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New Spectral Classification Technique

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New Spectral Classification Technique. for Faint X-ray Sources: Quantile ... J. Hong, E. Schlegel & J.E. ... on an ideal (flat) response. S band, H ... – PowerPoint PPT presentation

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Title: New Spectral Classification Technique


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)/(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

3
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

4
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
5
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
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 C210 and C320

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) 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)

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)/(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 ?

?
15
Hardness ratio simulations (no background)
S0.3-2.0 keV H2.0-8.0 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 (sourcebackground 11)
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
  • 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
19
Overview of the QCCD phase space
20
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
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
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39
Swift XRT Observation of GRB Afterglow
  • GRB050421 Spectral softening with constant
    NH
  • GRB050509b Short burst afterglow, softer than
    the host Quasar

40
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

41
Future Work
  • Find better phase spaces.
  • Handle background subtraction better.
  • Find better error estimates half sampling, etc.
  • Implement Bayesian statistics?

42
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43
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.

44
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

45
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
46
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