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, 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 1 xenon 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 observed from a burst of J (5 pcu)

Remaining rate vs Good rate for a burst from J

The distribution of time intervals between adjacent events Dead time ~ 9  s

L1 + R1 L1R1 L1 R1 14 incident photons L1 + R1 L1R1 6 good event

Dead time correction

the incident rate on each signal chain R j 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

Blank sky #2 (Counts/s/PCU) Good VP Remaining LLD LLD LLD VX44025 VLE10090

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=2  Xe L1=XeR1=Xe

:: 0 photon:1 photon:2 photons The Poisson probability distribution should be considered.

L1R1VP L1R1 R1L1 R1VP L1VP VPR1 VPL1 0LLD(R1) 0LLD(L1) 0LLD(VP) The probability of that the photon does not exist should also be considered.

The prediction of the coincidence rate The parameters provided by K. Jahoda et al. are pressumed correct.

5s5s 9s9s 4s4s 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 (~9  s) following the first event of the coincident set. ( D. Wei, 2006 ) The dead time window is accounted for 4  s.

Good Remaining L1&R1 Output rates vs. incident rates

Estimate and subtract VP, 2LLD, 0LLD Caculate dead time X’ out = X out ? Adjust X in Output X in Yes No X in

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.