On the transport and propagation of cosmic rays in galaxies. I - Solution of the steady-state transport equation for cosmic ray nucleons, momentum spectra and heating of the interstellar medium

Details On the transport and propagation of cosmic rays in galaxies. I - Solution of the steady-state transport equation for cosmic ray nucleons, momentum spectra and heating of the interstellar medium On the transport and propagation of cosmic rays in galaxies. I - Solution of the steady-state transport equation for cosmic ray nucleons, momentum spectra and heating of the interstellar medium

Dec 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982mnras.201.1041l&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 201, Dec. 1982, p. 1041-1072.

Astronomy and Astrophysics

Astronomy

45

Cosmic Rays, Interstellar Matter, Nucleons, Particle Motion, Transport Theory, Astronomical Models, Energy Dissipation, Momentum, Power Spectra, Steady State

Scientific paper

We present exact analytical solutions to the equation describing the steady-state transport, in a direction perpendicular to the galactic plane, of cosmic ray nucleons which are being convected, diffused and may be either gaining or losing momentum. The solutions allow for: (i) a spatially varying convection velocity; (ii) a diffusion coefficient which is both momentum and position dependent; (iii) adiabatic deceleration effects; (iv) a term describing the ionization loss and/or Fermi acceleration which is also spatially dependent; (v) a point (spatial) injection source or a spatially more diffuse source; (vi) arbitrary momentum dependence of the injection source.
We calculate momentum spectra for the special case of momentum power- law injection spectra S ∝ p-ɛ and power-law momentum dependence of the diffusion coefficient D(p) = D0pa and discuss these solutions in detail. The comparison of the nucleon momentum spectrum with measurements near the Solar System yields ɛ = 2.4, α = 0.6 ± 0.2 and wind velocities near the Solar System smaller than 50 km s-1. The calculated cosmic ray ionization rate of the interstellar medium is strongly influenced by the absolute value of the diffusion coefficient. Measurements so far indicate a diffusion coefficient of the order D(p) ≃ 1027 [p/(GeV/c)]0.6 cm2 s-1 near the Solar System. The heating of interstellar gas in the galactic disc and corona is discussed. In the disc cosmic ray ionization yields heating rates of the order 10-25 erg cm-3 s-1. The cosmic ray pressure is calculated as a function of galactic height and is shown to be practically constant at ˜7.10-13 dyne cm-2for galactic heights smaller than several Kpc.

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