Thermal decoupling of WIMPs

Transcription

1 PPC 2010, Torino, July 2010 A link between particle physics properties and the small-scale structure of (dark) matter

2 Outlook Chemical vs kinetic decoupling of WIMPs Kinetic decoupling from first principles The size of the first protohalos Observational prospects Conclusions 2

3 Dark matter Existence by now (almost) impossible to challenge! Ω CDM =0.233 ± (WMAP) electrically neutral (dark!) non-baryonic (BBN) cold dissipationless and negligible free-streaming effects collisionless (bullet cluster) (structure formation) credit: WMAP 3

4 Dark matter Existence by now (almost) impossible to challenge! Ω CDM =0.233 ± (WMAP) electrically neutral (dark!) non-baryonic (BBN) cold dissipationless and negligible free-streaming effects collisionless (bullet cluster) (structure formation) credit: WMAP WIMPS are particularly good candidates: well-motivated from particle physics [SUSY, EDs, little Higgs,...] thermal production automatically leads to the right relic abundance 3

5 The WIMP miracle iracle IMP ed by ) 2 eq a 3 nχ ls bee unithe relic The number density of Weakly Interacting Massive Particles in the early universe: n χ eq increasing σv time Fig.: Jungman, Kamionkowski & Griest, PR 96 Jungman, Kamionkowski & Griest, PR 96 dn χ dt σv : +3Hn χ = σv χχ SM SM ( ) n 2 χ n 2 χeq (thermal average) 1) [for interaction strengths of the weak type] 4

6 The WIMP miracle iracle IMP ed by ) 2 eq a 3 nχ ls bee unithe relic The number density of Weakly Interacting Massive Particles in the early universe: n χ eq increasing σv time Fig.: Jungman, Kamionkowski & Griest, PR 96 Jungman, Kamionkowski & Griest, PR 96 Relic density (today): 1) [for interaction strengths of the weak type] dn χ dt σv : +3Hn χ = σv χχ SM SM ( ) n 2 χ n 2 χeq (thermal average) Freeze-out when annihilation rate falls behind expansion rate ( a 3 n χ const.) Ω χ h cm 3 /s σv for weak-scale interactions! O(0.1) 4

7 Freeze-out = decoupling! WIMP interactions with heat bath of SM particles: χ SM χ χ χ (annihilation) SM SM (scattering) SM 5

8 Freeze-out = decoupling! WIMP interactions with heat bath of SM particles: χ SM χ χ χ (annihilation) SM SM (scattering) SM Boltzmann suppression of n χ scattering processes much more frequent continue even after chemical decoupling ( freeze-out ) at T cd m χ /25 5

9 Freeze-out = decoupling! WIMP interactions with heat bath of SM particles: χ SM χ χ χ (annihilation) SM SM (scattering) SM Boltzmann suppression of n χ scattering processes much more frequent continue even after chemical decoupling ( freeze-out ) at T cd m χ /25 Kinetic decoupling much later: τ r (T kd ) N coll /Γ el H 1 (T kd ) Random walk in momentum space N coll m χ /T Schmid, Schwarz, & Widerin, PRD 99; Green, Hofmann & Schwarz, JCAP 05,... 5

10 Kinetic decoupling in detail Evolution of phase-space density f χ given by the full Boltzmann equation in FRW spacetime: E( t Hp p )f χ = C[f χ ] 6

11 Kinetic decoupling in detail Evolution of phase-space density f χ given by the full Boltzmann equation in FRW spacetime: d 3 p E( t Hp p )f χ = C[f χ ] recovers the familiar dn χ dt +3Hn χ = σv ( n 2 χ n 2 χeq)... 6

12 Kinetic decoupling in detail Evolution of phase-space density f χ given by the full Boltzmann equation in FRW spacetime: d 3 p E( t Hp p )f χ = C[f χ ] recovers the familiar T χ n χ dn χ dt d 3 p (2π) 3 p2 f χ (p) +3Hn χ = σv ( n 2 χ n 2 χeq)... Idea: consider instead the 2 nd moment ( d 3 p p 2 ) and introduce analytic treatment possible no assumptions about f χ (p) necessary Allows highly accurate treatment, to order O(T/m χ ) 10 3 Bertschinger, PRD 06; TB & Hofmann, JCAP 07; TB, NJP 09 6

13 The collision term χ p SM k p χ k SM C = d 3 k (2π) 3 2ω d 3 k (2π) 3 2 ω d 3 p (2π) 3 2Ẽ (2π)4 δ (4) ( p + k p k) M 2 g SM [( 1 g ± (ω) ) g ± ( ω)f( p ) ( 1 g ± ( ω) ) g ± (ω)f(p) ] g ± : thermal distribution 7

14 The collision term χ p SM k p χ k SM C = d 3 k (2π) 3 2ω d 3 k (2π) 3 2 ω d 3 p (2π) 3 2Ẽ (2π)4 δ (4) ( p + k p k) M 2 g SM [( 1 g ± (ω) ) g ± ( ω)f( p ) ( 1 g ± ( ω) ) g ± (ω)f(p) ] g ± : thermal distribution Expansion in ω/m χ T/m χ [ ] C c(t )m 2 χ m χ T p + p p +3 f(p) c(t )= g SM 6(2π) 3 m 4 dk k 5 ω 1 g ± ( 1 g ±) M 2 t=0 i χt 7

15 The collision term χ p SM k p χ k SM C = d 3 k (2π) 3 2ω d 3 k (2π) 3 2 ω d 3 p (2π) 3 2Ẽ (2π)4 δ (4) ( p + k p k) M 2 g SM [( 1 g ± (ω) ) g ± ( ω)f( p ) ( 1 g ± ( ω) ) g ± (ω)f(p) ] g ± : thermal distribution Expansion in ω/m χ T/m χ [ ] C c(t )m 2 χ m χ T p + p p +3 f(p) c(t )= g SM 6(2π) 3 m 4 dk k 5 ω 1 g ± ( 1 g ±) M 2 t=0 i χt Analytic solution if M 2 = M 2 0 (ω/m χ) 2 generic situation for dk k 5... = N M 2 0 m 2 χ T 7 m SM ω ω res 7

16 The WIMP temperature T χ Resulting ODE for : 4.5 dy dx =2m χc(t ) H g 1/2 T. Bringmann, 2009 ( 1 T χ T ) 4.0 T χ = T (T < T kd ) y = mχg 1/2 log 10 ( eff Tχ/T 2 ) T χ a 2 (T > T kd ) Example: x kd =m χ /T kd m χ = 100 GeV M 2 g 4 Y (E χ /m χ ) log 10 (x = m χ /T ) 8

17 The WIMP temperature T χ Resulting ODE for : 4.5 dy dx =2m χc(t ) H g 1/2 T. Bringmann, 2009 ( 1 T χ T ) y = mχg 1/2 log 10 ( eff Tχ/T 2 ) T χ a 2 T χ = T x kd =m χ /T kd (T < T kd ) (T > T kd ) Example: m χ = 100 GeV M 2 g 4 Y (E χ /m χ ) log 10 (x = m χ /T ) Fast transition allows straight-forward definition of T kd TB & Hofmann, JCAP 07; TB, NJP 09 8

18 T kd in SUSY Tkd [MeV] Implement all SM-neutralino scattering amplitudes Scan MSSM and msugra parameter space (~10 6 models, 3 σ WMAP, all collider bounds OK) Higgsino (Z g < 0.05) mixed (0.05 Z g 0.95) Gaugino (Z g > 0.95) F K I J QCD T. Bringmann, 2009 xkd = mχ/tkd Higgsino (Z g < 0.05) mixed (0.05 Z g 0.95) Gaugino (Z g > 0.95) TB, NJP 09 T. Bringmann, m χ [GeV] x cd = m χ /T cd 9

19 The smallest protohalos Free streaming of WIMPs after t kd washes out density contrasts on small scales e.g. Green, Hofmann & Schwarz, JCAP 05 Similar effect from baryonic oscillations Loeb & Zaldarriaga, PRD 05 Bertschinger, PRD 06 Cutoff in power spectrum corresponds to smallest gravitationally bound objects in the universe M fs = ( 1 + ln ( m χ 100 GeV 1 g 4 eff T kd 30 MeV M ao = ( T kd g 14 eff 50 MeV ) /18.6 ) 1 2 g 1 4 eff ( Tkd 30 MeV ) 1 2 ) 3 M 3 M 10

20 The smallest protohalos Free streaming of WIMPs after t kd washes out density contrasts on small scales e.g. Green, Hofmann & Schwarz, JCAP 05 Similar effect from baryonic oscillations Loeb & Zaldarriaga, PRD 05 Bertschinger, PRD 06 Cutoff in power spectrum corresponds to smallest gravitationally bound objects in the universe Strong dependence on particle physics properties, no typical value of! Mcut/M M cut 10 6 M I K J Higgsino (Z g < 0.05) mixed (0.05 Z g 0.95) Gaugino (Z g > 0.95) m χ [GeV] T. Bringmann, 2009 F (see also Profumo, Sigurdson & Kamionkowski, PRL 06) 10

21 Other DM candidates Formalism applicable to any DM candidate that is nonrelativistic before kinetic decoupling Many WIMPs have smaller spread in than neutralinos, e.g. Kaluza-Klein DM (Number of free parameters in the theory ) M cut Mcut/M Formalism does not allow to compute m LKP [GeV] T. Bringmann, 2009 KK dark matter (mued, ΛR = 20, 30, 40) WMAP 3σ M cut if DM has never been in thermal equilibrium, like the axion for hot or warm DM decaying DM e.g Tkd [MeV] 11

22 Survival of microhalos N-body simulations can follow evolution until z~26 (for field halos and adopting a special multi-scale technique) Diemand, Moore & Stadel, Nature 05 General expectation afterwards: tidal disruption important, but compact core should survive... Berezinsky et al., PRD 03, PRD 08; Moore 05, Diemand, Kuhlen & Madau ApJ 06; Green & Goodwin, MNRAS 07, Goerdt et al., MNRAS 07;......though prospects might be much worse. Details not well understood and still under debate, more input from simulations needed! Zhao et al., ApJ 07 12

23 Indirect detection of WIMPs DM indirect detection: DM e + _ p "! DM! e + Total flux: Φ SM ρ 2 χ = (1 + BF) ρ χ 2 Fig.: Bergström, NJP 09 13

24 Indirect detection of WIMPs DM indirect detection: DM e + _ p "! DM! e + Total flux: Φ SM ρ 2 χ = (1 + BF) ρ χ 2 Boost factor Fig.: Bergström, NJP 09 each decade in Msubhalo contributes about the same depends on uncertain form of microhalo profile ( (large extrapolations necessary!) (still) important to include realistic value for! M cut e.g. Diemand, Kuhlen & Madau, ApJ 07 c v...) and dn/dm 13

25 Observational prospects Is there a way to directly probe? M cut 14

26 Observational prospects Is there a way to directly probe? M cut Point sources? sources rather dim; difficult to resolve strong limits from background Pieri, Branchini & Hofmann, PRL 05 Pieri, Bertone & Branchini, MNRAS 08 Kuhlen, Diemand & Madau, ApJ 08 14

27 Observational prospects Is there a way to directly probe? M cut Point sources? sources rather dim; difficult to resolve strong limits from background Proper motion? strong limits from background only for rather large masses Pieri, Branchini & Hofmann, PRL 05 Pieri, Bertone & Branchini, MNRAS 08 Kuhlen, Diemand & Madau, ApJ 08 Koushiappas, PRL 06 Ando et al., PRD 08 14

28 Observational prospects Is there a way to directly probe? M cut Point sources? sources rather dim; difficult to resolve strong limits from background Proper motion? strong limits from background only for rather large masses Pieri, Branchini & Hofmann, PRL 05 Pieri, Bertone & Branchini, MNRAS 08 Kuhlen, Diemand & Madau, ApJ 08 Koushiappas, PRL 06 Ando et al., PRD 08 Gravitational lensing? virial radius much larger than Einstein radius multiple images of time-varying sources in strong lensing systems!? Moustakas et al.,

29 Observational prospects Is there a way to directly probe? M cut Point sources? sources rather dim; difficult to resolve strong limits from background Proper motion? strong limits from background only for rather large masses Pieri, Branchini & Hofmann, PRL 05 Pieri, Bertone & Branchini, MNRAS 08 Kuhlen, Diemand & Madau, ApJ 08 Koushiappas, PRL 06 Ando et al., PRD 08 Gravitational lensing? virial radius much larger than Einstein radius multiple images of time-varying sources in strong lensing systems!? Moustakas et al., Anisotropy probes? angular correlations in EGRB [again mostly large masses] γ -ray flux (one-point) probability function Ando et al., PRD Fornasa et al., PRD 09 Lee, Ando, & Kamionkowski, JCAP 09 14

30 Observational prospects Is there a way to directly probe M cut? Point sources? sources rather dim; difficult to resolve strong limits from background Proper motion? strong limits from background only for rather large masses Waiting for clever ideas! Pieri, Branchini & Hofmann, PRL 05 Pieri, Bertone & Branchini, MNRAS 08 Kuhlen, Diemand & Madau, ApJ 08 Koushiappas, PRL 06 Ando et al., PRD 08 Gravitational lensing? virial radius much larger than Einstein radius multiple images of time-varying sources in strong lensing systems!? Moustakas et al., Anisotropy probes? angular correlations in EGRB [again mostly large masses] γ -ray flux (one-point) probability function Ando et al., PRD Fornasa et al., PRD 09 Lee, Ando, & Kamionkowski, JCAP 09 14

31 Conclusions Dark Matter decouples in two stages: chemical decoupling kinetic decoupling For WIMPs, relic density size of smallest mini-clumps M M cut 10 3 M strong dependence on particle physics properties! An analytic treatment from first principles allows to determine the cutoff with a precision of O(T/m χ )

32 Conclusions Dark Matter decouples in two stages: chemical decoupling kinetic decoupling For WIMPs, relic density size of smallest mini-clumps M M cut 10 3 M strong dependence on particle physics properties! An analytic treatment from first principles allows to determine the cutoff with a precision of O(T/m χ ) 10 3 Observational consequences determination of boost factor for indirect DM detection direct measurement of cutoff: challenging but not impossible 15

33 Conclusions Dark Matter decouples in two stages: chemical decoupling kinetic decoupling For WIMPs, relic density size of smallest mini-clumps M M cut 10 3 M strong dependence on particle physics properties! An analytic treatment from first principles allows to determine the cutoff with a precision of O(T/m χ ) 10 3 Observational consequences determination of boost factor for indirect DM detection direct measurement of cutoff: challenging but not impossible A new window into the particle nature of dark matter!? 15