GLAST DC2 Kickoff 1

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Algorithm for LAT On-board / On-ground GRB
Trigger and Localization Jay Norris
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The Detection Problems - 1

• On-ground Detection
• Near threshold GRB signal (5-10 ?s, 40 s, gt 50
  MeV), with 2 Hz bckgnd rate ? 1/300 count ?-1 ( ?
  sq. deg.), or 2 counts in 15 radius.
• For extended emission ( 103 s) in a bright
  burst, the corresponding bckgnd total is 50
  counts, perhaps comparable to the signal.
  Recourse more severe cuts, probably removing
  more low-energy signal. Use Likelihood.
• Notes
• 2 Hz bckgnd means total sky rate sources
  extragalactic galactic diffuse residual
  particle bckgnd. (Possibly higher with looser
  cuts for maximum GRB signal.)

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The Detection Problems - 2
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Straightforward LAT GRB Detection Localization
Algorithm

• Philosophy (On-ground analysis)
• Usually, negligible bckgnd and only one source
  (the GRB)
• High-energy ?s provide accuracy, but are less
  numerous.
• More low-energy ?s, and they are bunched in
  time.
• ? Optimal algorithm should be unbinned in time
  (thereby exploit bunching) and in space (exploit
  high-energy ?s).
• Starting from all-sky sample, algorithm should
  be able to bootstrap GRB position with very few
  false positives.
• This same conclusion applies for on-board
  trigger/localization, but it is constraint of GBM
  position (rather than ground filters) that lowers
  the bckgnd rate sufficiently, AND pinpoints GRB
  onset (thereby greatly reducing Ntrials).

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?s distances ?t intervals
Swift/BAT z 0.547
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Algorithm

• An N-event sliding window is used as the
  bootstrap step in searching for significant
  temporal-spatial clustering. Compute the Log
  Joint (spatialtemporal) likelihood for the
  tightest spatial cluster of events in the
  temporal sliding window
• Log(P) ? Log 1 cos(di) /
  1 cos(?max)
• ? Log 1 exp(-R?ti)
  
• Log(P) is measured against the near real-time
  bckgnd rate (R). Trigger threshold is also set as
  a function of the bckgnd, such that high GRB
  trigger efficiency is realized (events w/ 5-10
  ?s detected), and formal expectation for false
  positive lt 10-6/day.
• Localization algorithm collects all events
  between 1st and last windows which trigger within
  a time limit, 150 s computes an
  energy-weighted centroid. Probable particle
  events are IDedby virtue of difference between
  actual and predicted distances from centroidand
  then deweighted. Convergence one iteration.

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Implementation

• On-board Trigger and Localization Sequence
• Send LAT telemetry event stream to GRB processor.
• Apply additional filters, reduce background rate
  to 60 Hz.
• Run spatial/temporal sliding-window
  trigger/localization algorithm.
• Option to utilize GBM trigger time and position
  to reduce windows.
• Telemeter localization and other GRB information
  to ground.
• Option to send alert message with 10 highest
  energy GRB events to ground for rapid
  localization analysis.

• Some Adjustable/Variable Parameters
• On-board / On-ground filters
• Nevents in sliding window(s) Nmove events per
  trial
• GBM positional uncertainty
• Inclusion radius (? threshold energy) for GRB ?s
• This trigger-active search interval
• Trigger threshold(s)
• Nsigma distance threshold for deweighting
  putative particle events

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Bckgnd rate 32 Hz, 60-event sliding window
Burst 2
Localization from 10 events telemetered for
ground analysis. Events IDed using pseudo
on-board recon, and GBM position.
Localization from all 129 events IDed on ground
(results same, w/ or w/o GBM position) ?Ground
1/2 ?Alert
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Bckgnd rate 32 Hz, 60-event sliding window
Burst 3
Localization from 10 events telemetered for
ground analysis. Events IDed using pseudo
on-board recon, and GBM position.
Localization from all 27 events IDed on ground
(results same, w/ or w/o GBM position) ?Ground
1/2 ?Alert
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Error Estimation Energy Weighting
dumbck where(distset gt 2.photerrs, nbck) if
(nbck gt 0) then photerrs (dumbck)
distset(dumbck) W 1. / photerrs W2 W2 Y
W2 thetaset X W2 phiset
sin(thetaset) W2tot total(W2) Xavg total(X)
/ W2tot Yavg total(Y) / W2tot One
sqrt(Nphots / (Nphots-1)) Fact sqrt(max(W) /
total(W)) errX One sqrt( total( ((X/W2 -
Xavg)W2)2) / W2tot2 ) Fact errY One
sqrt( total( ((Y/W2 - Yavg)W2)2) / W2tot2 )
Fact avgtheta Yavg avgphi Xavg /
sin(avgtheta) errtheta errY errphi errX /
sin(avgtheta) errrho sqrt(errX2 errY2)
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Comparison Ground vs. Alert vs. On-board
Ground ?true 0.5-1 ? Alert ?true 0.5 ?
On-board ?true
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Summary

• Algorithm unbinned in time, space utilizes most
  of the available information On-board or
  On-ground. Fast.
• Probably sufficient for IDing photons in
  bursts of lt 100 s duration. Extended emission
  ( 103 s) use Likelihood.
• GBM position and additional on-board filters
  necessary to reduce bckgnd rate, enable a clean
  LAT localization.
• Alert to ground containing 10 highest energy
  LAT ?s for quicklook analysis probably
  better accuracy than on-board.

• Lest we forget The smallest possible LAT
  localization, delivered quickly to the community,
  means that larger ground-based telescopes can
  participate in afterglow searches at earlier
  epochs. Even past the Swift era, it is likely
  that spectroscopic redshifts will still be
  superior to pseudo redshifts (presently very
  immature) obtained from burst prompt emission
  properties. Know redshift ? Know energetics.