New Spectral Classification Technique
This presentation is the property of its rightful owner.
Sponsored Links
1 / 46

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


  • 115 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

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

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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.


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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 1:15:1

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


New spectral classification technique for faint x ray sources quantile analysis

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 bandSensitive 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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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.


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

Hardness ratio & X-ray colors

  • Use counts in predefined sub-energy bins.

    • Count dependent selection effect

    • Misleading spacing in the diagram


New spectral classification technique for faint x ray sources quantile analysis

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 bandSensitive to Median

0.3 – 4.2,4.2 – 8.0 keV ~ 04.2 keV

0.3 – 1.5,1.5 – 8.0 keV ~ 11.5 keV

0.3 – 0.6,0.6 – 8.0 keV ~ 20.6 keV


New spectral classification technique for faint x ray sources quantile analysis

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 bandSensitive to Median

0.3 – 4.2,4.2 – 8.0 keV ~ 04.2 keV

0.3 – 1.5,1.5 – 8.0 keV ~ 11.5 keV

0.3 – 0.6,0.6 – 8.0 keV ~ 20.6 keV


New spectral classification technique for faint x ray sources quantile analysis

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)


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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 <


New spectral classification technique for faint x ray sources quantile analysis

Hardness ratio simulations (no background)

S:0.3-2.0 keV

H:2.0-8.0 keV

Fractional cases with

upper or lower limits


New spectral classification technique for faint x ray sources quantile analysis

Hardness Ratio vs Median

(no background)

Hardness Ratio

0.3-2.0-8.0 keV

Median

0.3-8.0 keV


New spectral classification technique for faint x ray sources quantile analysis

Hardness Ratio vs Median

(source:background = 1:1)

Hardness Ratio

0.3-2.0-8.0 keV

Median

0.3-8.0 keV


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

Overview of the QCCD phase space


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

Realistic simulations

E50%=

ACIS-S effective area

& energy resolution

An ideal detector


New spectral classification technique for faint x ray sources quantile analysis

100 count source with no background

Quantile Diagram

0.3-8.0 keV

Conventional Diagram

0.3-0.9-2.5-8.0 keV


New spectral classification technique for faint x ray sources quantile analysis

100 source count/ 50 background count

Quantile Diagram

0.3-8.0 keV

Conventional Diagram

0.3-0.9-2.5-8.0 keV


New spectral classification technique for faint x ray sources quantile analysis

50 count source without background

Quantile Diagram

0.3-8.0 keV

Conventional Diagram

0.3-0.9-2.5-8.0 keV


New spectral classification technique for faint x ray sources quantile analysis

50 source count/ 25 background count

Quantile Diagram

0.3-8.0 keV

Conventional Diagram

0.3-0.9-2.5-8.0 keV


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

Energy resolution and Quantile Diagram

E/E = 10% at 1.5 keV

E/E = 100% at 1.5 keV


New spectral classification technique for faint x ray sources quantile analysis

Sgr A*

(750 ks Chandra)


New spectral classification technique for faint x ray sources quantile analysis

Sgr A*

(750 ks Chandra)


New spectral classification technique for faint x ray sources quantile analysis

Sgr A*

(750 ks Chandra)


New spectral classification technique for faint x ray sources quantile analysis

Sgr A*

(750 ks Chandra)


New spectral classification technique for faint x ray sources quantile analysis

Sgr A*

(750 ks Chandra)


New spectral classification technique for faint x ray sources quantile analysis

Swift XRT Observation of GRB Afterglow

  • GRB050421 : Spectral softening with ~ constant NH

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


New spectral classification technique for faint x ray sources quantile analysis

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


New spectral classification technique for faint x ray sources quantile analysis

Future Work

  • Find better phase spaces.

  • Handle background subtraction better.

  • Find better error estimates: half sampling, etc.

  • Implement Bayesian statistics?


New spectral classification technique for faint x ray sources quantile analysis

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.


New spectral classification technique for faint x ray sources quantile analysis

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%


New spectral classification technique for faint x ray sources quantile analysis

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


  • Login