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

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

3. 28 April 2005Aspen Workshop The HiRes Data Here’s the HiRes spectraHere’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

4. 28 April 2005Aspen Workshop  2 = 114/37  = -3.12(1) Features What are the features of the spectrum?What are the features of the spectrum? –Fit to broken power law –No BP, bad fit

5. 28 April 2005Aspen Workshop  2 = 46.0/35  1  = -3.31(3)  2  = -2.91(3) log 10 E = 18.45(2) Features What are the features of the spectrum?What are the features of the spectrum? –Fit to broken power law –No BP, bad fit –1 BP, Ankle

6. 28 April 2005Aspen Workshop  2 = 30.1/33  1  = -3.32(4)  2  = -2.86(4) log 10 E 12 = 18.47(6)  3  = -5(1) log 10 E 23 = 19.79(9) Features What are the features of the spectrum?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 break11 events above break Expect 28 with red lineExpect 28 with red line Poisson prob. 2.4x10 -4Poisson prob. 2.4x10 -4 Is the HE suppression the GZK?Is the HE suppression the GZK?

7. 28 April 2005Aspen Workshop Integral Spectra One measure of the energy of the suppression is E ½One measure of the energy of the suppression is E ½ –Due to Berezinsky –Where integral flux is half of expected with no suppression

8. 28 April 2005Aspen Workshop Integral Spectra One measure of the energy of the suppression is E ½One measure of the energy of the suppression is E ½ –Due to Berezinsky –Where integral flux is half of expected with no suppression Use red line extension of broken power law as no- suppression expectationUse red line extension of broken power law as no- suppression expectation

9. 28 April 2005Aspen Workshop Integral Spectra One measure of the energy of the suppression is E ½One measure of the energy of the suppression is E ½ –Due to Berezinsky –Where integral flux is half of expected with no suppression Use red line extension of broken power law as no- suppression expectationUse red line extension of broken power law as no- suppression expectation –Find log 10 E ½ = 19.77 +0.15 -0.06 –Berezinsky et al, predict log 10 E ½ = 19.72 for the GZK

10. 28 April 2005Aspen Workshop The HiRes Data (again) Want to fit the HiRes spectra…Want to fit the HiRes spectra…

11. 28 April 2005Aspen Workshop The HiRes Data (again) Want to fit the HiRes spectra…Want to fit the HiRes spectra… –And also take into account the HiRes composition measurements QGSJet Iron QGSJet protons

12. 28 April 2005Aspen Workshop The HiRes Data (again) Want to fit the HiRes spectra…Want to fit the HiRes spectra… –And also take into account the HiRes composition measurements Make one simplifying assumption:Make one simplifying assumption: –Composition determines origin Iron is GalacticIron is Galactic Protons are ExtragalacticProtons are Extragalactic –Use fit to composition But assume all protons at 100 EeVBut assume all protons at 100 EeV –Fit spectrum by varying extragalactic model, galactic spectrum determined from this “Toy Model” assumption

13. 28 April 2005Aspen Workshop Uniform Source Model (XG) Assume uniform sources of extragalactic protonsAssume uniform sources of extragalactic protons –Identical spectral slope  –Uniform luminosity density at any epoch –Luminosity density can vary as (1+ z ) m Protons lose energyProtons lose energy –Average energy loss rate from Berezinsky et al

14. 28 April 2005Aspen Workshop Uniform Source Model (XG) Assume uniform sources of extragalactic protonsAssume uniform sources of extragalactic protons –Identical spectral slope  –Uniform luminosity density at any epoch –Luminosity density can vary as (1+ z ) m Protons lose energyProtons 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 processHave to use MC for this process

15. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.0004

16. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.0006

17. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.001

18. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.0016

19. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.0025

20. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.004

21. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.006

22. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.01

23. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.016

24. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.025

25. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.04

26. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.06

27. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.1

28. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.16

29. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.25

30. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.4

31. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=0.6

32. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=1

33. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=1.6

34. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=2.5

35. 28 April 2005Aspen Workshop Uniform Source Model (XG) Z=4

36. 28 April 2005Aspen Workshop Uniform Source Model (XG) All the shells togetherAll the shells together –  = 2.4 – m = 2.5 Each energy dominated by different range in zEach energy dominated by different range in z –Given energy is somewhat flat in z up to maximum –Allows one to do cosmology

37. 28 April 2005Aspen Workshop Uniform Source Model (XG) All the shells togetherAll the shells together –  = 2.4 – m = 2.5 Each energy dominated by different range in zEach 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 fittingSum of shells gives spectrum for fitting

38. 28 April 2005Aspen Workshop Uniform Source Model (XG) All the shells togetherAll the shells together –  = 2.4 – m = 2.5 Each energy dominated by different range in zEach 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 fittingSum of shells gives spectrum for fitting Actually need finer set of shellsActually need finer set of shells

39. 28 April 2005Aspen Workshop Best USM Fit to HiRes Fit USM varying m and Fit USM varying m and  –  = 2.38 – m = 2.55 –Galactic spectrum falls steeply above 100 PeV Galactic Extragalactic

40. 28 April 2005Aspen Workshop Best USM Fit to HiRes Fit USM varying m and Fit USM varying m and  –  = 2.38 – m = 2.55 –Galactic spectrum falls steeply above 100 PeV Statistical UncertaintyStatistical Uncertainty –  = 0.035 – m = 0.25  2 Contours for Spectrum Fit

41. 28 April 2005Aspen Workshop Best USM Fit to HiRes  2 Contours for Spectrum Fit Fit USM varying m and Fit USM varying m and  –  = 2.38 – m = 2.55 –Galactic spectrum falls steeply above 100 PeV Statistical UncertaintyStatistical Uncertainty –  = 0.035 – m = 0.25 Systematic UncertaintySystematic Uncertainty –  = 0.03 – m = 0.3

42. 28 April 2005Aspen Workshop Where the Fit Works Well… The fit works best in the Ankle regionThe fit works best in the Ankle region –Understand the Ankle as coming from e + e - pair production energy losses –Spectral slope (  ) mostly determined by rise from Ankle (HiRes-I dominates) –Evolution ( m ) determined by fall into Ankle (HiRes-II dominates) Galactic Extragalactic

43. 28 April 2005Aspen Workshop …and Where it Doesn’t GZK regionGZK region –Fit is above the data –Perhaps… Some sources have E max of order GZK thresholdSome sources have E max of order GZK threshold 2 nd Knee Region2 nd Knee Region –There isn’t one –Perhaps… The input spectral slope changes?The input spectral slope changes? Evolution of sources changes?Evolution of sources changes? Galactic Extragalactic

44. 28 April 2005Aspen Workshop What if Evolution Changes? QSO surveys show a break in the redshift spectra at z = ~1.6QSO surveys show a break in the redshift spectra at z = ~1.6 Recall USM modelRecall USM model – z = 1.6 corresponds to E = 3x10 17 eV –Using m = 1 for z > 1.6 gives a 2 nd Knee SDSS Lines: (1+z) 3

45. 28 April 2005Aspen Workshop What if Evolution Changes? QSO surveys show a break in the redshift spectra at z = ~1.6QSO surveys show a break in the redshift spectra at z = ~1.6 Recall USM modelRecall USM model – z = 1.6 corresponds to E = 3x10 17 eV –Using m = 1 for z > 1.6 gives a 2 nd Knee

46. 28 April 2005Aspen Workshop What if Evolution Changes? QSO surveys show a break in the redshift spectra at z = ~1.6QSO surveys show a break in the redshift spectra at z = ~1.6 Recall USM modelRecall USM model – z = 1.6 corresponds to E = 3x10 17 eV –Using m = 1 for z > 1.6 gives a 2 nd Knee

47. 28 April 2005Aspen Workshop Spectrum Overview

48. 28 April 2005Aspen Workshop Spectrum Overview

49. 28 April 2005Aspen Workshop Conclusion HiRes has measured the UHECR spectrum from 10 17.2 eV to just above 10 20 eVHiRes has measured the UHECR spectrum from 10 17.2 eV to just above 10 20 eV HiRes Prototype/MIA and HiRes Stereo have measured the of UHECR from 10 16.9 eV to 10 19.4 eVHiRes Prototype/MIA and HiRes Stereo have measured the of UHECR from 10 16.9 eV to 10 19.4 eV Broken power law fit to spectrum finds the Ankle at 10 18.5 eV and evidence for a suppression at 10 19.8 eVBroken power law fit to spectrum finds the Ankle at 10 18.5 eV and evidence for a suppression at 10 19.8 eV HE suppression found consistent with being the GZK by examining integral spectrumHE 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 lossesWe 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