Fits of the HiRes Spectra to Fits of the HiRes Spectra to Astrophysical ModelsAstrophysical Models

Douglas Bergman

Rutgers University

ICRC 2003, Tsukuba, Japan

6 August 2003

HiRes Mono SpectraHiRes Mono Spectra Ankle is evident Hint of GZK Want to find the

significance of these features by fitting

Continuation above GZK?Continuation above GZK? Does the spectrum

continue at the same spectral index above the GZK?

Expect 29.8 see 11– Poisson probability

of 7.3 x 10-5

Fit to Event DistributionFit to Event Distribution All fits done using

binned maximum likelihood method on numbers of events

Two Component ModelTwo Component Model Use latest HiRes

composition measurements to constrain new fits– Assume the iron (heavy)

component comes from galactic sources

– Proton (light) component comes from extragalactic sources

33% protons at 1017 eV 80% protons at 1018 eV 100% protons at 1020 eV

Energy Loss in XG UHECR’sEnergy Loss in XG UHECR’s Model the GZK effect

in XG protons using the formalism of Berezinsky, Gazizov and Grigorieva (hep-ph/0904357)

Pion production causes high energy protons to loose energy quickly

Lower energy protons still loose energy due to electron pair production

Uniform Source ModelUniform Source Model Integrate over

uniform source density out to z = 4

Can allow density of sources to evolve as (1+z)m

– m = 0, 2 = 78.6/39

– m = 3, 2 = 64.7/39

– Source density is not static

Galactic Survey ModelGalactic Survey Model There is a local

over-density of galaxies, might be true of UHECR sources too

Use actual distribution of galaxies

This figure taken from Blanton et al. astro-ph/0009466

Galactic Survey ModelGalactic Survey Model Integrate over

observed galactic density out to z = 4

2 improves by 2-6 from introduction of galactic source density– m = 0, 2 = 72.8/39

– m = 3, 2 = 63.0/39

Best Evolution ParameterBest Evolution Parameter Allow m to vary

between 0 and 4 Best fit for m = 2.5

with an uncertainty of 0.5

Stellar Formation Rate evolves with

m = 3

HiRes Spectra: Galactic Survey FitHiRes Spectra: Galactic Survey Fit Best fit for m = 2.5

2 = 60.4/39 Some of 2 comes from

difference of energy scales between HiRes-I and HiRes-II

HiRes Mono & Fly’s Eye StereoHiRes Mono & Fly’s Eye Stereo Add Fly’s Eye Stereo

measurement into fit– Energy scaled down by

7%

– Helps constrain fit a lower energies

2 = 87.7/63 with

m = 2.4 Softening of spectrum

between second knee and ankle caused by e+e- pair production turning on

ConclusionConclusion The HiRes spectra are not consistent with a

continuation above the GZK at the same spectral slope seen above the “ankle”

The observed fluorescence spectra are consistent with a two component source model with protons from extragalactic sources subject to the GZK mechanism

Fits to the fluorescence spectra favor source densities which evolve with z in a similar way as the Stellar Formation Rate

2nd Knee and Ankle caused by e+e- pair production