Pile-up Modeling. John E. Davis. CXC 6th Chandra/CIAO Workshop, October 2008

Transcription

1 1 Pile-up Modeling

2 Outline Event Detection Grade Migration The Standard Model The Pile-up Model Data Preparation Using the model in sherpa and isis Examples 2

3 3 When a photon is absorbed in the silicon of a CCD, a charge cloud of electronhole pairs is formed ( 3.65 ev per pair). h γ The pulse-height is a measure of the number of pairs in the cloud.

4 4 For a bright source, there is a non-negligible probability for two or more photons to arrive in the same region during an integration time. The detector will be unable to distinguish the two events. This phenomena is called pileup. h 1 +h 2 h 1 γ 2 γ 1

5 5 Pile-up manifests itself by a lower event detection rate and an energy spectrum distorted towards higher energies. Expected Observed

6 6 The charge cloud is not necessarily confined to a single pixel. γ

7 Cosmic rays also produce charge clouds! 7 Cosmic Ray Cosmic Ray Fortunately, the charge cloud patterns, or grades, from cosmic rays are different from the patterns produced by X-rays.

8 8 X-rays are more likely to produce events with good grades. Grade 0 Grade 2 Grade 3 Grade 4 Grade 6 Grade 6

9 9 Cosmic rays are more likely to produce events with bad grades. Grade 1 Grade 5 Grade 7 Grade 7

10 Pile-up can also produce events with bad grades. 10 γ 2 γ 1 γ 2 γ 1 This effect is called Grade Migration.

11 The Standard Model 11 C(h) = (Nτ) de R(h, E)A(E)s(E) C(h) The number of counts in pulse-height bin h. dmextract s(e) Incident source flux sherpa A(E) Effective area, or ARF mkarf R(h, E) Detector redistribution matrix, or RMF mkrmf τ CCD frame time TIMEDEL N Total number of CCD frames Nτ = EXPOSURE

12 12 Data Std Model

13 The Pile-up Model Pile-up Modeling 13 C(h) = (Nτ)(1 f) de R(h, E)A(E)s(E) +Nne (τ/ḡ 0) de A(E)fs(E)/n α p 1 p=1 de R(h, E) [τa(e)fs(e)/n] p p! n The number of regions where pile-up occurs. f Total PSF fraction enclosed by the n pile-up regions. α Grade-migration survival probability. ḡ 0 Average branching ratio into good grades. p Convolution product ( ) p

14 14 Standard Model Pile-up Model Counts Flux

15 Data Preparation Pile-up Modeling 15 Know your lightcurve! The pile-up model assumes that photon arrival times are Poisson distributed. Use time-intervals where the incident flux is constant. Use either the counts in the wings of the PSF or in the readout streak to generate the lightcurve. HEG-1[Events/frame] HEG-1 lightcurve on ACIS-5[Obs-Id=3814] Exposure Number

16 16 II Peg Light Curve OBSID 1451, HETG/ACIS-S, Claude Canizares SKYX TIME[secs]

17 17 II Peg Light Curve OBSID 1451, HETG/ACIS-S, Claude Canizares SourceLightcurve0-12keV 0.6 Source Count Rate[events/frame] Exposure Number

18 II Peg Light Curve Pile-up Modeling StreakLightcurve:0-12keV Streak Count Rate[events/frame] Exposure Number

19 19 Use the right extraction region For an on-axis point source, it is recommended that a circular region with a 2 arc-second radius be used (4 ACIS pixels). A larger region will decrease the signal to noise ratio.

20 Using the pile-up model in sherpa 20.. sherpa> set_pileup_model(jdpileup.jdp); sherpa> jdp.f.min=0.85; sherpa> jdp.f.max=0.95; sherpa> jdp.f=0.9; sherpa> jdp.n = 1 sherpa> jdp.alpha = 0.5 sherpa> jdp.f = 0.95 sherpa> thaw (jdp.f, jdp.alpha); sherpa> freeze (jdp.n); sherpa> fit; sherpa> print(jdp);

21 Using the pile-up model in isis 21.. isis> set_kernel (1, "pileup"); isis> set_par ("pileup<1>.nregions", 1, 1); isis> set_par ("pileup<1>.alpha", 0.5, 0); isis> set_par ("pileup<1>.psffrac", 0.9, 0, 0.85, 0.95); isis> fit_counts; isis> print_kernel (1);

22 22 Example 1: Q OBSID 1450, HETG/ACIS-S, Claude Canizares Data Std Model

23 Pile-up Fit Pile-up Modeling 23 isis> fit_counts; Parameters[Variable] = 7[5] Data bins = 67 Chi-square = 63.1 Reduced chi-square = isis> list_par; phabs(1)*powerlaw(1) idx param tie-to freeze value min max 1 phabs(1).nh powerlaw(1).norm powerlaw(1).phoindex pileup<1>.nregions pileup<1>.g pileup<1>.alpha pileup<1>.psffrac

24 Spectral Fit Pile-up Modeling 24

25 Pile-up Fraction Pile-up Modeling 25 isis> print_kernel(1); 1: : : : : : : e e-05 8: e e-06 *** pileup fraction:

26 26 Confidence Contours 1.6 Q Spectral Index Pileup Model HETG Std Model N H [10 22 cm 2 ]

27 27 Example 2: NGC 4579 OBSID 807, ACIS-S, Michael Eracleous isis> fit_counts; Parameters[Variable] = 7[5] Data bins = 82 Chi-square = Reduced chi-square = isis> list_par; phabs(1)*powerlaw(1) idx param tie-to freeze value min max 1 phabs(1).nh powerlaw(1).norm powerlaw(1).phoindex pileup<1>.nregions pileup<1>.g pileup<1>.alpha pileup<1>.psffrac

28 Spectral Fit Pile-up Modeling 28

29 Pile-up Fraction Pile-up Modeling 29 isis> print_kernel(1); 1: : : : : : : e e-05 8: e e-06 *** pileup fraction:

30 30 Confidence Contours NGC 4579 Spectral Index Pileup Model Eracleous et al, ApJ 565,108(2002) N H [10 22 cm 2 ] 0.06

31 31 Example 3: Nucleus of M81 OBSID 735, ACIS-S, Douglas Swartz

32 32 isis> fit_counts; Parameters[Variable] = 7[5] Data bins = 99 Chi-square = Reduced chi-square = isis> list_par; phabs(1)*powerlaw(1) idx param tie-to freeze value min max 1 phabs(1).nh powerlaw(1).norm powerlaw(1).phoindex pileup<1>.nregions pileup<1>.g pileup<1>.alpha pileup<1>.psffrac

33 Spectral Fit Pile-up Modeling 33

34 Pile-up Fraction Pile-up Modeling 34 isis> print_kernel(1); 1: : : : : : : : : : : e-05 12: e-05 13: e-05 *** pileup fraction:

35 35 Confidence Contours Nucleus of M Pileup Model Spectral Index Swartz et al, ApJ 144,213(2003) Ishisaki et al, PASJ 48,237(1996) 0.1 N H [10 22 cm 2 ]