The Dead time correction for the light curve with millisecond time bin

Liang, Jau-shian

Institute of Physics, NTHU

2006/12/5

Reference

• K. Jahoda, J. H. Swank, et al., 1996 Proc. SPIE 2808, p. 59

• K. Jahoda, M. J. Stark, et al., 1999, Nucl. Phys. B (Proc. Suppl.), 69, 210

• Dennis Wei, 2006. Senior Thesis submitted to the MIT Dept. of Physics

• K. Jahoda, C. B. Markwardt, et al., 2006, ApJS, 163, 401

Outline

• Introduction• Recovery method

• Discussion

• Summary

Proportional counter

A proportional counter is a measurement device to count particles and photons of ionizing radiation and measure their energy.

Cross section view of one PCA detector

collimators

propane layer

xenon layer 1xenon layer 2

xenon layer 3

xenon veto layer

The propane layer is principally intended to act as a veto layer to reduce the background rate but could be used as a lower energy detector.

The “good” events that trigger only a single xenon chain.

Coincident events are likely particle events and thus are not included among the good events.

X-ray

Good event

q

5LLD event

• If the source is very bright, there is a non-negligible probability that two photons will arrive within the anti-coincidence window of each other, causing the PCA to mistakenly disqualify both photons.

Good and Coincidence rates observedfrom a burst of J1744-28.

(5 pcu)

Remaining rate vs Good rate for a burst from J1744-28

The distribution of time intervals between adjacent events

Dead time ~ 9 s

L1 + R1

L1R1

L1

R1

14 incident photons

L1 + R1

L1R16 good event

jjj

ii Dtout

outin

1

jjj

ii Dtin

inout

1

Dead time correction

the incident rate on each signal chain Rj where the index j runs from 1 to 7 and corresponds to L1, R1, L2, R2, L3, R3, and VP.

Dead time model (K. Jahoda, et. al. 1999)

Predicting the coincidence rate

1

Coincidence timing window

• There is not enough information to do dead time correction with millisecond time resolution.

• The missed coincidence photons should be added in.

• An available way is to construct a recovery method which needs only good rate.

Recovery method

10056-01-01-00 Blank sky #2

(Counts/s/PCU) (Counts/s/PCU)

Good 17800 35

VP 3800 70

Remaining 3400 700 2LLD 1900 80

3-8LLD 750 560

0LLD 360 0-5

VX 440 25

VLE 100 90

assumptions

• The 7 anodes are simplified into 3 anodes (VP, L1 and R1).

• The background of VP, L1 and R1 can be neglected.• The VP rate is proportional to the incident xenon rate.

VP=2Xe

L1=Xe R1=Xe

)(0

0 XeeXe )(220

0

2

1 XeeXe Xee 0 : :

0 photon : 1 photon : 2 photons

• The Poisson probability distribution should be considered.

L1 R1 VP

L1R1

R1L1

R1VP

L1VP

VPR1

VPL1

0LLD(R1)

0LLD(L1)

0LLD(VP)

)( 0 XeeXe )( 0 XeeXe )( 0 XeeXe )( 0 XeeXe

)( 0 XeeXe )( 0VPeVP )( 0 XeeXe

)( 0 XeeXe )( 0 XeeXe

)( 0VPeVP )( 0VPeVP )( 0VPeVP

Xee 1

VPpe

VPpe

VPpe

VPpe

Xee 1

Xee 1

Xee 1

Xee 1

Xee 1

Xee 1

Xee 1

)(20

0

2

1 XeeXe

)(20

0

2

1 XeeXe

)(20

0

2

1 VPeVP

• The probability of that the photon does not exist should also be considered.

VPXe peeXeRL 0221211

)(1

01)(2 VPXeXep eeVPXeVPXe

XeVPXeVPXe eeVPeeeXeLLD p 1010 220

20 2

10

The prediction of the coincidence rate

•The parameters provided by K. Jahoda et al. are pressumed correct.

5s9s

4s

The first event of a coincident set will appear to be a good event (or a propane event) and will trigger the ADC before being labelled “bad” upon the arrival of the second event of the coincident set. The ADC is nonetheless busy for a time (~9s) following the first event of the coincident set. (D. Wei, 2006)

• The dead time window is accounted for 4s.

Good

Remaining L1&R1

Output rates vs. incident rates

Estimate and subtractVP, 2LLD, 0LLD

Caculate dead time

X’out = Xout ?

Adjust Xin

Output Xin

Yes

No

Xin

Prediction rates compare with slew data

Good

Remaining(data)Remaining(prediction)

VP(data)VP(prediction)

Prediction rates compare with data

Remaining(data)

Remaining(prediction)

VP(data)VP(prediction)

Light curve

Corrected light curve

Some results

Light curve

Corrected light curve

Discussion

• the advantages and weaknesses

• Are the dips possibly caused by bursts?

• particle bursts within milliseconds?

the advantages and weaknesses

• The prediction rates agree with the data well.

• The light curve can be corrected with only the observed good rate even blow the time scale 1/8s.

the advantages

the weaknesses

• Particle background is still unknown.

• The fluctuation is enlarged.

• Incident propane rate to incident xenon rate ratio is not constant.

• The parameters may be depend on the spectrum.

Are the dips possibly caused by bursts?

• It can be expected that the busts will cause the L1R1 coincidence rates increasing dramatically.

• The hypothesis should be rejected, since the L1R1 coincidence rates increasing are not be observed.

particle bursts within milliseconds?

• If the particles come in densely, that will also make the detector blind.

Good counts

particles

T. A. Jones inferred that these energetic events may be the consequence of particle showers produced in the RXTE spacecraft by cosmic rays.

•There are some indications that the events may caused by high energy particles.

Summary

• The light curve can be corrected with only the observed good rate even blow the time scale 1/8s.

• The burst hypothesis has been rejected, since the L1R1 coincidence rates increasing are not be observed.

• The millisecond dips may caused by high energy particles.