Method to extract the primary cosmic ray spectrum from very high energy $\ensuremath{\gamma}$-ray data and its application to SNR RX J1713.7-3946

Method to extract the primary cosmic ray spectrum from very high energy $γ$ -ray data and its application to SNR RX J1713.7-3946

F. L. Villante and F. Vissani

Phys. Rev. D 76, 125019 – Published 19 December 2007

Abstract

Supernova remnants are likely to be the accelerators of the galactic cosmic rays. Assuming the correctness of this hypothesis, we develop a method to extract the parent cosmic ray spectrum from the very high energy gamma-ray flux emitted by supernova remnants (and other gamma transparent sources). Namely, we calculate semianalytically the (inverse) operator which relates an arbitrary gamma-ray flux to the parent cosmic ray spectrum, without relying on any theoretical assumption about the shape of the cosmic ray and/or photon spectrum. We illustrate the use of this technique by applying it to the young SNR RX J1713.7-3946 which has been observed by the High Energy Stereoscopic System (H.E.S.S.) experiment during the last three years. Specific implementations of the method permit using as an input either the parametrized very high energy gamma-ray flux or directly the raw data. The possibility to detect features in the cosmic rays spectrum and the error in the determination of the parent cosmic ray spectrum are also discussed.

Received 19 July 2007

DOI:https://doi.org/10.1103/PhysRevD.76.125019

Authors & Affiliations

F. L. Villante^1,* and F. Vissani²

¹Università di Ferrara and INFN, Ferrara, Italy
²INFN, Laboratori Nazionali del Gran Sasso, Assergi (AQ), Italy

^*Present and permanent address: Università dell’Aquila and INFN, Laboratori Nazionali del Gran Sasso, Assergi (AQ), Italy.

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Vol. 76, Iss. 12 — 15 December 2007

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Figure 1
The integral kernel $f [y, ε_{p}]$ as a function of $y \equiv \ln [E_{γ} / E_{p}]$ for selected values of the proton energy $ε_{p} \equiv \ln [E_{p} / 1 TeV]$ . We have chosen $ε_{p} = 0$ , 2.3, 4.6, 6.9 corresponding to $E_{p} ≃ 1$ , 10, 100, 1000 TeV, respectively.Reuse & Permissions
Figure 2
Absolute value and argument of the function $h [k]$ defined in Eq. (17).Reuse & Permissions
Figure 3
The $γ$ -ray spectrum of the RX J1713.7-3946 Supernova Remnant obtained by H.E.S.S. experiment. The black line represents the best fit to the data in the assumption of a power-law behavior of the photon spectrum. The blue (or dark gray) lines are obtained by assuming that the photon spectrum follows the BPL given by Eq. (21) in the assumption that the transition parameter is $S = 0.6$ (blue solid line) or $S = 0.45$ , 0.75 (blue dotted lines). The red (or gray) lines refers to the EC case, see Eq. (22), in the assumption that $β = 0.5$ (red solid line) or $β = 1.0$ (red dotted line).Reuse & Permissions
Figure 4
(Left panel) The effective CR flux $Φ_{p} [E_{p}]$ from the SNR RX J1713.7-3946 obtained from BPL and EC parametrizations of the gamma-ray flux measured by the H.E.S.S. experiment. The blue (or dark gray) lines are obtained from the best-fit BPL parametrizations with sharpness parameter $S = 0.6$ (blue solid line), $S = 0.45$ (blue dotted line) and $S = 0.75$ (blue dashed line). The red (or gray) lines correspond to best-fit EC parametrization with $β = 0.5$ (red solid line) and $β = 1.0$ (red dotted line). (Right panel) The CR energy distribution $J [E_{p}]$ calculated from Eq. (6) by assuming $R = 1 kpc$ and $N = 3.6 \times 10^{59}$ .Reuse & Permissions
Figure 5
(Left panel) The (smoothed) CR spectrum from the RX J1713.7-3946 SNR deduced from the raw data of the H.E.S.S. experiments. The solid line is obtained by continuing the $γ$ -ray spectrum at low and high energy with the best-fit BPL with sharpness parameter $S = 0.6$ , while the dashed line is obtained by using the best-fit EC with $β = 0.5$ . The shaded area represents the observational uncertainty and is obtained by propagating H.E.S.S. observational errors. (Right panel) The (smoothed) CR energy distribution calculated from Eq. (26) with $R = 1 kpc$ and $N = 3.6 \times 10^{59}$ .Reuse & Permissions
Figure 6
Correlation between the values of the (smoothed) proton spectrum obtained at two different energies. Light shadings correspond to values of the correlation index close to 1, while dark shadings correspond to values close to $- 1$ . The displayed contours correspond to a correlation index equal to 0.5 and to $- 0.5$ .Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology

Method to extract the primary cosmic ray spectrum from very high energy $γ$ -ray data and its application to SNR RX J1713.7-3946

F. L. Villante and F. Vissani

Phys. Rev. D 76, 125019 – Published 19 December 2007

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Physical Review D

covering particles, fields, gravitation, and cosmology

Method to extract the primary cosmic ray spectrum from very high energy γ-ray data and its application to SNR RX J1713.7-3946

F. L. Villante and F. Vissani

Phys. Rev. D 76, 125019 – Published 19 December 2007

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Method to extract the primary cosmic ray spectrum from very high energy $γ$ -ray data and its application to SNR RX J1713.7-3946