH - Perturbation also in material outside the boundary of fluctuation: outside R TH baryon recollapse fastened by increased density of DM  = 0  = 0.3

12. Spherical collapse in cDE models: Escaped baryon fraction - Barion fraction f b outside R TH at virialization for : - Mildly dependence on the scale 

13. Virialization in cDE models How to define virialization in cDE models? 1 - Only materials within top-hat considered: escaped baryon fraction neglected 2 - 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

14. Virialization in cDE models Our choice:1 - Only materials within top-hat considered: escaped baryon fraction neglected Potential energy made of three terms: self-interaction, mutual interaction, interaction with DE DM-DE energy exchange for fluctuation described by G*=  G Virialization condition: Kinetic and potential energies:

15. Virialization in cDE models Performing integrals… …but different baryons layers have different growth ratesnot valid for T b (R TH ) Density contrast

16. 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 neglected 2 - 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:

17. 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

18. Eqs. in physical coordinates Usual Friedmann-like equation for baryon shells Modified equation for DM shells