Penetration of Cosmic Rays into Dense Molecular Clouds: Role of Diffuse Envelopes^∗

Abstract

A flux of cosmic rays (CRs) propagating through a diffuse ionized gas can excite MHD waves, thus generating magnetic disturbances. We propose a generic model of CR penetration into molecular clouds through their diffuse envelopes, and identify the leading physical processes controlling their transport on the way from a highly ionized interstellar medium to a dense interior of the cloud. The model allows us to describe a transition between a free streaming of CRs and their diffusive propagation, determined by the scattering on the self-generated disturbances. A self-consistent set of equations, governing the diffusive transport regime in an envelope and the MHD turbulence generated by the modulated CR flux, is essentially characterized by two dimensionless numbers. We demonstrate a remarkable mutual complementarity of different mechanisms leading to the onset of the diffusive regime, which results in a universal energy spectrum of the modulated CRs. In conclusion, we briefly discuss implications of our results for several fundamental astrophysical problems, such as the spatial distribution of CRs in the Galaxy as well as the ionization, heating, and chemistry in dense molecular clouds. Subject headings: cosmic rays -ISM: clouds -turbulence -plasmas * This paper is dedicated to the memory of Prof. Vadim Tsytovich.

Impact of Low-Energy Cosmic Rays on Star Formation

“…The spectrum of MHD turbulence determines the magnitude of the CR diffusion coefficient and its dependence on the particle energy (Schlickeiser et al, 2016;Silsbee and Ivlev, 2019). However, MHD turbulence can also be driven by anisotropy in the CR distribution function (Skilling and Strong, 1976;Morlino and Gabici, 2015;Ivlev et al, 2018), which arises in response to CR absorption in dense cores. We begin by briefly summarising the basic principles of diffusive CR transport.…”

“…It has long been known (see Lerche, 1967;Kulsrud and Pearce, 1969) that a CR flux propagating through a plasma can excite MHD waves and thus create magnetic disturbances. However, the effect of these disturbances on the penetration of CRs into molecular clouds and on the resulting ionisation is still debated (Skilling and Strong, 1976;Cesarsky and Völk, 1978;Morlino and Gabici, 2015;Ivlev et al, 2018;Phan et al, 2018;Dogiel et al, 2018). Skilling and Strong (1976) predicted from a qualitative analysis of the problem a depletion of CR density inside the clouds.…”

Gas and Dust Temperature in Prestellar Cores Revisited: New Limits on Cosmic-Ray Ionization Rate

“…The magnitude of the CR ionization rate ζ ion measured in the outer envelopes of molecular clouds (in a range of the gas column densie-mail: ivlev@mpe.mpg.de e-mail: ksilsbee@mpe.mpg.de ties around N ∼ 10 21 cm −2 ) varies significantly from one object to another (Indriolo & McCall 2012;Neufeld & Wolfire 2017;Bacalla et al 2019). Given uncertainties in the leading transport regime(s) governing the CR penetration into the clouds (Ivlev et al 2018;Silsbee & Ivlev 2019), this introduces significant uncertainty in the value of ζ ion near the center; available theories (Padovani et al 2018b) predict ζ ion ∼ 10 −17 − 10 −16 s −1 for N ∼ 10 23 cm −2 .…”

The cosmic-ray content of the Orion-Eridanus superbubble

“…It implies that the same CR spectrum permeates the atomic and DNM phases even though the gas is denser and less ionised at the H i-H 2 transition than in the warm H i envelope. The North Rim DNM mass is large (of order 1.2×10 4 M at 160 pc), but the DNM gas column densities of 2 to 20×10 20 cm −2 are one to two orders of magnitude below the critical values for significant low-energy CR depletion (Ivlev et al 2018).…”