THB Source Catalog Meeting 12/21/05 1 Healpixels and Wavelets Toby Burnett and Bruce Lesnick University of Washington

THB Source Catalog Meeting 12/21/05 2 Problem with binning for images and source analysis Angular resolution varies dramatically with energy: –expect 1/E from multiple scattering –measure E -0.8 Images don’t show localization without removing low energies, increasing resolution Full information not used in point source searches Gamma energy (MeV) Resolution scale factor  (deg)  W Multiple scatter conversion Note: 68% containment is ~3  >3 decades of energy: >2 decades in resolution!

THB Source Catalog Meeting 12/21/05 3 HEALpix to the rescue Equal-area sky pixelization, invented by/for WMAP We use the Hierarchial aspect Level 3: 768 pixels Level 9: 3,145,728 pixels Level 10: 12,582,912 pixels Note: N pix = 12  4 level

THB Source Catalog Meeting 12/21/05 4 From the basic 12 to 48 pixels (level 0 to 1) (with “nested” indexing) Nesting is crucial to our variable-pixel scheme: divide by 4 to get “mother” pixel

THB Source Catalog Meeting 12/21/05 5 Application to GLAST: define a pixelized photon data base Take advantage of Hierarchical property, easy to correlate index for contained pixels. Create pixels in a sparse structure according to 8 bins in photon energy, sorted according to position. –Make selecting subset according to outer pixel level easy for projection integrals –Numerous low energy photons are effectively binned –Rare high energy photons occupy single pixels –Simplifies database indexing Gamma energy (MeV) Resolution scale factor  (deg) level Correlated bins in energy and position

THB Source Catalog Meeting 12/21/05 6 Apply it to the 56-day simulated data set (checkout3) Low levels: saturated, many photons/pixel. High levels: single photons (diffuse); multiple photons (point sources) 1.7M photons w/ E>100 MeV, front (thin) section  300 K pixels. Sparse structure, loads quickly from ROOT file

THB Source Catalog Meeting 12/21/05 7 Image generation: define a density function High energy photons are more localized: we express this by defining photons/area –Easily determined from the data base and the Healpix code. 3C273: density vs. all photons above 100 Mev

THB Source Catalog Meeting 12/21/05 8 The whole sky

THB Source Catalog Meeting 12/21/05 9 Density at the galactic center: the simulated EGRET source

THB Source Catalog Meeting 12/21/05 10 Sean’s Wavelets A projection function –constant or linear background cancels, so it is a measure of the signal strength in presence of background –Adjust width to optimize detection for our psf function: width depends on photon energy Evaluate using the pixelized photon data base –Assign width corresponding to average photon energy in the bin Use to measure: –Spectrum, measured value for each energy/healpix level –position: maximize value The “Mexican hat”

THB Source Catalog Meeting 12/21/05 11 Localization by maximizing the wavelet Galactic center: –generated at: –fit: (266.50, ) deviation 134 arc sec. –But expected error, predicted from curvature of the function, is 17 arc sec. The background degrades the precision: check a high- latitude source, like 3C273: –generated at: –fit: ( , ), deviation 4 arc sec, predicted 2. Vela 3C273 density Fit: (128.83, ) Deviation: 1 arc sec (13 predicted projection error)

THB Source Catalog Meeting 12/21/05 12 A look at many sources We get fits to all but one of the blazars. Fits to all 100 in a few min. (Starting at know positions) –About ½ within 100 arc sec, almost independent of flux, a surprise

THB Source Catalog Meeting 12/21/05 13 In progress: source detection Select candidates based on multiple photons in high- level pixels Apply wavelet fit to verify a likely source