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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 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?
7
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
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)
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