The Proton Spectrum in the 0.1-100 TeV Energy Range Obtained from Direct Measurements of the All-Particle Spectrum

Details The Proton Spectrum in the 0.1-100 TeV Energy Range Obtained from Direct Measurements of the All-Particle Spectrum The Proton Spectrum in the 0.1-100 TeV Energy Range Obtained from Direct Measurements of the All-Particle Spectrum

Jul 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003icrc....4.1841t&link_type=abstract

Proceedings of the 28th International Cosmic Ray Conference. July 31-August 7, 2003. Trukuba, Japan. Under the auspices of the I

Physics

Scientific paper

The proton spectrum was obtained as the difference between the allparticle flux and the flux of all nuclei with Z ≥ 2 The obtained spectrum has a `knee' at the energy of about 1 TeV. The spectral index βp = 2.6 - 2.7 in the energy range E < 1 TeV and βp = 3.0 - 3.1 in the energy range E ≥ 1 TeV. The proton spectrum Ip (E ) can be obtained from the obvious equality Io (E ) = Ip (E ) + Iz (E ), where Io is the all-particle spectrum, and Iz is the spectrum of all nuclei with Z ≥ 2. Multiplying all the terms of this equality by E 2.6 and inter-substituting Io and Ip , we obtain: E 2.6 Ip = E 2.6 Io - E 2.6 Iz (1) In a broad range of energies E 2.6 Iz = const = Φz , therefore, expression (1) can be rewritten as E 2.6 Ip = E 2.6 Io - Φz . In the energy range E < 1 TeV E 2.6 Io = const = 0.248 ± 0.005m-2 s-1 sr -1 T eV 1.6 [1] and Φz = 0.138 ± 0.005m-2 s-1 sr -1 T eV 1.6 , hence, E 2.6 Ip = const = 0.11 ± 0.009m-2 s-1 sr -1 T eV 1.6 . Thus, βp = 2.6. In the energy range E > 1 TeV the all-particle spectrum index β = 2.88 ± 0.04, therefore, βp should be greater than 2.6. The value of βp at E > 1T eV can be obtained from the all-particle spectrum characteristics, if we rewrite the proton spectrum in a somewhat simplified form: as Ip (E ) ˜ E -2.6 at E ≤ Ec and as Ip ˜ E -βp at E > Ec . For such a proton spectrum the all-particle spectrum will have the following form: E 2.6 Io (E ) = be -(βp -2.6) + Φz . At E = Ec we have E 2.6 Io = Φ1 and b= (Φ1 - Φz )Ecβp -2.6) . Therefore, E 2.6 Io (E ) = (Φ1 - ( Φz )(E /Ec )-(βp -2.6) + Φz . The sum of two power-law functions be -γ1 + C E -γ2 can be substituted with good accuracy by one power-law function D E -γ , where γ = C BB γ1 + C +B γ2 [2]. In our case γ1 = βp - 2.6 and b= Φ1Φ1Φz ,γ2 = 0 and C - + C = Φz /Φ1 . Therefore, the power index of the sum of the spectra will be equal to Φ 1 -Φ z (βp - 2.6). In the E > Ec energy range the spectral index of the all particle Φ1

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