Diffuse Galactic Gamma Rays from Shock-Accelerated Cosmic Rays

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  • Diffuse Galactic Gamma Rays from Shock-Accelerated Cosmic Rays

    Charles D. Dermer*

    Space Science Division, Code 7653, Naval Research Laboratory, Washington, D.C. 20375-5352, USA(Received 9 June 2012; published 29 August 2012)

    A shock-accelerated particle flux / ps, where p is the particle momentum, follows from simpletheoretical considerations of cosmic-ray acceleration at nonrelativistic shocks followed by rigidity-

    dependent escape into the Galactic halo. A flux of shock-accelerated cosmic-ray protons with s 2:8provides an adequate fit to the Fermi Large Area Telescope -ray emission spectra of high-latitude and

    molecular cloud gas when uncertainties in nuclear production models are considered. A break in the

    spectrum of cosmic-ray protons claimed by Neronov, Semikoz, and Taylor [Phys. Rev. Lett. 108, 051105

    (2012)] when fitting the -ray spectra of high-latitude molecular clouds is a consequence of using a

    cosmic-ray proton flux described by a power law in kinetic energy.

    DOI: 10.1103/PhysRevLett.109.091101 PACS numbers: 95.85.Pw, 98.38.j, 98.70.Rz, 98.70.Sa

    Introduction.One hundred years after the discoveryof cosmic rays by Hess in 1912 [1], the sources of thecosmic radiation are still not conclusively established.Theoretical arguments developed to explain extensiveobservations of cosmic rays and Galactic radiationsfavor the hypothesis that cosmic-ray acceleration takesplace at supernova remnant (SNR) shocks [2]. A crucialprediction that follows from this hypothesis is thatcosmic-ray sources will glow in the light of raysmade by the decay of neutral pions created as secon-daries in collisions between cosmic-ray protons and ionswith ambient matter. The p p! 0 ! 2 spectrumformed by isotropic cosmic rays interacting with parti-cles at rest is hard and symmetric about m0=2 67:5 MeV in a log-log representation of photon numberspectrum vs energy [3].The AGILE and Fermi -ray telescopes have recently

    provided preliminary evidence for a 0 ! 2 feature inthe spectra of the W44, W51C, and IC 443 SNRs [4].Whether this solves the cosmic-ray origin problem de-pends on disentangling leptonic and hadronic emissionsignatures, including multizone effects [5], and findingout if the nonthermal particles found in middle-agedSNRs as inferred from their spectral maps have the prop-erties expected from the sources of the cosmic rays.Supporting evidence that cosmic rays are accelerated at

    shocks comes from the diffuse Galactic -ray emission.High-latitude Galactic gas separate from -ray pointsources, dust, and molecular gas provides a clean targetfor -ray production from cosmic-ray interactions.Because the cosmic-ray electron and positron fluxes are* 20 times smaller than the cosmic-ray proton flux at GeVenergies [6], the 0-decay -ray flux strongly dominatesthe electron bremsstrahlung and Compton fluxes. The dif-fuse Galactic -ray spectrum can be deconvolved to givethe cosmic-ray proton spectrum, given accurate nuclear-ray production physics. Data from the Fermi LargeArea Telescope (LAT) offer an opportunity to derive

    the interstellar cosmic-ray spectra unaffected by Solarmodulation [7,8].This problem is revisited in order to address a recent

    claim [8] that fits to the diffuse Galactic -ray emission ofGould belt clouds imply a break at Tk;br 935 GeV in thecosmic-ray proton spectrum that represents a new energyscale. Note that a break in the kinetic-energy representationof the proton spectrum has been reported before [9]. In thisLetter, we show that when uncertainties in nuclear produc-tion models are taken into account, a power-law momen-tum spectrum favored by cosmic-ray acceleration theoryprovides an acceptable fit to Fermi LAT -ray data ofdiffuse Galactic gas and produces a break in a kineticenergy representation at a few GeV from elementarykinematics. Comparison of theoretical -ray spectra withdata supports a nonrelativistic shock origin of the cosmicradiation, consistent with the SNR hypothesis.Production spectrum of rays from cosmic-ray colli-

    sions.The -ray production spectrum divided by thehydrogen density nH is given, in units of (s GeV1, by


    4kZ 1Tp;min


    dpp!0!2Tp; d

    : (1)

    Here and below, jTp is the cosmic-ray proton intensity inunits of cosmic-ray protons cm2 s sr GeV1, and k, thenuclear enhancement factor, corrects for the compositionof nuclei heavier than hydrogen in the cosmic rays andtarget gas [10]. The term dpp!0!2Tp; =d is thedifferential cross section for the production of a photonwith energy by a proton with kinetic energy Tp, in GeV,

    and momentum p in GeV=c.The much studied and favored model for cosmic-ray

    acceleration is the first-order Fermi mechanism, whichwas proposed in the late 1970s [11]. Test particles gainenergies by diffusing back and forth across a shock front

    PRL 109, 091101 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

    31 AUGUST 2012

    0031-9007=12=109(9)=091101(5) 091101-1 Published by the American Physical Society

  • while convecting downstream. The downstream steady-

    state distribution function is given by fp / p3r=r1,where p is the momentum and r is the compressionratio. Consequently, the particle momentum spectrum /p2fp / pA, where A 2 r=r 1 is the well-known test-particle spectral index that approaches 2 (equalenergy per decade) in the limit of a strong nonrelativisticshock with r! 4 [12]. After injection into the interstellarmedium with A 2:12:2, characteristic of SNR shocks,cosmic-ray protons and ions are transported from the ga-lactic disk into the halo by rigidity-dependent escape [13],which softens their spectrum by 0:50:6 units, leavinga steady-state cosmic-ray spectrum dN=dp / ps, wheres A 2:72:8. Thus, we consider a cosmic-ray flux

    jshTp / TpdN


    / Tp





    / pTps:


    Gamma-ray production from cosmic-raymatter inter-actions.Secondary nuclear production in proton-protoncollisions is described by isobar formation at energies nearthreshold Tp 0:28 GeV [3] and scaling models at high-energies Tp mp. Uncertainties remain in the productionspectra at Tp few GeV, where most of the secondary-ray energy is made in cosmic-ray collisions.Figure 1 compares two models for -ray production

    from p-p collisions using an empirical fit to the demodu-lated cosmic-ray flux measured [14] in interstellar spacegiven by [15]

    jdemTp 2:2Tp mp2:75: (3)

    The model of Dermer [15] describes low-energy resonanceproduction in terms of the 1232 resonance throughSteckers model [3], and high-energy production by thescaling model of Stephens and Badhwar [16], with the tworegimes linearly connected between 3 and 7 GeV. Themodel of Kamae et al. [17] is a parametric representationof simulation programs and includes contributions fromthe 1232 isobar and N1600 resonance cluster, non-scaling effects, scaling violations, and diffractive pro-cesses. This model is represented by functional formsthat are convenient for astrophysical calculations.Figure 1 shows that the two models agree within 20% at

    > 100 MeV, but display larger differences at &

    10 MeV, where the -ray production is energetically in-significant. Both models are in general agreement in thehigh-energy asymptotic regime, with the Kamae et al.model giving fluxes larger by 13% due to the inclusionof diffractive processes. The spectral peak in a F repre-sentation occurs at 500 MeV to 1 GeV for this protonspectrum. The most significant discrepancy in the twomodels is by 30% at the pion production peak near67.5 MeV [18]. Because of the different approaches ofthe models and little improvement in nuclear databasesfrom laboratory studies between model development, thiscomparison indicates that our knowledge of the -rayproduction spectrum in p-p collisions is uncertain, atworst, by 30% near the pion-production peak and is betterthan 15% at * 200 MeV.

    Fits to Fermi LAT -ray data.The Fermi LAT data [7]of the diffuse galactic radiation are fit using a shockspectrum given by Eq. (2). Guided by the high-energyasymptote of Eq. (3), we let

    jCRTp 2:2ps; (4)

    with s 2:75. The data shown in Fig. 2 are from regions inthe third quadrant, with Galactic longitude from 200 to260, and galactic latitudes jbj ranging from 22 to 60.There are no molecular clouds in these regions, the ionizedhydrogen column density is small with respect to thecolumn density of neutral hydrogen, and -ray emissionfrom point sources is removed. The linear increase of theemissivity as traced by 21 cm line observations allowsresidual galactic and extragalactic radiation to be sub-tracted, leaving only the -ray emission resulting fromcollisions of cosmic rays with neutral gas, allowing foran absolute normalization to be derived for the emissivity.As can be seen, the shock-acceleration spectrum gives anacceptable fit to the data and restricts the value of k to be&1:8. Given that there must be some residual cosmic-rayelectron-bremsstrahlung and Compton radiations at theseenergies, the restriction on k could be larger.The spectrum in Fig. 3 from the analysis of Fermi LAT

    data given in Ref. [8] shows the averaged -ray flux frommolecular clouds in the Gould belt. The derived flux,which extends to 100 GeV, matches the spectrum of

    FIG. 1 (color online). Production spectra of secondary raysmade in p-p collisions from the models of Dermer [15] andKamae et al. [17], using the empirical demodulated cosmic-rayproton spectrum given by Eq. (3).

    PRL 109, 091101 (2012) P HY S I CA L R EV I EW LE T T E R Sweek ending

    31 AUGUST 2012


  • diffuse Galactic gas emission used by the Fermi team intheir analysis of the extragalactic diffuse -ray intensity[19], supporting the assumption that the clouds are porousto cosmic rays. The cosmic-ray pr


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