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 n from
past SN that form a diffuse flux? What role n play in the nucleosynthesis associated with SN?
Basic concepts:
Cosmological principle: All positions are equivalent and
hence 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 smaller
than the radius of the visible universe ~1028 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 = 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 y
There 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 r. The critical density rc corresponds to the
``flat’’ universe that is expanding now but asymptotically
comes to rest. If r > rc the universe is closed and eventually
will recontract, if r < rc the universe is open and will expand
forever.
Elementary derivation of rc:
For a test particle of mass m, kinetic energy T = 1/2 m (dR/dt)2
potential energy U = -GN (4p/3) (R3 rm)/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 p GN rc
(note that the lefthand side is simply H02)
Therefore rc = (3 H02)/(8 p GN) = 1.05x104 h1002 eV cm-3
Curious note: rc is energy density, hence rc = e4 ,
To calculate e multiply rc by (hc)3 to obtain e ~ 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 cm
Planck time [GNh/c5]1/2 = 5.4x10-44 s
Note: Dimension of GN is (energy x length/mass2)
Taking these units as ``natural” we see that the Universe
is old and large.
t0/tPl ~ 1061, R/rPl ~ 1062
Another custom is to express the density (and its components)
as fractions of rc, as Wi = ri/rc.
It follows from Einstein’s equations that if Wtot = 1 now then W(t) = 1 was at
all times, while if W < 1 then W(t) ~ 1/t thus it would require fine tuning to
have W ~ 1 now unless it is true that Wtot = 1 as inflation suggests.
From study of
CMB, galaxy
surveys, and
observations
of SNI (standard
candles) one
concludes that
indeed W ~ 1.
Best fit to all data gives:
Wtot = 1.02 +-0.02
Wdark energy = 0.73 +- 0.04
Wdark matter = 0.22 +- 0.04
Wbaryon = 0.044 +- 0.004
Note that the local (galactic) densities are much
higher, rdisk ~ 2-7 GeV/cm3, rhalo ~ 0.1-0.7 GeV/cm3.
This evidence comes mostly from the observation of rotational
curves, i.e. orbital velocity as a function of the enclosed mass:
vH2/r = GN M(r)/r2 thus vH 2= GN M(r)/r
But empirically vH does not decrease like ~1/r outside the
region of visible stars. Instead, it remains about constant
(flat rotational curves)
To actually observe these primordial neutrinos is a major
challenge. But there is little doubt that this neutrino sea
must exist.
Ideas how to observe primordial neutrinos:
Coherent effect: momentum <p> ~ 3T ~ 5x10-4 eV
Flux for massless neutrinos ~1013 /cm2 s
for 1 eV neutrinos v = <p>/m ~ 5x10-4
and the flux is correspondingly reduced.
The deBroglie wavelength is
l= hc/pc = (197x10-7x2p)/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)
Big Bang Nucleosynthesis (BBN)
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  (nB/ng) = 274 WBh2 ) 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 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)
BBN – Predicted and measured primordial abundances
4He
mass fraction,
note the scale
BBN abundances of
D, 3He and 7Li are
density limited. Their
values can be used
to determine 10..
7Li
7Be
Deuterium is the
Baryometer of
choice. From D
and Standard BBN
10 = 6 ± 0.4
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
SBBN (20 min) & CMB (380 kyr) remarkably AGREE !
10 Likelihoods
CMB
SBBN
The expansion rate (H  Hubble parameter)
provides a probe of Non-Standard Physics
S  H/ H  (r/r)1/2  (1 + 7Nn / 43)1/2
Nn represents the deviations from Nn = 3.
r  r + Nn rn
4He
and
Nn
 3 + Nn
depends on the number of relativistic degrees of
freedom and therefore it is sensitive to S while
D probes 
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 rR (S or Nn)
 
Nn = 1, 3, 5
The CMB is an early - Universe Chronometer
BBN (D &
4He)
Nn
& CMB AGREE !
vs. 10
CMB
BBN
Another strange numerical coincidence:
Earlier I have shown that the `dark energy’ is characterized by
e~ 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 p2/15 (kT/hc)3kT ~ 0.26 eV/cm3.
Those who did not believe in Big Bang argued that this energy
could have come from the formation of 4He.
Since WB ~ 0.044  rB = WBrc ~ 250 eV/cm3 and nB ~ 2.5x10-7 cm-3.
4He weight fraction is ~0.25, hence n
He = nB/16.
4He binding energy is 28 MeV, thus the energy `stored’ in 4He is
nB/16 x B(4He) = 0.41 eV/cm3.
This is (we know that accidentally) rather close to the CMB energy
density.
These two were already discussed
This provides a constraint
on the sum M = Smi of
neutrino masses
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).
Dodelson
Cosmological bounds on Smi 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 --> n + n (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
Supernova Energetics
Supernova Neutrino Emission
Supernova Neutrino Detection
IMB
KamII
Observation of SN neutrinos is a source of information on
Supernova physics (models, black holes, progenitors…)
Particle physics (neutrino properties, new particles, …)
A detector on Earth would ideally detect and distinguish four
classes of SN neutrino events:
a) Charged current events initiated by ne (easy with free
protons in the detector)
b) Charged current events initiated by ne (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.
Discovered by observing 44Ti, T1/2=60y
decay lines. Must have been very close,
yet no historical record. Probably wrong.
running now
no longer running
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 ne 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
W*~0.005~ 25eV/cm3
• The ne number density is then rn ~ W*/(100 Mp) ~
~2.5x10-10n/cm3
• The flux is crn ~ 8n/(cm2s)
Relic Supernova Neutrinos,
depend on the past SN rates
and on `typical’ n 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 ne could be measured.
(M. Malek)
Cosmological neutrino mass limit:
If we accept that W ~ 1 and the existence of the
primordial neutrino sea, we can derive a very general
mass limit.
Neutrino sea contributes to the energy density
rn = S mn (eV) x 112/cm3
This must not exceed rc ~ 5000 eV/cm3
Therefore Smn < 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, tn > 1010 y