Event Analysis for the Gamma-ray Large Area

Space Telescope

Robin Morris, RIACS

Johann Cohen-Tanugi INFN, Pisa

Why study gamma-rays?• Gamma-rays are produced by some of the highest energy

events in the universe, events that are not yet fully understood.

• Study of these events is critical to understanding the origins and evolution of the universe.

• The distribution of gamma-rays (both across the sky and in terms of energy) can confirm theories about the early universe.

• The Large Area Telescope is designed to map the incidence of gamma-rays.

• We are developing a Bayesian methodology for the analysis of the instrument response.

(background - distribution of gamma-rays from EGRET)

The Large Area Telescope (LAT)

• For each incident gamma ray photon, we want to know its incident direction and energy

• The LAT has three components:– Anticoincidence detector -

eliminates responses due to incident charged particles

– Array of conversion towers - the heart of the detector

– Imaging calorimeter - measures the residual energy in the particles generated by an incident gamma ray photon

How the conversion towers work• Alternating conversion and

detection layers• Incident gamma rays are

converted into electron/positron pairs

• The electron and positron cascade through the detector– Undergo secondary scattering– Produce further electrons and

photons

• Each time they cross a detection layer, they trigger the silicon microstrip detectors, producing a readout

• The output from an event is a set of (x,y,z) positions of the silicon microstrips that were triggered (+ calorimeter response)

Examples (from the GLEAM simulator)

200MeV photon• blue line - incident photon and

electron/positron• orange - microstrip detectors• blue cubes - calorimeter• green - anticoincidence detector

points to note:• inherent ambiguity in the number of

particles at each layer• significant secondary scattering• production of secondary electrons

(hits to left of main track)• anticoincidence detector fired by

secondary electrons• opening angle depends on energy

GLEAM - GLAST Event Analysis Machine

Examples (from the GLEAM simulator)

100GeV photon

• secondary photons are suppressed in the figure (to enable the secondary electron tracks to be seen)

• very small opening angle• huge number of secondary

electrons (black “cloud”)• lots of firing from the secondary

electrons• firings well away from the main

track (from secondary photons converted into charged particles)

Physics ProcessesPair production• conversion of gamma ray photons into

electron/positron pairs

multiple coulomb scattering• charged particles are deflected on interacting

with (primarily) atoms

positron anihilation• positron + electron => photons

ionisation• liberation of electrons from atoms by the transfer

of (at least) the binding energy from a particle to the electron

bremsstrahlung• radiation emitted by a charged particle undergoing acceleration (typically deceleration when passing through the field of atomic nuclei)

photoelectric effect• ejection of electrons from the surface of material by incident photons

compton scattering• transfer of energy from photons to electrons; may liberate bound electrons

Pair Production - energy and angles

• The tungsten conversion foils are 0.105mm thick, resulting in a conversion probability of ~2% for photons of 1GeV

• The lowest 4 foils are 0.723mm thick (~10% conversion probability)

• Compromise between pair production and multiple scattering and other physics processes that hide the primary event

• The energy of the incident photon is divided between the electron and positron

• The electron/positron angle depends stochastically on the electron/positron energy

photonE

electron

Ee

positron

Ep

e

p

Pair Production - energy and angles

• Distribution of energy split between electron and positron as a function of photon energy

• Distribution of electron/positron angle

where u is distributed as above

€

φ±=mec

2

E±

u

Other electron/positron processes

Currently we include

multiple scattering ionisation bremsstrahlung

Using the Geant4 physics simulation toolkit, we simulate the interaction of electrons with the tungsten foils, and estimate the scattering distributions

Apart from the tails, the distribution can be approximated by a gamma distribution

We currently neglect other physics processes/particles

Simplified Simulation

Using the physics distributions described so far, we implemented a simulation of the detector• uses the LAT geometry• only includes the primary electron and positron• doesn’t include energy deposition by particles as they pass through matter

Over-simplified Simulation

• Reduce the detector to 2D• Keep the physical distributions

–conversion–energy distribution–opening angle–scattering distributions

- neglect all other physics processes

Probabilistic event analysis

Incorporate data one layer at a time:

• p()

• p( | d1) p(d1 | )p()

• p( | d1,d2) p(d2 | )p(d1 | )p()

• p( | d1,d2,…dN)

p(dN | )p(dN-1 | ) … p(d2 | )p(d1 | )p()

Probabilistic event analysis

Incorporate data one layer at a time:

• p()

• p( | d1) p(d1 | )p()

• p( | d1,d2) p(d2 | )p(d1 | )p()

• p( | d1,d2,…dN)

p(dN | )p(dN-1 | ) … p(d2 | )p(d1 | )p()

Probabilistic event analysis

Likelihood:

• p(d | )

• This is zero-one - if the trajectory described by triggers all the detectors that fired, then p(d | )=1, else p(d | )=0

• This makes applying MCMC directly somewhat difficult.

• This is a simplification of the likelihood– some detectors fire spuriously– some particles pass through gaps between microstrips– information regarding the particles energy

Computation• The basic idea:

– run the forward simulation a very large number of times, keeping those runs which triggered the same detectors that were triggered in the event we are analysing

– compute the mean, variance etc of the photon direction and energy from the runs that are retained

– clearly this is computationally infesable (and becomes more so the more physics processes we include)

• Instead:

– use ideas from sequential importance sampling to only generate runs that with high probability trigger the detectors that fired

– non-parametric representation of the distribution that allows for tracking of multiple hypotheses

ComputationA combination of ideas from Particle Filters and MCMC

• represent p( | {d}) by a set of particles

• propagate the set of particles down the stack– use importance sampling distributions that generate trajectories

that intersect, with high probability, with the detectors that fired (0-1 likelihood)

– weight the particles by the ratio of the physics distribution to the importance sampling distribution

– re-sample the set of weighted particles

• apply mcmc steps to the particles after each layer– because the event has no dynamics between layers (the photon

angle does not change), “particle starvation” can be a problem

Over-simplified simulation

• Only analyse the incident photon angle and position• Also estimate the “nuisance” variables - the vertex position (shown) and scattering angles at

each layer (not shown)• Assume the energy split between the electron and positron is known (see later)

Over-simplified simulation

• The energy split is almost equal, so the “opening angle” is symmetric (107:93MeV)• Because the positron (blue) is scattered much less, a good fit to the data is a slightly offset

photon angle, with more even scattering down the two trajectories

Over-simplified simulation

• Very small opening angle, so energy split is less important (actual split is 154:46MeV)• Estimate is unbiased, but the remaining uncertainty is larger

Simplified Simulation

• Show the results for the estimate of the photon angles for the first four levels

(after that particle starvation became an issue)

Future work• Add more physics

– add the analysis of the energy of the photon, and consider also the deposition of energy by the particles as they interact with the detector

– addition of the processes which produce secondary particles will complicate the analysis significantly

• the dimensionality of the particles will vary

• Improve the likelihood:

– currently we use a simple 1-0 likelihood

– model the physics of the silicon microstrip detectors• the microstrips give information about the quantity of charge deposited• the number of strips that fire depends on the energy of the incident

particles

Future work• Analysis of the energy

– the angle distribution is highly dependent on the energy split between the electron and positron

photon200MeV

electron80MeV

positron120MeV

e

p

photon200MeV

electron190MeV

positron10MeV

e p

Conclusion

“If you have to use statistics, go back and design the experiment properly”

Lord Rutherford

“If you have to use statistics, think about the statistics at the same time as you design the experiment”

Me