Fermi LAT data analysis

Transcription

1 Fermi LAT data analysis PSR J VER J

2 Fermi Gamma-ray Space Telescope Large Area Telescope (LAT) ~20 MeV to >300 GeV FOV: 2.4 sr Credit: NASA E/PO, Sonoma State University, Aurore Simonnet Gamma-ray Burst Monitor (GBM) ~10 kev to ~25 MeV FOV: >8 sr

3 Fermi Science Support Center (FSSC)

4 The Cicerone Cicerone means a person who conducts sightseers; guide documentation/cicerone/

5 Analysis Threads scitools/

6 LAT Data Extraction

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8 LAT Data Extraction target source circular region centered at the target source } start and end times of observation default: 100 MeV GeV The region of interest (ROI) selection later on should be no bigger than this. Plan ahead or you have to download the data again!

9 Data Selection gtselect - defines data sub-selection criteria: region of interest (ROI), energy range, time range... gtmktime - selection of good-time intervals (GTIs)

10 Data Selection - gtselect zenith cone buffer region INDEF allows the parameters to be read from the header keywords { ROI Time range Energy range Max. zenith angle (Associated with the previous Pass6 IRFs) Event class (hidden!)

11 Data Selection - gtmktime Good-time intervals - time intervals in which the data is good Yes : excludes time intervals where the buffer region intersects with the ROI

12 Data Exploration - gtbin gtbin - bin selected event list into image specify that you are making a counts map dimensions of the counts map {

13 Data Exploration - gtbin PSR J VER J

14 HEASARC Web Tools Coordinate converter

15 HEASARC Web Tools Time converter

16 Likelihood Analysis

17 Likelihood Analysis Q: Given an input model (a set of parameters), what is the probability of obtaining/reproducing the observed data from the model? The probability is termed the... Likelihood L Our model: describes the gamma-ray sources in the sky (spatially + spectrally)

18 Likelihood Analysis Suppose the data is binned according to their positions in the sky and their energies. The number of counts in each bin is characterized by the Poisson distribution. The probability of detecting ni photons in the i-th bin is given by: where mi is the number of predicted photons by the model in that bin. The likelihood function L is defined as the product of the probabilities: To get the model which best describes the data, we wish to maximize L. In other words, we wish to find out the set of model parameters such that L is maximized.

19 Unbinned Likelihood Analysis Good for small data sets (short observation time) Re-writing L... is the total number of predicted photons. If we let the size of each bin to be infinitesimally small, then ni will be 0 or 1. The unbinned likelihood To make life simpler, we deal with the logarithm:

20 Likelihood Analysis The Test Statistic (TS) is defined as ( likelihood-ratio test ): where Lmax,0 = the maximum likelihood value for a model without an additional source (the null hypothesis ) Lmax,1 = the maximum likelihood value for a model with the additional source at a specified location Wilk s Theorem: If the number of photons is sufficiently large, the TS for the null hypothesis is distributed like a 2 distribution, where is the difference in the number of parameters between the models with and without the additional source. Detection significance

21 Likelihood Analysis - The Source Model describes the gamma-ray sources in the sky (spatially + spectrally) Source Model point sources : position in the sky spectral model e.g. simple power law, power law with exponential cutoff galactic diffuse and isotropic all-sky (extragalactic) emission other sources (diffuse templates ) In ordinary analysis, we treat as.

22 Likelihood Analysis - The Instrumental Response Functions (IRFs) The model is folded with the instrumental response functions (IRFs) to obtain the number of predicted counts in the measured quantity space: Effective area Energy dispersion PSF

23 Likelihood Analysis The log-likelihood becomes: where The likelihood will be evaluated many times during model fitting. To save CPU time, an exposure map (cube) is computed in advance (integral of total response over ROI data-space): which is independent of the source model.

24 Likelihood Analysis - gtltcube & gtexpmap Exposure map: total exposure for a given position in the sky producing counts in the ROI Pre-requisite: the time that a given position in the sky is observed at a given inclination angle (this is called the livetime ) has to be known This livetime (exposure) cube quantity is pre-computed by the tool gtltcube. specifies the grid of the livetime cube the livetime cube is used as an input to compute the exposure map specifies the grid of the exposure map

25 Spectral Models Simple power law Power law with exponential cutoff e.g. pulsars Log-parabola e.g. blazars The LAT 2-year Point Source Catalog is based on these models.

26 Building the Model -... make2fglxml.py Example use:... from make2fglxml import * mymodel = srclist('gll_psc_v07.fit', 'eventfile.fits', 'mylatxmlmodel.xml') match the names! mymodel.makemodel('gal_2yearp7v6_v0.fits', 'gal_2yearp7v6_v0', 'iso_p7v6source.txt', 'iso_p7v6source', Templates ) $FERMI_DIR/refdata/fermi/galdiffuse/gal_2yearp7v6_v0.fits $FERMI_DIR/refdata/fermi/galdiffuse/isotropic_iem_v02_P6_V11_DIFFUSE.txt

27 Building the Model - the XML file [ (1) spectral part [ (2) spatial part

28 Building the Model - the XML file Galactic diffuse and isotropic all-sky emission

29 Likelihood Analysis - gtdiffrsp Point-source: S is a delta-function, the integral is relatively easy Diffuse source: the integral is computational-intensive In the likelihood calculations, it is assumed that the spatial and spectral parts of a source model factor in such a way that the integral over spatial distribution of a source can be performed independently of the spectral part... Input source model, to determine: (1) whether pre-computed diffuse responses are present (2) whether an extended source is present in the model IRFs to use

30 Likelihood Analysis - gtlike keep your results! (for reference and for further iterations) { we are performing unbinned likelihood analysis optimizer used for fitting, in general: (1) DRMNFB (2) NEWMINUIT store the screen output into a file! [command] >& [file]

31 Likelihood Analysis - gtlike......

32 Likelihood Analysis - gttsmap dimensions of the output TS map {

33 Likelihood Analysis - gttsmap Goal: to find sources that are barely detectable. Model the strong, known, wellidentified sources -> look for point sources that are not present in the model Moving a putative point source through a grid of locations in the sky and maximizing -log(likelihood)