4) Neutrinos in astrophysics and cosmology.

In this last lecture we will explore the unique relation betweenneutrino physics and astrophysics/cosmology.

There are various aspects of this. One deals with the existence ofthe 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 makesit possible to use the “observational cosmology” to deduce limitsand possibly values of the neutrino mass.Here also belongs the discussion of the role played by neutrinosin 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 canwe gather from a galactic supernova? Can we detect the frompast SN that form a diffuse flux? What role play in the nucleo-synthesis associated with SN?

Basic concepts:Cosmological principle: All positions are equivalent andhence the universe is homogeneous and isotropic.This is true provided we average over distances ~1026cm ~ 30 Mpc,the scale larger than clusters of galaxies, but significantly smallerthan the radius of the visible universe ~1028 cm.

The standard model of cosmology is based on thenon-stationary solution of Einstein’s equations,starting with the Big-Bang singularity. (Friedmann expansion). This is consistent with theobservation of the cosmological red shift.If interpreted as a Doppler shift it leads to theconclusion that distant galaxies are moving withthe velocity proportional to their distance from us.

Thus v = H0 r,where Ho is the Hubble parameter

(Note that H0 has the dimension time-1, for a flat matter dominated universe H0 = 2/(3t0), where t0 is the time since Big-Bang)

It is customary to use units of 100 km s-1 Mpc-1 = (9.8x109 y)-1. The Hubble parameter is then denoted as h100 or just h., H0 =h/ 9.8x109 yThere have been a long running dispute about the true value of h100, whether 0.5 or 1.0 is correct. Presently h100 = 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 expandforever.

Elementary derivation of c:For a test particle of mass , kinetic energy T = 1/2 (dR/dt)2

potential energy U = -GN (4/3) (R3 )/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 GN c

(note that the lefthand side is simply H02)

Therefore c = (3 H02)/(8 GN) = 1.05x104 h100

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.

In cosmology it is customary to use the Planck units,based on a combination of GN, c, and h.Planck mass [hc/GN]1/2 = 1.2x1019 GeV/c2

Planck length [hGN/c3]1/2 = 1.6x10-33 cmPlanck time [GNh/c5]1/2 = 5.4x10-44 sNote: Dimension of GN is (energy x length/mass2)

Taking these units as ``natural” we see that the Universeis old and large.

t0/tPl ~ 1061, R/rPl ~ 1062

Another custom is to express the density (and its components) as fractions of c, as iic.

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.

From study ofCMB, galaxysurveys, andobservationsof SNI (standardcandles) one concludes thatindeed ~ 1.

Best fit to all data gives:tot = 1.02 +-0.02dark energy = 0.73 +- 0.04dark matter = 0.22 +- 0.04baryon = 0.044 +- 0.004

Note that the local (galactic) densities are much higher, disk ~ 2-7 GeV/cm3, halo ~ 0.1-0.7 GeV/cm3.

This evidence comes mostly from the observation of rotationalcurves, i.e. orbital velocity as a function of the enclosed mass:vH

2/r = GN M(r)/r2 thus vH 2= GN M(r)/r

But empirically vH does not decrease like ~1/r outside theregion of visible stars. Instead, it remains about constant(flat rotational curves)

To actually observe these primordial neutrinos is a majorchallenge. But there is little doubt that this neutrino seamust exist.

Ideas how to observe primordial neutrinos:

Coherent effect: momentum <p> ~ 3T ~ 5x10-4 eVFlux for massless neutrinos ~1013 /cm2 sfor 1 eV neutrinos v = <p>/m ~ 5x10-4

and the flux is correspondingly reduced.

The deBroglie wavelength is = hc/pc = (197x10-7x2)/5x10-4 ~ 2 mmSo the neutrinos could in principle interact with very manynuclei 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 (vanishingthreshold), are not really feasible. (Volpe et al. 2007)

BBN (~ 20 Minutes) & The CMB (~ 400 kyr) provide complementary probes of the early evolution of the universeDo predictions and observations of the baryon density (10 (nB/n) = 274 Bh2 ) and the expansion rate (H) of the Universe agree at these different epochs ?

4He, d, 3He and 7Li 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, 3He, 7Li abundance depends on baryon density 10, they are potential BARYOMETERS. On the other hand the mass fraction of 4He is almostindependent on but depends on the number of relativistic degrees of freedom (or nonstandard physics).

The anisotropy of CMB also depends on and nonstandard physics (amongother things)

Big Bang Nucleosynthesis (BBN)

BBN – Predicted and measured primordial abundances

4He mass fraction,note the scale

BBN abundances ofD, 3He and 7Li aredensity limited. Theirvalues can be usedto determine 10..

Deuterium is theBaryometer ofchoice. From Dand Standard BBN10 = 6 ± 0.4

7Li7Be

CMB temperature anisotropy spectrum (T2 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

10 Likelihoods

SBBNCMB

SBBN (20 min) & CMB (380 kyr) remarkably AGREE !

S H/ H (/)1/2 (1 + 7N / 43)1/2

N represents the deviations from N = 3.

The expansion rate (H Hubble parameter) provides a probe of Non-Standard Physics

4He depends on the number of relativistic degrees offreedom and therefore it is sensitive to S while D probes

+ N and N 3 + N

BBN (D, 4He) joint fit to S and 10

YP & yD 105 (D/H)

4.0 3.0 2.0

0.25

0.24

0.23

D & 4He Isoabundance Contours

CMB Temperature anisotropy spectrum depends on the radiation density R (S or N)

The CMB is an early - Universe Chronometer

N = 1, 3, 5

BBN (D & 4He) & CMB AGREE !

N vs. 10

CMB

BBN

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 thatsignificant? Some people thing so.

Here is another example, now of dubious significance:The energy density of CMB is 2/15 (kT/hc)3kT ~ 0.26 eV/cm3.Those who did not believe in Big Bang argued that this energycould have come from the formation of 4He.Since B ~ 0.044 B = Bc ~ 250 eV/cm3 and nB ~ 2.5x10-7 cm-3.4He weight fraction is ~0.25, hence nHe = nB/16.4He binding energy is 28 MeV, thus the energy `stored’ in 4He isnB/16 x B(4He) = 0.41 eV/cm3.This is (we know that accidentally) rather close to the CMB energydensity.

These two were already discussed This provides a constrainton the sum M = mi ofneutrino masses

Dodelson

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

Cosmological bounds on mi in recent publications

Neutrinos and core collapse supernovae:(SN type II and (for historical reasons) Ib,Ic)

~ 8 - 40 Msun progenitor (< 0.1 Gyr)iron white dwarf in core of star, mass ~ 1.4 Msun;neutrinos reveal (gravitational) explosion energy;hot and dense --> + (seconds)

Neutrinos from SNII:Seen once, from SN 1987A

But only ~ 20 eventsDiffuse background from past SNII not seen yet

Limits on MeV background from Super-K

Supernova Energetics

Supernova Neutrino Emission

Supernova Neutrino Detection

Observation of SN neutrinos is a source of information onSupernova physics (models, black holes, progenitors…)

Particle physics (neutrino properties, new particles, …)

IMB

KamII

A detector on Earth would ideally detect and distinguish fourclasses 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 enoughinformation to deduce the corresponding flux, some characteristicenergy, and all that as a function of time.

Discovered by observing 44Ti, T1/2=60ydecay lines. Must have been very close, yet no historical record. Probably wrong.

no longer running

running now

running now

running now

running now

running now

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 ~2x1057 Mp

• Number of emitted e happens to be also 2x1057

( 5x1052erg = 30x1057MeV, <E> ~ 15 MeV)• Assume that SN cores contain ~1% of the mass of

luminous stars, which in turn have *~0.005~ 25eV/cm3

• The e number density is then ~ */(100 Mp) ~

~2.5x10-10/cm3

• The flux is c/(cm2s)

Relic Supernova Neutrinos, depend on the past SN ratesand on `typical’ spectrum

Ando, Sato, and Totani, Astropart. Phys. 18, 307 (2003)

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)

Cosmological neutrino mass limit:

If we accept that ~ 1 and the existence of theprimordial neutrino sea, we can derive a very generalmass limit.

Neutrino sea contributes to the energy density = m (eV) x 112/cm3

This must not exceed c ~ 5000 eV/cm3

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, > 1010 y