Cosmic rays and neutrinos from supernova remnants from VHE gamma

ray data

F.L. Villanteab and F. Vissanib

aUniversita dell’Aquila, Dipartimento di Fisica, L’Aquila, Italy

bINFN, Laboratori Nazionali del GranSasso, Assergi (AQ), Italy

Motivated by the possibility that cosmic rays (CR) originate from supernova remnants, we ask ourselves whatwe learn on CR and ν produced in these systems from the emitted very high energy (VHE) γ radiation. Weanswer to this question in a simple, accurate and model-independent way.

1. Introduction

The idea that cosmic ray (CR) could origi-nate in supernovae has been put forward alreadyin 1934 but the first quantitative formulation ofthe conjecture that the young supernova rem-nants (SNR) refurnish the Milky Way of cosmicrays, compensating the energy losses, is due toGinzburg and Syrovatskii [1]1. In recent times,great progresses have been made in the under-standing and in the observation of these systems.In particular, the High Energy Stereoscopic Sys-tem (H.E.S.S.) has determined quite precisely theγ−ray spectra of few SNRs, showing that they ex-tend above 10 TeV. This is naturally expected ifSNRs are effective site of acceleration of CR. Theinteractions of accelerated CR with ambient hy-drogen result, indeed, in the production of mesonswhich subsequently decay producing gamma rayand neutrinos. New and crucial observations arebeing collected and the hadronic origin of the ob-served γ radiation seems to be favored for certainSNRs, such as Vela Jr and RX J1713.7-3946.

In this paper we take the hadronic origin as aworking hypothesis and we ask ourselves: whatcan we learn on CR and ν from the observed veryhigh energy (VHE) γ radiation? This questionis particularly urgent in view of the forecoming,large ν telescopes.

1Due to space limitation, we provide in this paper a lim-ited reference list. For complete list of references see [2,3]

2. The primary CR spectrum

Let us begin by studying what we can learnon the CR spectrum from the VHE γ−ray data.The mathematical problem is to invert an integralequation:

Φγ [Eγ ] =

∫∞

Eγ

dEp

Ep

Φp[Ep] Fγ

[Eγ

Ep

, Ep

](1)

Here, Φγ [Eγ ] is the photon flux produced on adetector placed at a distance R and Φp[Ep] is the”effective” CR flux in the SNR defined as follows:

Φp[Ep] =c σ[Ep]

4πR2

∫d3r n[r]

dnp[r, Ep]

dEp

(2)

where np and n represent the proton CR andproton target densities and σ is the total inelas-tic p-p cross-section. The adimensional distribu-tion function Fγ [x, Ep] describes hadronic inter-actions, according to the usual definition:

dσγ

dEγ

=σ[Ep]

Ep

Fγ

[Eγ

Ep

, Ep

](3)

We note that for Fγ [x, Ep] = (1 − x)4/x thatsomehow resembles the true hadronic interactionkernel an analyical solution can be found:

Φp[Ep] = −E4

24

d5

dE5[EΦγ [E]] (4)

This result can be generalized. Namely, a similarsimple formula can be obtained also for the true

Nuclear Physics B (Proc. Suppl.) 188 (2009) 261–263

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kernel (we use the analytical parameterization ofRef.[4]). Indeed, taking advantage to the scalingproperties of hadronic cross sections, the eq.(1)can be approximated as follows

Φγ [Eγ ] =

∫∞

Eγ

dEp

Ep

Φp[Ep] Fγ

[Eγ

Ep

, Ep = Ep,0

](5)

This has the form of a convolution integral in thevariable ε = log[E/1TeV] and can be treated withstandard Fourier techniques. Furthermore, by ap-proximating the Fourier transform of the inversekernel with a a polynomial, one can show that theprimary CR flux is given by

Φp[E] =

5∑i=0

ai

(E

d

dE

)i

Φγ [E] (6)

with a precision of several percent. The valueof the numerical coefficients ai can be found inRef.[2]

3. The neutrino flux

The gamma ray and neutrino fluxes producedby the interactions of CR protons in SNRs withambient hydrogen depend linearly on the flux ofthe primary cosmic ray. We, thus, expect thata linear relation also exists between photon andneutrino fluxes, which can formally be expressedas:

Φν [Eν ] =

∫dEγ

Eγ

Kν [Eν/Eγ ] Φγ [Eγ ]. (7)

In order to determine the kernels Kν [x], we onlyneed to know the relative production rate Ri[E]of the various mesons in hadronic interactions. Inthe assumption that the production rates of thevarious mesons fi = Ri/Rπ0 (rescaled to that ofπ0) are approximately constant, one shows that(see [3,5]):

Kν [x] = −1

2(1 + 0.39fη)

∑i

fi

dωiν [x]

d lnx(8)

where i = π+, π−, K+, K− and the quantityωiν [x] dx, with x = Eν/E, represents the spec-trum of neutrinos ν produced in the decay chainof the i−meson. The factors fi can be calculatedfrom hadronic interaction models. In ref.[3] we

calculated them by using the results of [8]. Wealso performed a comparison with other param-eterizations of hadronic cross sections, showingthat the fi factors are practically unchanged inthe various cases.

Neutrinos fluxes produced in SNRs differ fromthose observed at earth due to the effect of neu-trino oscillations. These can be included by defin-ing the “oscillated” kernel given by:

Koscνμ

[x] = Pμμ Kνμ[x] + Peμ Kνe

[x]. (9)

A similar relation hold for νμ. In Ref.[3] we evalu-ated the the oscillation probabilities P��′ , showingthat the error on Φνμ

(and Φνμ) arising from neu-

trino mixing parameters is very small (at the levelof 2%), as a result of the partial cancellation ofthe anti-correlated contributions of Peμ and Pμμ

to the total error budget.As a final result, one obtains a simple analytic

expression:

Φνμ[E] = 0.38Φγ[2.34E] + 0.013Φγ[1.05E]

+

∫ 1

0

dx

xkνμ

[x] Φγ [E/x] (10)

where the first two terms describe neutrinos pro-duced in pions and kaons decays, while the kernelkνμ

[x], given explicitely in [3], accounts for neutri-nos produced by muon decay. A similar relationholds for Φνμ

.

4. Application to SNR RXJ1713.7-3946

Eqs.(6) and (10) have a general validity andcan be applied directly to observational data sincethey do not require any specific parametrizationof the photon spectrum. We apply them toSNR RXJ1713.7-3946 which has been studied byH.E.S.S. during three years from 2003 to 2005 [7].The obtained results are shown in Fig.1, wherethe left panel refers to the primary CR spectrum,while the right panel shows the νμ and νμ fluxes.

We see that the primary CR spectrum is welldescribed by a by power-law with spectral indexΓ =1 .7−2 at low energy with a cutoff/transitionregion between Ep = 30 − 100 TeV. The limitedprecision of the data does not allow to extractsmall scale features of the CR spectrum, sincefluctuations of the γ−ray data on small scales

F.L. Villante, F. Vissani / Nuclear Physics B (Proc. Suppl.) 188 (2009) 261–263262

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Fig. 1: The (smoothed) CR spectrum, ϕp = ΦpE2.5p , and the ν fluxes from SNR RXJ1713.7-3946.

are amplified in the CR flux, as can be under-stood from eq.(6). For this reason, we applied agaussian filter to the data (a sort of ’image pro-cessing’) before extracting the CR spectrum (seeRef.[2] for details). The two curves corresponds todifferent extrapolations of γ−ray spectrum out-side the energy region probed by H.E.S.S. andallow to estimate the systematic uncertainty in-troduced by the ignorance of the high and/or lowenergy behaviour of the photon flux. The shadedarea are obtained by propagating errors in theγ−ray data and show that the observational un-certainty is less than 10% at low energy and re-mains smaller than 20% for Ep ≤ 300 TeV.

The solid (dashed) line in the right panel ofFig.1 is the νμ flux (νμ flux) expected from RXJ1713.7-3946 derived from the H.E.S.S. observa-tional γ−ray data (see [3] for details). We cansee that the neutrino and antineutrino spectra arewell described by a power law with spectral indexγ � 2 at low energies and a cutoff/transition re-gion at Eν ∼ 3 − 5 TeV. The ratio Φνμ

/Φνμis

nearly constant and equal to about 0.93. Wee seethat neutrino fluxes are well constrained at lowenergies where the observational errors (shadedareas) are at few per cents level. For comparison,we also show with (blue) dotted line the muonneutrino flux given in [6] The red dashed line inFig. 1 provides an estimate of the atmosphericneutrino background and is obtained by integrat-ing the muon neutrino flux in the vertical direc-tion over a circular observation window with anangular diameter equal to 2.0◦. We see that the

spectral region in which the signal is expected tobe larger than the background is above ∼ 1TeVquite close to cutoff in the ν spectrum.

The above method has been used in Ref.[3]to discuss wheter future neutrino telescopes havethe potential to observe neutrinos from SNRs. Itseems possible, at least for the best observed SNR(RX J1713.7-3946), to detect a neutrino signalwith exposures of the order of year× km2, pro-vided that the detection threshold in future neu-trino telescopes will be not higher than ∼ 1TeV.Due to the presence of the atmospheric neutrinobackground, it does not seem really useful tolower the threshold much below the TeV region.

REFERENCES

1. V.L. Ginzburg and S.I. Syrovatsky, Origin ofCosmic Rays (1964), Moscow.

2. F. L. Villante and F. Vissani, Phys. Rev. D76 (2007) 125019

3. F. L. Villante and F. Vissani, Phys. Rev. D,in press; arXiv:0807.4151 [astro-ph].

4. S. R. Kelner et al. Phys. Rev. D 74 (2006)034018

5. F. Vissani, Astropart. Phys. 26 (2006) 310[arXiv:astro-ph/0607249].

6. F. Vissani and F. L. Villante, Nucl. Instrum.Meth. A 588 (2008) 123.

7. F. Aharonian [HESS Collaboration], Astron.Astrophys. 464 (2007) 235.

8. H. B. J. Koers, A. Pe’er and R. A. M. Wijers,arXiv:hep-ph/0611219.

F.L. Villante, F. Vissani / Nuclear Physics B (Proc. Suppl.) 188 (2009) 261–263 263