Post on 29-Jan-2016
Searching for a Diffuse Flux of Neutrinos with AMANDA-II
Jessica Hodges
November 5, 2004Prelim Exam
Outline
● Why study neutrinos? ..... Cosmic ray and neutrino physics
● AMANDA-II detector .... Description of detector
● Analysis techniques .... How data is analyzed
● Diffuse neutrino analysis .... Work completed on the 2000 data set
● Future work .... Progress made on the 2000-2003 data set and what is to come
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What are neutrinos?
● Neutral lepton that follows the rules of weak interactions
● Three flavors: electron (e), muon (), tau ()
● Have some mass, although not yet determined● Neutrinos can oscillate or change between flavors
or types● First experimentally proved to exist by Cowan
and Reines in the 1950s
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Types of cosmic accelerators
● GRBs (Gamma Ray Bursts), supernova remnants, x-ray binaries, mini-quasars
● AGNs (Active Galactic Nuclei)
● Topological defects, primordial black holes, dark matter and other exotic phenomena
● ?
Crab Nebula (supernova remnant) 4
p + X +/- + Y +/- + ()
e+/- + e(
e) + ()
The above process also occurs with the decay of kaons (in place of pions).
p + + n + +
+ +
e+ + e+
p + p + o 2
The interacting proton splits its energy evenly between these two processes – one which creates neutrinos and one which creates gamma rays.
How are neutrinos created?
5
Cosmic rays hit the atmosphere and produce many particles, including muons and neutrinos which are detected by AMANDA
6Reference: University of Adelaide Astrophysics webpage
Cosmic Ray Spectrum
dN/dE ~ E-2.7 cosmic rays
dN/dE ~ E-3.7
atmospheric neutrinos created from the decay of cosmic rays
It is predicted that neutrinos created in cosmic accelerators will have...
dN/dE ~ E-2
Atmospheric neutrinos
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How you get an E-2 spectrum ?
● Particles experience Fermi acceleration
E=kEo
N=P k No
dN/dE ~ E -1 and = ln P / ln After derivation, = -1
dN/dE ~ E-2 Eo = Initial energy
No = Number of particles with energy E
o
P = Probability of crossing shockk = Number of times that the shock is crossed
Reference frame....
of the shock
of the downstream material
of the upstream material
v2=(1/4)v
1v
1= |U|
(3/ 4) U
(3/ 4) U
The particle gains the same amount of energy every time it crosses the shock, regardless of which direction it is crossing.
8 Reference: Longair (1994)
Why study neutrinos instead of cosmic rays?
Neutrinos carry directional information. Cosmic rays have electric charge and are thus deflected by magnetic fields.
Neutrinos interact with matter via charged current scattering. This creates a lepton which triggers the detector.
l + N l _ + X l + N l + + X 9
Outline
● Why study neutrinos? ..... Cosmic ray and neutrino physics
● AMANDA-II detector .... Description of detector
● Analysis techniques .... How data is analyzed
● Diffuse neutrino analysis .... Work completed on the 2000 data set
● Future work .... Progress made on the 2000-2003 data set and what is to come
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AMANDA-II
AMANDA-II is a collection of 677 optical modules (“OMs”) buried in the ice at the South Pole
the 60 cm diameter holes were drilled with hot water and the OMs were lowered in before the ice refroze
19 strings each contain about 36 OMs
each OM contains a photomultiplier tube inside a pressure resistant glass sphere
all of the OMs on a string are connected to a main cable which transmits the information from the light pulses to the electronics at the surface
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Amundsen-Scott South Pole Station
South PoleDome
Summer camp
AMANDA
road to work
1500 m
2000 m
[not to scale]
Where are we ?
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What do OMs do?
The OMs contain the photomultiplier tubes which detect the Cherenkov light emitted by particles that pass through the ice.
Muon track Electron cascade
Particles emit Cherenkov light when they travel faster than the speed of light in that medium.
{~15 m
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Which way is up?“Up-going”
(from Northern sky)“Down-going”(from Southern sky)
The PMT is pointing down (away from the South Pole surface)
Zenith angle = 0o Zenith angle = 180o
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“Down-going”(from Southern sky)
“Up-going”(from Northern sky)
Outline
● Why study neutrinos? ..... Cosmic ray and neutrino physics
● AMANDA-II detector .... Description of detector
● Analysis techniques .... How data is analyzed
● Diffuse neutrino analysis .... Work completed on the 2000 data set
● Future work .... Progress made on the 2000-2003 data set and what is to come
15
Background events
The goal is to detect extraterrestrial neutrinos. What background will be seen by the detector?
1) muons or muon bundles created when cosmic rays interact with the atmosphere
Downgoing muons need at least 2 MeV / cm * 1500 m = 300 GeV to make it through the ice to the detector. Muons created on the other side of the Earth lose all of their energy before making it to the detector.
2) neutrinos created when cosmic rays interact with the atmosphere
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“Signal”
Rate of Events
The trigger rate for AMANDA-II is about 80 Hz. These are predominately downgoing cosmic ray muons.
In 2000, the detector was triggered every time at least 24 OMs were hit within a 2.5 s interval. Once the detector is triggered, all hits from a 32 s interval are read out.
There is a chance that two particles went through the detector at the same time.
This leads to another type of background that we simulate in the detector – coincident muons.
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Coincident Muons
Coincident muons refer to the situation where two or more muons or muon bundles from different cosmic ray showers interact with the ice and hit the detector within the same trigger window.
How two downgoing muons can be reconstructed as an upgoing eventblue hits occur just prior to the purple hits, but all within a 32 s window of the trigger 18Orange = reconstructed track
Viewing the Events
Data event from the cascade analysis
Energy ~175 TeV
Energy ~10 TeV
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Muon Neutrino event
Outline
● Why study neutrinos? ..... Cosmic ray and neutrino physics
● AMANDA-II detector .... Description of detector
● Analysis techniques .... How data is analyzed
● Diffuse neutrino analysis .... Work completed on the 2000 data set
● Future work .... Progress made on the 2000-2003 data set and what is to come
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Diffuse Muon Neutrino Fluxes
Test Spectrum
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-
-
-
-
-
-
1) Nellen et al: pp interactions in the core of AGNs2) Stecker & Salamon: p- interactions in the core of AGNs3) Mannheim et al: p- interactions in extragalactic photoproduction sources4) Mannheim: p- interactions in blazar jets5) Rachen & Biermann: p- interactions in radio galaxies6) Mannheim: pp interactions in host galaxies of blazar jets7) Waman & Bahcall: gamma-ray bursts8) Sigl et al and Birkel & Sarkar: topological defects
Reference: Learned and Mannheim
General premise of the Diffuse Analysis
1) Remove the muon background. Make cuts on the data based on the fact that a lot of the data looks like downgoing muon background or coincident muons.
2) The remaining data is assumed to be a combination of atmospheric neutrinos or signal neutrinos. Separate the atmospheric and signal Monte Carlo with an energy cut optimized with the Model Rejection Potential.
3) Apply all of the cuts to the data to get the final number of events.
4) Compute a limit based on the number of observed events, number of predicted background events, and number of predicted signal events.
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Initial zenith cut
1) First, an 80o zenith angle cut was applied to the data set to quickly eliminate downgoing muons2) Many misreconstructed downgoing muons survived this zenith cut3) Four cuts were then chosen as good ways to separate these misreconstructed downgoing muons from neutrinos that have traveled all the way through the Earth
Number of Events Surviving this Cut (197 / 2 = 98.5 days)Downgoing Muon MC Coincident Muon MC Atmospheric Neutrino MC Signal MC Data
44550 2655 1955 323 245857
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South Pole
Events cut out
80o
The Four Quality Cuts
These four cuts were moved from very “loose” levels (passing most events) to very “tight” levels (letting very few events through)
The cut level established for the analysis was the level at which all of the misreconstructed downgoing muon background Monte Carlo had just been entirely removed by the cuts
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Num
ber
of e
vent
s
Parameter X
Each red line is a possible cut level Cut Parameters chosen:track lengthnumber of direct hitslikelihood ratio (up to down)smoothness of hits along the track
Cut Parameters
By recording hit time and amplitude, many parameters can be constructed which allow you study the data. Some of the most useful parameters are:
number of optical modules hit: usually referred to as nchannel or nch
smoothness: how smooth the hits are along the track
track length: length of the reconstructed particle path
number of direct hits: number of hits that are very close to an optical module
zenith angle: angle of the reconstructed track
jkchi: -log(likelihood L)
[jkchi(down)-jkchi(up) = likelihood ratio = log (L up
/ L down
)]25
Viewing the Events
Data event from the cascade analysis
Energy ~175 TeV
Energy ~10 TeV
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Muon Neutrino event
Cuts Applied:track lengthsmoothnessnumber of directs hitsNot Applied:likelihood ratio
Cut Keep
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Atms MCSignal MC
A portion of the remaining data events (circled in yellow) are simulated only by coincident muons (not by atmospheric or signal neutrinos).
cuts applied in these plots:track length
likelihood ratio of going up to downsmoothness of hits along the track
number of direct hits along the track
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Conclusion Drawn:Must find a coincidentmuon cut and reoptimize the cuts
MC
MuonMC
Signal MC
A large fraction of the signal Monte Carlo is also removed by this cut, but further investigation showed that this did not have a large effect on the limit setting ability of the analysis.
Consider a coincident muon cut on the reduced upgoing likelihood
cutkeep
keepkeep
keep cut
cut cut
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Coincident muon MC
Signal MCMC
Cuts Applied:likelihood ratiotrack lengthnumber of directs hitssmoothnessNot Applied:reduced upgoing likelihood
Keep
Cut
Reduced upgoing likelihood30
Atms MCSignal MCCoincident muon MC
Atmospheric neutrino MCSignal MC
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We know that atmospheric neutrinos and signal neutrinos have different energy spectrum. Thus it makes sense to look for a parameter that scales like the energy and use it to make an “energy” cut.
log10
[True Energy in GeV]
of the Monte Carlo
Number of Optical Modules hit32
True Energy ~ 103.6 GeVTrue Energy ~ 105 GeV
Key Point: Events with higher energy reconstruct with higher numbers of optical modules hit.
Number of Optical Modules Hit
Distribution of “ number of OMs hit ” before the energy cut is applied
The slope of the atmospheric neutrino Monte Carlo drops off before the signal Monte Carlo.
Need to find a cut to best separate the atmospheric and signal Monte Carlo.
= number of OMs hit33
Note that the data and atmospheric neutrino MC agree reasonably well
Atms MCSignal MCAtms MCSignal MC
# data events = 154# atmospheric events = 180.5# signal events = 39.9
The Model Rejection Potential is a way of quantifying the limit setting potential of an experiment.
If NO signal is observed, THEN an upper limit can be set for the highest possible flux that the events could have had.
(E, ) 90% confidence interval
= (E, )theoretical
The value of 90
is determined by Feldman – Cousins statistics.
This value CAN NOT be defined until the cuts have been set and a number of data events in the final sample has been determined. To optimize the cuts that determine the final sample, work with the average upper limit,
90, instead.
Model Rejection Potential
90(n
obs,n
b)
ns
Observed events
Predicted backgroundevents
Predicted signalevents
34Reference: Feldman-Cousins (1998) and Hill and Rawlins (2002)
How to calculate the Average Upper Limit
To optimize the cuts without looking at the data, use the average upper limit
90
Assume that there is no signal ns = 0
Find the expected number of background events, nb
Find the upper limit for each possible value of observed events
Add up all of the upper limits and weight them by their Poisson probability
By looking only at Monte Carlo files, you can define the Model Rejection Factor = MRF =
90 / n
signal . The best limit for the analysis can be set when
the MRF is at a minimum.
average upper limit, 90
35Reference: Hill and Rawlins (2002)
Model rejection factor plot
Model Rejection Factor
90
ns
Choose Nch (number of OMs registering hits) cut where the Model Rejection Factor is a minimum
= number of OMs hit
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Final Energy Cut on the Number of OMs Hit (Nch) Parameter
According to the Model Rejection Potential, the energy cut should be placed at nch > 80.
cut keep
First, count... 1) number of data events2) number of signal MC events3) number of background MC events Then, set a limit using the Feldman-Cousins method.
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Atms MCSignal MC
= number of OMs hit
Diffuse 2000 Results...10 data events in 197-day sample (“1 year”)
with normalization, expected number of events for 197 days:
atmospheric 's = 9.4 events
signal 's = 25.0 events
The Feldman-Cousins signal event upper limit for 10 observed events on a background of 9.4 events is
90%
= 7.5
Thus, the neutrino flux limit is:
E290%
= E2 * * 90%
/ nsignal
= 10-6 * 7.5 / 25
E2 limit = 3 * 10-7 GeV / cm2 *s *sr
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Initially used a test spectrum of E2 = 10 - 6 GeV/ cm2 * s * sr
{
Reference: Feldman-Cousins (1998) and Hill and Rawlins (2002)
104.0 GeV = 10 TeV 106.25 GeV = 1.8 PeV
log10
(true energy)
True Energy Spectrum of the Monte Carlo
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AMANDA-II Limit 1yr (this work)
Test Spectrum
-
-
-
-
-
-
-
Diffuse Muon Neutrino Fluxes
1) Nellen et al: pp interactions in the core of AGNs2) Stecker & Salamon: p- interactions in the core of AGNs3) Mannheim et al: p- interactions in extragalactic photoproduction sources4) Mannheim: p- interactions in blazar jets5) Rachen & Biermann: p- interactions in radio galaxies6) Mannheim: pp interactions in host galaxies of blazar jets7) Waman & Bahcall: gamma-ray bursts8) Sigl et al and Birkel & Sarkar: topological defects
Reference: Learned and Mannheim
Outline
● Why study neutrinos? ..... Cosmic ray and neutrino physics
● AMANDA-II detector .... Description of detector
● Analysis techniques .... How data is analyzed
● Diffuse neutrino analysis .... Work completed on the 2000 data set
● Future work .... Progress made on the 2000-2003 data set and what is to come
41
Diffuse 2000-2003 Status
• My collaborators at DESY-Zeuthen in Germany processed the data and neutrino simulation files for the 4-year data set
• I am generating downgoing muon Monte Carlo and coincident muon Monte Carlo for each of these years
• I am replicating their processing chain by using the Datahandler software that they provided for me
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I will look at 100 % of the data set AFTER all of the cuts have been developed on the Monte Carlo and I am approved for unblinding.
Diffuse 2000-2003 Status
4-year Monte Carlo sample
The neutrino files are prepared and normalized, as are a limited number of coincident muon files. Downgoing muon files are in processing and coincident muon generation continues.
This is the nch plot before any of the quality cuts have been applied
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Atms MCSignal MCCoincident muon MC
= number of OMs hit
Preliminary look at cuts
4-year Monte Carlo sample
cuts made on:likelihood ratio (up to down)
track lengthnumber of direct hits
smoothnessreduced upgoing likelihood
* The cuts applied correspond to the cut levels for the 2000 analysis. The cuts for the 4-year analysis are not yet optimized.
Nch plot with preliminary quality cuts applied
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Atms MCSignal MCCoincident muon MC
= number of OMs hit
Optimizing the nch cut with the Model Rejection Potential
IF THE CUTS stay exactly the same as they were for the single year (2000) analysis, then
1) the best nch cut will be at 124
(it was 80 for the single year analysis)
2) Model Rejection Factor = 0.0848
expected upper limit = 0.0848 * 10-6
= 8.5 * 10-8
for 807 days
(“four years”)
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Optimizing the nch cut with the Model Rejection Potential
Cuts will be determined after coincident muons are ready.
It is expected that any coincident muons that survive the quality cuts will be removed by the much tighter final energy (nch) cut.
Note the nch cut is expected to move from nch = 80 for the single year analysis to nch = 124 for the 4-year analysis.
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IceCube 3yrs
AMANDA-II Limit: 1yr
Test Spectrum
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Predicted AMANDA-II Limit: 4 yr
Diffuse Muon Neutrino Fluxes
1) Nellen et al: pp interactions in the core of AGNs2) Stecker & Salamon: p- interactions in the core of AGNs3) Mannheim et al: p- interactions in extragalactic photoproduction sources4) Mannheim: p- interactions in blazar jets5) Rachen & Biermann: p- interactions in radio galaxies6) Mannheim: pp interactions in host galaxies of blazar jets7) Waman & Bahcall: gamma-ray bursts8) Sigl et al and Birkel & Sarkar: topological defects
Reference: Learned and Mannheim
References
Cooley-Sekula, Jodi, dissertation, 2003.Desiati, Paolo, presentation for ECRS Firenze, 2004.Feldman, Gary and Robert Cousins, Unified approach to the classical statistical analysis of small signals, 1998.Halzen, Francis, Summer School proceedings, 2004. Hill, Gary, Experimental and Theoretical Aspects of High Energy Neutrino Astrophysics, September 1996.Hill, Gary and Katherine Rawlins, Unbiased cut selection for optimal upper limits in neutrino detectors: the
model rejection potential technique, 2002.Hill, Gary, Matthias Leuthold, Jodi Cooley for the AMANDA collaboration, Search for Diffuse Fluxes of
Extraterrestrial Muon-Neutrinos with the AMANDA Detectors.Kowalski, Marek, dissertation.Longair, Malcolm, High Energy Astrophysics, 1994.Woschnagg, Kurt, presentation for Neutrino 2004.Plot from http://www.physics.adelaide.edu.au/astrophysics/cr_new.html
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