Gamma-Rays Produced in Cosmic-Ray Interactions and

C.-Y .Huang,S.-E.Park,M.Pohl and C.

D.Daniels

Department of Physics and Astronomy,Iowa State University,Ames,IA 50011

Abstract.We employ the Monte Carlo particle collision code DPMJET3.04to determine the multiplicity spectra of various secondary particles (in addition to π0’s)with γ’s as the final decay state,that are produced in cosmic-ray (p ’s and α’s)interactions with the interstellar medium.We derive an easy-to-use γ-ray production matrix for cosmic rays with energies up to about 10PeV .This γ-ray production matrix is applied to the GeV excess in diffuse Galactic γ-rays observed by EGRET,and we conclude the non-π0decay components are insufficient to explain the GeV excess,although they have contributed a different spectrum from the π0-decay component.We also test the hypothesis that the TeV-band γ-ray emission of the shell-type SNR RX J1713.7-3946observed with HESS is caused by hadronic cosmic rays which are accelerated by a cosmic-ray modified shock.By the χ2statistics,we find a continuously softening spectrum is strongly preferred,in contrast to expectations.A hardening spectrum has about 1%probability to explain the HESS data,but then only if a hard cutoff at 50-100TeV is imposed on the particle spectrum.Keywords:cosmic rays,γ-rays,hadronic interactions,supernova remnants PACS:96.50.S-,96.60.tk,98.70.Sa,98.58.Mj γ-ray production matrix in hadronic Interactions This work presents a careful study of the γ-ray production in cosmic-ray (both p and α)interactions,by accounting for all decay processes including the direct production.For that purpose we employ the event generator DPMJET-III [1]to simulate secondary productions in both p-generated and He-generated interactions.We include all relevant secondary particles with γ-rays as the final decay products.For the composition of the ISM,we assume 90%protons,10%helium nuclei,0.02%carbon,and 0.04%oxygen.Around the energy of π0production threshold,where DPMJET appears unreliable,we apply a parametric model [2],that includes the resonance production for the πproduction.We thus derive a γ-ray production matrix for cosmic rays with energies up to about 10PeV that can be easily used to interpret the spectra of cosmic γ-ray sources.We consider all the decay channels and their decay fractions published by the Particle Data Group to account for all secondaries (resonances included)calculated by DPMJET and the parametric method.The calculation shows the non-π0resources in hadronic interactions have contributed about 20%of the total γ-ray photons,mostly from directly produced γ-rays and decays of η,K 0L and K 0S [3].In the cosmic-ray interactions,we calculate the γ-ray spectrum contributed by decays of unstable secondary particles

Q γ(E γ)=∑k

n ISM

E CR dE CR N CR (E CR )c βCR σ(E CR )dn k ,γdE γis the γ-ray decay spectrum from secondary species k .Eq.(1)can be re-written into

Q γ(E i )=∑j n ISM ∆E j N CR (E j )c βj σ(E j )∑k

dn k ,γdE |E γ=E i ,E CR =E j ,

with j being the index for the generating

cosmic-ray particle (p or α)and i being the index indicating the γ-ray energy.The energy binnings E i and E j are defined with good resolutions [3].

We use the γ-ray production matrix to analyze the observed spectra of diffuse Galactic emission and of the shell-type SNR RX J1713.7-3946.We find that the GeV excess is probably not the result of an inappropriate model of hadronic γ-ray production.We also test the hypothesis that the TeV-band γ-ray emission of SNR RX J1713.7-3946observed with

Application:the GeV-bandγ-ray spectrum and the TeV-band spectrum of RX J1713.7-3946 With theγ-ray production matrix,we calculate the diffuseγ-ray spectrum generated by the observed cosmic-ray spectrum[4].Fig.1(Left)shows the observed GeV-bandγ-ray emission from the inner Galaxy[5]in comparison with the contributions fromπ0decay as well as bremsstrahlung emission describe by a power-law spectrumΦB(E):

ΦB(E)≃1.3×10−8ωe

1022cm−2

· E cm2sec sr(3)

with power-law spectral indexΓe=2.1,the electron energy densityωe=0.1,0.4,0.8eV/cm3,and the gas column density N ISM=3×1022,8×1021,3×1021cm−2,respectively.The generating cosmic-rays are assumed with an energy densityρE=0.75eV/cm3.Models based on the locally observed cosmic-ray spectra generally predict a softer spectrum for the leptonic components,even after accounting for inverse Compton emission[5],so we may in fact overestimate the GeV-band intensity of the leptonic contribution.Nevertheless,it is clearly seen in thisfigure,that in the total intensity an over-shooting around Eγ≃300-600MeV appears in the modelledγ-ray energy distribution, whereas a deficit is present above1GeV.The observed spectrum of diffuse emission is always harder than the model spectrum,and we therefore conclude that an inaccurate description of hadronicγ-rays is ruled out as the origin of the GeV excess.

For the TeV-bandγ-ray spectrum of the shell-type SNR J1713.7-3946observed by the HESS collaboration[6],we use theγ-ray production matrix to test cosmic-ray acceleration models[7,8],which predict a continuous hardening of the cosmic-ray spectrum up to a high-energy cutoff.We therefore parametrize the spectrum of accelerated hadrons as

N(E)=N0 E E0Θ[E max−E](4)

whereΘis the step function and E0=15TeV is a normalization chosen to render variations in the power-law index s statistically independent from the choice of spectral curvature,σ.The cutoff energy,E max,is a free parameter.The normalization N0is obtained by normalizing both the data and the model to the value at0.97TeV.By theχ2statistics, we obtain the best-fitting values and the confidence ranges of the three parameters,E max,s,andσ,given values as s=2.13,σ=−0.25,and E max 200TeV,i.e.no cutoff.The bestfit,shown in Fig.1(Right),involves a continuous softening and is thus not commensurate with expectations based on acceleration at a cosmic-ray modified shock[7,8]. Noted that very valuable would be data in the energy range between1GeV and200GeV that may be provided by GLAST in the near future.Fig.2shows the confidence ranges of the parameters in Eq.(4),with confidence levels of 1,2and3sigma.The analysis strongly suggests a negative spectral curvature,σ<0,with confidence more than95%, in contrast to the expectation of standard cosmic-ray modified shock models.

Conclusion

We have considered a full picture of the hadronicγ-rays in cosmic-ray interactions and introduced an easy-to-useγ-ray production matrix which can be used for arbitrary cosmic-ray spectrum.The matrices are available for download at website http://cherenkov.physics.iastate.edu/gamma-prod.We apply the production matrix to calculate theγ-ray GeV excess and also the TeV-band spectrum of SNR RX J1713.7-3946.We conclude that1)the modifications in the GeV-bandγ-ray emission of hadronic origin are insufficient to explain the GeV excess in diffuse galacticγ-rays;2)a soft cut-off at about100TeV is statistically required in the particle spectrum if the TeV-band spectrum of RX J1713.7-3946 as observed with HESS is caused by cosmic-ray nucleons;3)no evidence for efficient nucleon acceleration to energies near the knee in the cosmic-ray spectrum,nor evidence of the spectral curvature and hardness predicted by standard models of cosmic-ray modified shock acceleration.We emphasize the need for GLAST data to better constrain the γ-ray spectrum below100GeV.

Grant support from NASA with award No.NAG5-13559is gratefully acknowledged.

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