1

Determining the Neutrino HierarchyFrom a Galactic Supernova

David WebberAPS 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)

http://www.spitzer.caltech.edu/search/image_set/20?search=sig08-016 http://chandra.harvard.edu/photo/printgallery/2004/

Cassiopeia A~300 years ago

11,000 light years (3.4 kPc)

http://www.spitzer.caltech.edu/search/image_set/20?search=ssc2005-14c

2Adapted from Fuller, NDM09

Neutrino emission:•10% gravitational binding energy•Ln ~ 1051-1053 erg s-1

•10-30 seconds•Neutrino spectral swaps

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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

1Keil, Raffelt, Janka. Astrophys. J. 590,971(2003)

Ignore

Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)

0 60 MeV

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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

|ne>

|nx>

|nx>+|ne>

|ne>+|nx>

0 60 MeV0 60 MeV

Normal Hierarchy

Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011) Fig adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)

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The features of the flavor swap depend on the neutrino hierarchy

http://www.lbl.gov/Science-Articles/Archive/sabl/2006/Jul/03.html

The energy shape gives a handle on the hierarchy

n2

n1

n3n2

n1

n3

0 60 MeV

Normal Hierarchy

“Normal” “Inverted”

Inverted Hierarchy

Energy spectra figs adapted from: Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)

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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 kT10 kPc to supernova

~20000 events

LBNE Liquid Argon 17 kT10 kPc to supernova

~1500 events

SN 1987A160,000 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

http://hubblesite.org/newscenter/archive/releases/1995/49/image/a/

How many events are needed to distinguish the neutrino hierarchy?

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n reaction cross-sections

https://wiki.bnl.gov/dusel/index.php/Event_Rate_Calculations

nepe Dominant reaction:

Water Argon

Dominant reaction:KeAr 40-40 e

Cros

s-se

ction

(10-3

8 cm

2 )

102

10-7

102

Neutrino Energy (MeV) Neutrino Energy (MeV)10-7

10010 10010

Inverse beta decay

Quasi-elastic scattering

ne 160

ne 160

Quasi-elastic scatteringCros

s-se

ction

(10-3

8 cm

2 )

NC 160

ne 40Ar

ne 40Ar

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Observed spectral shapes

Larger detector, more events Sharper, nonthermal features

Normal HierarchyInverted Hierarchy

Water 100kT Argon 17kTNormal Hierarchy

Inverted Hierarchy

Even

ts/0

.5 M

eV/s

*

Even

ts/0

.5 M

eV/s

*

Energy (MeV) Energy (MeV)

* one-second late-time slice

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A log-likelihood ratio discriminates between neutrino hierarchies

10%

12.6 s

log likelihood NH – log likelihood IH

1000 events“Normal”

1000 events“Inverted”

1000 simulated spectral fits

Define “significance (s)” as hierarchy distinguishability

*fit assuming known spectrum

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Finding the required number of events to distinguish the neutrino hierarchy

*fit assuming known spectrum

Sign

ifica

nce

(s)

11

Finding the required number of events to distinguish the neutrino hierarchy

*fit assuming known spectrum

Sign

ifica

nce

(s)

12

Finding the required number of events to distinguish the neutrino hierarchy

*fit assuming known spectrum

Sign

ifica

nce

(s)

13

Fitting simultaneously is better than fitting separately

*fit assuming known spectrum

Crab Nebula (SN1054) galactic center Milky Waydiameter

SN1987A

most probable distance

Sign

ifica

nce

(s)

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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+0.3circa 1870*

25,000 light years (7.7 kPc)*City of Anaheim, CA incorporated

Feb 10, 1870.

Backup

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189 events in argon

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1645 events in water

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1014 events in water, 75 events in argonwater

normal hierarchy

waterinverted hierarchy

argonnormal hierarchy

argoninverted hierarchy

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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)

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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

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A more robust estimator uses log likelihood

•Water Detector•30% PMT coverage•HQE tubes•IBD reaction

10%

14.5 s

22Slide created by:Fuller, NDM09

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Galactic supernovae occur roughly twice per century

YEARAD

CONSTELLATIONname

VISIBILITYperiod

BRIGHTNESSmagnitude

REMNANTfeature

DISTANCE(l.y.)

185 Centaurus 20 months -6? G315.4-2.3 7500

386 Sagittarius 3 months ? G11.2 -0.3? 15000

393 Scorpius 8 months ? G348.7 +0.3? ?

1006 Lupus Few years -9 P 1459 -41 7000

1054 Taurus 24 months -5 Crab Nebula 6500

1181 Cassiopeia 6 months +1? 3C58 10500

1572 Cassiopeia 18 months <-1 Tycho's SN 3C10 8000

1604 Ophiuchus 12 months -3 Kepler's SN 9500

1667 Cassiopeia Not seen >4? Cass-A 11000

1870 Sagittarius Not seen >5? G1.9+0.3 28000

http://www.spaceacademy.net.au/watch/snova/galactic.htmhttp://chandra.harvard.edu/photo/2008/g19/

G1.9+0.3~1870*

25,000 light years (7.7 kPc)

Known galactic supernovae in the last 2000 years

*City of Anaheim, CA incorporated Feb 10, 1870.

Core-Collapse Supernova rateFrom 26Al abundance:1.9 +/- 1.1 per centuryDiehl et. al., Nature 439

~40% chance to see SN with next-genn detector, even if optically invisible.

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