1. Stereo Spectrum of UHECR Showers at the HiRes Detector  The Measurement Technique  Event Reconstruction  Monte Carlo Simulation  Aperture Determination  Preliminary Results The 28 th International Cosmic Ray Conference August 2, 2003 R. Wayne Springer, for the HiRes Collaboration University of Utah

2. The Air Fluorescence Technique ShowerDevelopment AtmosphericMonitoring Detector Response and Calibration Need to understand  Shower Development  Atmospheric Monitoring  Detector Response and Calibration Need to KnowFluorescenceYield

3. The Measurement of the Energy Spectrum Important to understand the following…  Energy Measurement  Detector Calibration  Shower Geometry (STEREO HELPS!!)  Atmospheric Conditions  Aperture  Detector Calibration  Trigger Thresholds  Reconstruction  Atmospheric Conditions Note that the atmosphere has greatest effect on the aperture at enegies below 10 EeV!!!! Need to ensure that there are no tails in Energy distribution!!!!

4. Stereoscopic Event Reconstruction Determination of Shower Geometry The geometry of the air shower is determined simply by finding the intersection of the shower- detector planes Reduced Uncertainty in Energy Determination

5. Stereoscopic Event Reconstruction Determination of shower profile ➢ HiRes-I binning ➢ 1.5 degree angular bins ➢ Ray tracing to determine detector acceptance ➢ HiRes-II binning ➢ Time based binning ➢ Measure intensity and direction of light spot every 100ns ➢ Ray tracing to determine detector acceptance ➢ Profile fit ➢ Signal fit to shower profile function ➢ Cerenkov correction calculated based on geometry. ➢ dE/dX determined from fit ➢ Primary particle total energy calculated using “standard” relationship between EM and total energy.... Depth [g/cm 2 ] Signal

6. Stereoscopic Event Reconstruction Energy Resolution ➢ Choose best of HR1 or HR2 ➢ Basic cuts: ➢ Profile chi2/d.o.f<15 ➢ Nbin>3 ➢ Xmax<Xbottom+100g /cm ➢ Xmax>Xtop-300g/cm ➢ Tight cuts ➢ Energy uncertainty/energy <5.0 ➢ Xbottom-Xtop>100 g/cm ➢ Xmax>Xtop-200 g/cm ➢ 400 g/cm <Xmax<1200 g/cm ➢ Zenith angle<70 degrees ➢ Cuts need to OPTIMIZE Energy and Statistics HR2 no cuts Entries=8828 RMS=57.9 Sigma=15.8 Entries=8758 RMS=62.5 Sigma=25.5 Entries=8006 RMS=62.3 Sigma=25.5 Entries=7002 RMS=62.3 Sigma=25.5 HR1 no cuts Basic Cuts Tight Cuts Num events % fractional resolution

7. Stereoscopic Event Reconstruction Data/Monte Carlo Comparison ➢ Reweight MC events to agree with Data energy distribution ➢ 76-24 mixture of proton and iron events to get agreement with data Xmax distribution ➢ Still unable to model tails in Xmax distribution perfectly ➢ Compare MC and data distributions for other observables using reweighted MC events.... Log Energy Number events MC/Data Ratio

8. Stereoscopic Event Reconstruction Data/Monte Carlo Comparison Zenith and Azimuth angle distributions MC/Data Ratio Number events

9. Determination of Aperture ➢ Aperture=  thrown area*  where  (E)=Nrecon/Nthrown is the efficiency to reconstruct thrown events at Energy E. ➢ Generate Events using both a 1/E and a 1/E3 spectrum to obtain sufficient statistics at both low and high energies. ➢ Mix Proton and Iron events to obtain xmax distribution of data ➢ Calculate both thrown energy and reconstructed energy apertures Nsuccess v. logE Efficiency v log E Aperture v log E Nthrown v. logE Nsuccess v. logE Nthrown v. logE Aperture v log E Efficiency v log E 1/E thrown spectrum 1/E3 thrown spectrum

10. HiRes Stereoscopic Aperture ➢ Calculated for “average atmospheric conditions” of VSH=1.0km and HAL=25.0km ➢ 76% Proton 24% Iron mixture ➢ Aperture exceeds 10,000 km2-sr above 100 EeV Km2-sr Aperture v log Ethrown Mix Aperture v log Erecon Mix Log E(eV) Km2-sr

11. HiRes Stereo Flux Measurement Energy Distributions Good Weather cuts 1006 hours 1588 events NoWeather cuts 1291 hours 1944 events Number events Log E(eV)

12. Measuring The UHECR Energy Spectrum ➢ Count Particles vs. Energy ➢ Observe UV fluorescence signal ➢ Determine Geometry of shower ➢ Bin Shower profile and reconstruct energy ➢ “Fill histogram” Number v Energy ➢ Determine Exposure vs. Energy ➢ Determine detector on-time ➢ Determine aperture for each detector configuration ➢ Divide Count/Exposure  Energy Spectrum

13. HiRes Stereo Flux Measurement Energy**3 * Flux HiRes Stereo Spectrum is consistent With Monocular Spectrum Change in spectral index weakly observed at an energy of 10 18.6 eV. STATISTICAL ERRORS ONLY Log E(eV) E 3 J(E)

14. Conclusion ● Still evaluating sources of systematic uncertainty – Energy scale – Atmospheric effects – Fluorescence Yield ● Indication of structure in spectrum – Ankle at ~10 18.6 eV ● Need More Statistics – HiRes is still collecting data…. – GZK effect????

15. HiRes Stereo Flux Measurement Fit to Energy Distribution Number predicted events Log Energy For 1000 hours Flyseye spectrum prediction Of 3 events at 100 EeV !!!!

16. HiRes Stereo Flux Measurement Fit to Energy Distribution

18. HiRes Stereo Flux Measurement Energy**3 * Flux HiRes Stereo Spectrum is consistent With Monocular Spectrum Change in spectral index weakly observed at an energy of 10 18.6 eV. STATISTICAL ERRORS ONLY

19. HiRes Stereo Flux Measurement Aperture and Flux

20. Stereoscopic Event Reconstruction Data/Monte Carlo Comparison Rp distributions