Fitting the HiRes Data

1. Fitting the HiRes Data Douglas Bergman Rutgers University 28 April 2005

2. The HiRes Data • Here’s the HiRes spectra Aspen Workshop

3. The HiRes Data • Here’s the HiRes spectra • Actually fit to numbers of events using calculated aperture • Use binned maximum likelihood method • Two empty bins for each of HiRes-I and HiRes-II Aspen Workshop

4. c2 = 114/37 g = -3.12(1) Features • What are the features of the spectrum? • Fit to broken power law • No BP, bad fit Aspen Workshop

5. c2 = 46.0/35 g1= -3.31(3) log10E = 18.45(2) g2= -2.91(3) Features • What are the features of the spectrum? • Fit to broken power law • No BP, bad fit • 1 BP, Ankle Aspen Workshop

6. c2 = 30.1/33 g1= -3.32(4) log10E12 = 18.47(6) g2= -2.86(4) log10E23 = 19.79(9) g3= -5(1) Features • What are the features of the spectrum? • Fit to broken power law • No BP, bad fit • 1 BP, Ankle • 2 BP, HE suppression • 11 events above break • Expect 28 with red line • Poisson prob. 2.4x10-4 • Is the HE suppression the GZK? Aspen Workshop

7. Integral Spectra • One measure of the energy of the suppression is E½ • Due to Berezinsky • Where integral flux is half of expected with no suppression Aspen Workshop

8. Integral Spectra • One measure of the energy of the suppression is E½ • Due to Berezinsky • Where integral flux is half of expected with no suppression • Use red line extension of broken power law as no-suppression expectation Aspen Workshop

9. Integral Spectra • One measure of the energy of the suppression is E½ • Due to Berezinsky • Where integral flux is half of expected with no suppression • Use red line extension of broken power law as no-suppression expectation • Find log10E½ = 19.77+0.15-0.06 • Berezinsky et al, predict log10E½ = 19.72 for the GZK Aspen Workshop

10. The HiRes Data (again) • Want to fit the HiRes spectra… Aspen Workshop

11. The HiRes Data (again) • Want to fit the HiRes spectra… • And also take into account the HiRes composition measurements QGSJet protons QGSJet Iron Aspen Workshop

12. The HiRes Data (again) • Want to fit the HiRes spectra… • And also take into account the HiRes composition measurements • Make one simplifying assumption: • Composition determines origin • Iron is Galactic • Protons are Extragalactic • Use fit to composition • But assume all protons at 100 EeV • Fit spectrum by varying extragalactic model, galactic spectrum determined from this “Toy Model” assumption Aspen Workshop

13. Uniform Source Model (XG) • Assume uniform sources of extragalactic protons • Identical spectral slope g • Uniform luminosity density at any epoch • Luminosity density can vary as (1+z)m • Protons lose energy • Average energy loss rate from Berezinsky et al Aspen Workshop

14. Uniform Source Model (XG) • Assume uniform sources of extragalactic protons • Identical spectral slope g • Uniform luminosity density at any epoch • Luminosity density can vary as (1+z)m • Protons lose energy • Average energy loss rate from Berezinsky et al • Pion production causes proton to loose a large fraction of its energy • Have to use MC for this process Aspen Workshop

15. Uniform Source Model (XG) Z=0.0004 Aspen Workshop

16. Uniform Source Model (XG) Z=0.001 Aspen Workshop

17. Uniform Source Model (XG) Z=0.004 Aspen Workshop

18. Uniform Source Model (XG) Z=0.01 Aspen Workshop

19. Uniform Source Model (XG) Z=0.04 Aspen Workshop

20. Uniform Source Model (XG) Z=0.1 Aspen Workshop

21. Uniform Source Model (XG) Z=0.4 Aspen Workshop

22. Uniform Source Model (XG) Z=1 Aspen Workshop

23. Uniform Source Model (XG) Z=4 Aspen Workshop

24. Uniform Source Model (XG) • All the shells together • g = 2.4 • m = 2.5 • Each energy dominated by different range in z • Given energy is somewhat flat in z up to maximum • Allows one to do cosmology Aspen Workshop

25. Uniform Source Model (XG) • All the shells together • g = 2.4 • m = 2.5 • Each energy dominated by different range in z • Given energy is somewhat flat in z up to maximum • Allows one to do cosmology • Sum of shells gives spectrum for fitting Aspen Workshop

26. Uniform Source Model (XG) • All the shells together • g = 2.4 • m = 2.5 • Each energy dominated by different range in z • Given energy is somewhat flat in z up to maximum • Allows one to do cosmology • Sum of shells gives spectrum for fitting • Actually need finer set of shells Aspen Workshop

27. Best USM Fit to HiRes • Fit USM varying m and g • g = 2.38 • m = 2.55 • Galactic spectrum falls steeply above 100 PeV Extragalactic Galactic Aspen Workshop

28. Best USM Fit to HiRes c2 Contours for Spectrum Fit • Fit USM varying m and g • g = 2.38 • m = 2.55 • Galactic spectrum falls steeply above 100 PeV • Statistical Uncertainty • g = 0.035 • m = 0.25 Aspen Workshop

29. Best USM Fit to HiRes c2 Contours for Spectrum Fit • Fit USM varying m and g • g = 2.38 • m = 2.55 • Galactic spectrum falls steeply above 100 PeV • Statistical Uncertainty • g = 0.035 • m = 0.25 • Systematic Uncertainty • g = 0.03 • m = 0.3 Aspen Workshop

30. Where the Fit Works Well… • The fit works best in the Ankle region • Understand the Ankle as coming from e+e- pair production energy losses • Spectral slope (g) mostly determined by rise from Ankle (HiRes-I dominates) • Evolution (m) determined by fall into Ankle (HiRes-II dominates) Extragalactic Galactic Aspen Workshop

31. …and Where it Doesn’t • GZK region • Fit is above the data • Perhaps… • Some sources have Emax of order GZK threshold • 2nd Knee Region • There isn’t one • Perhaps… • The input spectral slope changes? • Evolution of sources changes? Extragalactic Galactic Aspen Workshop

32. Spectrum Overview Aspen Workshop

33. Spectrum Overview Aspen Workshop

34. Conclusion • HiRes has measured the UHECR spectrum from 1017.2 eV to just above 1020 eV • HiRes Prototype/MIA and HiRes Stereo have measured the <Xmax> of UHECR from 1016.9 eV to 1019.4 eV • Broken power law fit to spectrum finds the Ankle at 1018.5 eV and evidence for a suppression at 1019.8 eV • HE suppression found consistent with being the GZK by examining integral spectrum • We have used the composition measurements to separate the galactic and extragalactic components of the spectrum and fit the extragalactic component to a uniform source model with variable evolution and with proton energy losses Aspen Workshop