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Analysis of low surface brightness sources with EPIC

Analysis of low surface brightness sources with EPIC. Alberto Leccardi. EPIC background working group meeting. Palermo, 11 April 2007. If background dominates and spectra have few counts. Apply correct statistic. Control systematics. APPLY THE CORRECT STATISTIC.

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Analysis of low surface brightness sources with EPIC

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  1. Analysis of low surface brightness sources with EPIC Alberto Leccardi EPIC backgroundworking group meeting Palermo, 11 April 2007

  2. If background dominates and spectra have few counts Applycorrectstatistic Controlsystematics

  3. APPLY THE CORRECT STATISTIC The counting process of the number of photonscollected by a detector during a time intervalis a typical example of a Poisson process A spectrum is univocally definedby the observed counts, Oi, in each channel Given a model, the expected counts, Ei,in each channel can be calculated

  4. APPLY THE CORRECT STATISTIC The probability, P, of obtaining a particular spectrumfollows a Poisson distributionand is a function of the model parameters, α:

  5. APPLY THE CORRECT STATISTIC Given a measured spectrum,astronomers wish to determinethe best set of model parameters The maximum likelihood methoddetermines the parameters which maximize P One is likely to collect those datawhich carry the highest chance to be collected The Cash (Cash, 1979) and the χ2 statisticsare based on these concepts The former is more appropriatewhen analyzing low count spectra

  6. MAXIMUM LIKELIHOOD ESTIMATORS The Cash and the χ2 statistics are basedon maximum likelihood methods From the literature (e.g. Eadie 1971)it is well known that: ML estimators could be biasedespecially in the case ofhighly non linear model parameters(e.g. kT of a bremsstrahlung model) Bias: difference between expected and true value

  7. THERMAL SOURCE ONLY CASE Bias appears for low count spectra The Cash estimator is asymptotically unbiased

  8. Sourcedominates Bkg dominates INTRODUCING A BACKGROUND When using the Cash statisticthe background has to be modeled (Cash, 1979) The bias depends on:1) the background contribution2) the spectrum total number of counts

  9. WORK IN PROGRESS… For the realistic caseno definitive solution has been found Quick and dirty solution: the triplet method Correct the posterior probability density functions(Leccardi & Molendi, 2007 A&A submitted) Long term solution: ? Find different estimators (e.g. 1/kT, log(kT), …)Explore the Bayesian approach

  10. If background dominates and spectra have few counts Applycorrectstatistic Controlsystematics

  11. SYSTEMATIC UNCERTAINTIES Imperfect MOS-pn cross-calibration Defective background knowledge The energy band is very important

  12. SYSTEMATIC UNCERTAINTIES Measuring the temperature of hot GC Using the energy band beyond 2 keV • Cross-calibration is relatively good • Internal background continuum is well described by a power law • Al and Si fluorescence lines are excluded • Local X-ray background is negligible

  13. BACKGROUND BEYOND 2 keV Internal background: continuum and lines (Quiescent) soft protons Cosmic X-ray background

  14. pn MOS1 MOS2 INTERNAL BACKGROUND

  15. INTERNAL BKG: CONTINUUM When analyzing different observationswe found typical variationsof 15% for PL normalization and negligible variations for PL index PL index is ~0.23 for MOS and ~0.33 for pnit does not show spatial variations MOS: SB is roughly constant over all detectorpn: SB presents a hole due to electronic board,inside the hole the continuum is more intense

  16. INTERNAL BKG: LINES When analyzing different observationswe found typical variations of the norm of the linesof the same order of the associated statistical error MOSweak lines pnintenseNi-Cu-Znblend lines pn MOS1 MOS2

  17. THE R PARAMETER R depends only on the selected inner regionand on the instrument R is independent of the particular observation R is roughly equal to the area ratio for MOS, not for pn Once measured the PL normalization out of the FOV, this scale factor allows to estimate rather preciselythe PL normalization in the selected region of the FOVfor every observation.

  18. SOFT PROTONS Light curve in a hard band (beyond 10 keV) and GTI filtering with a semi-fixed threshold Light curve in a soft band (2-5 keV)and GTI filtering with a 3 σ threshold IN/OUT ratio to evaluate the contribution of quiescent soft protons Caveat ! Extended sources which fill the whole FOVand emit beyond 5-6 keV

  19. SOFT PROTONS Goal:estimate QSP contribution for MOS spectra Stack many blank field observations (~1.5 Ms) Use the Cash statistic  Background modeling Model the total spectrum CXB + QSP + Int. bkg continuum + Int. Bkg lines with PL + PL/b + PL/b + (several) GA/b

  20. SOFT PROTONS & COSMIC BKG Data Int. bkg CXB QSP

  21. SOFT PROTONS & COSMIC BKG • Int. bkg continuum is fixed • PL index from CLOSED • PL norm = R*normOUT Data Int. bkg CXB Int. bkg line norm is free QSP QSP and CXBparameters are free We measure both CXB and QSP components

  22. SOFT PROTONS & COSMIC BKG Work in progress Soft proton index is poorly constrained,conversely the normalization uncertainty is 15% CXB uncertainties are rather largebecause we are modeling 3 components * CXB norm is expressed in photons cm-2 s-1 sr-1 keV-1

  23. SOFT PROTONS & COSMIC BKG We eliminate QSP component andfit the same data only with CXB and int. bkg The index is substantially unchanged,norm increases by 15% due to QSP not to real CXB,uncertainties are strongly reduced * CXB norm is expressed in photons cm-2 s-1 sr-1 keV-1

  24. SOFT PROTONS & COSMIC BKG De Luca & Molendi have used renormalized background subtraction Results are consistentthe difference could be due to the cosmic variance (~7%) We can infer that also this result could be biased by 10-15%and the uncertainties could be too small * CXB norm is expressed in photons cm-2 s-1 sr-1 keV-1

  25. Goal:measure temperature profiles of hotintermediate redshift galaxy clusters

  26. OUR TECHNIQUE Galaxy clusters are extended sources. They fill the FOV (intermediate redshift)but in outer regions thermal emission is very small,therefore IN/OUT technique is reliable. They are hot  exponential cutoff at high energies, therefore we use the energy band beyond 2 keV. We use the Cash statistic (more suitable than χ2). Cash statistic requires background modeling.

  27. Data Int. bkg CXB GC OUR TECHNIQUE NOW We consider an external ring (10’-12’ in FOV)to estimate the norm of CXB and int. bkg GC is fixed(iterative estimate) Int. bkg and CXB:index fixednorm free QSP is excluded:- degeneracy- int. bkg and CXBcontain alsoinformation on QSP

  28. OUR TECHNIQUE NOW We rescale so called CXB and int. bkg normto the inner regions using area ratio In the inner regions CXB and int. bkg normare semi-fixed:they are allowed to vary in a small rangearound the rescaled values Montecarlo simulations tell ushow important is the systematic introduced We found a bias of ~5-10% in the ring 5’-7’where the background dominates

  29. IN THE FUTURE… If we find a tight relation betweenthe IN/OUT ratio and the QSP normalization,we could model and fix the bulkof QSP component. This could reduce the bias of 5-10%. We will implement simulations to evaluatewhich is the best procedure andto quantify the intensity of introduced bias.

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