Neutrinos from galactic sources of cosmic rayswith known c-ray spectra

Francesco Vissani *

INFN, Laboratori Nazionali del Gran Sasso, Assergi (AQ), Italy

Received 5 May 2006; received in revised form 4 July 2006; accepted 10 July 2006Available online 24 August 2006

Abstract

We describe a simple procedure to estimate the high-energy neutrino flux from the observed c-ray spectra of galactic cosmic raysources that are transparent to their gamma radiation. We evaluate in this way the neutrino flux from the supernova remnant RXJ1713.7-3946, whose very high-energy c-ray spectrum (assumed to be of hadronic origin) is not a power law distribution according toH.E.S.S. observations. The corresponding muon signal in neutrino telescopes is found to be about five events per km2 per year in anideal detector.� 2006 Elsevier B.V. All rights reserved.

PACS: 98.70.Sa; 95.85.Pw; 98.38.Mz

Keywords: Neutrinos from CR; Observations of c-rays; SNR in Milky Way

1. Context and motivations

The recent observations of c-rays above TeV byH.E.S.S. are of great interest [1,2]. They will certainlyhelp in answering the old question of the origin of thecosmic rays till the knee [3–7] and at the same timethey could provide us a reliable guidance for what weshould expect in neutrino telescopes, at least for certainsources.

This is evident for the main candidate sources of galac-tic cosmic rays, supernova remnants (SNR) [8,9]. Thehuge kinetic energy of the gas of the SNR could beeffectively converted into cosmic rays by diffusive shockacceleration [10], producing enough cosmic rays to com-pensate the losses from the Milky Way. When the SNRis surrounded by matter that can act as a target for cos-mic rays, we would have a point source of very high-

energy (VHE) gamma radiation, which seems in agree-ment with certain H.E.S.S. observations. Since we expectthat the matter around SNR is not too dense anyway, thec-rays are not significantly absorbed, and there is a ratherdirect relation between VHE c-rays and neutrinos.

More in general, we think that it is important to takeadvantage of the detailed observations of c-rays wheneverthey exist in order to formulate definite expectations forneutrino telescopes. This is certainly true after the mostrecent H.E.S.S. observations, that are beginning to findVHE c-ray spectra that deviate from power law distribu-tions above 10 TeV or so [2].

Our recipe to calculate the neutrino fluxes is described inSection 2 and the application to the SNR RX J1713.7-3946is in Section 3. In essence, these results are a straightfor-ward application of standard techniques [11] (and we fol-low as much as possible the conventions of [4] toemphasise this fact) but we hope that they are useful inthe present moment, when the high-energy gamma astron-omy is flourishing and the neutrino telescopes are finallybecoming a reality.

0927-6505/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.astropartphys.2006.07.005

* Tel.: +39 862 437 205.E-mail address: vissani@lngs.infn.it

www.elsevier.com/locate/astropart

Astroparticle Physics 26 (2006) 310–313

2. Deriving the neutrino flux from the c-ray flux

Let us assume that the VHE c-ray flux Fc observed froma certain source is of hadronic origin and that it is not sig-nificantly absorbed – the source is c-transparent.1 From thewell-known relation F cðEÞ ¼

R1E dE02F p0ðE0Þ=E0 valid for

high-energy c-rays we find:

F p0ðEÞ ¼ �E2

dF c

dEð1Þ

that implies that the c-ray flux has to be strictly decreasing.This equation, together with the approximate isospin-invariant distribution of pions:

F p � F p0 � F pþ � F p� ð2Þpermits us to predict the flux of neutrinos using the ob-served c-ray flux. It is important to note that the chargeasymmetry has a small or negligible impact on the observa-ble ml flux, compare [13,14]. The ml flux from the decayp+! l+ml is

F mlðEÞ ¼F cðE=ð1� rÞÞ

2ð1� rÞ ð3Þ

where r = (ml/mp)2. The neutrinos from muon decaylþ ! �mlmeeþ have a more implicit expression:

F mðEmÞ ¼Z 1

0

dyy

F lðElÞ ðg0ðyÞ � �P lðElÞg1ðyÞÞ ð4Þ

where El = Em/y and gi are known polynomials: g0 = 5/3 �3y2 + 4/3y3 and g1 = 1/3 � 3y2 + 8/3y3 when m ¼ �ml, whileg0 = 2 � 6y2 + 4y3 and g1 = � 2 + 12y � 18y2 + 8y3 whenm = me [11]. The muon flux (from p+) that appears inprevious formula is

F lðEÞ ¼F cðEÞ � F cðE=rÞ

2ð1� rÞ ð5Þ

while the muon polarisation averaged over the pion distri-bution is given by

�P lðEÞ � F lðEÞ ¼ �F cðEÞ þ F cðE=rÞ

2ð1� rÞ

þ r

ð1� rÞ2Z E=r

EF cðE0Þ

dE0

Eð6Þ

It is easy to check that in the special case of power law dis-tributions these equations reproduce the results of Section7.1 of [4] (e.g., Eq. (7.14) there).

We include the contribution to c flux from g! cc(resp., the contribution to m flux from the leptonic K±

decay) in the simplest conceivable approximation: namely,we declare that the relevant flux of eta mesons (resp., theone of charged kaons) is proportional to the one of the

neutral pions (resp., of the charged pions) with a fixed coef-ficient fg = 10% (resp. fK = 25% · 0.635). Thus: (1) all for-mulae above should be multiplied by 1/(1 + fg), and then(2) we add a neutrino contribution that has the same formas the one from charged pions, but replacing r = (ml/mK)2

and including the multiplicative factor fK.Finally, we incorporate three neutrino oscillations

replacing:

F ml ! F ml P ll þ F me P el ð7Þ

and the same for antineutrinos. The numerical values of theoscillation probabilities are Pll = 0.39 ± 0.05 and Pel =0.22 � 0.05 where the quoted errors, approximately equaland opposite, are mostly (0.04) due to the spread of h23

around maximal mixing and partly (0.02) to the spreadof h13 around zero; the effect of the uncertainty in h12 issmaller. See [13] for more discussion, [15] for a resume ofneutrino data, and [16] for further references.

We note in passing a stricter condition on the behaviourof the flux of VHE secondaries with the energy. Considerthe connection with the primary cosmic rays F pðEÞ /R1

E dE0F pðE0ÞkðE=E0Þ=E, that we assume for simplicity tobe protons. When we go from E = E1 to E = E2 withE2 > E1, the integral decreases because (1) the lower limitincreases; (2) the scaling distribution k in the integrand isa decreasing function; (3) there is an explicit factor 1/E.Thus, also fp(E) � EFp(E) decreases. The same can be saidof the function fc(E) = EFc(E), since fcðEÞ ¼2R 1

0dzfpðE=zÞ; in other words the flux of hadronic c-rays

decreases at least as 1/E at high energies.2

3. Application: neutrinos from RX J1713.7-3946

We apply the formalism of the previous section toobtain the expected neutrino flux from RX J1713.7-3946on the basis of H.E.S.S. observations [2]. We use twoparameterisations of the c-ray flux that describe well theobservations [2]:

Fig. 1. Expected ml fluxes corresponding to the two c-ray spectra of Eq.(8).

1 Therefore, this procedure is not of direct application for a number ofpossible galactic sources of neutrinos such as micro-quasars [12] that areintrinsically non-transparent or even for extragalactic sources since the IRphotons background absorbs the VHE gammas above �10 TeV; see also[23].

2 Such a very hard spectrum would follow from a hypotheticalpopulation of very energetic primaries. In fact, consider Fp(E 0) =d(E0 � E0): when E� E0 we find that the pions have Fp(E) / 1/E sincek(0) 5 0; thus, the c-rays would obey the 1/E distribution.

F. Vissani / Astroparticle Physics 26 (2006) 310–313 311

F cðEÞ ¼

20:4E�1:98 expð�E=12Þ½exponential cutoff

20:1E�2:06½1þ ðE=6:7Þ2:5�0:496

½broken power law

8>>><>>>:

ð8Þ

where the units are 10�12/(TeV cm2 s) for the flux Fc(E)and TeV for the energy E. We do not use the third para-metrization proposed in [2], Fc / E�2.08�0.3logE, namelythe distribution with energy dependent photon index: infact, this cannot result from p0s, since this is just a Gauss-ian in the logarithmic variable logE, that increases ratherthan decreasing before 40 GeV. Note that a relatively lowcutoff implied by H.E.S.S. observations is consistent withthe present theoretical expectations [17] (however, ratherdifferent models of the same object are also discussed[18]). The result for muon neutrinos according to formulae(3), (4) and (7) is presented in Fig. 1 and Table 1; in ourapproximation, the flux of antineutrinos is the same.

We can estimate the number of through-going events ina neutrino telescope with Eth = 50 GeV, / = 42�50 0

(ANTARES location) following [13]. Considering neutri-nos with energies below Em,max = 300 TeV (that is not a sig-nificant limitation), we find:3

N lþ�l ¼4:8 per km2 per year ½exponential cutoff 5:4 per km2 per year ½broken power law

(

ð9Þthat can be compared with Nlþ�l ¼ 8:8 of [13], obtainedassuming a power law distribution. Thus, the newH.E.S.S. data suggest a signal about 8 times weaker thangiven in [19] (resp., 2 times weaker than in [13]) thatadopted a power law distribution extrapolated from thefirst observations of CANGAROO (resp., of H.E.S.S.).

One can gain something if some events above the hori-zon are accepted; e.g., with 5� more, one can go from afraction of time useful for observation of 78% (used forthe numbers quoted in Eq. (9)) to 88%. This is similar toeffects here neglected, e.g., other contributions of g and K

meson decays or the deviations of h23 from maximal mix-ing, and should be comparable with the error of themethod of calculation we proposed. The effect of finitedetection efficiency for realistic detector configurationsinstead should be more important (comparable with theeffect of the deviation from a power law distribution

discussed here) for the events are not expected to be partic-ularly energetic: the distribution of parent neutrino ener-gies has a median of 3 TeV for both distributions ofEq. (8).

4. Summary and discussion

In summary, we presented a simple procedure to convertthe observations of high-energy c-rays into expectations forhigh-energy neutrinos, assuming that the source is gamma-transparent and that the flux of VHE c-ray is due to cosmicray interactions (=it is of hadronic origin). The latterhypothesis shows that our flux should be thought as anupper bound for gamma-transparent sources. As an appli-cation, we calculated the neutrino flux from RX J1713.7-3946 expected on the basis of new H.E.S.S. results andfound that the expected number of events decreases by40–50% and that the signal consists of relatively low energyevents.

In the future, it will be interesting to repeat the samesteps for other intense sources of VHE c-rays, e.g., VelaJr (RX J0852.0-4652), that is almost continuously visiblefrom ANTARES (95% of time). In the region E 6 10 TeV[1] the spectrum is described by Fc = 21E�2.1 (same units asin Eq. (8)). Suppose that the future observations will dem-onstrate a milder exponential cutoff, described by a multi-plicative factor exp(�E/Ecut) with Ecut = 50(150) TeV. Inthis case we would find N lþ�l ¼ 10ð14Þ events per km2 peryear with a median neutrino energy of 5.5 (8.5) TeV (if,again, we assume that all c-rays are hadronic). If insteadRX J1713.7-3946 should turn out to represent a typicalSNR in a typical stage, it will be important to understandthe cosmic rays from a few hundred TeV till the knee, e.g.,considering other galactic point sources of cosmic raysand/or further phases of cosmic ray acceleration.

These results emphasise even further the importance toobtain c-ray observations in the region from 10 to100 TeV and to understand well the experimental back-ground coming from atmospheric neutrinos.

5. Note added in proof

After the present paper was submitted for publication and when it waspresented at Vulcano 2006 conference (May 2006), a number of interestingnew works appeared: [20] where the background and possible strategiesfor neutrino search are quantitatively discussed; [21] where a detailedparameterizations of neutrino and gamma yields is offered; [22] whereneutrinos events from Vela Jr are estimated (though, without describingthe details of the calculation) using a fixed m/c conversion coefficient =1/2.

Table 1First line: selected values of neutrino energy. Second line: sum of the yields of muons and antimuons (including Earth absorption), times the reference areaA = 1 km2 and observation time T = 1 year. Third and fourth line: the F ml=F c ratio for the c-ray fluxes of Eq. (8), which varies significantly with the energy

E [TeV] .1 .3 1 3 10 30 100 300

AT ðY l þ Y �l) [cm2 s] 1.0E9 2.3E10 2.8E11 1.9E12 1.1E13 3.5E13 9.2E12 1.6E14Exponential cutoff .26 .26 .25 .21 .14 .06 .02 .01Broken power law .25 .25 .25 .21 .14 .13 .13 .13

3 The same numbers are obtained using F ml þ F �ml ¼ 0:37F c.

312 F. Vissani / Astroparticle Physics 26 (2006) 310–313

Acknowledgements

We gratefully thank F. Aharonian, V. Berezinsky, P.L.Ghia, D. Grasso and especially P. Lipari for useful discus-sions and M.L. Costantini for help.

References

[1] See e.g., H.E.S.S. Collaboration, Astron. Astrophys. 437 (2005) L7,95, 135;H.E.S.S. Collaboration, Astron. Astrophys. 439 (2005) 1013;H.E.S.S. Collaboration, Astrophys. j. 636 (2006) 777.

[2] F. Aharonian et al., The HESS Collaboration, A detailed spectraland morphological study of the gamma-ray supernova remnant RXJ1713.7-3946 with HESS, Astron. Astrophys. 449 (2006) 223.

[3] V.S. Berezinsky, S.V. Bulanov, V.A. Dogiel, V.L. Ginzburg, V.S.Ptuskin (Ed.), Astrophysics of Cosmic Rays, (Russian edition) 1984,North Holland, 1990.

[4] T. K Gaisser, Cosmic Rays and Particle Physics, CambridgeUniversity Press, 1990.

[5] T. Stanev, High Energy Cosmic Rays, Springer, 2003.[6] F. Aharonian, Very High Energy Cosmic c Radiation, World

Scientific, 2004.[7] V.S. Ptuskin, Origin of galactic cosmic rays: sources, acceleration,

and propagation, Rapporteur talk at 29th ICRC, vol. 10, 2005, p.317.

[8] W. Baade, F. Zwicky, Phys. Rev. 45 (1934) 138.[9] V.L. Ginzburg, S.I. Syrovatsky, Origin of Cosmic Rays, Moscow,

1964.[10] For reviews see L.O’C. Drury et al., Space Sci. Rev. 99 (2001) 329;

M.A. Malkov, L.O’C. Drury, Rep. Prog. Phys. 64 (2003) 429;A.M. Hillas, J. Phys. G: Nucl. Part. Phys. 31 (2005) R95.

[11] P. Lipari as quoted in the caption of tab. 7.2 of [4]. See also L.V.Volkova, Proceedings of Erice 1988 Cosmic c-rays, Neutrinos, andRelated Astrophysics p. 139;S.M. Barr, T.K. Gaisser, P. Lipari, S. Tilav, Phys. Lett. B 214 (1988)147.

[12] C. Distefano, D. Guetta, E. Waxman, A. Levinson, Astrophys. J. 575(2002) 378;See W. Bednarek, G.F. Burgio, T. Montaruli, New Astron. Rev. 49(2005) 1, for a review of possible galactic neutrino sources.

[13] M.L. Costantini, F. Vissani, Astropart. Phys. 23 (2005) 477.[14] V. Cavasinni, D. Grasso, L. Maccione. Available from: <astro-ph/

0604004>.[15] A. Strumia, F. Vissani, Nucl. Phys. B 726 (2005) 294;

A. Strumia, F. Vissani. Available from: <hep-ph/0606054>;G.L. Fogli, E. Lisi, A. Marrone, A. Palazzo. Available from: <hep-ph/0506083>.

[16] S.M. Bilenky, B. Pontecorvo, Phys. Rept. 41 (1978) 225;J. Learned, S. Pakvasa, Astroparticle Phys. 3 (1995) 267;R.M. Crocker, F. Melia, R.R. Volkas, Astroph. J. Suppl. 130 (2000)339;H. Athar, M. Jezabek, O. Yasuda, Phys. Rev. D 62 (2000) 103007;R.M. Crocker, F. Melia, R.R. Volkas, Astroph. J. Suppl. 141 (2002)147;J.F. Beacom, N.F. Bell, D. Hooper, S. Pakvasa, T.J. Weiler, Phys.Rev. D 68 (2003) 0930005.

[17] E.G. Berezhko, H.J. Volk. Available from: <astro-ph/0602177>.[18] M.A. Malkov, P.H. Diamond, R.Z. Sagdeev, Astrophys. J. 624 (2005)

L37.[19] J. Alvarez-Muniz, F. Halzen, Astrophys. J. 576 (2002) L33.[20] P. Lipari. Available from: <astro-ph/0605535>.[21] S.R. Kelner, F.A. Aharonian, V.V. Bugayov. Available from: <astro-

ph/0606058>.[22] U.F. Katz. Available from: <astro-ph/0606068>.[23] H.E.S.S. Collaboration, Nature 440 (2006) 1018.

F. Vissani / Astroparticle Physics 26 (2006) 310–313 313