The Dead time correction for the light curve with millisecond time bin
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The Dead time correction for the light curve with millisecond time bin
Liang, Jau-shian
Institute of Physics, NTHU
2006/12/5
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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
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Outline
• Introduction• Recovery method
• Discussion
• Summary
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Proportional counter
A proportional counter is a measurement device to count particles and photons of ionizing radiation and measure their energy.
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Cross section view of one PCA detector
collimators
propane layer
xenon layer 1xenon layer 2
xenon layer 3
xenon veto layer
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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.
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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
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• 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.
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Good and Coincidence rates observedfrom a burst of J1744-28.
(5 pcu)
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Remaining rate vs Good rate for a burst from J1744-28
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The distribution of time intervals between adjacent events
Dead time ~ 9 s
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L1 + R1
L1R1
L1
R1
14 incident photons
L1 + R1
L1R16 good event
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jjj
ii Dtout
outin
1
jjj
ii Dtin
inout
1
Dead time correction
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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
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1
Coincidence timing window
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• 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
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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
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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
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)(0
0 XeeXe )(220
0
2
1 XeeXe Xee 0 : :
0 photon : 1 photon : 2 photons
• The Poisson probability distribution should be considered.
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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.
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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.
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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.
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Good
Remaining L1&R1
Output rates vs. incident rates
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Estimate and subtractVP, 2LLD, 0LLD
Caculate dead time
X’out = Xout ?
Adjust Xin
Output Xin
Yes
No
Xin
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Prediction rates compare with slew data
Good
Remaining(data)Remaining(prediction)
VP(data)VP(prediction)
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Prediction rates compare with data
Remaining(data)
Remaining(prediction)
VP(data)VP(prediction)
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Light curve
Corrected light curve
Some results
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Light curve
Corrected light curve
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Discussion
• the advantages and weaknesses
• Are the dips possibly caused by bursts?
• particle bursts within milliseconds?
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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
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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.
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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.
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particle bursts within milliseconds?
• If the particles come in densely, that will also make the detector blind.
Good counts
particles
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T. A. Jones inferred that these energetic events may be the consequence of particle showers produced in the RXTE spacecraft by cosmic rays.
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•There are some indications that the events may caused by high energy particles.
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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.