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

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

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

Ignore

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

0 60 MeV

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

|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)

5

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)

6

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 eventsLBNE Liquid Argon 17 kT

10 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?

7

n reaction cross-sections

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

nepe nDominant reaction:

Water Argon

Dominant reaction:KeAr 40-40 en

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

8

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

9

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

10

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)

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+0.3circa 1870*

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

Feb 10, 1870.

Backup

16

189 events in argon

17

1645 events in water

18

1014 events in water, 75 events in argonwater

normal hierarchy

waterinverted hierarchy

argonnormal hierarchy

argoninverted 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

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

10%

14.5 s

22Slide created by:Fuller, NDM09

23

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)