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Smoot Group Technical Report 2012-11-01.a_BG

Title: Prediction of UBAT Detection Rates and Estimation of UBAT Duty Cycle

Author: Bruce Grossan

Version Number: 1.0

Original Date: 2012-10-31

This Version Date: 2012-11-01

(SSL Technical Report number to follow)

<pre>

Summary: I estimate Rate_UBAT ~ 4.5 GRB/yr with large uncertainty * Assuming same detector response characteristics as Swift * Assuming Van Allen Belt Passage is similar to Swift SAA-grazing (orbit after SAA max) passage to determine duty cycle due to high background regions wiping out sensitivity. * Assuming FOV Scales as HCFOV and that our HCFOV is 1.17 Sr

1. Duty Cycle: Using Swift's Background, and assuming Swift's orbit after SAA max passage gives the same background as Van Allen Belt passage, I estimate a polar orbit X-ray instrument duty cycle to be around 19%, or around 20% of Swift's duty Cycle. The loss of duty cycle to flipping the orientation of the spacecraft, etc. has been ignored.

2. Field of View (FOV): Swift BAT's HCFOV is 1.4 Sr (bat_descrip.html). UBAT's HCFOV I have as 1.17 Sr (SEE NOTE 1 - important - this may be listed wrong in publication.)

3. Sensitivity, Collecting Area: From the Grossan Malaga presentation, assuming a 6.5 sigma rate trigger criteria, a 191 cm^2 EXACT Swift-BAT SCALED INSTRUMENT should measure 27 GRB/year. This includes nothing about background on-orbit, operational duty cycle, etc.

4. Final: Rate_UBAT/Rate_Swift ~ f(A,N(E))/f_Swift * FOV/FOV_Swift * DutyCycle/DutyCycle_Swift = 27 * 0.20 * (1.17 / 1.4 Sr) = 4.5 per yr. where f(A,N(E)) is the factor for the sensitivity (based on collecting area scaling) and spectral response of the detector; *I assumed that the sensitivity and spectral response of the UBAT was the same as Swift Because the method of calculating van allen belt passage background is uncertain, the duty cycle estimate could be off by 50%. For camparison, MAXI, on the 40 deg. inclined space station orbit, has frequent SAA passages and has a duty cycle of 50%. However, they do not have 4 Van Allen belt passages/orbit, so UFFO polar orbit should be _considerably_ worse, therefore, 19% is reasonable. ==================================================== I. Equation: —————— UBAT Rate may be determined from Swift Rates based on the following: R= f(a_detect,N(S(E)))/f_SWIFT * D(orbit)/D_swift * FOV/FOV_Swift * R_Swift (BG12) f(a_detect,N(S(E)))) is fraction of Bursts detectable with your sensitivity; a_detect = collecting area, N(S(E)) is spectral response of the instrument D=duty cycle including requirement for low background FOV= Field of View in which bursts may be localized (i.e. HCFOV) R_Swift is the Swift GRB rate In my Malaga presentation (BG12), I showed that for a 6.5 sigma trigger threshold, for 190 cm^2 collecting area, ASSUMING the same energy response, FOV, Duty cycle as Swift, 27 GRB would result. II. Estimate of the Duty Cycle: —————————————- On the maps of MeV electrons (Stassinopoulos, G., 1970, NASA SP-3054, Goddard Space Flight Center) You find typically for polar orbit: 1. a 20 degree wide band; passage time=20/360 *2* 90 min = 10 min ; 2. a 10 degree wide band ; passage time = 20/360 * 2*90 min= 5 min; 3. SAA (-95 to +55=140 deg. E-W; -65 to +10=75 deg. N-S); The contours of these regions are extremely tight; i.e. the density rises exponentially, and so the boundaries are very hard and all of these regions must be considered very high background, with complete loss of operation. IN ADDITION, there is time for activation and secondary emission background to decay -We can use actual Swift background to make an estimate of this decay time. *Here I base my analysis on a pass through Van Allen belts ~ Next Swift orbit AFTER passage through SAA max; with 1000 sec before useful data after exit of region. See Figure Attached.

The time for decay for grazing passage is ~ 650 s (=10.1 min). Decay time after passage through SAA is 2000 s. To take an optimistic view, limited operation might commence about 1000 s =16.7 min after passage through a high background (not SAA) region.

This gives us therefore: Good orbits: long. -180 to -100, +60 to +180 or 200/360 = 55% SAA Grazing Orbits, only about 15 deg. total = 4% ============⇒ Neglect. SAA Orbits - ~ 30 % include substantial passages

We can add up the times of passage plus the decay times for each high-background region. (With long decay, is there overlap? Consider S to N orbit at -120 long.(See Map Figure): N band stops at +60; S band starts at -76; so they are 44 deg. away. or 11 minutes away. For a 1000 s=16.7 min decay time, there is indeed overlap and we must write out sequence of passages, just below.)

A. Good orbit Calculating at -120 deg for “typical”, starting at +40 and moving North: data loss long,lat event ———– ——— —————–

  1. ——Moving North from +40

00 min -120,50 N belt entry 2.5 min -120,60 N belt exit 7.5 min -120,90 Decay (truncated)

  1. ———>Now moving South

4.75 min +60,71 Decay(trundated); enter N belt 2.75 min +60,60 exit N belt 16.7 min +60,-7 Decay ends 00 min +60, -45 enter S belt 4 min +60,-61 exit S belt 7.25 min +60,-90 Decay (truncated) 3.5 min -120,-76 decay(truncated); enter S belt 3.75 min -120,-61 exit S belt 16.7 min -120,+5.8 Decay Ends


69.4 minutes ==⇒ Duty Cycle of 23%

(Swift Duty Cycle is > 90% as SAA passages are not so frequent, and the Van Allen Belts are never touched, inclination =20.5 deg.)

B. SAA passage orbits about 30% of polar orbits hit the SAA. This is typically 45 deg. N-S Since (going S to N) there are around 52 deg = 13 minutes to the next belt, and since the decay time is 33 min, there is no time on the SAA hemisphere that will be useful.

data loss long,lat event ———– ——— —————–

  1. ——Moving North from -90

00 min -60,-90 Decaying ….. S belt entry …. S belt exit ….decay …. SAA entry … SAA exit … decay … N belt entry … N belt exit … 45 min -60,+90 decay (truncated) —–> hemisphere Completely lost

  1. ———>Now moving South

4.5 min +120,+72 Decay(trundated); enter N belt 2.5 min +60,+62 exit N belt 16.7 min +60,-4.8 Decay ends 00 min +60, -43 enter S belt ———→ Here was the only useful time, 38.2 deg (9.55 min) ….. exit S belt, decay 11.75 min -120,-90 Decay truncated


80.45 min =======⇒ Duty cycle of 11%


Total Duty Cycle ~ .7 * .23 + .3 *.11 = 19.4%

D/D_swift ~ .20 using 95% for Swift

Sanity Checks: i) MAXI,in a 40 deg. inclination orbit on the ISS, in http://arxiv.org/pdf/1102.0891v1.pdf, shows an elevation of count rate of > 100X when it touches the Van Allen Belts and the SAA (See figure). ii) Motoko Serino of the MAXI team told me at the malaga conference that MAXI has a 50% duty cycle from SAA passages (though they have data on Van Allen best grazing passages, MAXI rarely passes through the belts). Therefore a polar orbit duty cycle must be much, much worse, because you add the Van Allen Belt Passages and decay time.

Next Step: Try to get data from MAXI nearest approach to Van Allen Belt. ISS has inclination of 51.6 deg so grazes the South Belt.


BAT_vs_taftersaa.png THE ABOVE FIGURE IS NOT ORIGINAL WORK AND MUST BE REFERENCED AS The Ajello+08, Astrophysical Journal 689 (2008) 666<Screen Shot 2012-10-31 at 4.28.04 PM.png> THE ABOVE FIGURE IS NOT ORIGINAL WORK AND MUST BE REFERENCED AS Stassinopoulos, G., 1970, NASA SP-3054, Goddard Space Flight Center

e- counts

THE ABOVE FIGURE IS NOT ORIGINAL WORK AND MUST BE REFERENCED AS Sugizaki, M. et al. 2011PASJ…63S.635S

Notes: NOTE 1 Re: Solid Angle - I have the HCFOV = 68 Deg. X 68 Deg, from the following references: (BGPC1) Email Paul Connell to Bruce Grossan PST 2012 feb 22 03:56. (BGPC2) Email Paul Connell to Bruce Grossan PST 2012 feb 22 03:42; PC said mask-detector separation is 0.5 + 280+D mm, D=1.0-2.0 mm, TBD; I used 1.5 mm above. (BGPC3) I used Tan theta_hcfov/2 = mask_width/2/mask_detector_separation and mask_detector_separation 282 mm (incl. absorption length).

UBAT_DAU.ppt by Victor, and verified in Heuijin Lim's email of 10/1/2010, has 65.2deg. X65.2 deg.= 1.18 Sr.

* Note that 43.2degX43.2 deg is given in Proc_SPIE_JEKIM_V103.doc = 0.54 Sr. * Please check these values and use the right one in publication.*** ←pre>

public/grbratepredict.txt · Last modified: 2021/01/12 00:50 (external edit)