GLAST LAT Project Gammaray Large Area Space Telescope

GLAST LAT Project Gamma-ray Large Area Space Telescope Astrostatistics Workshop, HEAD meeting, 10 September 2004 Challenges in Analyzing Data from the GLAST Large Area Telescope James Chiang GLAST SSC/ UMBC James Chiang (GSSC/UMBC) 1

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 GLAST Large Area Telescope (LAT) Spectrum Astro • • Within its first few weeks, the LAT will double the number of celestial gamma rays ever detected 5 -year design life, goal of 10 years 1. 8 m Tracker ACD Years Ang. Res. (100 Me. V) Ang. Res. (10 Ge. V) Eng. Rng. (Ge. V) EGRET 1991– 00 5. 8° 0. 5° 0. 03– 10 750 1. 4 × 106 AGILE 2005– 4. 7° 0. 2° 0. 03– 50 1, 500 4 × 106/yr AMS 2005+? – – 0. 1° 0. 3– 300 1, 600 7 × 105/yr 0. 1° 0. 02– 300 25, 000 1 × 108/yr GLAST LAT 2007– 3. 5° James Chiang (GSSC/UMBC) Aeff Ω (cm 2 sr) # g-rays e+ e– g 3000 k Calorimeter 2

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Scanning the Gamma-Ray Sky with the LAT Will also observe GRBs, Galactic diffuse emission, Dark Matter searches James Chiang (GSSC/UMBC) 3

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Scanning the Gamma-Ray Sky with the LAT Will also observe GRBs, Galactic diffuse emission, Dark Matter searches James Chiang (GSSC/UMBC) 4

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Analyzing LAT Data • Sources must be fit simultaneously. – Broad and energydependent PSFs: 68 < 3. 5º for 100 Me. V (on axis) and < 0. 1º for 10 Ge. V – Emission from nearby point sources overlap. – Intrinsic source spectrum affects the degree of source confusion. – “Source region” must be significantly larger than the “region-of-interest” (ROI). James Chiang (GSSC/UMBC) • Anticenter region: 5

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Analyzing LAT Data • Each event effectively has its own response function: – Large FOV, 2. 4 sr – Strong variation of response as a function of photon incident angle, Aeff cos – Scanning mode of operation: 95 min orbit continuous aspect changes of 4º/min. James Chiang (GSSC/UMBC) 6

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Galactic Diffuse Emission • Emission results from cosmic ray interactions with interstellar gas. • Models rely on HI & CO observations for the gas distribution • These observations reveal structures on angular scales similar to the PSF: James Chiang (GSSC/UMBC) 7

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Extragalactic Diffuse • Pushing the confusing limit: – If it is composed of unresolved blazars, we expect the LAT to find 103 -104 new sources outside of the Galactic plane. – Implications for blazar luminosity function (Chiang & Mukherjee 1998; Salomon & Stecker 1996; Willis 1996) James Chiang (GSSC/UMBC) 8

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Nuts and bolts of the Statistical Model • Use a standard factoring of the total response, R: A = effective area, D = energy dispersion, P = psf, E = photon energy, p = photon direction, L(t) represents the time variation of the instrument orientation and internal degrees of freedom, primes indicate measured quantities. • The Source Model: This accounts for point sources, Galactic diffuse emission, extragalactic diffuse, and other diffuse and possibly time varying sources (e. g. , LMC, Moon, SNRs, etc. ). James Chiang (GSSC/UMBC) 9

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Convolving with the Instrument Response • The region-of-interest (ROI) is the extraction region for the data in measured energy, direction, and arrival time. • Folding the source model through the instrument response yields the event distribution function, M, (i. e. , the expected counts given the model) in the space of measured quantities: The “source region”, SR, is the part of the sky defined to contain all sources that contribute significantly to the ROI. • For standard analyses, we will treat “steady” sources, so that James Chiang (GSSC/UMBC) 10

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 The Unbinned Likelihood • The objective function we would like to maximize is – The sum is taken over all events, indexed by j, lying within the ROI. Compare to binned Poisson likelihood: • The predicted number of observed events is the integral of M over the ROI: James Chiang (GSSC/UMBC) 11

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Performance • An example fit, the 17 strongest 3 EG sources in the Galactic anticenter region (34 free parameters): – black points: 1 day simulation time, 1. 7 k events, 98 cpu secs on a 2. 8 GHz Pentium 4 machine. – blue: 1 week, 11 k events, 745 cpu secs. – Similar results are found when Galactic and extragalactic diffuse components are included (for a factor ~ 4 more events). – Execution time ~O(Nevents) binned analysis? James Chiang (GSSC/UMBC) 12

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Source Detection and Localization • Following EGRET analyses, we rely on “test-statistic” maps for detailed source detection and localization: – A point source is moved from each map location to the next and the maximum log-likelihood is evaluated. – The peak of the resulting Ts map is taken as the best fit location, and the 50, 68, 95, & 99% C. L. contours correspond to Ts = 1. 4, 2. 3, 6. 0, & 9. 1 according to Wilks’ Theorem (Mattox et al. 1996). – Accurate source positions rely on the other sources being accurately modeled. As with EGRET, an iterative “clean” algorithm will likely be required. James Chiang (GSSC/UMBC) 13

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Example Ts Map Calculation • Source model: 3 C 279, 3 C 273, Galactic and extragalactic diffuse. • Normalization of Galactic diffuse component must be correct in order to obtain accurate source locations. James Chiang (GSSC/UMBC) 14

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Source Detection Methods • Test statistic maps are useful for positional error contours, but for finding candidate sources, faster methods will be needed. • “Fast” methods include: – Continuous wavelet transform (CWT, e. g. , Damaini et al. 1997) – “MRfilter” – Haar wavelet transform (Stark) – Bayesian Blocks – 2 D/3 D generalization of Scargle’s 1 D method – Optimal filter – 2 D analog of Weiner filter • All of these methods still need a separate algorithm for identifying candidate sources. James Chiang (GSSC/UMBC) 15

GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 Open Issues & Conclusions • LAT data require computational intensive analysis. • Uncertainties in the Galactic diffuse model limit how well other discrete components can be characterized using likelihood. • Extended vs point sources: – Maximum likelihood and ratio test for extended emission parameters – however, see Protossav et al. (2002) – For Gaussian PSFs, CWT gives a clear prescription. • Deconvolution of Galactic diffuse emission: – Use EGRET data, then 1 st year survey. – EMC 2 applicable? • Generalization to full Celestial sphere? • Energy dependent PSF? James Chiang (GSSC/UMBC) 16