Transcript Neutrino Masses, Dark Matter and the Mysterious Early Quasars

R.D. Viollier
University of Cape Town

Observational facts: Earliest quasar SDSS J114816.64
+525 150.3 has redshift z = 6.42 corresponding to
receding velocity v/c = 0.96. Quasar light was emitted
at te = 0.85 Gyr and is observed today at to = 13.7 Gyr
after the Big Bang (WMAP-3).

Simplest interpretation: Quasar is temporarily
(Δt < 30 Myr) powered by isotropic accretion of
baryonic matter onto a supermassive black hole of mass
M = 3×109 M☼, radiating at the Eddington luminosity

gravitational force on protons
dominates
Fgrav (r ) 

GM (r )m p
r
σT - Thomson
cross section
of the electron
LE (r ) T

4 r 2 c
8
T 
3
2
mp proton
mass
2
radiational force on electrons
dominates
Frad
M(r) - mass
enclosed
within r
LE(r) - nett
luminosity
crossing r
outwards
 e2 
 0.665 1024 cm 2

2 
 me c 

local neutrality of plasma implies
Fgrav(r) = Frad(r) or
Eddington luminosity

differential equation
dM BH 1   M
L
1 M
M
1

 L E2 
 L BH  M BH
dt
M
c
M
tE

tE 
T c
 450.5 Myr
4 Gmp
 M tE

 50.1 Myr
1 M L

εM = 0.1 is the standard efficiency
εL = L/LE = 1 for the Eddington limit
Eddington time
characteristic time
solution
M BH (t )  M BH (0) e
t

 M BH (0) 2
t
t2
mass doubling time
Answer:
1
210 ~ 103  230 ~ 109
t E ln30
2 mass
34 Myr
doubling times
L
 t = 30 × 35 Myr = 1.05 Gyr
M
with t2   ln 2 
1 M 
for the formation of supermassive black holes
massive star
~ 25 M⊙
stellar
mass BH
~ 3 M⊙
SN
explosion
accretion of
baryonic
matter
supermassive BH
~ 3×109 M⊙
HOWEVER:
Compare
this
tform
> 1.437
• the massive
star
can
only
form Gyr to the observed times of te ~ 0.85 Gyr
after zreion ~ 11 or treion ~ 0.365 Gyr
 this scenario does not work!
reionization  molecular hydrogen

initial BH mass should be
MBH(0) = 1.4×105 M☼ instead of MBH(0) = 3 M☼
 population III stars?

allowing super-Eddington accretion with
e.g. εL = 2 instead of εL = 1
 non-spherical accretion?

lowering the efficiency from
εM = 0.1 to εM = 0.05
(dark matter has εM = 0!)
X
X
√

P. Minkowski, Phys. Lett. B67 (1977) 421: add 3 right-handed (or
sterile) neutrinos  invention of the seesaw mechanism
 renormalizable Lagrangean which generates Dirac and Majorana
masses for all neutrinos
LMSM  LSM
~ MI c
 N Iiγ   N I  FαI Lα N I Φ 
N I N I  h.c.
2

LSM: Lagrangean of the Standard Model
~
Φi = εij Φj*: Higgs doublet
Lα (α=e,μ,τ): lepton doublet
NI (I=1,2,3): sterile neutrino singlet
kinetic
energy
Yukawa
terms terms
coupling
Majorana mass
MD = FαI ‹Ф›exp
terms MI

In comparison with the SM, the νMSM has 18 new parameters:
18 new parameters of νMSM
3 Majorana
masses of NI

15 Yukawa couplings in leptonic sector
3 Dirac
masses
6 mixing angles
6 CP-violating
phases
these parameters can be chosen such as to be consistent with the solar,
atmospheric, reactor and accelerator neutrino experiments

the baryon asymmetry comes out correctly

the Majorana masses are below the weak interaction symmetry breaking scale

the lowest mass right-handed (or sterile) neutrino has a mass of O(10 keV) and
is quasi-stable: it could be the dark matter particle
unstable,
observable at
accelerators
M. Shaposhnikov
arxiv: 0706.1894v1 [hep-ph]
13.06.2007
quasi-stable dark
matter particle,
observable through
its radioactive decay

to fix our ideas, we assume

production process: scattering
that the lightest sterile
of active neutrinos out of
neutrino νs has
equilibrium
Majorana mass
• m = 15
mixing:
resonant or
non-resonant ≡
vacuum
L. Wolfenstein
(1978)
keV/c2
Mixing angle of νs with νe
• ϑ = 10-6.5
Lepton asymmetry
• L(νe) = (n(νe) – n(͞νe))/n(γ) = 10-2

production process is
number densities of νe, ͞νe, γ
necessarily linked with decay
• n(νe), n(͞νe), n(γ)
process!

νs’s produced at T ~ 328 (mc2/15 keV)1/3 MeV/K with
Ωs= 0.24 through resonant and non-resonant scattering of
active neutrinos

~ 22 min after Big Bang, the νs’s are non-relativistic

νs’s dominate the expansion of the universe ~ 79 kyr after Big
Bang

degenerate νs-balls form between 650 Myr and 840 Myr

mass contained within the free-streaming length at matter-radiation equality at
79 kyr is
resonant
production, cold
non-resonant
production, warm

since part of the neutrinos may be ejected, the minimal mass that may collapse is
perhaps Mmin ~ 106 M☼ .

the maximal mass that a self-gravitating degenerate neutrino ball can support is
the Oppenheimer-Volkoff limit
Planck
mass
m-dependent
for the formation of supermassive black holes
supermassive
νs-ball
650 Myr < t <
840 Myr
M.C. Richter, G.B. Tupper, R.D. Viollier
JCAP 0612 (2006) 015; astro-ph/0611552
attraction of
H2-cloud to
center of
νs-ball
massive star
M ~ 25 M⊙
stellar mass
BH
M ~ 3 M⊙
supermassive
BH through
accretion of
νs-ball
antihierarchical
formation of quasars
and active galactic
nuclei

Bernoulli’s equation for a

Bernoulli’s equation is now

Here, v(x) fulfils the Lane-Emden
steady-state flow
• u(r):
• vF(r):
• φ(r):
• rH:

flow velocity of infalling
degenerate sterile neutrino fluid
Fermi velocity
gravitational potential
radius of the halo
the flow is trans-sonic, i.e.
equation
Total mass enclosed
within a radius r = bx is
Solutions of the Lane-Emden equation with
constant mass M = MC + MH = 2.714 M⊙

mass accretion rate into a sphere, containing a mass MC
within a radius rC from the centre is
μ = MC /M

with universal time scale

and shut-off parameter, defined as
rC = bxC is now the
radius at which the
escape velocity is c
M.C. Richter, G.B. Tupper, R.D. Viollier
JCAP 0612 (2006) 015; astro-ph/0611552
4 main characteristics of the symbiotic scenario:

no Eddington limit for νs-ball formation and accretion onto BH

matter densities in νs-balls much larger than any form of baryonic
matter of the same total mass

νs-balls have for m ~15 keV/c2 the same mass range as
supermassive BH

different escape velocities from the center of the νs-balls may
explain antihierarchical formation of quasars