Preliminary Post-DC2/Handoff Instrument Response Functions (IRFs) and Point Source Sensitivity
description
Transcript of Preliminary Post-DC2/Handoff Instrument Response Functions (IRFs) and Point Source Sensitivity
C&A at Stockholm 29 Aug 06 1T. Burnett
PreliminaryPreliminaryPost-DC2/HandoffPost-DC2/Handoff
Instrument Response Instrument Response Functions (IRFs)Functions (IRFs)
and and Point Source SensitivityPoint Source Sensitivity
Toby Burnett University of Washington
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Generation of test data set (“all-Generation of test data set (“all-gamma”)gamma”)
• Energy: uniformly in log(energy) from 18 MeV to 178 (or 356 GeV)
• Angles: Uniform in upper GLAST hemisphere
• Position: uniform over 6 m2
disk (1.38 m radius) perpendicular to incoming, centered at GLAST coordinate origin.
– About 2/3 miss
• Current Data set: 20 M generated– Bill used 2M.
• Start with basic cuts
z
y
x
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Effective Area, FOVEffective Area, FOVLoose cutsCount number in each bin, divide by total generated in that bin, multiply by 6 m^2
66 cut
Angular detail (1-10 GeV)Angular detail (1-10 GeV)
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66 cut
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Acceptance: integrate over angles, Acceptance: integrate over angles, >66>66
Relevant for scanning mode sensitivity
PSFPSF
• Front (thin) vs. back (thick) – factor of 2 in width– Separate, measure independently
• Energy dependence: E-0.8
– Factor of 100 from 100 MeV to 10 GeV!– Bin in energy, fit scaled deviation
• CTBCORE– Introduced by Atwood– Function of other variables,
trained to predict good PSF
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From Atwood
PSF representationPSF representation
• Two traditional measures– Scale: 68% containment radius– Shape: ratio of 95% to 68% radius– (assume azimuthally symmetric)
• Simple function has two parameters: for scale, for shape (power-law).
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M
0 1 2 3 4 50
0.5
1
gamma=2.5gaussian
PSF functional form
scaled deviation
dens
ity
11
2
2
PSF fitsPSF fits
• Categories: front/back, 8 bins in log energy, 8 bins in cos()
• Also fit combined angles, 0-66
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Front,CTBCORE>0.5
Note: =2 corresponds to 95%/68% ratio =3.
This is of course Monte Carlo: the beam test must validate it!
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Check PSF in CTBCORE intervalsCheck PSF in CTBCORE intervals
1
2
34
100 GeV
10GeV
1GeV
Data sets
Combined 0-66 degrees
0.01 0.1 1 10 1000
0.2
0.4
0.6
0.8
1
class1class2class3class4
sigma, front
energy (GeV)
sigm
a
0.01 0.1 1 10 1000
0.2
0.4
0.6
0.8
1
class1class2class3class4
sigma, back
energy (GeV)
sigm
a
Point-source sensitivityPoint-source sensitivity
• Figure of merit combining FOV, effective area, PSF
• What is the weakest E-2 power law source, in the presence of the nominal EGRET extra galactic diffuse background, that is detectable with a likelihoodTS >25 for a one year livetime, in a scanning mode?
• Current estimate: 4E-9 cm-2 s-1, E>100 MeV
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From GLAST LAT performance
The ingredients: for each event classThe ingredients: for each event class
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signal, background assumption From all-gamma analysis, average over 0-66deg.
s E( ) signal fluxA E( ) acceptance
b E( ) background flux E( ) total scale factor
E( ) PSF power law
t total live timeangular integrals convertedto u signal multiplier u
1
2
E( )
2
photon count, differential in E and u P E u t A E( ) s E( ) fPSF u E( ) b E( ) 2 E( )
2
total photons N Emin
Emax
E0
umax
uP E u
d
d
expected log likelihood as function of
logL Emin
Emax
E
0
umax
uP E u 1( ) lnP E u
N
d
d
test statistic corresponds to number of sigmas in Gaussian likelihood case
TS 2 logL 0( ) logL 1( )( )
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Sensitivity Calculation Sensitivity Calculation
b Mf 0( ) s Mf 1( ) b
100 1 103
1 104
1 105
1 103
0.01
0.1
1
10
100
1 103
1 104
1 105
si
bi
E2i
s b
0 0.5 1 1.5 20
5
10
15
20
frontback
signal fraction
TS
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Point source sensitivity: Point source sensitivity: Check TS for 4E-9 cmCheck TS for 4E-9 cm-2 -2 ss-1-1, one year livetime, one year livetime
• E-2 power law• Standard EGRET extragalactic background• Combined 0-66 deg in one bin, scanning mode• Ignore effects of dispersion
ClassCTBCORE
range
TS
front back
#1 0.1-0.5 1.90 0.27
#2 0.5-0.7 4.42 1.40
#3 0.7-0.85 7.30 3.65
#4 0.85-1 6.86 4.14
(Sum) 20.48 9.46
2-4 combined 0.5-1 19.10 8.94
DC2 classA 21.0 10.0
‘5” requirement: (TS) > 25
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Status/PlansStatus/Plans
• No post-DC2 surprises: parameterizations used then still seem applicable
• Preliminary set of IRFs ready for Science Tools• Need to reconcile with beam test• Generate ~100M All-gamma data set
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DispersionDispersion
• R. Rando’s formula, compared with Gaussian with same variance
disp x t w( )1 x( )
t
1 expx
w
gauss x 0.5 exp 0.5x
2
t 16 w 0.025
0.5 0 0.51 10
3
0.01
0.1
1
disp x t w( )
gauss x 0.076( )
x
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Fit results (typical)Fit results (typical)
Tail contents may be a problem: let’s cut on that good energy measurement guy!
3.7%3.9%
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Cut on CTBBestEnergyProb>0.5Cut on CTBBestEnergyProb>0.5
This tail was in the DC2 data
Consequence for the sensitivity:TS = 15.5 +7.6
Reduced acceptance
2.4% ~0%