Gravitational clustering of relic neutrinos in galactic halos and their detection

Transcription

1 Gravitational clustering of relic neutrinos in galactic halos and their detection Andreas Ringwald ringwald DESY in collaboration with Yvonne Wong, arxiv:hep-ph/ Seminar, Laboratori Nazionali del Gran Sasso, Assergi L Aquila, I November 2004

2 Gravitational clustering of relic neutrinos in galactic halos and their detection 1 1. Introduction Big Bang cosmology: Cosmic microwave background (CMB) Cosmic neutrino background (CνB) Firm predictions: n νi 0 = n νi 0 ßÞ Ð CνB p νi 0 = p νi 0 ßÞ Ð CνB = 3 22 n γ ßÞÐ 0 4 = 3 CMB = 56 cm 3 CMB 1/3 Tγ 0 ßÞÐ 11 = ev Big bang relic neutrinos as abundant as relic photons [ratio (6 3)/22 = 9/11] Relic neutrinos non-relativistic as long as m νi (1 + z) ev [CERN]

3 Gravitational clustering of relic neutrinos in galactic halos and their detection 2 1. Introduction Big Bang cosmology: Cosmic microwave background (CMB) Cosmic neutrino background (CνB) Firm predictions: n νi 0 = n νi 0 ßÞ Ð CνB = 3 22 n γ ßÞÐ 0 CMB = 56 cm 3 Big bang relic neutrinos as abundant as relic photons [ratio (6 3)/22 = 9/11] Relic neutrinos non-relativistic as long as m νi (1 + z) ev

4 Gravitational clustering of relic neutrinos in galactic halos and their detection 3 1. Introduction Big Bang cosmology: Cosmic microwave background (CMB) Cosmic neutrino background (CνB) Firm predictions: n νi 0 = n νi 0 ßÞ Ð CνB = 3 22 n γ ßÞÐ 0 CMB = 56 cm 3 Big bang relic neutrinos as abundant as relic photons [ratio (6 3)/22 = 9/11] p νi 0 = p νi 0 ßÞ Ð CνB 4 1/3 = 3 Tγ 0 11 ßÞÐ CMB = ev At least two neutrino mass eigenstates nonrelativistic (m νi (1+z) ev)

5 Gravitational clustering of relic neutrinos in galactic halos and their detection 4 Nonrelativistic relic neutrinos subject to gravitational clustering on cold dark matter (CDM) and baryonic structures Neutrino density might be enhanced in the halo of the Milky Way or in the halos of other galaxies/clusters of galaxies CνB has not been detected in laboratory: Neutrinos interact only weakly Smallness of neutrino mass small momentum-transfer Only evidence for/inference about CνB from other cosmological measurements: Big bang nucleonsynthesis (BBN) (1.8 N ν 4.5) Large scale structure data together with CMB ( m νi 1.8 ev) Design of possible direct, scattering-based detection experiment: Requires precise knowledge of phase space distribution of relic neutrinos Possible now with much more accuracy then ever!

6 Gravitational clustering of relic neutrinos in galactic halos and their detection 5 Further content: 2. Gravitational clustering of relic neutrinos 3. Implications for detection 4. Conclusions

7 Gravitational clustering of relic neutrinos in galactic halos and their detection 6 2. Gravitational clustering of relic neutrinos In context of flat ΛCDM model, neutrino component perturbation On cosmological scales, ρ ν / ρ m < 0.2 free streaming even smaller on cluster/galactic scales CDM component ρ m dominates in gravitational potential φ Neutrino clustering in cold dark matter halos from ΛCDM simulations [Singh,Ma 03; AR,Wong 04] Neutrino phase space distributions f νi (x,p,τ), depending on x = r/a(t), p = am νi ẋ, dτ = dt/a(t), obey the Vlasov, or collisionless Boltzmann, equation, Df νi Dτ f ν i τ + ẋ f ν i x am ν i φ f ν i }{{} p = 0 ṗ

8 Gravitational clustering of relic neutrinos in galactic halos and their detection 7 Poisson equation ) 2 φ = 4πGa (ρ 2 m (x,τ) ρ m (τ) } {{ } δ m (x,τ) ρ m (τ) relates φ to density fluctuation δ m with respect to physical mean ρ m Vlasov equation conservation of f νi along characteristics {x(τ), p(τ)}, dx dτ = p dp, am νi dτ = am ν i φ Complete set of characteristics coming through every point in phase space exactly equivalent to Vlasov equation Particle-based solution methods (N-body simulations): Follow a sufficiently large, but still manageable set of characteristics selected from the initial phase space distribution

9 Gravitational clustering of relic neutrinos in galactic halos and their detection 8 Velocity of unperturbed ν distribution, ( ) ev v ν (1 + z) m ν km/s ( < ) velocity dispersion of galaxy (cluster) km/s (10 3 km/s) today For sub-ev neutrinos, clustering on small scales can only have been a z < 2 event In this epoch, exploit ρ m of CDM halos, conform to a universal shape, e.g. the Navarro Frenk White profile, ρ halo (r) = ρ s (r/r s )(1 + r/r s ) 2, [Navarro et al. 04]

10 Gravitational clustering of relic neutrinos in galactic halos and their detection 9 Comparative analysis for various {m ν, M vir }: Neutrino free-streaming: n ν / n ν flattens out at small radii ρ ν /ρ m drops substantially below ρ ν / ρ m Improved clustering for increasing M vir a/o m ν : Overdensity M vir for fixed r, m ν Overdensity m ν (1 3) for fixed r, M vir Linear approximation fails, unless n ν / n ν < 2 [AR,Wong 04]

11 Gravitational clustering of relic neutrinos in galactic halos and their detection 10 Comparative analysis for various {m ν, M vir }: Neutrino free-streaming: n ν / n ν flattens out at small radii ρ ν /ρ m drops substantially below ρ ν / ρ m Improved clustering for increasing M vir a/o m ν : Overdensity M vir for fixed r, m ν Overdensity m ν (1 3) for fixed r, M vir Linear approximation fails, unless n ν / n ν < 2 [AR,Wong 04]

12 Gravitational clustering of relic neutrinos in galactic halos and their detection 11 Comparative analysis for various {m ν, M vir }: Neutrino free-streaming: n ν / n ν flattens out at small radii ρ ν /ρ m drops substantially below ρ ν / ρ m Improved clustering for increasing M vir a/o m ν : Overdensity M vir for fixed r, m ν Overdensity m ν (1 3) for fixed r, M vir Linear approximation fails, unless n ν / n ν < 2 [AR,Wong 04]

13 Gravitational clustering of relic neutrinos in galactic halos and their detection 12 Comparative analysis for various {m ν, M vir }: Neutrino free-streaming: n ν / n ν flattens out at small radii ρ ν /ρ m drops substantially below ρ ν / ρ m Improved clustering for increasing M vir a/o m ν : Overdensity M vir for fixed r, m ν Overdensity m ν (1 3) for fixed r, M vir Linear approximation fails, unless n ν / n ν < 2 [AR,Wong 04]

14 Gravitational clustering of relic neutrinos in galactic halos and their detection 13 Comparative analysis for various {m ν, M vir }: Neutrino free-streaming: n ν / n ν flattens out at small radii ρ ν /ρ m drops substantially below ρ ν / ρ m Improved clustering for increasing M vir a/o m ν : Overdensity M vir for fixed r, m ν Overdensity m ν (1 3) for fixed r, M vir Linear approximation fails, unless n ν / n ν < 2 [AR,Wong 04]

15 Gravitational clustering of relic neutrinos in galactic halos and their detection 14 Phase space distribution of neutrinos in neighbourhood of Earth (r 8 kpc)? Central region of Milky Way (< 10 kpc) dominated by baryonic matter in form of disk + bulge (+ bar?) Use N-one-body method with following φ mass distribution MWnow: present day one from observations; static NFWhalo: NFW profile for Milky Way parameters; dynamic [AR,Wong 04]

16 Gravitational clustering of relic neutrinos in galactic halos and their detection 15 Momentum distribution of neutrinos in neighbourhood of Earth (r 8 kpc): almost isotropic: p r 0 2 p 2 r p 2 T flat at low momenta, with common value 1/2 turning point at p esc m ν v esc m ν 2 φ(r ) matches Fermi-Dirac at high momenta nν yr y nν T y yr 2 y2 T y2 Fermi Dirac MWnow mν = 0.6 ev ev ev ev NFWhalo mν = 0.6 ev ev ev ev y = p/t ν,0 = m ν v/t ν,0

17 Gravitational clustering of relic neutrinos in galactic halos and their detection 16 Momentum distribution of neutrinos in neighbourhood of Earth (r 8 kpc): almost isotropic: p r 0 2 p 2 r p 2 T flat at low momenta, with common value 1/2 turning point at p esc m ν v esc m ν 2 φ(r ) matches Fermi-Dirac at high momenta [AR,Wong 04]

18 Gravitational clustering of relic neutrinos in galactic halos and their detection 17 Phase space bounds? f max(f 0 ): Final coarse-grained f must not exceed maximum of initial fine-grained f 0 [Lynden-Bell 67] f saturates bound up to pesc, semi-degenerate state that can only be made denser by filling in states above p esc Stronger bound: [Tremaine,Gunn 79; Kull et al. 96] Sum semi-degenerate distribution only up to p esc, n ν < m3 νvesc 3 n ν 9ζ(3)Tν,0 3 applicable: large Mvir (m ν ) [AR,Wong 04]

19 Gravitational clustering of relic neutrinos in galactic halos and their detection 18 Phase space bounds? f max(f 0 ): Final coarse-grained f must not exceed maximum of initial fine-grained f 0 [Lynden-Bell 67] f saturates bound up to pesc, semi-degenerate state that can only be made denser by filling in states above p esc Stronger bound: [Tremaine,Gunn 79; Kull et al. 96] Sum semi-degenerate distribution only up to p esc, n ν < m3 νvesc 3 n ν 9ζ(3)Tν,0 3 applicable: large Mvir (m ν ) [AR,Wong 04]

20 Gravitational clustering of relic neutrinos in galactic halos and their detection Implications for detection Gravitational clustering of relic neutrinos significant for their detection? Consider detection methods based on scattering processes, involving the relic neutrinos either as a beam or as a target: Coherent elastic scattering of the relic neutrino flux off target matter in a terrestrial detector (flux detection) Scattering of extremely energetic particles (accelerator beams or cosmic rays) off the relic neutrinos as a target (target detection)

21 Gravitational clustering of relic neutrinos in galactic halos and their detection 20 Flux detection Low average momentum of relic neutrinos corresponds to a (reduced) de Broglie wavelength of macroscopic dimension, λ = 1/ p = 0.12 cm/ y Envisage scattering processes in which many target atoms act coherently over a macroscopic volume λ 3 elastic scattering rate enhanced by N A A ρ t λ ( )( ) ( 100 ρt λ A g/cm cm ) 3 compared to case where neutrinos are elastically scattered coherently only on the individual nuclei of the target [Shvartsman et al. 82; Smith,Lewin 83]

22 Gravitational clustering of relic neutrinos in galactic halos and their detection 21 Test body will experience neutrino wind force through random neutrino scattering: a t ν, ν [Shvartsman et al. 82; Smith,Lewin 83;...; Duda et al. 01] n ν v ßÞ rel Ð flux 4π 3 N2 A ρ t r 3 t σ νn 2 m ν v ßÞ rel Ð mom. transfer nν 10 3 c ρt rt n ν v rel g/cm 3 λ Majorana neutrinos: suppressed by factor (v rel /c) 2 s 2 3 cm At present, smallest measurable acceleration > cm/s 2, using conventional Cavendish-type torsion balance. Improvements to > cm/s 2 proposed [Hagmann 99] Detection possible in years, if neutrinos are Dirac particles [Smith 03]

23 Gravitational clustering of relic neutrinos in galactic halos and their detection 22 Test body will experience neutrino wind force through random neutrino scattering: a t ν, ν [Shvartsman et al. 82; Smith,Lewin 83;...; Duda et al. 01] n ν v ßÞ rel Ð flux 4π 3 N2 A ρ t r 3 t σ νn 2 m ν v ßÞ rel Ð mom. transfer nν 10 3 c ρt rt n ν v rel g/cm 3 λ s 2 3 cm Majorana neutrinos: suppressed by factor (v rel /c) 2 Laser Resonator At present, smallest measurable acceleration > cm/s 2, using conventional Cavendish-type torsion balance. Improvements to > cm/s 2 proposed [Hagmann 99] Detection possible in years, if neutrinos are Dirac particles [Smith 03] A B Neutrino Target [Hagmann 99] Persistent Magnet Suspension Magnet Balancing Mass

24 Gravitational clustering of relic neutrinos in galactic halos and their detection 23 Test body will experience neutrino wind force through random neutrino scattering: a t ν, ν [Shvartsman et al. 82; Smith,Lewin 83;...; Duda et al. 01] n ν v ßÞ rel Ð flux 4π 3 N2 A ρ t r 3 t σ νn 2 m ν v ßÞ rel Ð mom. transfer nν 10 3 c ρt rt n ν v rel g/cm 3 λ s 2 3 cm Majorana neutrinos: suppressed by factor (v rel /c) 2 At present, smallest measurable acceleration > cm/s 2, using conventional Cavendish-type torsion balance. Improvements to > cm/s 2 proposed [Hagmann 99] Detection possible in years, if neutrinos are Dirac particles [Smith 03] MWnow mν = nν nν λ = 1 p v 0.6 ev cm ev cm ev cm ev cm NFWhalo mν = 0.6 ev cm ev cm ev cm ev cm

25 Gravitational clustering of relic neutrinos in galactic halos and their detection 24 Target detection For center-of-mass energies below W- and Z-resonances, cf. 2mν E 4.5 ( mν ) ( ) 1/2 1/2 E MeV ev 10 TeV weak interaction cross sections grow rapidly with energy Exploit a flux of extremely energetic particles accelerator beams from cosmic rays for scattering on relic neutrinos as target

26 Gravitational clustering of relic neutrinos in galactic halos and their detection 25 Exploit accelerator beams: Scattering rate [B. Müller 87; Melissinos 99, Weiler 01] R ν A Z N ν, ν n ν σ ν A Z N L I/(Z e) nν mν A 2 n ν ev Z Too small to give rise to an observable effect in the foreseeable future (LHC, VLHC) Need Ultimate Large Hadron Collider Few elastic scattering events per year; hard to detect, due to small momentum transfers ( 1 GeV at E N 10 7 TeV) Alternative: exploit inverse beta decay A Z N + ν e A Z+1 N + e detect A Z+1N on exit of machine EN 10 TeV L 100 km I 0.1 A [Melissinos 99; Zavattini unpubl] yr 1 R accel. N E N L I νa n ν nν m ν ev [TeV] [km] [A] [yr 1 ] p LHC Pb VLHC p Pb ULHC p

27 Gravitational clustering of relic neutrinos in galactic halos and their detection 26 Exploit cosmic rays: Before ULHC: target detection only via extremely energetic cosmic rays Unique: resonant annihilation of extremely energetic cosmic neutrinos (EHECν) E res ν = m2 Z ev 2m ν m ν ev with relic ν into Z-bosons [Weiler 82] Absorption dips in EHECν spectrum [Weiler 82;...; Eberle,AR,Song,Weiler 04] Emission features (Z-bursts): [Fargion et al. 99; Weiler 99;...; Fodor,Katz,AR 01, 02] protons and photons with energies above the predicted Greisen Zatsepin Kuzmin (GZK) cutoff at E GZK ev [Greisen 66; Zatsepin,Kuzmin 66]

28 Gravitational clustering of relic neutrinos in galactic halos and their detection 27 Exploit cosmic rays: Before ULHC: target detection only via extremely energetic cosmic rays Unique: resonant annihilation of extremely energetic cosmic neutrinos (EHECν) E res ν = m2 Z ev 2m ν m ν ev with relic ν into Z-bosons [Weiler 82] Absorption dips in EHECν spectrum [Weiler 82;...; Eberle,AR,Song,Weiler 04] Emission features (Z-bursts): [Fargion et al. 99; Weiler 99;...; Fodor,Katz,AR 01, 02] protons and photons with energies above the predicted Greisen Zatsepin Kuzmin (GZK) cutoff at E GZK ev [Fodor,Katz,AR 02] [Greisen 66; Zatsepin,Kuzmin 66]

29 Gravitational clustering of relic neutrinos in galactic halos and their detection 28 Exploit cosmic rays: Before ULHC: target detection only via extremely energetic cosmic rays Unique: resonant annihilation of extremely energetic cosmic neutrinos (EHECν) E res ν = m2 Z ev 2m ν m ν ev with relic ν into Z-bosons [Weiler 82] Absorption dips in EHECν spectrum [Weiler 82;...; Eberle,AR,Song,Weiler 04] Emission features (Z-bursts): [Fargion et al. 99; Weiler 99;...; Fodor,Katz,AR 01, 02] protons and photons with energies above the predicted Greisen Zatsepin Kuzmin (GZK) cutoff at E GZK ev [Fargion,Mele,Salis 99] [Greisen 66; Zatsepin,Kuzmin 66]

30 Gravitational clustering of relic neutrinos in galactic halos and their detection 29 Exploit cosmic rays: Before ULHC: target detection only via extremely energetic cosmic rays Unique: resonant annihilation of extremely energetic cosmic neutrinos (EHECν) E res ν = m2 Z ev 2m ν m ν ev with relic ν into Z-bosons [Weiler 82] Absorption dips in EHECν spectrum [Weiler 82;...; Eberle,AR,Song,Weiler 04] Emission features (Z-bursts): [Fargion et al. 99; Weiler 99;...; Fodor,Katz,AR 01, 02] protons and photons with energies above the predicted Greisen Zatsepin Kuzmin (GZK) cutoff at E GZK ev [Eberle,AR,Song,Weiler 04] [Greisen 66; Zatsepin,Kuzmin 66]

31 Gravitational clustering of relic neutrinos in galactic halos and their detection 30 Exploit cosmic rays: Before ULHC: target detection only via extremely energetic cosmic rays Unique: resonant annihilation of extremely energetic cosmic neutrinos (EHECν) E res ν = m2 Z ev 2m ν m ν ev with relic ν into Z-bosons [Weiler 82] Absorption dips in EHECν spectrum [Weiler 82;...; Eberle,AR,Song,Weiler 04] Emission features (Z-bursts): [Fargion et al. 99; Weiler 99;...; Fodor,Katz,AR 01, 02] protons and photons with energies above the predicted Greisen Zatsepin Kuzmin (GZK) cutoff at E GZK ev [Fodor,Katz,AR 02] [Greisen 66; Zatsepin,Kuzmin 66]

32 Gravitational clustering of relic neutrinos in galactic halos and their detection 31 Absorption spectroscopy: [Eberle,AR,Song,Weiler 04] Presently planned EHECν detectors appear to be sensitive enough to lead us, within the next decade, into an era of relic neutrino absorption spectroscopy, provided EHECν flux at resonant energies close to current observational bounds neutrino mass sufficiently large, m ν > 0.1 ev In this case, the associated Z-bursts likely to be seen as post-gzk events at the planned cosmic ray detectors

33 Gravitational clustering of relic neutrinos in galactic halos and their detection 32 Absorption spectroscopy: [Eberle,AR,Song,Weiler 04] Presently planned EHECν detectors appear to be sensitive enough to lead us, within the next decade, into an era of relic neutrino absorption spectroscopy, provided EHECν flux at resonant energies close to current observational bounds neutrino mass sufficiently large, m ν > 0.1 ev In this case, the associated Z-bursts likely to be seen as post-gzk events at the planned cosmic ray detectors

34 Gravitational clustering of relic neutrinos in galactic halos and their detection 33 Absorption spectroscopy: [Eberle,AR,Song,Weiler 04] Presently planned EHECν detectors appear to be sensitive enough to lead us, within the next decade, into an era of relic neutrino absorption spectroscopy, provided EHECν flux at resonant energies close to current observational bounds neutrino mass sufficiently large, m ν > 0.1 ev In this case, the associated Z-bursts likely to be seen as post-gzk events at the planned cosmic ray detectors

35 Gravitational clustering of relic neutrinos in galactic halos and their detection 34 Absorption spectroscopy: [Eberle,AR,Song,Weiler 04] Presently planned EHECν detectors appear to be sensitive enough to lead us, within the next decade, into an era of relic neutrino absorption spectroscopy, provided EHECν flux at resonant energies close to current observational bounds neutrino mass sufficiently large, m ν > 0.1 ev In this case, the associated Z-bursts likely to be seen as post-gzk events at the planned cosmic ray detectors

36 Gravitational clustering of relic neutrinos in galactic halos and their detection 35 Implications of clustering for absorption spectroscopy: sensitive to relic neutrino background at z 1 clustering (z < 2) can only show up as secondary dips with small, unresolvable widths in energy emission spectroscopy: sensitive to relic neutrino content of local universe (r GZK < 50 Mpc z < 0.01) neutrino density contrasts, above free-streaming scale λ fs 2 (ev/m ν ) Mpc, approximately track those of underlying CDM no substantial neutrino overdensity over the whole GZK volume ( r 3 GZK ) no significant enhancement of overall emission rate by gravitational clustering relic neutrino tomography: for 1 angular resolution and m ν ev, expect 8 55 increase in number of events from Virgo

37 Gravitational clustering of relic neutrinos in galactic halos and their detection 36 Implications of clustering for absorption spectroscopy: sensitive to relic neutrino background at z 1 clustering (z < 2) can only show up as secondary dips with small, unresolvable widths in energy emission spectroscopy: sensitive to relic neutrino content of local universe (r GZK < 50 Mpc z < 0.01) neutrino density contrasts, above free-streaming scale λ fs 2 (ev/m ν ) Mpc, approximately track those of underlying CDM no substantial neutrino overdensity over the whole GZK volume ( r 3 GZK ) no significant enhancement of overall emission rate by gravitational clustering relic neutrino tomography: for 1 angular resolution and m ν ev, expect 8 55 increase in number of events from Virgo [Da Costa et al. 96]

38 Gravitational clustering of relic neutrinos in galactic halos and their detection 37 Implications of clustering for absorption spectroscopy: sensitive to relic neutrino background at z 1 clustering (z < 2) can only show up as secondary dips with small, unresolvable widths in energy emission spectroscopy: sensitive to relic neutrino content of local universe (r GZK < 50 Mpc z < 0.01) neutrino density contrasts, above free-streaming scale λ fs 2 (ev/m ν ) Mpc, approximately track those of underlying CDM no substantial neutrino overdensity over the whole GZK volume ( r 3 GZK ) no significant enhancement of overall emission rate by gravitational clustering relic neutrino tomography: for 1 angular resolution and m ν ev, expect 8 55 increase in number of events from Virgo [Fodor,Katz,AR 02; AR,Wong 04]

39 Gravitational clustering of relic neutrinos in galactic halos and their detection 38 Implications of clustering for absorption spectroscopy: sensitive to relic neutrino background at z 1 clustering (z < 2) can only show up as secondary dips with small, unresolvable widths in energy emission spectroscopy: sensitive to relic neutrino content of local universe (r GZK < 50 Mpc z < 0.01) neutrino density contrasts, above free-streaming scale λ fs 2 (ev/m ν ) Mpc, approximately track those of underlying CDM no substantial neutrino overdensity over the whole GZK volume ( r 3 GZK ) no significant enhancement of overall emission rate by gravitational clustering relic neutrino tomography: for 1 angular resolution and m ν ev, expect 8 55 increase in number of events from Virgo [Jarrett [2MASS] 04]

40 Gravitational clustering of relic neutrinos in galactic halos and their detection Conclusions Study of gravitational clustering of big bang relic neutrinos onto existing CDM and baryonic structures within flat ΛCDM model Clustering properties on galaxy cluster, galactic, and sub-galactic scales for a range of allowed neutrino masses Local universe: Overdensity 1000 ( 100) for m ν = 0.6 ev (= 0.15 ev) for inner part (< 100 kpc) of Virgo and Centaurus Local neighbourhood of Earth: Overdensity 20 ( 2) for m ν = 0.6 ev (= 0.15 ev) Coarse-grained momentum spectrum semi-degenerate, f 1/2, up to escape momentum Higher density needs non-standard theory No tremendous increase of rate for scattering-based detection Visible in non-linear matter power spectrum? [Abazajian et al., talk in Trento, Oct 04]