Determining the neutrino hierarchy from a galactic supernova using a next-generation detector David M. 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 2D. M. Webber

Initial neutrino spectra “Pinched thermal” distribution 1 e “freeze-out” later than , , at lower temp Initial 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 D. M. Webber

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 MeV0 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 II (1 kton) detected 11 IMB (3.3 kton) detected 8 Baksan (0.2 kton) detected 5 How many events are needed to distinguish the neutrino hierarchy? 6D. M. Webber

reaction cross-sections Dominant reaction: WaterArgon Dominant reaction: 7 Cross-section ( cm 2 ) Neutrino Energy (MeV) inverse beta decay elastic scattering e 16 0 elastic scattering Cross-section ( cm 2 ) NC 16 0 e 40 Ar D. M. Webber SNOwGLoBES K. Scholberg L11 6

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 D. M. Webber

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 D. M. Webber

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

189 events in argon 11D. M. Webber Normal HierarchyInverted Hierarchy

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

1645 events in water 13D. M. Webber Normal HierarchyInverted Hierarchy

14 Finding the required number of events to distinguish the neutrino hierarchy *fit assuming known spectrum Significance (  ) D. M. Webber

events in water, 76 events in argon water normal hierarchy water inverted hierarchy argon normal hierarchy argon inverted hierarchy

Fitting simultaneously is better than fitting separately 16 *fit assuming known spectrum Significance (  ) D. M. Webber SN Distance from Earth, O(10’s kPc)

Summary Core-collapse supernovae emit a lot of neutrinos Spectra will not be known ab-initio ~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 study – More neutrino flux models – Time-evolution of neutrino flux – Parameterize uncertainty 17 G circa 1870* 25,000 light years away (7.7 kPc) *City of Anaheim, CA incorporated Feb 10, D. M. Webber

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Fitting simultaneously is better than fitting separately 19 *fit assuming known spectrum Crab Nebula (SN1054)galactic centerMilky Way diameter SN1987A most probable distance Significance (  ) D. M. Webber SN Distance from Earth, O(10’s kPc)

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) 20D. M. Webber

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 21D. M. Webber

A more robust estimator uses log likelihood Water Detector 30% PMT coverage HQE tubes IBD reaction 10% 14.5  22D. M. Webber

Slide created by: Fuller, NDM09 23D. M. Webber

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. 24D. M. Webber

25 Fig 4 from Duan and Friedland, Phys. Rev. Lett. 106, (2011) D. M. Webber