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 6×10 19 eV. Propagation through CMBR ?

ExperimentFly’s Eye AGASAHiResAugerOWL Energy range (eV) × × × Energy Resolution 20 %30 %< 20%25%14% Aperture (km 2 -str) eV / array 3×10 6 Duty cycle10%100%10 %100%10% Events/year /array3000 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 ~10 6 pixels, ~10 6 km 2 sr Inclined air shower

owl Large collection aperture 3×10 6 km 2 sr events/year with energies > 3×10 19 eV. Challenging aspect is the need to keep simple compact configuration.

Shower Generation. Geometry generation. Energy generation. Profile generation.

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.

X o :the point of the first interaction (g/cm 2 ) simulated with an exponential function. X max : the point of the maximum development of the shower (g/cm 2 ) sampled from a Gaussian function. : constant 70 g/cm 2. : shower size at maximum.

Parameters X max Gaussian function parameters. Sigma = Elongation Rate (ER) = X max mean 18 )= Mean = X max + ER * (log10(energy) ) X o : Exponential function parameters. Mean = 35.0 Sigma = 35.0

Simulated event Y-axis angular position vs. X-axis angular position Pixel size is 0.07 o, FOV on ground is 1km 2 /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 : normal to the plane. :direction of the pixel :number of photoelectrons triggering the pixel. :angular error of the pixel ~ 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 1 st and 2 nd 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.

Profile Reconstruction :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 / m 2 vs. X max (gm/cm 2 )

Reconstruction of the simulated event Energy Direction Composition (X max )

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 > 93 0 Opening angle between the reconstructed SD’s planes >10 0

Quality cuts Track length > 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 3×10 19 eV Number of events vs. Fractional energy error 14% shift in the mean

Energy resolution histogram 1×10 20 eV Number of events vs. Fractional energy error -2% shift in the mean

Energy resolution histogram 3×10 20 eV Number of events vs. Fractional energy error -3% shift in the mean Energy resolution gets better with higher energies

Angular resolution histogram 3×10 19 eV Number of events vs. Angular error (deg) Half of the events are better than 0.9 o

Angular resolution histogram 1×10 20 eV Number of events vs. Angular error (deg) Half of the events are better than 0.6 o

Angular resolution histogram 3×10 20 eV Number of events vs. Angular error (deg) Half of the events are better than 0.3 o Angular resolution also gets better with higher energies

Aperture calculation To calculate the aperture we need to find. First the Generation aperture

Aperture calculation Find the triggered aperture (Monte Carlo integration) Find the reconstructed aperture

Trigger Aperture Aperture (×10 6 km 2 sr) vs. Log(E(EeV)) Note: that it saturate at 2.4×10 6 km 2 sr

Reconstruction Aperture Aperture (10 6 km 2 sr) vs. Log(E(EeV))

Large drop between the trigger and the reconstruction aperture at 3×10 19 eV 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 eV. 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 E i = 5 × eV and E f = 3 × eV is equal to 2376 events. Number of events per energy bin.

Log(E(Eev)) #events Log(E(Eev)) #events Number of events per energy bin.

From the simulation results Angular resolution ( 0.3 o 0.9 o ). 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 ~ 1×10 19 eV, the threshold of the reconstructed aperture is much higher ~ 4×10 19 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 (40 0 FOV) Pixel size is , 4.4mm on the focal plane with FOV of (1km 2 /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

Without a corrector The steps of the simulation Given the incident ray direction, and a simulated random position. Calculate the point of incidence with the mirror and the direction of the reflected ray that did not intersect with the focal surface.

Without a corrector Calculate the point of interaction between the reflected ray and the focal surface. Looping over the previous process we obtain the shape and the size of the reflected image (The Spot )

Lego plot (m) without the corrector, angle of incidence =0 0 ~18 pixels across each side Note: coma

Lego plot (m) without the corrector, angle of incidence =10 0 ~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 R d : the radius of the entrance from center

Lego plot (m) with the corrector plate, angle of incidence =0 0 The size of the center is comparable to a pixel

Lego plot (m) with the corrector plate, angle of incidence =10 0 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)

AngleMean without corrector plate (mm) Means with corrector plate (mm) 0o0o o5o o o o 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 ~ 4×10 19 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??)