Determining the Neutrino Hierarchy From a Galactic Supernova

1. Determining the Neutrino Hierarchy • From a Galactic Supernova http://www.spitzer.caltech.edu/search/image_set/20?search=sig08-016 http://chandra.harvard.edu/photo/printgallery/2004/ http://www.spitzer.caltech.edu/search/image_set/20?search=ssc2005-14c 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) David Webber APS April Meeting May 3, 2011

2. Neutrino emission: • 10% gravitational binding energy • Ln ~ 1051-1053 erg s-1 • 10-30 seconds • Neutrino spectral swaps Adapted from Fuller, NDM09

3. Initial neutrino spectra • “Pinched thermal” distribution1 • ne “freeze-out” later than nm, nt, at lower temp • Observed Spectrum will be modified by • Spectral (flavor) swaps • Turbulence and shockwave • Detector resolution 0 60 MeV Ignore Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011) 1Keil, Raffelt, Janka. Astrophys. J. 590,971(2003)

4. 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 |nx>+|ne> |ne> |nx> |ne>+|nx> Normal Hierarchy 0 60 MeV 0 60 MeV Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011) Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)

5. The features of the flavor swap depend on the neutrino hierarchy “Normal” “Inverted” n2 n1 n3 n2 n1 n3 0 60 MeV http://www.lbl.gov/Science-Articles/Archive/sabl/2006/Jul/03.html The energy shape gives a handle on the hierarchy Normal Hierarchy Inverted Hierarchy Energy spectra figs adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)

6. Next-generation detectors will see lots of (anti)neutrinos from a galactic SN LBNE Water-Cherenkov 100 kT 10 kPc to supernova ~20000 events LBNE Liquid Argon 17 kT 10 kPc to supernova ~1500 events http://hubblesite.org/newscenter/archive/releases/1995/49/image/a/ Fig: Steve Hentschel Via Bruce Baller SN 1987A 160,000 LY (50 kPc) (galactic SN 5-15 kPc) How many events are needed to distinguish the neutrino hierarchy? Kamiokande II (1 kton) detected 11  IMB (3.3 kton) detected 8 Baksan (0.2 kton) detected 5 Fig: S. Kettell

7. n reaction cross-sections Water Argon 102 102 ne40Ar ne160 Inverse beta decay ne40Ar Cross-section (10-38 cm2) ne160 Cross-section (10-38 cm2) NC160 Quasi-elastic scattering Quasi-elastic scattering 10-7 10-7 10 Neutrino Energy (MeV) 100 Neutrino Energy (MeV) 10 100 Dominant reaction: Dominant reaction: https://wiki.bnl.gov/dusel/index.php/Event_Rate_Calculations

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

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

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

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

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

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

14. 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 http://chandra.harvard.edu/photo/2008/g19/ G1.9+0.3 circa 1870* 25,000 light years (7.7 kPc) *City of Anaheim, CA incorporated Feb 10, 1870.

15. Backup

16. 189 events in argon

17. 1645 events in water

18. 1014 events in water, 75 events in argon water normal hierarchy argon normal hierarchy argon inverted hierarchy water inverted hierarchy

19. To study different SNB spectra, need “effective” spectra generator Use basis: (ne, ne, nx, nx, ny, ny) nx=cos(q23)nm-sin(q23)nt ny=cos(q23)nm+sin(q23)nt Tunable Knobs: Relative flavor luminosity, eg. L(ne)/L(ne), L(nx)/L(ne) Average Energies, <Ei> Luminosity: (1.0, 1.0, 1.5, 1.5, 1.5, 1.5) <Energy> (MeV): (12, 15, 20, 20, 20, 20)

20. 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 10-100 MeV (docDB 2687) • 15% PMT coverage

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

22. Slide created by: Fuller, NDM09

23. Galactic supernovae occur roughly twice per century Core-Collapse Supernova rate From 26Al abundance: 1.9 +/- 1.1 per century Diehl et. al., Nature 439 Known galactic supernovae in the last 2000 years http://www.spaceacademy.net.au/watch/snova/galactic.htm http://chandra.harvard.edu/photo/2008/g19/ G1.9+0.3 ~1870* 25,000 light years (7.7 kPc) ~40% chance to see SN with next-gen n detector, even if optically invisible. *City of Anaheim, CA incorporated Feb 10, 1870.

24. Fig 4 from Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)