Gamma rays and neutrinos from a cosmic ray source in the Galactic Center region
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Gamma rays and neutrinos from a cosmic ray sourcein the Galactic Center region
A. D. Supanitsky*
Instituto de Astronoma y Fsica del Espacio (IAFE),CONICET-UBA, CC 67, Suc. 28, C1428ZAA Buenos Aires, Argentina
(Received 15 October 2013; published 7 January 2014)
The center of the our Galaxy is a region where very energetic phenomena take place. In particular,powerful cosmic ray sources can be located in that region. The cosmic rays accelerated in these sourcesmay interact with ambient protons and/or low energy photons producing gamma rays and neutrinos.The observation of these two types of secondary particles can be very useful for the identification ofthe cosmic ray sources and for the understanding of the physical processes occurring during acceleration.Motivated by the excess in the neutrino spectrum recently reported by the IceCube Collaboration, we studyin detail the shape of the gamma ray and neutrino spectra originating from the interaction of cosmic rayprotons with ambient protons for sources located in the Galactic Center region. We consider differentmodels for proton acceleration and study the impact on the gamma ray and neutrino spectra. We alsodiscuss the possibility to constrain and even identify a particular neutrino source by using the informationgiven by the gamma ray spectrum, taking advantage of the modification of the spectral shape caused by theinteraction of the gamma rays with the photons of the radiation field present in the interstellar medium,which strongly depends on the source distance.
DOI: 10.1103/PhysRevD.89.023501 PACS numbers: 95.85.Ry, 98.70.Sa
Gamma rays and neutrinos can be generated in cosmicray sources due to the interaction of the cosmic rays withambient photons and/or protons. Powerful cosmic rayaccelerators can be located in the Galactic Center region;therefore, the observation of gamma rays and neutrinoscoming from the Galactic Center is of great importancefor the identification and understanding of the Galactic cos-mic ray sources. It is worth noting that, in contrast withcharged cosmic rays, these two types of secondary particlesare not deviated by the magnetic fields present in theinterstellar medium and they point back to its source.The IceCube Collaboration has recently reported the
observation of 28 neutrino events in the energy range from30 TeV to 1.2 PeV [1,2], while only 10.64.63.9 events wereexpected considering a conventional atmospheric neutrinobackground. This corresponds to a 4.3 excess. Despitethe large angular uncertainty of these events (10), wecan observe that 5 of the 28 events come from the GalacticCenter region. However, there is a degeneracy about the ori-gin of these neutrinos because they can also originate outsideour Galaxy. It has been pointed out that the gamma ray fluxassociatedwith the neutrino flux can be useful to constrain oreven identify the candidate neutrino sources . In particu-lar, in Refs. [7,8] it is found that the gamma ray data taken byFermi LAT at lower energies are consistent with a Galacticorigin of these five events. However, the upper limits on
the diffuse gamma ray flux obtained by different experimentsat higher energies disfavor this hypothesis .On the other hand, the region in the cosmic ray energy
spectrum where the transition from the Galactic to extraga-lactic cosmic rays takes place is still unknown (see Ref. for a review). Two possible regions for this transition arethe second knee, a steepening of the spectrum which isgiven at an energy of 0.5 EeV, and the ankle, a hardeningof the spectrum placed at an energy of 3 EeV. In Ref. it has been pointed out that the identification of Galacticneutrino sources and the observation of their spectra cancontribute to finding the region where the transition fromGalactic to extragalactic cosmic rays takes place. This isdue to the fact that the end of the neutrino energy spectrumis correlated with the maximum energy at which the cosmicrays are accelerated in the source. Following Ref. , theobservation of the end of the neutrino spectrum, of a givenGalactic source, at Emax 1 PeV favors the scenario inwhich the transition takes place in the second knee region,whereas the observation of Emax 810 PeV favors thescenario in which the transition is given at the ankle region.The most probable mechanism for the production of
gamma rays and neutrinos in Galactic cosmic ray sourcesis the interaction of cosmic rays with ambient protons .In this work we study in detail the shape of the gamma rayand neutrino spectra that originate from the proton-protoninteraction in Galactic cosmic ray sources placed in theGalactic Center region, which is motivated by the recentIceCube results. We consider different shapes of theproton spectrum based on acceleration models. We alsoconsider the values for the maximum energy of firstname.lastname@example.org
PHYSICAL REVIEW D 89, 023501 (2014)
1550-7998=2014=89(2)=023501(9) 023501-1 2014 American Physical Society
corresponding to the Galactic to extragalactic transition inthe second knee region and in the ankle region. The propa-gation of the gamma rays and neutrinos from the GalacticCenter to the Solar System is included in these calculations.While neutrinos suffer flavor oscillation during propaga-tion, gamma rays can interact with the photons of theGalactic interstellar radiation field (ISRF) and the cosmicmicrowave background (CMB) which is the most importantone . In particular, we find that the ratio between theneutrino and gamma ray spectra depends on the cosmic rayproton spectrum, which can be used to study the conditionsunder which the cosmic ray protons are accelerated in thesource. Finally, we study the possibility to discriminatebetween the Galactic and extragalactic origins of a neutrinospectrum observed in the direction of the Galactic Centerby observing the associated gamma ray flux, which in prin-ciple will be possible with the planned high energy gammaray observatories.
II. GAMMA RAYS AND NEUTRINOS INJECTEDBY A COSMIC RAY SOURCE
Gamma rays and neutrinos can be produced as a result ofthe interaction of the cosmic rays with ambient protonspresent in the sources. Gamma rays are mainly producedby the decay of neutral pions; mesons also contributeto the gamma ray flux. The generation of neutrinos is domi-nated by the decay of charged pions. Positive (negative)charged pions mainly decay into an antimuon and a muon(antimuon) neutrino,
The subsequent decay of the muons and antimuonsproduces more neutrinos,
e e ; e e :
It is believed that the Galactic cosmic rays are acceleratedprincipally at supernova remnants (see e.g. Ref. ) bymeans of the first order Fermi mechanism. Also, the exper-imental evidence indicates that the injected composition ofthe Galactic sources is dominated by protons . Thespectrum of protons which are accelerated via the first orderFermi mechanism and escape from the acceleration region,obtained without taking account of energy losses, can bewritten as
where A is a normalization constant, is the spectral index,Emax refers to the maximum energy which indicates the endof the spectrum (note that protons can be accelerated tohigher energies than Emax), and comes from the energydependence of the diffusion coefficient in the accelerationregion, k E (see Appendix A for details).Cosmic rays can suffer energy losses during the accel-
eration process due to the presence of strong magneticfields and ambient low energy photons [13,14]. The spec-trum near its end can have different shapes, including pile-ups and sudden cutoffs, depending on the type of energyloss dominating in the acceleration region. Then, in the sub-sequent analyses a proton spectrum with a sudden cutoff inEmax is also considered,
pEp A8 Emax: (2)
Figure 1 shows the proton spectra for 2 and for 1=3 (Kolmogorov spectrum), 1=2 (Kraichnanspectrum), and 1 (completely disordered field) .The spectrum corresponding to the sudden cutoff is alsoshown. The maximum energy considered is Emax 2 104 TeV, which corresponds to the transition betweenthe Galactic and extragalactic cosmic rays in the region ofthe second knee. As expected, the steepening of the spectrais more pronounced for increasing values of .Given the proton spectrum, the spectra of gamma rays
and neutrinos generated by the interaction with the ambientprotons are calculated following Ref. . In that workthe proton-proton interaction was simulated by using thehadronic interaction model Sibyll 2.1 . The gammaray spectrum is calculated from
/TeV)pElog(1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
)) 0E( p
Sudden cutoff = 1/3 = 1/2 = 1
FIG. 1. Logarithm of the proton spectra multiplied by E2
as a function of the logarithm of the proton energy. The spectralindex considered is 2 and the maximum energy isEmax 2 104 TeV. The spectra multiplied by E2 are normal-ized at an energy E0 10 TeV.
A. D. SUPANITSKY PHYSICAL REVIEW D 89, 023501 (2014)
where C is a normalization constant and inel is the proton-proton inelastic cross section. inel and F are taken fromRef. . The neutrino and antineutrino spectra areobtained in a similar way, and the corresponding functionsare also taken from Ref. .Figure 2 shows the gamma ray and neutrino1 spectra at
the source for 2, Emax 2 104 TeV, and 1=2.Note that the results obtained in this work are in very goodagreement with the ones obtained in Ref. . From Fig. 2it can be seen that the gamma ray spectrum is larger than theone corresponding to the electron neutrino and muon neu-trino. Also, the end of the neutrino spectra takes place at asmaller energy than the one corresponding to gamma rays.1
III. GAMMA RAYS AND NEUTRINOS AT EARTH
A. Precise calculation
Gamma rays and neutrinos produced at a given sourcepropagate through the interstellar medium to reach theEarth. The electron and muon neutrinos oscillate duringpropagation; therefore, the flavor ratio observed at theEarth is different from the one in the source. It is believedthat the neutrino oscillations originate from the fact thatthe flavor states, ji with e, , , are not the masseigenstates, jji with j 1, 2, 3. The flavor and the massbasis are related by 
where U is a unitary matrix which can be parametrized bythe mixing angles 12, 23, and 13 and a CP violatingphase CP. The transition probability can be written as 
In the so-called tribimaximal mixing approximation the parameters of the mixing matrix are taken as12 arcsin1=
p , 23 =4, 13 0, and CP 0.By using this approximation it can be seen that a flavorratio 120 in the source goes to 111 after propagation.In this work a more precise estimation of the mixingangles is used in which 13 is different from zero :sin2212 0.857, 23 =4, and sin2213 0.096.It is also assumed that CP 0. By using this new estima-tion of the parameters the flavor ratio 120 goes to1.050.990.95, which is very close to the tribimaximalmixing approximation. Therefore, the propagated spectraare calculated from
where the elements of the P matrix are given by P P and
0 are the neutrino spectra at the source.
Note that in this case 0 0.Gamma rays interact with photons of different back-
grounds when they propagate from the source to theEarth; the most important ones are the CMB and theISRF . The most important process at the energies con-sidered is the electron-positron pair production. Figure 3shows the mean free path of photons, , as a functionof energy for the CMB. The calculation has been done fol-lowing Ref. . From the figure it can be seen that forenergies of order of 1 PeV 9 kpc, which is very closeto the distance from the Solar System to the Galactic Center(D 8.5 kpc). Therefore, at these energies the attenuationin the CMB becomes quite important.The attenuation factor is given by TE; D
expE; D, where D is the distance from the sourceto the Earth and
E; D Z
Thus, the gamma ray flux at the Earth is given by
log(E/TeV)1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
e + e
FIG. 2 (color online). Logarithm of the gamma ray and neutrinospectra multiplied by E2 as a function of the logarithm of theenergy for 2, Emax 2 104 TeV, and 1=2. Also in thiscase E0 10 TeV.
1Hereafter, neutrino spectrum will refer to the sum of theneutrino and antineutrino spectra of a given flavor.
GAMMA RAYS AND NEUTRINOS FROM A COSMIC RAY PHYSICAL REVIEW D 89, 023501 (2014)
E TE; D0E
Figure 4 shows the attenuation factor for the CMB andISRF (taken from Ref. ) as a function of the energyfor two different positions of the source: One is placedat the Galactic Center and the other at 4 Mpc from theSolar System in the direction of the Galactic Center. Theattenuation factor for the ISRF is taken from Ref. ;the one corresponding to the extragalactic source isobtained by integrating 1 E;l from a distance of28.5 kpc in the direction of the Galactic center [seeEq. (7)]. It can be seen that the attenuation caused bythe interaction with the CMB photons is more importantthan that corresponding to the ISRF.
The top panel of Fig. 5 shows the gamma ray andneutrino spectra at the Earth for a Galactic cosmic raysource, like the one considered in Sec. II ( 2,Emax 2 104 TeV, and 1=2), located in theGalactic Center. In this figure the effects of the attenuationin the gamma ray spectra are evident. Also, the neutrinospectra for the different flavors become similar after propa-gation. The bottom panel of Fig. 5 shows the ratio R= ofthe neutrino spectra to the gamma ray spectrum. It can beseen that it is not constant in a large energy range due to theattenuation suffered by the gamma rays and the differentends of the neutrino and gamma ray spectra. In particular,the first maximum of R= corresponds to the attenuationof the gamma rays in the ISRF, whereas the second andlarger one corresponds to the attenuation in the CMB.The shape of the end of the gamma ray and neutrino
spectra depends on the shape of the proton spectrum.Figure 6 shows the gamma ray and the total neutrino
log(E/TeV)1 2 3 4 5 6 7 8
FIG. 3 (color online). Logarithm of the mean free path ofgamma rays as a function of the logarithm of the primary energyfor electron-positron pair production in the CMB.
log(E/TeV)1 2 3 4 5 6 7 8
D = 8.5 kpc
D = 4 Mpc
FIG. 4 (color online). Attenuation factor of gamma rays as afunction of the logarithm of energy. The photon backgroundsconsidered are the CMB and the ISRF. One so...