new spectral classification technique for faint x-ray sources: quantile analysis jaesub hong spring,...

New Spectral Classification Techniquefor 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.

Extracting Spectral Properties or Variationsfrom Faint X-ray sources

• Hardness RatioHR1 =(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 colorC32 = 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

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


Cons• Different sub-binning among different analysis• Many cases result in upper or lower limits• Spectral bias built in sub-band selection

Hardness Ratio


Cons• Different sub-binning among different analysis• Many cases result in upper or lower limits • Spectral bias built in sub-band selection


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 1:15:1

0.3 – 0.6 : 0.6 – 8.0 keV = 1:24 1:41:1

Hardness Ratio


Cons• Many cases result in upper or lower limits • Spectral bias built in sub-band selection


Cons• Many cases result in upper or lower limits • Spectral bias built in sub-band selection


S band : H band Sensitive to (HR~0)0.3 – 4.2 : 4.2 – 8.0 keV ~ 00.3 – 1.5 : 1.5 – 8.0 keV ~ 10.3 – 0.6 : 0.6 – 8.0 keV ~ 2

X-ray Color-Color Diagram

C21 = log10(C2/C1) C32 = log10(C3/C2)

C1 : 0.3-0.9 keVC2 : 0.9-2.5 keVC3 : 2.5-8.0 keV

Power-Law : & NH

Intr

insi

cally

Hard

More

Absorption


• 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.


• 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

Use counts in predefined sub-energy bins.

• Count dependent selection effect• Misleading spacing in the diagram



Hardness ratio & X-ray colors





Hardness ratio & X-ray colors


S band, H band Sensitive to Median0.3 – 4.2, 4.2 – 8.0 keV ~ 0 4.2 keV0.3 – 1.5, 1.5 – 8.0 keV ~ 1 1.5 keV0.3 – 0.6, 0.6 – 8.0 keV ~ 2 0.6 keV

Search energies that divide photons

into predefined fractions.

: median, terciles, quartiles, etc

Search energies that divide photons

into predefined fractions.

: median, terciles, quartiles, etc

How about Quantiles?


S band, H band Sensitive to Median0.3 – 4.2, 4.2 – 8.0 keV ~ 0 4.2 keV0.3 – 1.5, 1.5 – 8.0 keV ~ 1 1.5 keV0.3 – 0.6, 0.6 – 8.0 keV ~ 2 0.6 keV

Quantiles

• Quantile Energy (Ex%) and Normalized 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)

Quantiles

• Low count requirements for quantiles: spectral-independent

2 counts for median3 counts for terciles and

quartiles

• No energy binning required• Take advantage of energy resolution• Optimal use of information

Hardness Ratio

HR1 = (H-S)/(H+S)

-1 < HR1 < 1

HR1 = (H-S)/(H+S)

-1 < HR1 < 1 HR2 = log10[ (1+HR1)/(1-

HR1) ]

m=Q50= (E50%-Elo)/(Eup-Elo)

0 < m < 1

m=Q50= (E50%-Elo)/(Eup-Elo)

0 < m < 1

Median

HR2 = log10(H/S)

- < HR2 <

HR2 = log10(H/S)

- < HR2 <

qDx= log10[ m/(1-m) ]

- < qDx <

qDx= log10[ m/(1-m) ]

- < qDx <

Hardness ratio simulations (no background)

S:0.3-2.0 keV H:2.0-8.0 keV

Fractional cases withupper or lower limits

Hardness Ratio vs Median(no background)

Hardness Ratio0.3-2.0-8.0 keV

Median0.3-8.0 keV

Hardness Ratio vs Median(source:background = 1:1)

Hardness Ratio0.3-2.0-8.0 keV

Median0.3-8.0 keV

Quantile-based Color-Color Diagram (QCCD)

• Quantiles are not independent

• m=Q50 vs Q25/Q75

• Power-Law : & NH

• Proper spacing in the diagram

• Poor man’s Kolmogorov -Smirnov (KS) testAn ideal detector

03-8.0 keV

IntrinsicallyHard

More

Absorp

tion

E50%=

Overview of the QCCD phase space

Color estimate distributions (68%) by simulationsfor 1000 count sources

Quantile Diagram0.3-8.0 keV

Conventional Diagram0.3-0.9-2.5-8.0 keV

E50%=

Realistic simulations

ACIS-S effective area & energy resolutionAn ideal detector

E50%=

100 count source with no background



100 source count/ 50 background count



50 count source without background



50 source count/ 25 background count



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 keVto ~ 7.8 keV



• E/E = 20% at 1.5 keV





• E/E = 50% at 1.5 keV





• E/E = 100% at 1.5 keV





• E/E = 200% at 1.5 keV





• E/E = 500% at 1.5 keV



E/E = 10% at 1.5 keV E/E = 100% at 1.5 keV


Sgr A* (750 ks Chandra)

Swift XRT Observation of GRB Afterglow

• GRB050421 : Spectral softening with ~ constant NH

• GRB050509b : Short burst afterglow, softer than the host Quasar

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

Score Board

Future Work

• Find better phase spaces.

• Handle background subtraction better.

• Find better error estimates: half sampling, etc.

• Implement Bayesian statistics?

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.

• In principle, by simulations: slow and redundant

• Maritz-Jarrett Method : bootstrapping

• Q25 & Q75: not independentMJ overestimates by ~10%

• 100 count source:consistent within ~5%

Quantile Error Estimates

Quantile Error Estimatesby 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

new spectral classification technique for faint x-ray sources: quantile analysis jaesub hong spring,...

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