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

2. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 2 Spectrum Astro GLAST Large Area Telescope (LAT) e+e+ e–e– Calorimeter Tracker ACD 1.8 m 3000 kg 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 Years Ang. Res. (100 MeV) Ang. Res. (10 GeV) Eng. Rng. (GeV) A eff Ω (cm 2 sr) #  rays EGRET 1991 – 00 5.8°0.5° 0.03 – 10 7501.4 × 10 6 AGILE 2005 – 4.7°0.2° 0.03 – 50 1,5004 × 10 6 /yr AMS 2005+? –– 0.1° 0.3 – 300 1,6007 × 10 5 /yr GLAST LAT 2007 – 3.5°0.1° 0.02 – 300 25,0001 × 10 8 /yr

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

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

5. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 5 Analyzing LAT Data Sources must be fit simultaneously. –Broad and energy- dependent PSFs:  68 < 3.5º for 100 MeV (on axis) and < 0.1º for 10 GeV –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). Anticenter region:

6. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 6 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, A eff  cos  –Scanning mode of operation: 95 min orbit  continuous aspect changes of 4º/min.

7. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 7 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:

8. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 8 Extragalactic Diffuse Pushing the confusing limit: –If it is composed of unresolved blazars, we expect the LAT to find 10 3 -10 4 new sources outside of the Galactic plane. –Implications for blazar luminosity function (Chiang & Mukherjee 1998; Salomon & Stecker 1996; Willis 1996)

9. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 9 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.).

10. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 10 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

11. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 11 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:

12. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 12 Performance An example fit, the 17 strongest 3EG sources in the Galactic anticenter region (34 free parameters): –black points: 1 day simulation time, 1.7k events, 98 cpu secs on a 2.8 GHz Pentium 4 machine. –blue: 1 week, 11k 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(N events )  binned analysis?

13. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 13 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 T s map is taken as the best fit location, and the 50, 68, 95, & 99% C.L. contours correspond to  T s = 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.

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

15. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 15 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 – 2D/3D generalization of Scargle’s 1D method –Optimal filter – 2D analog of Weiner filter All of these methods still need a separate algorithm for identifying candidate sources.

16. GLAST LAT Project Astrostatistics Workshop, HEAD meeting, 10 September 2004 James Chiang (GSSC/UMBC) 16 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. –EMC2 applicable? Generalization to full Celestial sphere? Energy dependent PSF?