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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
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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 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?
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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
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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)
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Finding the required number of events to distinguish the neutrino hierarchy
*fit assuming known spectrum
Sign
ifica
nce
(s)
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Finding the required number of events to distinguish the neutrino hierarchy
*fit assuming known spectrum
Sign
ifica
nce
(s)
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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.
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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
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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.
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24Fig 4 from Duan and Friedland, Phys. Rev. Lett. 106, 091101 (2011)