Determining the Neutrino Hierarchy From a Galactic Supernova David Webber APS April Meeting May 3, 2011 SN 1572 “Tycho’s Nova” 7,500 light years (2.3 kPc) SN 1604 “Kepler’s Nova” ~20,000 light years (6 kPc) Cassiopeia A ~300 years ago 11,000 light years (3.4 kPc) 1

Adapted from Fuller, NDM09 Neutrino emission: 10% gravitational binding energy L ~ erg s seconds Neutrino spectral swaps 2

Initial neutrino spectra “Pinched thermal” distribution 1 e “freeze-out” later than , , at lower temp Observed Spectrum will be modified by – Spectral (flavor) swaps – Turbulence and shockwave – Detector resolution 1 Keil, Raffelt, Janka. Astrophys. J. 590,971(2003) Ignore 3 Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, (2011) 060 MeV

The initial flux is modified by spectral swaps ● Near the Supernova, at high neutrino densities, neutrinos self-interact ● Self-interaction will introduce a collective flavor swap e>e> x>x>  x >+  e >  e >+  x > 060 MeV 4 0 Normal Hierarchy Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, (2011)

The features of the flavor swap depend on the neutrino hierarchy The energy shape gives a handle on the hierarchy       MeV Normal Hierarchy “Normal”“Inverted” Inverted Hierarchy Energy spectra figs adapted from: Duan and Friedland, Phys. Rev. Lett. 106, (2011)

Next-generation detectors will see lots of (anti)neutrinos from a galactic SN Fig: S. Kettell Fig: Steve Hentschel Via Bruce Baller LBNE Water-Cherenkov 100 kT 10 kPc to supernova ~20000 events LBNE Liquid Argon 17 kT 10 kPc to supernova ~1500 events SN 1987A 160,000 LY (50 kPc) (galactic SN 5-15 kPc) Kamiokande IIKamiokande II (1 kton) detected 11 IMBIMB (3.3 kton) detected 8 BaksanBaksan (0.2 kton) detected 5 How many events are needed to distinguish the neutrino hierarchy? 6

reaction cross-sections Dominant reaction: WaterArgon Dominant reaction: 7 Cross-section ( cm 2 ) Neutrino Energy (MeV) Inverse beta decay Quasi-elastic scattering e 16 0 Quasi-elastic scattering Cross-section ( cm 2 ) NC 16 0 e 40 Ar

Observed spectral shapes Larger detector, more eventsSharper, nonthermal features Normal Hierarchy Inverted Hierarchy Water 100kT Argon 17kT 8 Normal Hierarchy Inverted Hierarchy Events/0.5 MeV/s* Energy (MeV) * one-second late-time slice

A log-likelihood ratio discriminates between neutrino hierarchies 10% 12.6  9 log likelihood NH – log likelihood IH 1000 events “Normal” 1000 events “Inverted” 1000 simulated spectral fits Define “significance (  )” as hierarchy distinguishability *fit assuming known spectrum

10 Finding the required number of events to distinguish the neutrino hierarchy *fit assuming known spectrum Significance (  )

11 Finding the required number of events to distinguish the neutrino hierarchy *fit assuming known spectrum Significance (  )

12 Finding the required number of events to distinguish the neutrino hierarchy *fit assuming known spectrum Significance (  )

Fitting simultaneously is better than fitting separately 13 *fit assuming known spectrum Crab Nebula (SN1054)galactic centerMilky Way diameter SN1987A most probable distance Significance (  )

Summary Core-collapse supernovae emit a lot of neutrinos ~40% chance to observe a galactic supernova in next-gen detectors Non-thermal features in the observed energy-spectrum will distinguish hierarchy Water and argon detectors, fit simultaneously, will give the most information Further work – more neutrino flux models – parameterize uncertainty 14 G circa 1870* 25,000 light years (7.7 kPc) *City of Anaheim, CA incorporated Feb 10, 1870.

Backup

189 events in argon 16

1645 events in water 17

events in water, 75 events in argon water normal hierarchy water inverted hierarchy argon normal hierarchy argon inverted hierarchy

To study different SNB spectra, need “effective” spectra generator ● Use basis: ( e, e, x, x, y, y ) ● x =cos(  23 )  -sin(  23 )  ● y =cos(  23 )  +sin(  23 )  ● Tunable Knobs: ● Relative flavor luminosity, eg. L( e )/L( e ), L( x ) /L( e ) ● Average Energies, Luminosity: (1.0, 1.0, 1.5, 1.5, 1.5, 1.5) (MeV): (12, 15, 20, 20, 20, 20) 19

Miscellaneous Supernova – 10% of rest energy emitted – 99% of energy emitted as neutrinos Caveats – Neglected Turbulence – Assumed energy spectrum known exactly – Have not explored time-dependence Distances – Milky Way is 30 kPc across – Sun is 8.5 kPc from center of Milky Way Energy resolution – 10-12% for water from MeV (docDB 2687) – 15% PMT coverage 20

A more robust estimator uses log likelihood Water Detector 30% PMT coverage HQE tubes IBD reaction 10% 14.5  21

Slide created by: Fuller, NDM09 22

Galactic supernovae occur roughly twice per century YEAR AD CONSTELLATION name VISIBILITY period BRIGHTNESS magnitude REMNANT feature DISTANCE (l.y.) 185Centaurus20 months-6?G Sagittarius3 months?G ? Scorpius8 months?G ?? 1006LupusFew years-9P Taurus24 months-5Crab Nebula Cassiopeia6 months+1?3C Cassiopeia18 months<-1 Tycho's SN 3C Ophiuchus12 months-3Kepler's SN CassiopeiaNot seen>4?Cass-A SagittariusNot seen>5?G G ~1870* 25,000 light years (7.7 kPc) Known galactic supernovae in the last 2000 years *City of Anaheim, CA incorporated Feb 10, Core-Collapse Supernova rate From 26 Al abundance: 1.9 +/- 1.1 per century Diehl et. al., Nature 439 ~40% chance to see SN with next-gen detector, even if optically invisible. 23

24 Fig 4 from Duan and Friedland, Phys. Rev. Lett. 106, (2011)