Cosmic Rays

Galactic cosmic rays (CRs) are a ubiquitous source of ionization and heating of the interstellar gas. In dense astrophysical environments – such as molecular clouds and pre-stellar cores, where UV and X-ray photons cannot penetrate – the ionization and heating are completely dominated by CRs. One of the principal aims of the CAS-Theory group is to understand properties and transport mechanisms of low-energy CRs, and to derive a bigger picture relating the local CR spectra to the physics of Galactic CRs. The ultimate goal of these efforts is to enable self-consistent modelling of the key physical and chemical processes governed by CRs in molecular clouds. Several recent highlights of our research are presented below.

Re-evaluation of the cosmic-ray ionization rate in diffuse molecular clouds

A universal parameter characterizing impact of CRs on a medium is the ionization rate (CRIR), which is usually estimated from observed abundances of certain ions that can only be produced by CRs. All previous estimates of CRIR rely on model-dependent assessments of the gas density along the probed sight lines, and the resulting values of CRIR typically exceed the values derived for the CR spectra measured by the Voyager spacecraft by an order of magnitude.

In Obolentseva et al. (2024), we utilized high-resolution 3D dust extinction maps by Edenhofer et al. (2024) (recently developed by our neighbours at MPA in the group of PD Dr. Torsten Enßlin), which allowed us to precisely identify the location of molecular clouds probed in each measurement, and also to derive the gas density in these clouds. Hence, we were able to evaluate CRIR in each cloud without involving any model-dependent assumption about the environment.

Our results illustrated in Fig. 1 indicate that (i) values of CRIR probed in individual diffuse molecular clouds in the local Galactic environment may vary significantly from cloud to cloud, while the average CRIR value is (ii) a factor of ~10 smaller than that derived previously, and (iii) consistent with the CR spectra measured by the Voyager spacecraft.

Left: Re-evaluated values of the CRIR per H2 molecule (ζH2) obtained from the analysis of observations toward different stars (indicated by their HD catalogue numbers), and earlier results for these sight lines. The grey curve represents the CRIR derived from the Voyager data. The horizontal axis indicates the gas column density of molecular clouds where the CRIR was measured. Right: The circles show locations of the gas clumps that were probed along the detection sight lines (projected onto the Galactic plane), the color-coding depicts the derived value of the CRIR. — Left: Re-evaluated values of the CRIR per H₂ molecule (ζ_H2) obtained from the analysis of observations toward different stars (indicated by their HD catalogue numbers), and earlier results for these sight lines. The grey curve represents the CRIR derived from the Voyager data. The horizontal axis indicates the gas column density of molecular clouds where the CRIR was measured. Right: The circles show locations of the gas clumps that were probed along the detection sight lines (projected onto the Galactic plane), the color-coding depicts the derived value of the CRIR.

Left: Re-evaluated values of the CRIR per H₂ molecule (ζ_H2) obtained from the analysis of observations toward different stars (indicated by their HD catalogue numbers), and earlier results for these sight lines. The grey curve represents the CRIR derived from the Voyager data. The horizontal axis indicates the gas column density of molecular clouds where the CRIR was measured. Right: The circles show locations of the gas clumps that were probed along the detection sight lines (projected onto the Galactic plane), the color-coding depicts the derived value of the CRIR.

Self-modulation of cosmic rays penetrating dense molecular clouds

Several years ago, we developed a theory of CR self-modulation in dense molecular clouds (Ivlev et al. 2018). We showed that the modulation occurs due self-generated Alfvénic turbulence, resonantly excited by the penetrating CRs in diffuse envelopes surrounding the clouds. In a subsequent paper (Dogiel et al. 2018) we applied the theory to investigate whether the mechanism of self-modulation can explain gamma-ray features observed in the Galactic center. Assuming a simplified cloud model, with a dense core and a diffuse surrounding envelope of a constant gas density about 10 cm^–3, we showed that gamma-ray emission is noticeably suppressed at GeV energies for the cloud column densities over 10²³ cm⁻². However, the 3D dust extinction maps by Edenhofer et al. (2024) indicate that the gas distribution in envelopes is highly inhomogeneous, decreasing monotonically from the cloud center, and typical density values are substantially lower than that assumed in Dogiel et al (2018).

In Chernyshov et al. (2024)a we have now generalized the theory of CR self-modulation for inhomogeneous envelopes, making it applicable to arbitrary monotonically decreasing density profiles. In this case, we found that noticeable suppression of GeV gamma rays already occurs when the gas column density exceeds a few times 10²² cm⁻². We obtained excellent quantitative agreement with recent Fermi LAT observations of nearby giant molecular clouds (Yang et al. 2023) showing deficits in the gamma-ray residual map at energies below a few GeV (see Fig. 2).

The above results obtained for relativistic CRs suggest that the impact of self-generated turbulence on penetration of lower-energy CRs, responsible for ionization in the cloud interior, may be dramatic. Our preliminary analysis shows that attenuation of the CRIR with gas column density traversed by CRs may be substantially steeper than that predicted by traditional models of CR propagation, implying a notable redaction of the ionization in dense cores with column densities over 10²² cm⁻².

Comparison between gamma-ray observations of giant molecular clouds and our theoretical model. The grey and black symbols represent the measured emissivity reported in Yang et al. (2023) for the surrounding diffuse gas and dense molecular clumps, respectively. The grey solid line represents the theoretical emissivity computed for the unmodulated spectrum of CRs. The emissivity for modulated spectra obtained from our model is shown by different lines illustrating contributions of different CR nuclei, as indicated in the legend.

Comparison between gamma-ray observations of giant molecular clouds and our theoretical model. The grey and black symbols represent the measured emissivity reported in Yang et al. (2023) for the surrounding diffuse gas and dense molecular clumps, respectively. The grey solid line represents the theoretical emissivity computed for the unmodulated spectrum of CRs. The emissivity for modulated spectra obtained from our model is shown by different lines illustrating contributions of different CR nuclei, as indicated in the legend.

Self-consistent model of the Galactic cosmic-ray halo

Formation of the CR Galactic halo is the long-standing problem. There have been a large number of different halo models developed so far, some of them are currently broadly implemented in advanced numerical codes such as e.g., GALPROP. The main disadvantage of many available models, however, is that they depend on two arbitrary parameters whose values are ambiguously defined, namely the CR diffusion coefficient in the halo and its size (i.e., the height above the disk mid-plane starting from which CRs freely escape the Galaxy). Therefore, it is necessary to self-consistently describe the processes of generation and damping of MHD turbulence in the halo and connect this to the CR transport.

In Chernyshov et al. (2022) and (2024)b we developed a self-consistent model of the CR halo, and used it to compute the Galactic spectra of stable and unstable secondary nuclei. We assume that the confinement of CRs in the Galaxy is entirely determined by the self-generated turbulence, whose spectrum is controlled by a balance of the resonant streaming instability generated by escaping CRs and nonlinear Landau damping of Alfvén waves in fully ionized dilute gas in the halo.

As illustrated in Fig. 3, our results are in excellent agreement with the measured spectrum of CR protons in a wide range of energies, including the spectral features observed between ∼10 GeV and ∼10 TeV. The figure also shows that the model predicts a reasonable halo size (of about 1 kpc at 1 GeV) slowly increasing with CR energy. Furthermore, the model is able to reproduce observational abundance ratios of secondary to primary nuclei as well as of unstable to stable secondary nuclei (Chernyshov et al. 2024b). Agreement with observations at lower energies may be further improved by taking into account the effect of ion-neutral damping of turbulence, operating near the Galactic disk.