New Spectral Classification Technique

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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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Extracting Spectral Properties or Variations from
Faint X-ray sources

• Hardness Ratio
• HR1 (H-S)/(HS) 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

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Hardness Ratio

• Pros
• Easy to calculate
• Require relatively low statistics (gt 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

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Hardness Ratio

• Pros
• Easy to calculate
• Require relatively low statistics (gt 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 11 41 271 0.3 1.5
1.5 8.0 keV 15 11 51 0.3 0.6
0.6 8.0 keV 124 14 11
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Hardness Ratio

• Pros
• Easy to calculate
• Require relatively low statistics (gt 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 (HR0) 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
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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
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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.

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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 C210 and C320

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Hardness ratio X-ray colors

• Use counts in predefined sub-energy bins.
• Count dependent selection effect
• Misleading spacing in the diagram

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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
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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
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Quantiles

• Quantile Energy (Ex) and Normalized Quantile
  (Qx)
• x of total counts at E lt Ex
• Qx (Ex-Elo) / (Elo-Eup), 0ltQxlt1
• e.g. Elo 0.3 keV, Eup8.0 keV in 0.3 8.0 keV
• Median (mQ50)
• Terciles (Q33, Q67)
• Quartiles (Q25, Q75)

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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

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Hardness Ratio
HR1 (H-S)/(HS) -1 lt HR1 lt 1
HR2 log10(H/S) -? lt HR2 lt ?
?
HR2 log10 (1HR1)/(1-HR1)
Median
mQ50 (E50-Elo)/(Eup-Elo) 0 lt m lt 1
qDx log10 m/(1-m) -? lt qDx lt ?

?
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Hardness ratio simulations (no background)
S0.3-2.0 keV H2.0-8.0 keV
Fractional cases with upper or lower limits
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Hardness Ratio vs Median (no background)
Hardness Ratio 0.3-2.0-8.0 keV
Median 0.3-8.0 keV
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Hardness Ratio vs Median (sourcebackground 11)
Hardness Ratio 0.3-2.0-8.0 keV
Median 0.3-8.0 keV
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Quantile-based Color-Color Diagram (QCCD)
E50

• Quantiles are not independent
• mQ50 vs Q25/Q75
• Power-Law ? NH
• Proper spacing in the diagram
• Poor mans Kolmogorov -Smirnov (KS) test

More Absorption
Intrinsically Hard
An ideal detector 03-8.0 keV
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Overview of the QCCD phase space
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Color estimate distributions (68) by
simulations for 1000 count sources
E50
Quantile Diagram 0.3-8.0 keV
Conventional Diagram 0.3-0.9-2.5-8.0 keV
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Realistic simulations
E50
ACIS-S effective area energy resolution
An ideal detector
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100 count source with no background
Quantile Diagram 0.3-8.0 keV
Conventional Diagram 0.3-0.9-2.5-8.0 keV
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100 source count/ 50 background count
Quantile Diagram 0.3-8.0 keV
Conventional Diagram 0.3-0.9-2.5-8.0 keV
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50 count source without background
Quantile Diagram 0.3-8.0 keV
Conventional Diagram 0.3-0.9-2.5-8.0 keV
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50 source count/ 25 background count
Quantile Diagram 0.3-8.0 keV
Conventional Diagram 0.3-0.9-2.5-8.0 keV
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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

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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

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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

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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

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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

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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

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Energy resolution and Quantile Diagram
?E/E 10 at 1.5 keV
?E/E 100 at 1.5 keV
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Sgr A (750 ks Chandra)
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Sgr A (750 ks Chandra)
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Sgr A (750 ks Chandra)
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Sgr A (750 ks Chandra)
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Sgr A (750 ks Chandra)
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Swift XRT Observation of GRB Afterglow

• GRB050421 Spectral softening with constant
  NH
• GRB050509b Short burst afterglow, softer than
  the host Quasar

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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

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Future Work

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

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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.

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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

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Quantile Error Estimates by Maritz-Jarrett Method

• PL ? 2, NH5x1021cm-2
• gt30 count within 10
• lt30 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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