THB Source Catalog Meeting 12/21/05

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Healpixels and WaveletsHealpixels and Wavelets

Toby Burnett and Bruce LesnickUniversity of Washington

THB Source Catalog Meeting 12/21/05

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Problem with binning for images and Problem with binning for images and source analysissource 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)

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WMultiple scatter

conversion

Note: 68% containment is ~3

>3 decades of energy: >2 decades in resolution!

THB Source Catalog Meeting 12/21/05

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HEALpix to the rescueHEALpix 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 pixelsLevel 10: 12,582,912 pixels

Note: Npix = 124level

THB Source Catalog Meeting 12/21/05

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From the basic 12 to 48 pixels (level 0 to 1)From the basic 12 to 48 pixels (level 0 to 1)(with “nested” indexing)(with “nested” indexing)

0 1 2 3

4 5 6 7

8 9 10

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Nesting is crucial to our variable-pixel scheme: divide by 4 to get “mother” pixel

THB Source Catalog Meeting 12/21/05

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Application to GLAST: define a Application to GLAST: define a pixelized photon data basepixelized 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)

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78

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10111213

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Correlated bins in energy and position

THB Source Catalog Meeting 12/21/05

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Apply it to the 56-day simulated data set Apply it to the 56-day simulated data set (checkout3)(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

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Image generation: define a Image generation: define a densitydensity function 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

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The whole skyThe whole sky

THB Source Catalog Meeting 12/21/05

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Density at the galactic center: the Density at the galactic center: the simulated EGRET sourcesimulated EGRET source

THB Source Catalog Meeting 12/21/05

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Sean’s WaveletsSean’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

W

The “Mexican hat”

THB Source Catalog Meeting 12/21/05

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Localization by maximizing the waveletLocalization by maximizing the wavelet

• Galactic center: – generated at: <celestial_dir ra="266.51" dec="-28.86"/> – fit: (266.50, -28.88) 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: <celestial_dir ra="187.25" dec="2.17"/> – fit: (187.251, 2.16998), deviation 4 arc sec, predicted 2.

• Vela

3C273 density

<source name=" F_PSRB0833m45 " >     <spectrum escale="MeV"> <SpectrumClass name="PulsarSpectrum" params="F_B0833m45, 128.83, -45.18, 1.0e5, 3.0e8, 1, 61243, 3, 1e6, 8e6, -1.62, 1.7"/>     <use_spectrum frame="galaxy"/>    </spectrum> </source>

Fit: (128.83, -45.18)

Deviation: 1 arc sec (13 predicted projection error)

THB Source Catalog Meeting 12/21/05

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A look at many sourcesA 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

Blazar localization

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10 100 1000

flux

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THB Source Catalog Meeting 12/21/05

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In progress: source detectionIn progress: source detection

• Select candidates based on multiple photons in high-level pixels

• Apply wavelet fit to verify a likely source