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New Spectral Classification Technique for Faint X-ray Sources: Quantile Analysis

New Spectral Classification Technique for Faint X-ray Sources: Quantile Analysis. JaeSub Hong Spring, 2006 J. Hong, E. Schlegel & J.E. Grindlay, ApJ 614, 508, 2004 The quantile software (perl and IDL) is available at http://hea-www.harvard.edu/ChaMPlane/quantile.

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New Spectral Classification Technique for Faint X-ray Sources: Quantile Analysis

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  1. New Spectral Classification Technique for Faint X-ray Sources: Quantile Analysis JaeSub Hong Spring, 2006 J. Hong, E. Schlegel & J.E. Grindlay, ApJ 614, 508, 2004 The quantile software (perl and IDL) is available at http://hea-www.harvard.edu/ChaMPlane/quantile.

  2. Extracting Spectral Properties or Variations from Faint X-ray sources • Hardness Ratio • HR1 =(H-S)/(H+S) or HR2 = log10(H/S) • e.g. S: 0.3-2.0 keV, • H: 2.0-8.0 keV • X-ray colors • C21 = log10(C2/C1) : soft color • C32 = log10(C3/C2) : hard color • e.g. C1: 0.3-0.9 keV, • C2: 0.9-2.5 keV, • C3: 2.5-8.0 keV

  3. Hardness Ratio • Pros • Easy to calculate • Require relatively low statistics (> 2 counts) • Direct relation to Physics (count  flux) • Cons • Different sub-binning among different analysis • Many cases result in upper or lower limits • Spectral bias built in sub-band selection

  4. Hardness Ratio • Pros • Easy to calculate • Require relatively low statistics (> 2 counts) • Direct relation to Physics (count  flux) • Cons • Different sub-binning among different analysis • Many cases result in upper or lower limits • Spectral bias built in sub-band selection e.g. simple power law spectra (PLI = ) on an ideal (flat) response S band : H band ~ 0  ~ 1  ~ 2 0.3 – 4.2 : 4.2 – 8.0 keV = 1:1 4:1 27:1 0.3 – 1.5 : 1.5 – 8.0 keV = 1:5 1:1 5:1 0.3 – 0.6 : 0.6 – 8.0 keV = 1:24 1:4 1:1

  5. Hardness Ratio • Pros • Easy to calculate • Require relatively low statistics (> 2 counts) • Direct relation to Physics (count  flux) • Cons • Many cases result in upper or lower limits • Spectral bias built in sub-band selection e.g. simple power law spectra (PLI = ) on an ideal (flat) response S band : H band Sensitive to (HR~0) 0.3 – 4.2 : 4.2 – 8.0 keV ~ 0 0.3 – 1.5 : 1.5 – 8.0 keV ~ 1 0.3 – 0.6 : 0.6 – 8.0 keV ~ 2

  6. X-ray Color-Color Diagram C21 = log10(C2/C1) C32 = log10(C3/C2) C1 : 0.3-0.9 keV C2 : 0.9-2.5 keV C3 : 2.5-8.0 keV Power-Law :  & NH Intrinsically Hard More Absorption

  7. X-ray Color-Color Diagram • Simulate 1000 count sources with spectrum at the grid nods. • Show the distribution (68%) of color estimates for each simulation set. • Very hard and very soft spectra result in wide distributions of estimates at wrong places.

  8. X-ray Color-Color Diagram • Total counts required in the broad band(0.3-8.0 keV)to have at least one count in each of three sub-energy bands • Sensitive to C21~0 and C32~0

  9. Hardness ratio & X-ray colors • Use counts in predefined sub-energy bins. • Count dependent selection effect • Misleading spacing in the diagram

  10. Hardness ratio & X-ray colors • Use counts in predefined sub-energy bins. • Count dependent selection effect • Misleading spacing in the diagram e.g. simple power law spectra (PLI = ) on an ideal (flat) response S band,H band Sensitive to Median 0.3 – 4.2,4.2 – 8.0 keV ~ 0 4.2 keV 0.3 – 1.5,1.5 – 8.0 keV ~ 1 1.5 keV 0.3 – 0.6,0.6 – 8.0 keV ~ 2 0.6 keV

  11. How about Quantiles? Search energies that divide photons into predefined fractions. : median, terciles, quartiles, etc e.g. simple power law spectra (PLI = ) on an ideal (flat) response S band,H band Sensitive to Median 0.3 – 4.2,4.2 – 8.0 keV ~ 0 4.2 keV 0.3 – 1.5,1.5 – 8.0 keV ~ 1 1.5 keV 0.3 – 0.6,0.6 – 8.0 keV ~ 2 0.6 keV

  12. Quantiles • Quantile Energy (Ex%) andNormalized Quantile (Qx) • x% of total counts at E < Ex% • Qx= (Ex%-Elo) / (Elo-Eup), 0<Qx<1 • e.g. Elo = 0.3 keV, Eup=8.0 keV in 0.3 – 8.0 keV • Median (m=Q50) • Terciles (Q33, Q67) • Quartiles (Q25, Q75)

  13. Quantiles • Low count requirements for quantiles: • spectral-independent • 2 counts for median • 3 counts for terciles and quartiles • No energy binning required • Take advantage of energy resolution • Optimal use of information

  14. Hardness Ratio HR1 = (H-S)/(H+S) -1 < HR1 < 1 HR2 = log10(H/S) - < HR2 <   HR2 = log10[ (1+HR1)/(1-HR1) ] Median m=Q50= (E50%-Elo)/(Eup-Elo) 0 < m < 1 qDx= log10[ m/(1-m) ] - < qDx < 

  15. Hardness ratio simulations (no background) S:0.3-2.0 keV H:2.0-8.0 keV Fractional cases with upper or lower limits

  16. Hardness Ratio vs Median (no background) Hardness Ratio 0.3-2.0-8.0 keV Median 0.3-8.0 keV

  17. Hardness Ratio vs Median (source:background = 1:1) Hardness Ratio 0.3-2.0-8.0 keV Median 0.3-8.0 keV

  18. Quantile-based Color-Color Diagram (QCCD) E50%= • Quantiles are not independent • m=Q50 vs Q25/Q75 • Power-Law :  & NH • Proper spacing in the diagram • Poor man’s Kolmogorov -Smirnov (KS) test More Absorption Intrinsically Hard An ideal detector 03-8.0 keV

  19. Overview of the QCCD phase space

  20. Color estimate distributions(68%) by simulations for1000 count sources E50%= Quantile Diagram 0.3-8.0 keV Conventional Diagram 0.3-0.9-2.5-8.0 keV

  21. Realistic simulations E50%= ACIS-S effective area & energy resolution An ideal detector

  22. 100 count source with no background Quantile Diagram 0.3-8.0 keV Conventional Diagram 0.3-0.9-2.5-8.0 keV

  23. 100 source count/ 50 background count Quantile Diagram 0.3-8.0 keV Conventional Diagram 0.3-0.9-2.5-8.0 keV

  24. 50 count source without background Quantile Diagram 0.3-8.0 keV Conventional Diagram 0.3-0.9-2.5-8.0 keV

  25. 50 source count/ 25 background count Quantile Diagram 0.3-8.0 keV Conventional Diagram 0.3-0.9-2.5-8.0 keV

  26. Energy resolution and Quantile Diagram • Elo = 0.3 keV • Ehi = 8.0 keV • E/E = 10% at 1.5 keV • E50%: from Elo+ f Elo • to Ehi– f Ehi • from ~ 0.4 keV • to ~ 7.8 keV

  27. Energy resolution and Quantile Diagram • Elo = 0.3 keV • Ehi = 8.0 keV • E/E = 20% at 1.5 keV • E50%: from Elo+ f Elo • to Ehi– f Ehi • from ~ 0.4 keV • to ~ 7.6 keV

  28. Energy resolution and Quantile Diagram • Elo = 0.3 keV • Ehi = 8.0 keV • E/E = 50% at 1.5 keV • E50%: from Elo+ f Elo • to Ehi– f Ehi • from ~ 0.5 keV • to ~ 7.0 keV

  29. Energy resolution and Quantile Diagram • Elo = 0.3 keV • Ehi = 8.0 keV • E/E = 100% at 1.5 keV • E50%: from Elo+ f Elo • to Ehi– f Ehi • from ~ 0.7 keV • to ~ 6.5 keV

  30. Energy resolution and Quantile Diagram • Elo = 0.3 keV • Ehi = 8.0 keV • E/E = 200% at 1.5 keV • E50%: from Elo+ f Elo • to Ehi– f Ehi • from ~ 1.0 keV • to ~ 6.0 keV

  31. Energy resolution and Quantile Diagram • Elo = 0.3 keV • Ehi = 8.0 keV • E/E = 500% at 1.5 keV • E50%: from Elo+ f Elo • to Ehi– f Ehi • from ~ 1.2 keV • to ~ 5.0 keV

  32. Energy resolution and Quantile Diagram E/E = 10% at 1.5 keV E/E = 100% at 1.5 keV

  33. Sgr A* (750 ks Chandra)

  34. Sgr A* (750 ks Chandra)

  35. Sgr A* (750 ks Chandra)

  36. Sgr A* (750 ks Chandra)

  37. Sgr A* (750 ks Chandra)

  38. Swift XRT Observation of GRB Afterglow • GRB050421 : Spectral softening with ~ constant NH • GRB050509b : Short burst afterglow, softer than the host Quasar

  39. Score Board • Spectral Bias • Stability • Sub-binning • Phase Space • Sensitivity • Energy Resolution • Physics • Quantile • Analysis • None • Good • No Need • Meaningful • Evenly Good • Sensitive • Indirect • X-ray Hardness • Ratio or Colors • Yes • Upper/Lower Limits • Required • Misleading? • Selectively Good • Insensitive • Direct

  40. Future Work • Find better phase spaces. • Handle background subtraction better. • Find better error estimates: half sampling, etc. • Implement Bayesian statistics?

  41. Conclusion: Quantile Analysis • Stable spectral classification with limited statistics • No energy binning required • Take advantage of energy resolution • Quantile-based phase space is a good indicator • of spectral sensitivity of the detector. • The basic software (perl and IDL) is available at • http://hea-www.harvard.edu/ChaMPlane/quantile.

  42. Quantile Error Estimates • In principle, by simulations: • slow and redundant • Maritz-Jarrett Method : bootstrapping • Q25 & Q75: not independent • MJ overestimates by ~10% • 100 count source: • consistent within ~5%

  43. Quantile Error Estimates by Maritz-Jarrett Method • PL:  =2, NH=5x1021cm-2 • >~30 count : within ~ 10% • <~30 count : overestimate up to ~50% • MJ requires • 3 counts for Q50 • 5 counts for Q33, Q67 • 6 counts for Q25, Q75 mj/sim

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