Transcript ppt

Point Source Detection and
Localization
Using the UW HealPixel database
Toby Burnett
University of Washington
C&A 10April06
1
• 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
C&A 10April06
Resolution scale factor  (deg)
The UW pixelized photon data base
level
6
7
8
9
10
11
12
13
Gamma energy (MeV)
2
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
C&A 10April06
3
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
C&A 10April06
4
Point source analysis
1. Select conical region:
1. Known source, like Vela
2. Perugia wavelet analysis
3. …
2. Extract 8 sets of HealPixel lists from the data set
1. Analyze each level with maximum likelihood, signal fraction
and TS
3. Perform global optimization with respect to the direction
4. Perhaps repeat step 2
C&A 10April06
5
Simple Point Source Maximum Likelihood
•
Assumptions:
–
All events from the source in energy band/pixel level can be described by the same
PSF
•
•
•
–
Everything else is uniform
•
•
measured with AllGamma weighted according to 1/E2
Average over position in detector, detector polar angle, zenith angle, etc – measure using
AllGamma data set.

2
Use the power-law function
f (u;  )  1  1 1  u
u  12 
 



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:
–
–
–
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

1
f prob (u;  ,  )   f (u;  ) 
umax
where  is the signal fraction and fˆ is normalized over the range.
C&A 10April06
6
PSF fits
C&A 10April06
7
Example: MRF320
• Choose a high-latitude moderate-strength source: MRF320!
C&A 10April06
8
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
0
total
539.1
Only class A
front for now 
Coordinates
from catalog;
radius 10
Catalog: 7586
(different
likelihood
definition)
C&A 10April06
9
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
1.602e+004
3192
677.7
150.5
C&A 10April06
delta
0.0316
0.00607
0.00129
0.000287
ra
309.03
309.046
309.048
309.048
dec
-18.59
-18.618
-18.6237
-18.6249
error
0.0106
0.0104
0.0105
0.0105
10
Next Steps
• Systematic comparison with catalog sources, with
localization
• Improve speed
• Try to find new sources, near detection threshold
C&A 10April06
11