George M. FullerDepartment of Physics

&Center for Astrophysics and Space Science

University of California, San Diego

Neutron Stars and Neutrinos Arizona State University

Tempe, AZApril 12, 2010

Geor ge M. Ful l erDepar t ment of Physi cs

Neutrino Flavor Transformation :hot neutron stars

to the early universe

Neutrino mass physics is a theme common to both

Compact Objects (supernovae; neutron stars; holes; etc. . .)

Cosmology (structure formation; dark matter, etc. . .)

Synergy between laboratory/observational neutrino physicsand new developments and capabilitiesin observational astronomy

We have an exciting situation in neutrino physics and astrophysics

Experiment s are revealing t he propert ies of neut rinosand t his new dat a is driving int erest ing development sin nuclear and part icle ast rophysics. As I will show,t hese ast rophysical development s may feed back onour underst anding of neut rino propert ies.

This is classic particle/nuclear astrophysics,with a synergistic coupling of astrophysicsand low energy laboratory measurementsof physics beyond the Standard Model

Willy Fowler might appreciate this . . .

We know the mass-squared differences:

We do not know the absolute masses or the mass hierarchy:

Neutrino Mass: what we know and don’t know

We know 2 of the 4 vacuum 3X3 mixing parametersand we have a good upper limit on a third.

Neutrino energy (mass) states are not coincidentwith the weak interaction (flavor) states

The unitary transformation that relates these statesin vacuum has 4 parameters (exclusive of Majorana phases)

4 parameters

Maki-Nakagawa-Sakata matrix

δm232 ≈ 2.4 ×10−3 eV2

sin2 θ23 ≈ 0.50Atmospheric Neutrinos

“Solar”/KamLaND Neutrinos

δmsol2 ≈ 7.6 ×10−5 eV2

sin2 θ12 ≈ 0.31

The key mixing angle

limit on θ13 ⇒

sin2 θ13 < 0.040 ( 2σ)

My take on this is as follows:

(1) What we already know about neutrino mass/mixing has potentially big implications for astrophysics.

(2) Working out those implications may allow new insights into nucleosynthesis and unmeasured neutrino properties:e.g., a supernova neutrino signal could help us get at θ13 andthe neutrino mass hierarchy. And, vice versa, what we know aboutneutrino flavor mixing may give us insights into how supernovae work.Cosmology may give absolute masses --- gives best limits now.

MASS Main Seq.Entropy per baryon

CollapseEntropy per baryon

Iron core mass

Instability Mechanism

Fraction of rest mass radiated as neutrinos

12 to ~ 100 ~ 10 ~ 1 ~ 1.4

Electron capture /Feynman-ChandrasekharG.R. instab.

~ 10%Iron core mass

~ 100 to

~ 104~ 100 ~ 100 NONE pair

instability

~ 10%C/O burning core

~ 104

to~ 108

~ 1000no main seq.

~ 1000 NONE

Feynman-ChandrasekharG.R.Instability

~ 5%

Neutrino Trapping /Thermal equilibrium

Yes

Yes

No

Gravitational Collapse of Massive Stars

Cor e Col l apseSuper novae

The Core Collapse Supernova Phenomenonis Exquisitely Sensitive to Flavor ChangingProcesses and New Neutrino Physics:

Gravitational collapse results in high electron and νeFermi Energies (representing ~ 1057 units of e-lepton number);µ/τ charged leptons are absent and the correspondingneutrinos are pair-produced so they carry no net lepton number.Any process that changes flavor νe νµ/τ/s will open phasespace for electron capture as well as reducing e-lepton number.

Later, energy (10% of the core’s rest mass) is in seas of activeneutrinos of all flavors. Entropy and lepton number transportedby neutrinos.

Neutron/proton ratio (crucial for nucleosynthesis) determinedby electron degeneracy or by charged current neutrino capture:

Neutrinos Dominate the Energetics of Core Collapse Supernovae

Total optical + kinetic energy, 1051 ergs

Total energy released in Neutrinos, 1053 ergs

Neutrino diffusion time,

τν ≈ 2 s to

10 s

Lν ≈16

GMNS2

RNS

1τν

≈ 4 ×1051ergs s-1

Explosiononly ~1% of

neutrino energy

10% of star’srest mass!

EGRAV ≈35

G MNS2

RNS

≈ 3 ×1053ergs MNS

1.4Msun

210 km

RNS

ordinary MSW evolution of neutrino flavors

MSW resonance at neutrino energy

Eν =δm2 cos2θ2 A + B( )

≈ 0.02 MeV( ) δm2 cos2θ3×10−3 eV2

106 g cm-3

ρ Ye + Yν( )

sin2 2

θ MEν(MeV)

“coherent”λmfp>>res. width

λmfp <<res. width“incoherent”

ν e = cosθM t( )ν1 t( ) + sinθM t( )ν 2 t( )ντ = −sinθM t( )ν1 t( ) + cosθM t( )ν 2 t( )

time/position - dependentmixing angle and mass-states

At a given location expect only neutrinosin a narrow energy range to experience largeflavor mixing while anti-neutrino mixing is suppressed. With the small measuredneutrino mass-squared differences we expectsignificant flavor conversion only at low densities.

Neutrino Self Coupling - the source of nonlinearity

Coherent Flavor Evolution for Neutrino i

neutrino-electroncharged currentforward exchange scattering

neutrino-neutrinoneutral currentforward scattering

Effects beyond the mean field?Balantekin & Pehlivan (2007)Friedland & Lunardini (2003)

now self-consistently couple flavor evolution

on all neutrino trajectories . . . • Anisotropic, nonlinear quantum coupling of

all neutrino flavor evolution histories

Neutrino flavor evolutionin core collapse supernovae

Huaiyu Duan (UCSD/INT), George M. Fuller (UCSD)Joseph A. Carlson (LANL),Yong-Zhong Qian (U. Minn.)

(numerical simulations/analyses with coupled trajectories)

“Coherent Development of Neutrino Flavor in the Supernova Environment,”H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 97, 241101 (2006)“Simulation of coherent nonlinear neutrino flavor transformation in the supernova environment:Correlated neutrino trajectories,”

H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. D 74, 105014 (2006)“Analysis of Collective Neutrino Flavor Transformation in Supernovae,”H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. D 75, 125005 (2007)

“Neutrino Mass Hierarchy and Stepwise Spectral Swapping of Supernova Neutrino Flavors,”H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 99, 241802 (2007)

“A Simple Picture for Neutrino Flavor Transformation in Supernovae,”H. Duan, G.M. Fuller, & Y.-Z. Qian, Phys. Rev. D 76, 085013 (2007)

“Collective neutrino flavor transformation in supernovae,”H. Duan, G.M. Fuller, & Y.-Z. Qian, Phys. Rev. D 74, 123004 (2006)

“Simultaneous flavor transformation of neutrinos and antineutrinos with dominant potentialsfrom neutrino-neutrino forward scattering,”

G.M. Fuller & Y.-Z. Qian, Phys. Rev. D 73, 023004 (2006)

“Flavor Evolution of the Neutronization Neutrino Burst from an O-Ne-Mg Core Collapse Supernova,”H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 100, 021101 (2008)“Stepwise Spectral Swapping with Three Neutrino Flavors,”H. Duan, G.M. Fuller, Y.-Z. Qian, Phys. Rev. D 77, 085016 (2008) “Simulating Nonlinear Neutrino Flavor Transformation,” H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Computational Science & Discovery, 1, 015007 (2008)

Some other recent work on neutrino flavor evolutionin core collapse supernovae

S. Hannestad, G.C. Raffelt, G. Sigl, & Y.Y.Y. Wong, Phys. Rev. D 74, 105010 (2006)astro-ph/0608695 (the “flavor pendulum”)

G.C. Raffelt & G. Sigl astro-ph/0608695

J.P. Kneller, G.C. McLaughlin, & J. Brockman, astro-ph/0705.3835

S. Pastor & G.C. Raffelt, Phys. Rev. Lett. 89, 191101 (2002)

A. Dolgov, S. Hansen, S. Pastor, S. Petcov, G. Raffelt, P. Semikoz hep-ph/0201287

K. Abazajian, J. Beacom, N. Bell astro-ph/0203442

G.C. Raffelt & A.Y. Smirnov, hep-ph/0705.1830

Ot her gr oups now have “ mul t i - angl e” codes . . .A. Esteban-Pretel, S. Pastor, R. Tomas, G.C. Raffelt, G. Sigl, astro-ph/0706.2498

G. Fogli, E. Lisi, A. Marrone, A. Mirizzi, hep-ph/0707.1998

A.B. Balantekin & H. Yuksel, New J. Phys. 7, 51 (2005)

R. F. Sawyer, Phys. Rev. D 72, 045003 (2005)

A. Friedland, B.H.J. McKellar, I. Ocuniewicz, Phys. Rev. D 73, 093002 (2006)

A. Friedland and C. Lunardini, J. High Energy Phys. 10, 043 (2003)

A great deal of work has now been done on this problem by many groups around the world.There is now a huge literature on this topic.See review on Collective Neutrino Oscillations:

H. Duan, G. M. Fuller, & Y.-Z. Qian, hep-ph/1001.2799

Results of Large-Scale Numerical Calculations

In the sample numerical calculations that follow we have taken:

The neutrino mass-squared difference to be

The effective 2 X 2 vacuum mixing angle to be either

The neutrino energy luminosities to be the same for all species and either

oras indicated.

for the NORMAL MASS HIERARCHY

for the INVERTED MASS HIERARCHY

neutrinos antineutrinos

r6 radius in units of 106 cm

cosi

ne o

f em

issi

on a

ngle

angl

e-av

erag

eden

ergy

spe

ctra

NO

RM

AL M

ASS H

IERA

RC

HY

neutrinos antineutrinos

r6 radius in units of 106 cm

cosi

ne o

f em

issi

on a

ngle

angl

e-av

erag

eden

ergy

spe

ctra

NO

RM

AL M

ASS H

IERA

RC

HY

neutrinos antineutrinos

r6 radius in units of 106 cm

cosi

ne o

f em

issi

on a

ngle

angl

e-av

erag

eden

ergy

spe

ctra

INVER

TED M

ASS H

IERA

RC

HY

survival probability

cosi

ne o

f ν tr

ajec

tory

ang

le w

rt. n

orm

al to

n.s.

surf

ace

consequences of neutrino mass and quantum coherence in supernovaeH. Duan, G. M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 97, 241101 (2006) astro-ph/0606616

normal m

ass hierarchyinverted m

ass hierarchy

Spectral Swap

The νe - νµ/τ Spectral Swap - a mass hierarchy signal ?

nor mal mass hi er ar chy i nver t ed mass hi er ar chy

cosi

ne o

f ne

utri

no e

miss

ion

angl

e

survival probability Pνν

neut r i no ener gy neut r i no ener gy

her e spect r al swap ener gy ECdecr eases wi t h decr easi ng θV

swap has its origin in nonlinear neutrino self- couplingH. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 99, 241802 (2007)

O- Ne- Mg Cor e Col l apse Super novaeThe progenitors of these events are stars in the mass range

K. Nomoto, Astrophys. J., 277, 791 (1984); 322, 206 (1987)

Post-collapse, these objects have a very steep matter densityprofile above the neutron star and behind the (viable) shock.

Modeling flavor transformation in the neutronization burstrequires a full 3X3 mixing treatment with neutrino self-coupling.

We find a sequence of neutrino spectral swaps which, if detected,could identify the neutrino burst as originating in an O-Ne-Mgevent instead of an ordinary Fe-core-collapse!

H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 100, 021101 (2008)C. Lunardini, B. Mueller, H.-Th. Janka, Phys. Rev. D 78, 023016 (2008)

Full 3X3 treatment (with both atmospheric and solar mass-squared differences) of the neutronization burst from an O-Ne-Mg core collapse: succession of spectral swaps

Distinctive pattern could tell us whether SN is an Fe-core or an O-Ne-Mg core collapse:

H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian, Phys. Rev. Lett. 100, 021101 (2008)

squa

red-

ampl

itude

to this end . . . open issues

e.g., the SASI and late re-heating Blondin & Mezzacappa Nature 445, 58 (2007)

Inhomogeneous matter/neutrino environments,e.g., what are the effects of inhomogeneities like turbulence or the shock on the neutrino signal, anisotropic neutrino emission? Friedland & Gruzinov (2006); Gava et al. (2009)Galais, Kneller, Volpe, & Gava (2009); review by H. Duan & J. Kneller (2009)

Full 3X3 flavor transformation in realistic environments,“multi-angle”, phase averaging - necessarye.g., A. Friedland hep-ph/1001.0996 (2010)

Extension to regime where scattering-induced de-coherenceis significant: the full Quantum Kinetic Equations.Abazaj i an, Ful l er , Pat el ( 2001) ; St r ack & Bur r ows (2005)Cardall (2007, 2009); Kishimoto & Fuller (2008)

Non-Spherical geometries . . . 3-D hydro

The experimental revolution in neutrino physics has given us some ofthe mass/mixing properties of the neutrinos. Modelers should include this physics in models of core collapse supernovaeand in the early universe.

Neutrino self coupling can alter neutrino flavor evolution in SN, ultimatelycausing large-scale flavor conversion deep in the supernova envelope,despite the small measured neutrino mass-squared differences. MSW-based analyses are inadequate.This could affect neutrino-heated nucleosynthesis and the neutrino signal.

Neutrino self coupling-induced flavor collective modesmay produce distinctive signatures which could allow a supernova neutrino signal to give us theneutrino mass hierarchy and θ13as well as give us an observational window on the deep interior of the coreand distinguish between Fe-core collapse and O-Ne-Mg core collapse.

CONCLUSIONS