This slide presentation gives an overview the Fermi Gamma-ray space telescope. It includes information on spectral fitting, useful considerations, and binned vs. unbinned likelihood

Hays, Elizabeth

NASA Technical Reports Server

Fermi 
Gamma-ray Space Telescope 
Analysis Workshop 
17 December 2009 
Advanced Likelihood 
E.Hays 
Goals 
• Quality checks on spectral fitting of point sources 
- Major gotchas 
- Simple checks 
- Models revisited 
- Spectral residuals 
- Spatial residuals 
• Useful considerations 
- Impact of region selection 
- Impact of zenith angle selection (relates to above ... ) 
- Impact of energy selection 
- Impact of spectral model 
• Binned vs. Unbinned likelihood 
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https://ntrs.nasa.gov/search.jsp?R=20100003049 2019-08-30T08:50:53+00:00Z
Major gotchas 
• Parameter estimate depends critically on calculating the 
proper exposure 
selection livetime response 
gtexpmap 
minimization 
gtseled: gtmktillle gttcube gIIlke 
gtsrcmap8 
• Examples of things that can screw this up 
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- fselect, fcopy selections do not update the header 
keywords used In the exposure calculation 
- Mismatch of data and IRF set 
- Mismatch of initial ROI selection and data cube 
(binned) ---•• 
- Mismatch of calculated diffuse response and model 
diffuse components - Use different names for 
different models 
Likelihood output - simple checks 
-----------------------------------------------Did the fit work and does it make sense? 
• Old the minimization converge? 
• Are the number of predicted photons reasonable? 
Do the parameter values make sense? 
- values hitting limits? 
- source with extremely soft spectrum or hard spectrum? 
• Do the parameter errors make sense? 
- Too small? Were enough parameters left free? 
- Larger than the parameter values - with low TS ... better luck 
next time 
• Consider the above for target source and field sources 
• All of the above become more critical for faint sources, 
complex regions, time-binned light curves ... 
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4 
2 
Likelihood - ROI selection 
How big? 
• Big enough to constrain model components - source of 
interest, diffuse emission, nearby sources 
• Small enough to avoid significant zenith cut losses to 
exposure 
- Practical advantagel less photons and less sources => less 
calculations for unbinned analysis 
- Analysis disadvantage I likelihood is an inclusive modeling 
strategy 
• Recommendations 
- 10 deg for isolated point source (E>100 MeV) 
- Larger regions (15-20 deg) benefit confused sources, aid in 
separating diffuse at low energy, improve error estimates 
• Test it 
- Are fit results reliable for different ROI radii? 
- What is the impact on GTls? 
I ' .aml Likelihood model - sources 
What should be included? 
• All sources that contribute photons to the selected region 
- Bright source list sources within -10 deg of the ROI 
boundary - accommodates tail of low energy PSF 
- Same goes for catalog sources once available 
• Galactic diffuse model 
• Isotropic diffuse model 
- Important for all parts of the sky ... provides a home for 
residual instrumental effects 
This is a starting point. Adapt to find what works best for 
your region and source. 
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3 
Likelihood Model· spectra 
What spectral shape? 
• Power laws are simple and well defined 
- For faint sources, difficult to justify more parameters 
• BUT lots of LA T sources are not simple power laws ... some 
tips to help motivate other spectral forms 
Bright pulsars? 
• Try simple exponentially cutoff power laws to improve 
fits for the pulsar itself and for nearby sources 
Check the energy distribution for an energy-dependent ROI 
selection 
Do the power-law fit parameters vary significantly for 
different minimum energy selections or fits in separate 
energy bins? 
• Most accurate and unbiased way to determine spectral 
parameters and errors is by testing that hypothesis using the 
likelihood fit 
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Spectral Residuals 
-----------------------------------------------
Un binned analysis produces 
predicted counts and residuals. 
Example is a long integration near 
the Galactic plane and a bright pulsar 
• Discrepancy at low energy is 
typical 
- likelihood uses true energy 
• Discrepancies strongly tied to 
diffuse model for most analysis 
- Diffuse mediates cross talk 
between your source and 
neighbors 
- Consider relative strength and 
test impact of model choices 
and selections on source of 
interest 
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Bright pulsar 
Isotropic 
Diffuse 
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Likelihood - reality checks 
Is anything missing in the model? 
• Visual inspection of count maps and residuals 
• Test Statistic maps (unbinned analysis) 
- gttsmap - Tests hypothesis of additional point source over 
a grid 
- Very Calculation Intensive 
• try small regions (5 deg) and large grid spacing (0.5 deg) 
- Note this can expose deficiencies in the diffuse model in 
addition to evidence for an additional source 
- Warning: gttsmap is not a tool for localization, gtfindsrc 
does that 
• Predicted and residual count maps (binned analysis) 
- Profiles, radial density, energy dependence 
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Likelihood - useful tests 
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------------------------------------------------
• Overall consistency -lots of good ways to get at this 
• Iteration 
- Consistent results if using output model is fit model? 
• Data selection consistency 
- Effects of energy selection? 
- Changes with ROI selection? (Keep in mind this also effects good 
time selection in combination with zenith cut) 
- Consistency with results in distinct energy bins (ala catalog) 
- Separate analysis of front and back events (using appropriate 
IRFs, diffuse response, and isotropic model) 
- Effects of time selection 
• Fit and Minimization choices 
- Impact of starting parameter values in the model? 
- Fit tolerence? (converging to true minimum?) 
Effects of optimizer? 
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Binned vs. Unbinned Likelihood 
Unbinned: Treats each photon independently (position, energy) 
- Best theoretical performance 
- More sensitive· important for faint sources 
- Best option for low statistics scenarios· light curves 
- Not for use with spatially extended sources 
More difficult to diagnose problems in individual source fit 
Binned: Treats the data in bins of position and energy. Minimal 
criteria· more photons than bins 
Less computationally intensive than unbinned 
- Handles templates for extended sources 
- Allows more straightforward diagnostics of fit (source maps, 
spatial profiles, energy dependent comparisons of prediction and 
model) 
- At highest energies, can run into low statistics even for long 
integrations 
Use of both allows consistency check 
(for data sets where both can be reasonably used) 
gtobssim 
• The ultimate test ... 
- Can you simulate what you found? 
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Fermi Gamma-Ray Space Telescope

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