Fitting the HiRes Data

Fitting the HiRes DataFitting the HiRes Data

Douglas BergmanDouglas BergmanRutgers UniversityRutgers University

28 April 200528 April 2005

28 April 200528 April 2005 Aspen WorkshopAspen Workshop

The HiRes DataThe HiRes Data• Here’s the HiRes spectraHere’s the HiRes spectra


The HiRes DataThe HiRes Data• Here’s the HiRes spectraHere’s the HiRes spectra

– Actually fit to numbers of Actually fit to numbers of events using calculated events using calculated apertureaperture

– Use binned maximum Use binned maximum likelihood methodlikelihood method

– Two empty bins for each of Two empty bins for each of HiRes-I and HiRes-IIHiRes-I and HiRes-II


2 = 114/37

= -3.12(1)

FeaturesFeatures• What are the features of What are the features of

the spectrum?the spectrum?– Fit to broken power lawFit to broken power law– No BP, bad fitNo BP, bad fit


2 = 46.0/35

1= -3.31(3)

2= -2.91(3)log10E = 18.45(2)


the spectrum?the spectrum?– Fit to broken power lawFit to broken power law– No BP, bad fitNo BP, bad fit– 1 BP, Ankle1 BP, Ankle


2 = 30.1/33

1= -3.32(4)

2= -2.86(4)log10E12 = 18.47(6)

3= -5(1)log10E23 = 19.79(9)


the spectrum?the spectrum?– Fit to broken power lawFit to broken power law– No BP, bad fitNo BP, bad fit– 1 BP, Ankle1 BP, Ankle– 2 BP, HE suppression2 BP, HE suppression

• 11 events above break11 events above break• Expect 28 with red lineExpect 28 with red line• Poisson prob. 2.4x10Poisson prob. 2.4x10-4-4

• Is the HE suppression the Is the HE suppression the GZK?GZK?


Integral SpectraIntegral Spectra• One measure of the energy One measure of the energy

of the suppression is Eof the suppression is E½½ – Due to BerezinskyDue to Berezinsky– Where integral flux is half of Where integral flux is half of

expected with no expected with no suppressionsuppression





• Use red line extension of Use red line extension of broken power law as no-broken power law as no-suppression expectationsuppression expectation





• Use red line extension of Use red line extension of broken power law as no-broken power law as no-suppression expectationsuppression expectation– Find logFind log1010EE½½ = 19.77 = 19.77+0.15+0.15

-0.06-0.06

– Berezinsky Berezinsky et al,et al, predict predict loglog1010EE½½ = 19.72 for the GZK = 19.72 for the GZK


The HiRes Data (again)The HiRes Data (again)• Want to fit the HiRes Want to fit the HiRes

spectra…spectra…



spectra…spectra…– And also take into account And also take into account

the HiRes composition the HiRes composition measurementsmeasurements

QGSJet Iron

QGSJet Iron

QGSJet protons

QGSJet protons



spectra…spectra…– And also take into account And also take into account

the HiRes composition the HiRes composition measurementsmeasurements

• Make one simplifying Make one simplifying assumption:assumption:– Composition determines Composition determines

originorigin• Iron is GalacticIron is Galactic• Protons are ExtragalacticProtons are Extragalactic

– Use fit to compositionUse fit to composition• But assume all protons at But assume all protons at

100 EeV100 EeV– Fit spectrum by varying Fit spectrum by varying

extragalactic model, galactic extragalactic model, galactic spectrum determined from spectrum determined from this “Toy Model” assumptionthis “Toy Model” assumption


Uniform Source Model (XG)Uniform Source Model (XG)• Assume uniform sources Assume uniform sources

of extragalactic protonsof extragalactic protons– Identical spectral slope Identical spectral slope – Uniform luminosity density Uniform luminosity density

at any epochat any epoch– Luminosity density can vary Luminosity density can vary

as (1+as (1+zz))mm

• Protons lose energyProtons lose energy– Average energy loss rate Average energy loss rate

from Berezinsky from Berezinsky et alet al


Uniform Source Model (XG)Uniform Source Model (XG)• Assume uniform sources Assume uniform sources

of extragalactic protonsof extragalactic protons– Identical spectral slope Identical spectral slope – Uniform luminosity density Uniform luminosity density

at any epochat any epoch– Luminosity density can vary Luminosity density can vary

as (1+as (1+zz))mm

• Protons lose energyProtons lose energy– Average energy loss rate Average energy loss rate

from Berezinsky from Berezinsky et alet al– Pion production causes Pion production causes

proton to loose a large proton to loose a large fraction of its energyfraction of its energy

• Have to use MC for this Have to use MC for this processprocess


Uniform Source Model (XG)Uniform Source Model (XG)Z=0.0004Z=0.0004


Uniform Source Model (XG)Uniform Source Model (XG)Z=1Z=1


Uniform Source Model (XG)Uniform Source Model (XG)Z=4Z=4


Uniform Source Model (XG)Uniform Source Model (XG)• All the shells togetherAll the shells together

– = 2.4= 2.4– mm = 2.5 = 2.5

• Each energy dominated by Each energy dominated by different range in different range in zz– Given energy is somewhat Given energy is somewhat

flat in flat in zz up to maximum up to maximum– Allows one to do cosmologyAllows one to do cosmology



– = 2.4= 2.4– mm = 2.5 = 2.5



• Sum of shells gives Sum of shells gives spectrum for fittingspectrum for fitting



– = 2.4= 2.4– mm = 2.5 = 2.5



• Sum of shells gives Sum of shells gives spectrum for fittingspectrum for fitting

• Actually need finer set of Actually need finer set of shellsshells


Best USM Fit to HiResBest USM Fit to HiRes• Fit USM varying Fit USM varying mm and and

– = 2.38= 2.38– mm = 2.55 = 2.55– Galactic spectrum falls Galactic spectrum falls

steeply above 100 PeVsteeply above 100 PeV

Galactic

Extragalactic


Best USM Fit to HiResBest USM Fit to HiRes• Fit USM varying Fit USM varying mm and and


steeply above 100 PeVsteeply above 100 PeV• Statistical UncertaintyStatistical Uncertainty

– = 0.035= 0.035– mm = 0.25 = 0.25

2 Contours for Spectrum Fit


Best USM Fit to HiResBest USM Fit to HiRes2 Contours for Spectrum Fit• Fit USM varying Fit USM varying mm and and


steeply above 100 PeVsteeply above 100 PeV• Statistical UncertaintyStatistical Uncertainty

– = 0.035= 0.035– mm = 0.25 = 0.25

• Systematic UncertaintySystematic Uncertainty– = 0.03= 0.03– mm = 0.3 = 0.3


Where the Fit Works Well…Where the Fit Works Well…• The fit works best in the The fit works best in the

Ankle regionAnkle region– Understand the Ankle as Understand the Ankle as

coming from coming from ee++ee-- pair pair production energy lossesproduction energy losses

– Spectral slope (Spectral slope () mostly ) mostly determined by rise from determined by rise from Ankle (HiRes-I dominates)Ankle (HiRes-I dominates)

– Evolution (Evolution (mm) determined by ) determined by fall into Ankle (HiRes-II fall into Ankle (HiRes-II dominates)dominates)

Galactic

Extragalactic


……and Where it Doesn’tand Where it Doesn’t• GZK regionGZK region

– Fit is above the dataFit is above the data– Perhaps…Perhaps…

• Some sources have Some sources have EEmaxmax of of order GZK thresholdorder GZK threshold

• 22ndnd Knee Region Knee Region– There isn’t oneThere isn’t one– Perhaps…Perhaps…

• The input spectral slope The input spectral slope changes?changes?

• Evolution of sources Evolution of sources changes?changes?

Galactic

Extragalactic


Spectrum OverviewSpectrum Overview


ConclusionConclusion• HiRes has measured the UHECR spectrum from 10HiRes has measured the UHECR spectrum from 1017.217.2 eV to just above 10 eV to just above 102020

eVeV• HiRes Prototype/MIA and HiRes Stereo have measured the <HiRes Prototype/MIA and HiRes Stereo have measured the <XXmaxmax> of > of

UHECR from 10UHECR from 1016.916.9 eV to 10 eV to 1019.419.4 eV eV• Broken power law fit to spectrum finds the Ankle at 10Broken power law fit to spectrum finds the Ankle at 1018.518.5 eV and evidence eV and evidence

for a suppression at 10for a suppression at 1019.819.8 eV eV• HE suppression found consistent with being the GZK by examining integral HE suppression found consistent with being the GZK by examining integral

spectrumspectrum• We have used the composition measurements to separate the galactic and We have used the composition measurements to separate the galactic and

extragalactic components of the spectrum and fit the extragalactic extragalactic components of the spectrum and fit the extragalactic component to a uniform source model with variable evolution and with component to a uniform source model with variable evolution and with proton energy lossesproton energy losses

Fitting the HiRes Data

Documents

Transcript of Fitting the HiRes Data