Sterile Neutrinos in Cosmology and Astrophysics

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1 Kalliopi Petraki (UCLA) October 27, 2008

2 Particle Physics Neutrino Oscillation experiments: neutrinos have mass Cosmology and Astrophysics Plenty of unexplained phenomena Dark Matter Pulsar Kicks Supernova explosions Matter-Antimatter Asymmetry Can these issues be attacked on the same ground?

3 Neutrino masses The discovery of neutrino masses suggests the existence of right-handed, called sterile, neutrinos. The neutrino sector is extended to include: {ν e, ν µ, ν τ, N 1, N 2, N 3,...} The SM Lagrangian is extended to include the new states: L = L SM + N ai N a y αaε ij H i ( L α) j N a Ma 2 The neutrino mass mixing matrix becomes: M = 0 D 3 N N c an a + h.c. D T N 3 M N N where D 3 N y H are the Dirac masses and M N N are the Majorana masses of sterile states.

4 What can experiments and theoretical considerations tell us about sterile neutrinos? How many are there? theory: no upper limit experiment: at least 1 What is the scale of their Majorana masses?

5 Seesaw Mechanism and Yukawa couplings M = ( 0 D D T M ) The eigenvalues of this matrix are: D 2 /M and M In the Standard Model, the matrix D arises from the Higgs mechanism: D αa = y αa H The smallness of neutrino masses ( ) y H m ν y H M can be explained by either: - small Yukawa couplings y 1 - Large M and y 1

6 Seesaw Mechanism and Yukawa couplings M = ( 0 D D T M ) The eigenvalues of this matrix are: D 2 /M and M In the Standard Model, the matrix D arises from the Higgs mechanism: D αa = y αa H The smallness of neutrino masses ( ) y H m ν y H M can be explained by either: - small Yukawa couplings y 1 - Large M and y 1 Is y 1 better than y 1? Depends on the model: If y some intersection number in string theory, then y 1 is natural. If y comes from wave function overlap of fermions living on different branes in a model with extra-dimensions, then it can be exponentially suppressed, hence, y 1 is natural.

7 Seesaw Mechanism and Yukawa couplings M = ( 0 D D T M ) The eigenvalues of this matrix are: D 2 /M and M In the Standard Model, the matrix D arises from the Higgs mechanism: D αa = y αa H The smallness of neutrino masses ( ) y H m ν y H M can be explained by either: - small Yukawa couplings y 1 - Large M and y 1 Is y 1 better than y 1? Depends on the model: If y some intersection number in string theory, then y 1 is natural. If y comes from wave function overlap of fermions living on different branes in a model with extra-dimensions, then it can be exponentially suppressed, hence, y 1 is natural. In the absence of theory of the Yukawa couplings, consider all allowed values for the sterile neutrino masses.

8 What can experiments and theoretical considerations tell us about sterile neutrinos? How many are there? theory: no upper limit experiment: at least 1 What is the scale of their Majorana masses? anything What are the cosmological consequences of such particles? Light sterile neutrino as a Dark Matter candidate Heavy sterile neutrinos produced in supernovae

9 Dark Matter A sterile neutrino of mass kev can be Dark Matter A good candidate because: it is a plausible explanation of neutrino masses if it is sufficiently light (sub-mev), it is stable it constitutes Warm Dark Matter, of variable warmth, depending on the production mechanism Other hints in favor of such a particle: - Pulsar kicks, by asymmetric emission from the supernova core - Star Formation, by speeding up H 2 formation. - Matter - Antimatter asymmetry, via leptogenesis. Investigate production mechanisms and cosmological properties

10 CDM vs WDM In large scales, both CDM and WDM are in complete agreement with observations. In small scales, CDM predictions do not match observations: overprediction of satellite galaxies prediction of central cusps rather than cores

11 CDM vs WDM In large scales, both CDM and WDM are in complete agreement with observations. In small scales, CDM predictions do not match observations: overprediction of satellite galaxies prediction of central cusps rather than cores Quantitatively: - free-streaming length: cutoff scale of the power spectrum of density perturbations. ( ) kev λ F S 13 kpc p ( ) T m X Ω X - phase-space density: entropy content; observationally inferred from Dwarf Spheroidal Galaxies / 3 p 2 2 Q ϱ m 2

12 Production Mechanisms Sterile neutrinos can be produced in the early universe through: Oscillations - off-resonance [Dodelson, Widrow] at T prod 130 MeV; thermal spectrum - on-resonance, if there is large lepton asymmetry [Fuller, Shi] at T prod 150 MeV; non-thermal spectrum Cool DM

13 Production Mechanisms Sterile neutrinos can be produced in the early universe through: Oscillations - off-resonance [Dodelson, Widrow] at T prod 130 MeV; thermal spectrum - on-resonance, if there is large lepton asymmetry [Fuller, Shi] at T prod 150 MeV; non-thermal spectrum Cool DM Decays - inflaton decays into sterile neutrinos [Shaposhnikov, Tkachev] - Higgs decays, at the electroweak scale [Kusenko, KP]

14 The Majorana Masses L =L SM + N ai N a y αa ε ij H i ( L α) j N a Ma 2 N c an a +h.c.

15 The Majorana Masses In the SM, fermion masses arise via the Higgs mechanism. Can the Majorana masses of sterile neutrinos arise in the same way? L =L SM + N ai N a y αa ε ij H i ( L α) j N a Ma 2 N c an a +h.c.

16 The Majorana Masses In the SM, fermion masses arise via the Higgs mechanism. Can the Majorana masses of sterile neutrinos arise in the same way? L =L SM + N ai N a ( S)2 y αa ε ij H i ( L α) j N a fa 2 S N c an a +h.c.

17 The Majorana Masses In the SM, fermion masses arise via the Higgs mechanism. Can the Majorana masses of sterile neutrinos arise in the same way? L =L SM + N ai N a ( S)2 y αa ε ij H i ( L α) j N a fa 2 S N c an a V (H, S)+h.c.

18 The Majorana Masses In the SM, fermion masses arise via the Higgs mechanism. Can the Majorana masses of sterile neutrinos arise in the same way? L =L SM + N ai N a ( S)2 y αa ε ij H i ( L α) j N a fa 2 S N c an a V (H, S)+h.c. The singlet Higgs couples to the SM Higgs through a scalar potential: V (H, S) = µ 2 H H 2 + λ H H µ2 S S λ S S4 + 2λ HS H 2 S αs3 + ω H 2 S If the parameters of the potential are such that S 10 2 GeV, then the singlet Higgs will take part in the EWPT.

19 The Electroweak Phase Transition The presence of the singlet Higgs changes the nature of the EWPT S 0, H = 0 2nd order PT to H 0 1st order PT to the true vacuum It is possible that the singlet Higgs will be discovered at the LHC [Profumo, Ramsey-Musolf, G. Shaughnessy (2007); Barger et al. (2008)]

20 The Majorana Masses In the SM, fermion masses arise via the Higgs mechanism. Can the Majorana masses of sterile neutrinos arise in the same way? L = L SM + N ai N a+ 1 2 ( S)2 y αa ε ij H i ( L α) j N a fa 2 S N c an a V (H, S)+h.c. The singlet Higgs couples to the SM Higgs and takes part in the EWPT: V (H, S) = µ 2 H H 2 + λ H H µ2 S S λ S S4 + 2λ HS H 2 S αs3 + ω H 2 S Majorana masses may arise, after spontaneous symmetry breakdown, from the coupling of sterile neutrinos to a gauge-singlet Higgs: M = f S Sterile neutrinos are produced by decays of S bosons: S NN

21 Higgs singlet decays ( f Ω N ) 3 ( S m S ) ( ) 33 ξ Ω N does not depend on the mixing angle

22 Higgs singlet decays ( f Ω N ) 3 ( S m S ) ( ) 33 ξ Ω N does not depend on the mixing angle Take S m S, this sets f 10 8 For a sterile neutrino of mass m N singlet Higgs VEV has to be: S m N f kev to constitute all of dark matter, the kev GeV

23 Higgs singlet decays ( f Ω N ) 3 ( S m S ) ( ) 33 ξ Ω N does not depend on the mixing angle Take S m S, this sets f 10 8 For a sterile neutrino of mass m N kev to constitute all of dark matter, the singlet Higgs VEV has to be: S m N f kev GeV S lives in the electroweak scale and can affect the EW Phase Transition.

24 Higgs singlet decays ( f Ω N ) 3 ( S m S ) ( ) 33 ξ Ω N does not depend on the mixing angle For a sterile neutrino of mass m N kev to constitute all of dark matter, the singlet Higgs VEV has to be: S m N f kev GeV S lives in the electroweak scale and can affect the EW Phase Transition. ξ = g (T prod ) g (T today ) The ξ factor is important because it redshifts the sterile neutrinos and results in colder dark matter. This weakens the limits derived from the small-scale structure considerations [Kusenko (2006)].

25 Sterile neutrinos of m N kev are produced non-thermally from decays of a singlet Higgs. At production T 100 GeV: p N = T T 100GeV

26 Sterile neutrinos of m N kev are produced non-thermally from decays of a singlet Higgs. At production T 100 GeV: p N = T T 100GeV As universe expands, relativistic species decouple, releasing entropy. Sterile neutrinos produced at the EW scale appear redshifted at later times: p N = T ξ 1 3 where ξ = g (T prod ) g (T today ) T kev This is lower than for sterile neutrinos produced via off-resonance oscillations, at T 100 MeV, and modifies the small-scale structure limits

27 Chilling... Sterile neutrinos of m N kev are produced non-thermally from decays of a singlet Higgs. At production T 100 GeV: p N = T T 100GeV As universe expands, relativistic species decouple, releasing entropy. Sterile neutrinos produced at the EW scale appear redshifted at later times: p N = T ξ 1 3 where ξ = g (T prod ) g (T today ) T kev This is lower than for sterile neutrinos produced via off-resonance oscillations, at T 100 MeV, and modifies the small-scale structure limits Dark Matter candidate ν-chill

28 Dark Matters sterile neutrinos Warm DM via off-res. oscill. Cool DM via on-res. oscill. w. lepton asymm. ν-chill via Higgs decays at the EW scale free-streaming length (z = 0) kpc ( 2 ( ) ( kev ) g d m ( ) ( kev ) g d m 110 g d ) 1 3 ( kev ) m primordial phase-space density, in M /kpc3 (km/s) ( ) 5 m 3 kev ( ) 7 m 3 kev ( ) 5 m 3 kev observations Q [Gilmore] [Boyanovsky, Vega, Sanchez (2008); Boyanovsky (2008); KP (2008)]

29 Radiative Decay and X-ray detection Sterile neutrinos with m kev have lifetimes longer than the age of the universe, but they do decay into lighter neutrino states and photons: The rate of the radiative decay is: Γ N νγ ( sin 2 2θ ) ( mn ) 5 s 1 1 kev Decay rate is very small, but large lumps of dark matter emit some X-rays. [Abazajian, Fuller, Tucker; Dolgov, Hansen; Shaposhnikov et al.] Photon energy is m/2 detection with X-ray telescopes. Dwarf Spheroidal Galaxies: dark-matter dominated; X-ray quiet.

30 Supernovae won t explode... Simulations of core-collapse SN fail to reproduce the shock. Problem is: Gravitational energy erg initially trapped in the core. At the bounce, this energy is drained from the core by active neutrinos. The stalled shock needs only 1% of this energy, erg, to propagate successfully. Energy transport from the core to the shock front. What are we missing?

31 Supernovae won t explode... Simulations of core-collapse SN fail to reproduce the shock. Problem is: Gravitational energy erg initially trapped in the core. At the bounce, this energy is drained from the core by active neutrinos. The stalled shock needs only 1% of this energy, erg, to propagate successfully. Energy transport from the core to the shock front. What are we missing? it might be multi-dimensional hydrodynamic effects,

32 Supernovae won t explode... Simulations of core-collapse SN fail to reproduce the shock. Problem is: Gravitational energy erg initially trapped in the core. At the bounce, this energy is drained from the core by active neutrinos. The stalled shock needs only 1% of this energy, erg, to propagate successfully. Energy transport from the core to the shock front. What are we missing? it might be multi-dimensional hydrodynamic effects, or new physics

33 SN explosions from heavy sterile neutrino decay A neutral particle, produced in the core, that will decay inside the envelope increases the energy of the envelope melts nuclei in front of the shock

34 SN explosions from heavy sterile neutrino decay A neutral particle, produced in the core, that will decay inside the envelope increases the energy of the envelope melts nuclei in front of the shock A heavy sterile neutrino could do! - produced in the core from weak interactions - small mixing means it s not trapped: it streams-out freely from the core - heavy: carries out the right amount of energy erg - short-lived τ s: it decays in the vicinity of the shock

35 Limits mixing with ν µ mixing with ν τ [Kusenko, Pascoli, Semikoz (2005)] [Nédélec (2001)]

36 Calculations show that A sterile neutrino m s MeV mixing with ν µ or ν τ by sin 2 θ removes from a typical supernova core E s erg within 1-5 s

37 Calculations show that A sterile neutrino m s MeV mixing with ν µ or ν τ by sin 2 θ removes from a typical supernova core E s erg within 1-5 s Decay inside the envelope, in the vicinity of the shock: τ s 0.01 s or R 10 8 cm

38 Calculations show that A sterile neutrino m s MeV mixing with ν µ or ν τ by sin 2 θ removes from a typical supernova core E s erg within 1-5 s Decay inside the envelope, in the vicinity of the shock: τ s 0.01 s or R 10 8 cm Decay mode: N s ν µ,τ + π 0 ν µ,τ + 2γ γ-ray photons will thermalize quickly with surrounding matter High-energy neutrinos ( 80 MeV) produced will escape and provide an detectable signature, by galactic supernova neutrino observations

39 Sterile neutrinos are introduced to explain the observed neutrino masses. The same particles can account for a lot of astrophysical phenomena. If one of them is light, m s kev, it can be the Dark Matter. Different production mechanisms result in colder or warmer DM. S NN decays yield sufficient DM abundance that does not depend on the mixing angle and is in agreement with the small-scale structure. The same particle can explain the pulsar velocities, speed up the star formation, and account for the matter-antimatter asymmetry. possible through X-ray observations of nearby galaxies. Heavy sterile neutrinos, m s 200 MeV, produced in supernovae cores, can facilitate SN explosions, by enhancing the energy transport from the core to the shock front. possible through galactic supernova neutrino observations.