1. 4) Neutrinos in astrophysics and cosmology. In this last lecture we will explore the unique relation between neutrino physics and astrophysics/cosmology. There are various aspects of this. One deals with the existence of the relic neutrino background, analogous to the CMB (except not observed as yet and waiting for a really bright idea that would make its observation possible). Indirectly the existence of the RNB makes it possible to use the “observational cosmology” to deduce limits and possibly values of the neutrino mass. Here also belongs the discussion of the role played by neutrinos in the Big Bang Nucleosynthesis (BBN). Another topic is the role of neutrinos in the Supernovae. 99% of the SN energy is carried by neutrinos. What information can we gather from a galactic supernova? Can we detect the from past SN that form a diffuse flux? What role  play in the nucleo- synthesis associated with SN?

2. Basic concepts: Cosmological principle: All positions are equivalent and hence the universe is homogeneous and isotropic. This is true provided we average over distances ~10 26 cm ~ 30 Mpc, the scale larger than clusters of galaxies, but significantly smaller than the radius of the visible universe ~10 28 cm. The standard model of cosmology is based on the non-stationary solution of Einstein’s equations, starting with the Big-Bang singularity. (Friedmann expansion). This is consistent with the observation of the cosmological red shift. If interpreted as a Doppler shift it leads to the conclusion that distant galaxies are moving with the velocity proportional to their distance from us. Thus v = H 0 r, where H o is the Hubble parameter

3. (Note that H 0 has the dimension time -1, for a flat matter dominated universe H 0 = 2/(3t 0 ), where t 0 is the time since Big-Bang) It is customary to use units of 100 km s -1 Mpc -1 = (9.8x10 9 y) -1. The Hubble parameter is then denoted as h 100 or just h., H 0 =h/ 9.8x10 9 y There have been a long running dispute about the true value of h 100, whether 0.5 or 1.0 is correct. Presently h 100 = 0.73 -0.03 +0.04 is accepted. A homogeneous and isotropic universe is characterized by the energy density  The critical density  c corresponds to the ``flat’’ universe that is expanding now but asymptotically comes to rest. If  c the universe is closed and eventually will recontract, if  c the universe is open and will expand forever.

4. Elementary derivation of  c : For a test particle of mass , kinetic energy T = 1/2  (dR/dt) 2 potential energy U = -G N (4  /3) (R 3  )/R (since homogeneous matter outside of the sphere of radius R does not contribute to the potential energy). Steady state expansion is reached for T+U = 0  Thus [(dR/dt)/R] 2 = 8/3  G N  c (note that the lefthand side is simply H 0 2 ) Therefore  c = (3 H 0 2 )/(8  G N ) = 1.05x10 4 h 100 2 eV cm -3 Curious note:  c is energy density, hence  c =  4, To calculate  multiply  c by (hc) 3 to obtain  ~ 2.5x10 -3 eV, there is no other scale so small in physics, except the neutrino mass. It is not clear whether this similarity of scales has any significance.

5. In cosmology it is customary to use the Planck units, based on a combination of G N, c, and h. Planck mass [hc/G N ] 1/2 = 1.2x10 19 GeV/c 2 Planck length [hG N /c 3 ] 1/2 = 1.6x10 -33 cm Planck time [G N h/c 5 ] 1/2 = 5.4x10 -44 s Note: Dimension of G N is (energy x length/mass 2 ) Taking these units as ``natural” we see that the Universe is old and large. t 0 /t Pl ~ 10 61, R/r Pl ~ 10 62 Another custom is to express the density (and its components) as fractions of  c, as  i  i  c. It follows from Einstein’s equations that if  tot = 1 now then  (t) = 1 was at all times, while if  < 1 then  (t) ~ 1/t thus it would require fine tuning to have  ~ 1 now unless it is true that  tot = 1 as inflation suggests.

6. From study of CMB, galaxy surveys, and observations of SNI (standard candles) one concludes that indeed  ~ 1.

7. Best fit to all data gives:  tot = 1.02 +-0.02  dark energy = 0.73 +- 0.04  dark matter = 0.22 +- 0.04  baryon = 0.044 +- 0.004 Note that the local (galactic) densities are much higher,  disk ~ 2-7 GeV/cm 3,  halo ~ 0.1-0.7 GeV/cm 3. This evidence comes mostly from the observation of rotational curves, i.e. orbital velocity as a function of the enclosed mass: v H 2 /r = G N M(r)/r 2 thus v H 2 = G N M(r)/r But empirically v H does not decrease like ~1/r outside the region of visible stars. Instead, it remains about constant (flat rotational curves)

9. To actually observe these primordial neutrinos is a major challenge. But there is little doubt that this neutrino sea must exist.

10. Ideas how to observe primordial neutrinos: Coherent effect: momentum ~ 3T ~ 5x10 -4 eV Flux for massless neutrinos ~10 13 /cm 2 s for 1 eV neutrinos v = /m ~ 5x10 -4 and the flux is correspondingly reduced. The deBroglie wavelength is = hc/pc = (197x10 -7 x2  )/5x10 -4 ~ 2 mm So the neutrinos could in principle interact with very many nuclei at once, coherently. However, so far none of the proposed ideas would work (Langacker et al., 1983). Also, proposals to use radioactive nuclei as targets (vanishing threshold), are not really feasible. (Volpe et al. 2007)

11. BBN (~ 20 Minutes) & The CMB (~ 400 kyr) provide complementary probes of the early evolution of the universe Do predictions and observations of the baryon density (  10    (n B /n  ) = 274  B h 2 ) and the expansion rate (H) of the Universe agree at these different epochs ? 4 He, d, 3 He and 7 Li are primordial. They were formed in a series of nuclear reactions once the temperature was below T ~ 1 MeV and the weak interactions were no longer in equilibrium. D, 3 He, 7 Li abundance depends on baryon density  10, they are potential BARYOMETERS. On the other hand the mass fraction of 4 He is almost independent on  but depends on the number of relativistic degrees of freedom (or nonstandard physics). The anisotropy of CMB also depends on  and nonstandard physics (among other things) Big Bang Nucleosynthesis (BBN)

12. BBN – Predicted and measured primordial abundances 4 He mass fraction, note the scale BBN abundances of D, 3 He and 7 Li are density limited. Their values can be used to determine  10.. Deuterium is the Baryometer of choice. From D and Standard BBN  10 = 6 ± 0.4 7 Li 7 Be

13. CMB temperature anisotropy spectrum (  T 2 vs.  ) also depends on the baryon density. The CMB is an early Universe Baryometer.   10 = 4.5, 6.1, 7.5 This and following few slides use the results of V. Simha & G. Steigman

14.  10 Likelihoods SBBN CMB SBBN (20 min) & CMB (380 kyr) remarkably AGREE !

15. S  H/ H  (  /  ) 1/2  (1 + 7  N / 43) 1/2  N represents the deviations from N = 3. The expansion rate (H  Hubble parameter) provides a probe of Non-Standard Physics 4 He depends on the number of relativistic degrees of freedom and therefore it is sensitive to S while D probes     +  N  and N  3 +  N

16. BBN (D, 4 He) joint fit to S and  10  Y P & y D  10 5 (D/H) 4.03.02.0 0.25 0.24 0.23 D & 4 He Isoabundance Contours

17. CMB Temperature anisotropy spectrum depends on the radiation density  R (S or N ) The CMB is an early - Universe Chronometer N = 1, 3, 5  

18. BBN (D & 4 He) & CMB AGREE ! N vs.  10 CMB BBN

19. Another strange numerical coincidence: Earlier I have shown that the `dark energy’ is characterized by  ~ 2.5x10 -3 eV, the scale similar to neutrino masses. Is that significant? Some people thing so. Here is another example, now of dubious significance: The energy density of CMB is  2 /15 (kT/hc) 3 kT ~ 0.26 eV/cm 3. Those who did not believe in Big Bang argued that this energy could have come from the formation of 4 He. Since  B ~ 0.044   B =  B  c ~ 250 eV/cm 3 and n B ~ 2.5x10 -7 cm -3. 4 He weight fraction is ~0.25, hence n He = n B /16. 4 He binding energy is 28 MeV, thus the energy `stored’ in 4 He is n B /16 x B( 4 He) = 0.41 eV/cm 3. This is (we know that accidentally) rather close to the CMB energy density.

20. These two were already discussed This provides a constraint on the sum M =  m i of neutrino masses

22. Dodelson Neutrino mass & large scale structures. Effect of neutrino mass on the power spectrum (bigger masses suppress the structure formation at high k or smaller scales).

24. Cosmological bounds on  m i in recent publications

25. Neutrinos and core collapse supernovae: (SN type II and (for historical reasons) Ib,Ic) ~ 8 - 40 M sun progenitor (< 0.1 Gyr) iron white dwarf in core of star, mass ~ 1.4 M sun ; neutrinos reveal (gravitational) explosion energy; hot and dense --> + (seconds) Neutrinos from SNII: Seen once, from SN 1987A But only ~ 20 events Diffuse background from past SNII not seen yet Limits on MeV background from Super-K

26. Supernova Energetics

27. Supernova Neutrino Emission

28. Supernova Neutrino Detection Observation of SN neutrinos is a source of information on Supernova physics (models, black holes, progenitors…) Particle physics (neutrino properties, new particles, …) IMB KamII

29. A detector on Earth would ideally detect and distinguish four classes of SN neutrino events: a)Charged current events initiated by e (easy with free protons in the detector) b)Charged current events initiated by e (require complex nuclear targets) c)Neutrino-electron scattering events, that combine events caused by the charged and neutral currents. d)Neutral current events, that measure the total SN neutrino flux. Ideally, for each of these events we would like to get enough information to deduce the corresponding flux, some characteristic energy, and all that as a function of time.

30. Discovered by observing 44 Ti, T 1/2 =60y decay lines. Must have been very close, yet no historical record. Probably wrong.

31. no longer running running now

32. What about the diffuse neutrino flux of the past SN? Can we ever observe it, and what it would tell us? Back of the envelope estimate of the relic SN flux Typical SN has ~2x10 57 M p Number of emitted e happens to be also 2x10 57 ( 5x10 52 erg = 30x10 57 MeV, ~ 15 MeV) Assume that SN cores contain ~1% of the mass of luminous stars, which in turn have  * ~0.005~ 25eV/cm 3 The e number density is then  ~  * /(100 M p ) ~ ~2.5x10 -10 /cm 3 The flux is c    /(cm 2 s)

33. Relic Supernova Neutrinos, depend on the past SN rates and on `typical’  spectrum Ando, Sato, and Totani, Astropart. Phys. 18, 307 (2003)

34. Relative spectra when only single events are observed as in SK now. The chances of observation would be greatly enhanced of the correlated signal on e could be measured. (M. Malek)

35. Cosmological neutrino mass limit: If we accept that  ~ 1 and the existence of the primordial neutrino sea, we can derive a very general mass limit. Neutrino sea contributes to the energy density  =  m (eV) x 112/cm 3 This must not exceed  c ~ 5000 eV/cm 3 Therefore  m < 45 eV (this is a conservative limit, since we know that other components, dark energy, dark matter, etc. exceed the neutrino contribution, hence this limit can be improved) The only loophole involves possible neutrino decay,  > 10 10 y