Point Source Detection and Localization

1. Point Source Detection and Localization Using the UW HealPixel database Toby Burnett University of Washington

2. level 6 7 Resolution scale factor  (deg) 8 9 10 11 12 13 Gamma energy (MeV) The UW pixelized photon data base • Define 8 energy bands • Associate each level with a HealPixel level. • Fill structure with pixels in a sparse structure sorted by 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

3. 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

4. See the DC2 sky as a clickable map • See http://glast.phys.washington.edu/DC2/healpix/ • Also http://glast.phys.washington.edu/dc2/healpix/source_table.htm for a nice table

5. Point source analysis • Select conical region: • Known source, like Vela • Perugia wavelet analysis • … • Extract 8 sets of HealPixel lists from the data set • Analyze each level with maximum likelihood, signal fraction and TS • Perform global optimization with respect to the direction • Perhaps repeat step 2

6. Simple Point Source Maximum Likelihood • Assumptions: • All events from the source in energy band/pixel level can be described by the same PSF • measured with AllGamma weighted according to 1/E2 • Average over position in detector, detector polar angle, zenith angle, etc – measure using AllGamma data set. • Use the power-law function • Everything else is uniform • Ignore variations from exposure, galactic diffuse, nearby sources • Implementation details • Select pixels from the cone only within a given maximum u=umax. • Normalized probability function is:where  is the signal fraction and is normalized over the range. • Define log likelihood as weighted sum over pixels. • First and second derivatives with respect to  are quite simple, allowing fast solution • After the solution, calculate the TS

7. PSF fits

8. Example: MRF320 • Choose a high-latitude moderate-strength source: MRF320!

9. MRF320 spectral fit Loading data from file F:/glast/data/DC2/allsky.root, selecting event type 0 photons found: 840469 pixels created: 438524 Spectrum of source MRF0320 at ra, dec=309.03, -18.59 level events sig fraction TS 6 713 0.37 +/- 0.03 128.4 7 359 0.67 +/- 0.041 193.5 8 193 0.79 +/- 0.049 142.5 9 50 1 +/- 0.074 48.36 10 15 1 +/- 0.38 20.86 11 5 0.91 +/- 0.29 5.503 12 0 13 0total 539.1 Only class A front for now  Coordinates from catalog; radius 10 Catalog: 7586(different likelihood definition)

10. Localization • Algorithm: Newton’s method, add gradient and curvature for all levels, iterate until small change. Determine error circle radius from curvature. • Note that a simple “weighted sum” is not a good estimator, in fact disastrous if  ≤2. • Note differs by (0.018, -0.035) from catalog position, 4 sigma away. • How about a strong source? Vela localization is 0.003 deg. • Example: MRF320 Gradient delta ra dec error 1.602e+004 0.0316 309.03 -18.59 0.0106 3192 0.00607 309.046 -18.618 0.0104 677.7 0.00129 309.048 -18.6237 0.0105 150.5 0.000287 309.048 -18.6249 0.0105

11. Next Steps • Systematic comparison with catalog sources, with localization • Improve speed • Try to find new sources, near detection threshold