Characterization of Orbiting Wide-angle Light-collectors (OWL) By: Rasha Usama Abbasi.
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Transcript of Characterization of Orbiting Wide-angle Light-collectors (OWL) By: Rasha Usama Abbasi.
Characterization of Orbiting Wide-angle Light-collectors (OWL)
By:Rasha Usama Abbasi
OUTLINE Motivation Shower Generation and
Reconstruction OWL Simulation Study
Quality cuts Energy and Angular resolution Aperture calculations
OWL optical simulation and design Conclusion
Unsolved problems in Ultra-High Energy Cosmic Rays.
Motivation Origin of these rays. Acceleration mechanism. Determine Energies, chemical composition,
arriving direction . Discovering cosmic rays > Greisen-
Zatsepin-Kuzmin (GZK) cut off 6×1019 eV. Propagation through CMBR ?
Experiment
Fly’s Eye
AGASA
HiRes Auger OWL
Energy range (eV)
1017
6×1019
1018
1.5×1020
1017
4×1020
1019 1021
1019 1022
EnergyResolution
20 % 30 % < 20% 25% 14%
Aperture (km2-str)
40 @ 1020 eV
200 104 7000/array
3×106
Duty cycle 10% 100% 10 % 100% 10%
Events/year 0.4 2 10 70/array
3000
Comparison of UHECR Experiments
OWL Two satellites 1000 km height and 500 km
separation View common volume of the
atmosphere Tilted near the nadir point Obtain a large field of view
FOV with ~106 pixels, ~106 km2
sr
Inclined air shower
Shower Generation
Geometry generation Shower core : randomly simulated location could lie
outside the Field Of View (FOV) of the detector.
Shower direction: randomly simulated isotropic direction
Energy generation Energy is generated with several set of
fixed energies.
Shower generation
Profile generation Profile simulation is based on Gaisser-
Hillas (G-H) parameterization.
)exp()()( max)max(
max
max XX
XX
XXNN OXX
O
O
e
Xo :the point of the first interaction (g/cm2) simulated with an exponential function.
Xmax : the point of the maximum development of the shower (g/cm2) sampled from a Gaussian function.
: constant 70 g/cm2 .
: shower size at maximum.
)exp()()( max)max(
max
max XX
XX
XXNN OXX
O
O
e
maxN
Simulated event
Y-axis angular position vs. X-axis angular position
Pixel size is 0.07o , FOV on ground is 1km2/pixel
OWL Simulation Study
Goals of my study Aperture of the detector Number of events collected each year Energy and Angular resolution
Reconstruction Plane Reconstruction
Determines the Shower Detector (SD) plane that contains the detector and the shower track which depends on the triggered pixel direction.
Plane Reconstruction
N
ii
iiSnn
12
2 )ˆˆ(
n̂
in̂
2
i
iS
: normal to the plane.
:direction of the pixel
:number of photoelectrons triggering the pixel .
:angular error of the pixel ~ 0.07 0 .
Minimizing
Track Reconstruction Track
reconstruction SD’s depends on
triggered tube direction
Intersection between the SD planes of the
orbiting detectors.
Track Reconstruction fit for the 1st and 2nd
eye .
Time (micro seconds) vs. Θ (in degrees)
Profile Reconstruction
Profile reconstruction
Minimizing between the signal that is produced by the shower and detected in the pixels.
2
pfl
N
ii
p
i
m
i
pfl1
2
2
2 )(
Profile Reconstruction
N
ii
p
i
m
i
pfl1
2
2
2 )(
m
i
p
i
2
i
:number of photoelectrons detected per each pixel
:number of photoelectrons predicted by trial simulated event.
:error by adding Poisson fluctuation and ground light noise.
Observed shower profiles
Pe/ 1deg / m2 vs. Xmax (gm/cm2)
Reconstruction of the simulated event
Energy
Direction
Composition (Xmax)
Quality cuts
Optimization between best fractional energy, and angular error while maximizing a usable reconstructible aperture.
Energy and angular resolution
Quality cuts
Zenith angle of the shower > 930
Opening angle between the reconstructed SD’s planes >100
122 ndof
Quality cuts
Track length > 0.70
Geometry of the track
Photoelectron per good tube > 5.2
Low energy events and noise sources
Quality cut
Energy resolution vs. track length for a simulated shower
Energy resolution histogram 3×1019 eV
•Number of events vs. Fractional energy error 14% shift in the mean
Energy resolution histogram 1×1020 eV
•Number of events vs. Fractional energy error -2% shift in the mean
Energy resolution histogram 3×1020 eV
•Number of events vs. Fractional energy error -3% shift in the mean •Energy resolution gets better with higher energies
Angular resolution histogram 3×1019 eV
•Number of events vs. Angular error (deg)
•Half of the events are better than 0.9o
Angular resolution histogram 1×1020 eV
•Number of events vs. Angular error (deg)
•Half of the events are better than 0.6o
Angular resolution histogram 3×1020 eV
•Number of events vs. Angular error (deg)
• Half of the events are better than 0.3o
•Angular resolution also gets better with higher energies
Aperture calculation
To calculate the aperture we need to find.
First the Generation aperture 22RAgen
)(500 boundarylocationcoreofradiuskmR
srkmAgen
26105.2
Aperture calculation
eventsgenerated
eventstriggeredAA
gentrig #
#
Find the triggered aperture (Monte Carlo integration)
Find the reconstructed aperture
eventstriggered
eventstedreconstrucAA
trigrec #
#
Trigger Aperture
Aperture (×106 km2 sr) vs. Log(E(EeV)) Note: that it saturate at 2.4×106 km2 sr
Reconstruction Aperture
Aperture (106 km2 sr) vs. Log(E(EeV))
Large drop between the trigger and the reconstruction aperture at 3×1019eV because there is not enough photoelectrons to fit it to the G-H function (can not find minimum because of insufficient SNR).
Knowing that
The assumed flux j(E) is taken from Fly’s Eye spectrum, extrapolated to beyond 1020 eV.
)()( EjEATEN
Number of events per energy bin.
Fly’s Eye stereo spectrum
The number of events collected by the detector in a year duration (10% duty cycle) of time that holds energies between
Ei = 5 × 1019eV and Ef = 3 × 1020 eV
is equal to 2376 events.
fE
iE
dEEjEATN )()(
Number of events per energy bin.
Log(E(Eev))
#events Log(E(Eev))
#events
1.7 805 2.6 24
1.8 544 2.7 16
1.9 368 2.8 11
2.0 249 2.9 7
2.1 168 3.0 5
2.2 114 3.1 3
2.3 77 3.2 2
2.4 52 3.3 2
2.5 35 3.4 1
Number of events per energy bin.
From the simulation results
Angular resolution ( 0.3o 0.9o ) .
The directional accuracy of OWL is comparable to HiRes.
OWL does not provide us with an astronomical quality accuracy.
i.e. important for ID and sources.
From the simulation results
Although the threshold of the trigger aperture is ~ 1×1019 eV, the threshold of the reconstructed aperture is much higher ~ 4×1019 eV
High threshold is problematic: not knowing how the detector acts in low energies will compromise the accuracy of our experiment.
OWL optical simulation Construct a photon-by-photon ray
tracing simulation. Use the ray tracing simulation to
characterize the proposed system. Without a Schmidt corrector plate. With a Schmidt corrector plate.
Comparison.
OWL optics Wide angle viewing
camera (400 FOV)
Pixel size is 0.070, 4.4mm on the focal
plane with FOV of (1km2/pixel) on the ground.
OWL optics
Spherical mirror (7.1 m diameter , 6.0 m radius of curvature). Spherical focal plane surface ( 3.0
m radius of curvature, 3.15 m focal length and 2.3 m diameter)
3.0 m corrector plate with an aspherical front and a planer back surface .
Schmidt camera geometry
Lego plot (m) without the corrector, angle of incidence =00
~18 pixels across each side
Note: coma
Lego plot (m) without the corrector, angle of incidence =100
~18 pixels across each side Note: coma
Corrector plate The profile of the corrector plate is
T(r) : thickness of the corrector plate at a radial
distance r from the center f: focal length of the mirror n : the refractive index of the plate
Rd: the radius of the entrance from center
32
24
)1(32
)()0()(
fn
ArrTrT
22
3dRA
Lego plot (m) with the corrector plate, angle of incidence =00
The size of the center is comparable to a pixel
Lego plot (m) with the corrector plate, angle of incidence =100
The size of the center is comparable to a pixel
Number of particles/radial position vs. Radial position (without the corrector plate)
Entrance aperture
Number of particles/radial position vs. Radial position (with the corrector plate)
Angle Mean without corrector plate (mm)
Means with corrector plate (mm)
0o 7.3 5.5
5o 6.5 5.5
10o 8.0 5.5
15o 8.3 5.2
20o 8.3 5.3
Comparison of the Means for the image with and without the corrector plate
Optics Conclusions Corrector plate improves spot size and
quality:
Focal plane location is optimized by minimizing the spot size.
Improves spot size, suppression of coma.
The size of the spot is of the order of the pixel (when corrector is added)
Summary
OWL does not provide us with an astronomical quality.
The threshold of the reconstructed aperture is high ~ 4×1019 eV
Corrector plate improves the spot size and quality
Things to be done. Composition study Calculating the light loss (need to know
actual material used) Interface the optical simulation with the OWL simulation (Any volunteers??)