Cosmic Rays in Clouds and Disks

Galactic cosmic rays (CRs) are a ubiquitous source of ionisation of the interstellar gas. Along with UV and X-ray photons as well as natural radioactivity they determine the fractional abundance of electrons, ions and charged dust grains in molecular clouds and circumstellar discs, and thus substantially impact the dynamical and chemical processes occurring in these objects. One of the principal aims of the CAS-Theory group is to understand the physics of CRs in clouds and disks, by combining advanced theoretical methods of the kinetic theory and plasma physics and applying available observational constraints. These efforts enable self-consistent modeling of the key processes, including the evolution of dense cores and the formation of disks, coagulation of dust grains and the processing of ice mantles on their surface, chemical reactions ongoing on the dust and in the gas phase, etc.

The transport regime of the penetration of Galactic CRs and their further propagation in clouds and disks depend on a variety of conditions – CRs can stream freely along the magnetic field lines, or they experience significant scattering on the field fluctuations, and thus propagate diffusively. Below we highlight three topics illustrating our research:

Self-modulation of penetrating CRs.

In papers by Ivlev et al. (2018) and Dogiel et al. (2018) we showed that the Galactic spectrum of CR protons at energies below ~30 GeV could be significantly modified while CRs traverse the outer diffuse envelope of a dense cloud, even though the ionisation losses in the envelope are relatively low. The governing mechanism behind the effect is the excitation of MHD waves in the envelope by a flux of penetrating CRs. These self-generated magnetic disturbances effectively scatter CRs, which inhibits their free streaming into the cloud. We developed a self-consistent model of this essentially nonlinear phenomenon, describing the energy-dependent transition between a free streaming and diffusive propagation of CRs. One of our key findings is the existence of a certain threshold energy below which the penetrating flux is modulated. Figure 1 illustrates the modulation effect for the Central Molecular Zone (CMZ), showing that CRs can be significantly depleted in the interior of dense clouds.

Figure 1: Modulated energy spectrum of CR protons in the CMZ, calculated for the interstellar proton spectrum (thick dotted line). The solid lines represent the case where no effects of heavier CRs are included; the other curves are for an additional 10% of He nuclei (dashed lines) and for all elements (dotted line).

Magnetic mirroring and focusing in dense cores and disks.

Irrespective of their transport regime, CRs propagate along the local magnetic field lines. The magnetic configuration in dense astrophysical objects can be very complicated and the field strength can be much larger than the interstellar value. This leads to efficient mirroring of the penetrating CRs – their pitch angles increase in response to the growing field until reaching 90°, and thus more and more particles are reflected back. On the other hand, the convergence of field lines results in the CR focusing. In Silsbee et al. (2018) we have studied the combined impact of magnetic mirroring and focusing on the ionisation by CRs in dense molecular clouds and circumstellar disks. We rigorously showed that for effective column densities of up to ∼1025 cm –2 the two effects practically cancel each other out, provided the magnetic field strength has a single peak along field lines. On the other hand, in the presence of the local field minima – “magnetic pockets” (see Figure 2), the local ionization can be reduced drastically.

Figure 2: A sketch of the magnetic field strength B as a function of distance s along a field line. A situation is illustrated where B has multiple maxima. This results in multiple magnetic pockets, indicated by the shading.

Ionization in dense regions of disks.

The processes governing the CR propagation and ionisation become remarkably diversified at column densities N above ~1025 cm –2, relevant for the inner regions of collapsing clouds and circumstellar discs. Mechanisms of energy loss other than ionisation become dominant in this case. In a paper by Padovani et al. (2018) we carefully investigated attenuation of interstellar CRs at such high column densities, by including both the relevant energy loss and the particle production mechanisms and adopting appropriate models for the transport of primary and secondary CR particles. We found that for N above ≈ 3x1025 cm –2 the CR ionisation rate rapidly becomes dominated by electron-positron pairs, locally produced by secondary photons. Figure 3 shows contributions of the primary and secondary CRs into the total ionisation rate, demonstrating that the ionisation at very high column densities is expected to be much higher than previously thought.

Figure 3: Ionisation rate per H2 molecule due to primary and secondary CR species, ζ, plotted vs. the gas column density N. The black solid curve shows the total ionisation rate, the coloured curves represent partial contributions, as indicated in the legend. The horizontal dashed line is the ionisation rate set by long-lived radioactive nuclei (LLR). For comparison, the grey dotted curve shows ζ(N) which had been commonly used previously.

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