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Nuclear Instruments and Methods in Physics Research A 588 (2008) 22–25

www.elsevier.com/locate/nima

Diffuse gamma emission of the Galaxy from cosmic rays

C. Evolia, D. Gaggerob,c, D. Grassob,�, L. Maccionea,d

aSISSA, via Beirut, 2-4, I-34014 Trieste, ItalybINFN, Sezione di Pisa, Largo Bruno Pontecorvo, 3, I-56127 Pisa, Italy

cDipartimento di Fisica, Universita di Pisa, Largo Bruno Pontecorvo, 3, I-56127 Pisa, ItalydINFN, Sezione di Trieste, Via Valerio, 2, I-34127 Trieste, Italy

Available online 12 January 2008

Abstract

The diffuse g-rays and neutrino emissions of the Galaxy may provide a unique tool to probe galactic cosmic rays (CR) and their

interaction with the interstellar medium. At the same time, if not well understood, such emissions may be annoying backgrounds for dark

matter searches. Therefore, it is crucial to model them as better as possible. We do that by combining simulations of the CR propagation

with recent models of the gas distribution. Respect to previous works, we perform a treatment of CR diffusion which accounts for a more

realistic spatial dependence of the diffusion coefficients. Although our analysis is focused on the energy range above the TeV, we can

reliably extrapolate our predictions at lower energies and compare them with EGRET measurements finding a good agreement. Then, we

compare our predictions with MILAGRO and TIBET observations in several regions of the sky, including Cygnus and the Galactic

Centre. Finally, we briefly discuss the implication of our finding for neutrino astronomy.

r 2008 Elsevier B.V. All rights reserved.

PACS: 95.85.Pw; 95.85.Ry

Keywords: g-Rays; Neutrinos and cosmic rays

1. Introduction

Several orbital observatories (see Ref. [1] for a review),especially EGRET [2,3], found that, at least up to 10GeV,the Galaxy is pervaded by a g-ray diffuse radiation. Whilea minor component of that emission is likely to beoriginated by unresolved point-like sources, the dominantcontribution is expected to come from the interaction ofgalactic cosmic rays (CR) with the interstellar medium(ISM). The g-ray high energy range will be soon probed byGLAST [4] (up to 300GeV) and by air shower arrays(ASA) (e.g. MILAGRO [5,6] and TIBET [7]) (above theTeV). Above the GeV, the main g-ray emission processesare expected to be the decay of p0 produced by thescattering of CR nuclei onto the diffuse gas (hadronicemission) and the Inverse Compton (IC) emission ofrelativistic electron colliding onto the interstellar radiationfield (leptonic emission). It is unknown, however, what are

e front matter r 2008 Elsevier B.V. All rights reserved.

ma.2008.01.007

ing author.

ess: dario.grasso@pi.infn.it (D. Grasso).

the relative contributions of those two processes and howthey change with the energy and the position in the sky(the so-called hadronic–leptonic degeneracy). Several nu-merical simulations have been performed in order tointerpret EGRET data as well as forthcoming measure-ments at high energy (see e.g. Refs. [8,9]). Generally, theypredict the hadronic emission to be dominant, in theproximity of the Galactic Plane (GP), between 0.1GeV andfew TeV, while between 1 and 100TeV a comparable, oreven larger IC contribution may be allowed.The 1–100TeV energy range, on which we focus here, is

also interesting from the point of view of neutrinoastrophysics. In that energy window neutrino telescopes(NTs) can look for up-going muon neutrino and recon-struct their arrival direction with an angular resolutionbetter than 1�. Since hadronic scattering gives rise to g-raysand neutrinos in a known ratio, the possible measurementof the neutrino emission from the GP may allow to resolvethe hadronic–leptonic degeneracy.In this contribution we discuss the main results of a

recent work where we modelled the g-ray and neutrino

ARTICLE IN PRESSC. Evoli et al. / Nuclear Instruments and Methods in Physics Research A 588 (2008) 22–25 23

diffuse emission of the Galaxy due to hadronic scattering[10]. We improve previous analyses under several aspects:the distribution of CR sources, the way we treated CRdiffusion by accounting for spatial variations of thediffusion coefficients, the distribution of the atomic andmolecular hydrogen.

2. The spatial structure of the ISM

In order to assess the problem of the propagation of CRsand their interaction with the ISM we need the knowledgeof three basic physical inputs, namely: the distribution ofSuperNova Remnants (SNR) which we assume to tracethat of CR sources; the properties of the Galactic MagneticField (GMF) in which the propagation occurs; thedistribution of the diffuse gas providing the target for theproduction of g-rays and neutrinos through hadronicinteractions. In the following we assume cylindricalsymmetry and adopt the Sun galactocentric distancer� ¼ 8:5 kpc.

Several methods to determine the SNR distribution inthe Galaxy are discussed in the literature (see e.g. thatbased on the surface brightness–distance relation [11]).Here we adopt an SNR distribution inferred from obser-vations of pulsars and progenitor stars as done in Ref. [12].Such an approach is less plagued by systematics and itsresults agree with those inferred from the distribution ofradioactive nuclides like of 26Al. A similar approach wasfollowed in Ref. [13], where the contribution of typeI-a SNR (dominating in the inner 1 kpc) was, however,disregarded.

Concerning the GMF we adopt the following analyticaldistribution which is based on Faraday Rotation Measure-ments (RMs) of polarised radio sources [14,15]:

Bregðr; zÞ ¼ B0 exp �r� r�

rB

� �1

2 coshðz=zrÞ(1)

where B0 � Bdiskreg ðr�; 0Þ ’ 2mG is the strength at the Sun

circle. The parameters rB and zr are poorly known.However, we found that our final results are practicallyindependent of their choice. In the following we adoptedrB ¼ 8:5 kpc and zr ¼ 1:5 kpc.

More uncertain are the properties of the turbulentcomponent of the GMF. Here we assume that it strengthfollows the behaviour:

Branðr; zÞ ¼ sðrÞBregðr; 0Þ1

2 coshðz=ztÞ(2)

where sðrÞ parametrizes the turbulence strength andzt ¼ 3 kpc. From polarimetric measurements and RMs isknown GMF are chaotic on all scales below �100 pc. Thepower spectrum of the those fluctuations is also poorlyknown. Similarly to what done in previous works we adopthere a Kolmogorov ðB2ðkÞ / k�5=3Þ spectrum. In Ref. [10]we also considered a Kraichnan ðB2ðkÞ / k�3=2Þ powerspectrum.

Concerning the gas distribution we adopt a model whichis based on a suitable combination of different analyseswhich have been separately performed for the disk and thegalactic bulge. For the H2 and HI distributions in the bulgewe use a detailed 3D model recently developed by Ferriereet al. [16] on the basis of several observations. For themolecular hydrogen in the disk we use the well-knownBronfman’s et al. model [17]. For the HI distribution in thedisk, we adopt Wolfire et al. [18] 2D model. Similarly towhat done in Ref. [13] we adopt here a radially dependentvalue of the CO–H2 conversion factor ðXCOÞ. We assumeXCO ¼ 0:5� 1020 cm�2 K�1 km�1 s for ro2 kpc and 1:2�1020 (in the same units) for rX2 kpc.

3. CR diffusion

The ISM is a turbulent magneto-hydro-dynamic (MHD)environment. Since the Larmor radius of high energynuclei is smaller than Lmax, the propagation of thoseparticles takes place in the spatial diffusion regime. Thediffusion equation describing such a propagation is(see e.g. Ref. [19])

�riðDijðr; zÞrjNðE; r; zÞÞ ¼ QðE; r; zÞ (3)

where NðE; r; zÞ is the differential CR density averaged overa scale larger than Lmax, QðE; r; zÞ is the CR source termand DijðE; r; zÞ are the spatial components of the diffusiontensor. In the energy range considered in our work energyloss/gain can be safely neglected. Since we assumecylindrical symmetry the only physically relevant compo-nents of the diffusion coefficients are D? and DA,respectively, the diffusion coefficient in the directionperpendicular to Breg and the antisymmetric (Hall)coefficient. We adopted expressions for those coefficientsas derived by Monte Carlo simulations of charged particlepropagation in turbulent magnetic fields [20]. With respectto other works, where a uniform value of the diffusioncoefficient all over the magnetic halo was assumed and nodistinction was done between perpendicular and paralleldiffusion (see e.g. Ref. [9]), our approach is more realistic.We know, in fact, that the turbulence strength has to bespatially dependent and that the role of the regular GMF(which breaks isotropy) is likely to be not negligible at highenergies. We found that although the role of Hall diffusionis negligible up to several PeV’s, a realistic spatialdependence of D? gives rise to non-negligible effects.

4. Mapping the g-ray and n emission

Assuming that the primary CR spectrum is a power-lawand that the differential cross-section follows a scalingbehaviour (well justified at the energies considered in thispaper), the g-ray (muon neutrino) emissivity due tohadronic scattering can be written as

dngðnÞðE; b; lÞ

dE’ f NsppY gðnÞðaÞ

Zds IpðEp; r; zÞnHðr; zÞ. (4)

ARTICLE IN PRESS

15

10

5

0

15

10

5

0−100 −50 0 50 100 −10 −5 0 5 10

b (degrees)I (degrees)

Φ� (

>1Te

V) ∗

1010

(cm

-2 s

-1 s

r-1)

Fig. 1. The g-ray flux profiles along the galactic plane (left panel) and along l ¼ 0 (right panel) are shown. The flux is integrated over 1� � 1� angular bins.

The corresponding neutrino flux can be obtained by dividing the flux in these diagrams by 3.1.

I (degrees)

Φ� (

4 <

Ε <

10 G

eV) ∗

106

(cm

-2 s

-1 s

r-1)

12

10

8

6

4

2

0−200 −100 0 100 200

Fig. 2. The longitude profile of the simulated g-ray flux (red, continuous

line) along the galactic plane is compared with EGRET measurements

[2,3]. The flux has been integrated in energy between 4 and 10GeV and in

latitude for jbjo2�.

Table 1

In this table our predictions for the mean g-ray flux in some selected

regions of the sky are compared with some available measurements

Sky window Eg Fgð4EgÞ ðcm2 s srÞ�1

Our model Measurements

jljo10�; jbjp2� 4GeV ’ 4:7� 10�6 ’ 6:5� 10�6 [3]

20�plp55�; jbjp2� 3TeV ’ 5:7� 10�11 p3� 10�10 [7]

4GeV ’ 4:4� 10�6 ’ 5:3� 10�6 [3]

73:5�plp76:5�; jbjp1:5� 12TeV ’ 2:9� 10�12 ’ 6:0� 10�11 [6]

4GeV ’ 2:4� 10�6 ’ 3:96� 10�6 [3]

140�olo200�; jbjo5� 3:5TeV ’ 5:9� 10�12 p4� 10�11 [5]

4GeV ’ 5:9� 10�7 ’ 1:2� 10�6 [3]

Since measurements’ errors are much smaller than theoretical uncertain-

ties they are not reported here.

C. Evoli et al. / Nuclear Instruments and Methods in Physics Research A 588 (2008) 22–2524

Here IpðEp; r; zÞ is the proton CR differential flux at theposition ðr; zÞ as determined by solving the diffusionequation; spp is the pp cross-section; Y g ’ 0:04 andY nmþnm ’ 0:01 are the g-ray and muon neutrino yields,respectively, as obtained for a proton spectral slope a ¼ 2:7(see Fig. 7 in Refs. [10,21] and references therein); thefactor f N ’ 1:4 represents the contribution from all othernuclear species both in the CR and the ISM; s is thedistance from the Earth; b and l are the galactic latitudeand longitude. In Fig. 1 we show the expected g-ray fluxprofile above the TeV obtained by adopting the magneticfield and gas model discussed in Sections 2 and 3.

5. Discussion

Due to the number of poorly known astrophysicalparameters entering in our analysis, it is useful toextrapolate our results to low energy in order to comparethem with EGRET measurements of the galactic g-raydiffuse emission. Here we only use EGRET data in the4–10GeV energy range [3] since at lower energy the scalingapproximation adopted in our work does not hold and re-acceleration (which we disregarded) may not be negligible.It is evident from Fig. 2 that for low galactic latitudes,where the hadronic emission is expected to be the dominantemission process, our predictions are in good agreementwith EGRET measurements. Therefore we think that ourmethods and results are reliable.

In Table 1 we compare our predictions with measure-ments performed above the TeV with ASAs and NTs indifferent regions of the sky. We found that the predictedfluxes are significantly below the experimental limits, withthe exception of the Cygnus region (where one or moresources are likely to increase the local CR density).

Concerning neutrinos, the only available upper limit onthe flux from the Galaxy has been obtained by theAMANDA-II experiment [22]. Being located at the SouthPole, it cannot probe the emission from the GC. In theregion 33�olo213�; jbjo2�, and assuming a spectralindex a ¼ 2:7, their present constraint is Fnmþnmð41TeVÞo3:1� 10�9 ðcm2 s srÞ�1. According to our model the

ARTICLE IN PRESSC. Evoli et al. / Nuclear Instruments and Methods in Physics Research A 588 (2008) 22–25 25

expected flux in the same region is Fnmþnmð41TeVÞ ’4:2� 10�11 ðcm2 s srÞ�1. It will be hardly detectable even byIceCube. The perspectives of a km3 NT to be built in theNorth Hemisphere are slightly more promising. Such aninstrument, in fact, probes the GC region and have a betterangular resolution than NTs in ice, which should help todisentangle the almost uniform atmospheric neutrinobackground. Although we showed in Ref. [10] that theexpected neutrino flux is hardly detectable even by theKm3Net project, it is worth noticing that our analysis doesnot account for local CR over-densities. As suggested byrecent HESS observations of the GC region [23], andMILAGRO observations of the Cygnus region [6], a sourceover-density may be present in those regions enhancing theneutrino signal to a detectable level.

References

[1] J.B.G.M. Bloemen, Annu. Rev. Astron. Astrophys. 29 (1989) 469.

[2] S.D. Hunter, et al., Astrophys. J. 481 (1997) 205.

[3] A.N. Cillis, R.C. Hartman, Astrophys. J. 621 (2005) 291.

[4] N. Gehrels, P. Michelson, for the GLAST Collaboration, Astropart.

Phys. 11 (1999) 277 (experiment website: http://www-glast.stanford.

edu).

[5] R.W. Atkins, MILAGRO Collaboration, et al., Phys. Rev. Lett. 95

(2005) 251103.

[6] A.A. Abdo, et al., MILAGRO Collaboration, arXiv:astro-ph/

0611691.

[7] M. Amenomori, et al., TIBET AS g Collaboration, arXiv:astro-ph/

0511514.

[8] V.S. Berezinsky, T.K. Gaisser, F. Halzen, T. Stanev, Astropart. Phys.

1 (1993) 281.

[9] A.W. Strong, I.V. Moskalenko, O. Reimer, Astrophys. J. 613 (2004)

962.

[10] C. Evoli, D. Grasso, L. Maccione, J. Cosmol. Astropart. Phys. 0706

(2007) 003.

[11] G.L. Case, D. Bhattacharya, Astrophys. J. 504 (1998) 761.

[12] K.M. Ferriere, Rev. Mod. Phys. 73 (2001) 1031.

[13] A.W. Strong, et al., Astron. Astrophys. 422 (2004) L47.

[14] J.L. Han, G.J. Qiao, Astron. Astrophys. 288 (1994) 759.

[15] J.L. Han, et al., Astrophys. J. 642 (2006) 868.

[16] K. Ferriere, W. Gillard, P. Jean, Astron. Astrophys. 467 (2007)

611.

[17] L. Bronfman, et al., Astrophys. J. 324 (1988) 248.

[18] M.G. Wolfire, et al., Astrophys. J. 587 (2003) 278.

[19] V.S. Ptuskin, et al., Astron. Astrophys. 268 (1993) 726.

[20] J. Candia, E. Roulet, J. Cosmol. Astropart. Phys. 0410 (2004) 007.

[21] V. Cavasinni, D. Grasso, L. Maccione, Astropart. Phys. 26 (2006) 41.

[22] J.L. Kelley, IceCube Collaboration, et al., in: Proceeding of the 29th

International Cosmic Ray Conference, Pune, 2005 arXiv:astro-ph/

0509546.

[23] F.A. Aharonian, HESS Collaboration, et al., Nature 439 (2006) 695.