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

C&A at Stockholm 29 Aug 06 2T. Burnett

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

C&A at Stockholm 29 Aug 06 3T. Burnett

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)

C&A at Stockholm 29 Aug 06 T. Burnett 4

66 cut

C&A at Stockholm 29 Aug 06 5T. Burnett

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

C&A at Stockholm 29 Aug 06 T. Burnett 6

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).

C&A at Stockholm 29 Aug 06 T. Burnett 7

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

C&A at Stockholm 29 Aug 06 8T. Burnett

Front,CTBCORE>0.5

Note: =2 corresponds to 95%/68% ratio =3.

This is of course Monte Carlo: the beam test must validate it!

C&A at Stockholm 29 Aug 06 9T. Burnett

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

C&A at Stockholm 29 Aug 06 T. Burnett 10

From GLAST LAT performance

The ingredients: for each event classThe ingredients: for each event class

C&A at Stockholm 29 Aug 06 11T. Burnett

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( )( )

C&A at Stockholm 29 Aug 06 12T. Burnett

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

C&A at Stockholm 29 Aug 06 13T. Burnett

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

C&A at Stockholm 29 Aug 06 14T. Burnett

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

C&A at Stockholm 29 Aug 06 15T. Burnett

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

C&A at Stockholm 29 Aug 06 16T. Burnett

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%

C&A at Stockholm 29 Aug 06 17T. Burnett

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%