[Paper Review] Cosmic ray penetration in diffuse clouds

Giovanni Morlino, S. Gabici+1 more|arXiv (Cornell University)|Sep 17, 2015

Astrophysics and Star Formation Studies4 citations

TL;DR

This paper investigates cosmic ray (CR) penetration into diffuse molecular clouds using a steady-state kinetic transport model that includes diffusion, advection, and ionization energy losses. It finds a spectral break at ≈100 MeV, below which CR spectra inside clouds are significantly suppressed—especially for energies relevant to ionization—regardless of streaming instability, implying that CR ionization rates in diffuse clouds are substantially lower than previously assumed under ballistic propagation models.

ABSTRACT

Cosmic rays are a fundamental source of ionization for molecular and diffuse clouds, influencing their chemical, thermal, and dynamical evolution. The amount of cosmic rays inside a cloud also determines the $γ$-ray flux produced by hadronic collisions between cosmic rays and cloud material. We study the spectrum of cosmic rays inside and outside of a diffuse cloud, by solving the stationary transport equation for cosmic rays including diffusion, advection and energy losses due to ionization of neutral hydrogen atoms. We found that the cosmic ray spectrum inside a diffuse cloud differs from the one in the interstellar medium (ISM) for energies smaller than $E_{br}\approx 100$ MeV, irrespective of the model details. Below $E_{br}$, the spectrum is harder (softer) than that in the ISM if the latter is a power law $\propto p^{-s}$ with $s$ larger (smaller) than $\sim0.42$. As a consequence also the ionization rate due to CRs is strongly affected. Assuming an average Galactic spectrum similar to the one inferred from AMS-2 and Voyager 1 data, we discuss the resulting ionization rate in a typical diffuse cloud.

Motivation & Objective

• To understand how cosmic rays penetrate diffuse molecular clouds and influence their ionization, thermal, and dynamical evolution.
• To resolve discrepancies in the literature regarding CR exclusion from clouds, particularly the role of streaming instability and diffusion.
• To quantify the modification of the cosmic ray spectrum inside clouds due to energy losses from ionization of neutral hydrogen.
• To assess the impact of CR spectrum modification on ionization rates and gamma-ray emission from clouds.
• To provide a self-consistent model of CR transport that accounts for spatially varying diffusion, advection, and energy losses in a 1D magnetic flux tube.

Proposed method

• Solves the steady-state kinetic transport equation for cosmic rays along a magnetic flux tube threaded through a diffuse cloud.
• Models CR propagation with spatially dependent diffusion coefficient, advection via Alfvén speed, and energy losses from ionization of neutral hydrogen.
• Assumes a one-dimensional, sharp transition between the interstellar medium (ISM) and the cloud, with constant magnetic field and ion density.
• Uses parametrized Galactic CR spectra (minimum and maximum bounds) from Voyager 1 and AMS-02 data as input boundary conditions.
• Applies a power-law approximation for ionization energy loss timescale in the 100 keV–1 GeV range.
• Compares the resulting CR spectrum inside the cloud to the ISM spectrum to identify spectral breaks and suppression factors.

Experimental results

Research questions

• RQ1 What is the energy scale at which cosmic ray spectra inside diffuse clouds deviate from those in the interstellar medium?
• RQ2 How do energy losses from ionization of neutral hydrogen affect the cosmic ray spectrum inside a cloud?
• RQ3 To what extent is cosmic ray penetration into diffuse clouds suppressed below 100 MeV, independent of streaming instability?
• RQ4 How does the modified cosmic ray spectrum impact the ionization rate of molecular hydrogen in diffuse clouds?
• RQ5 What is the effect of CR spectral modification on the gamma-ray luminosity of diffuse clouds, particularly near the pion production threshold?

Key findings

• A spectral break at approximately 100 MeV (E_br ≈ 100 MeV) emerges in the cosmic ray spectrum inside diffuse clouds, regardless of the presence of streaming instability.
• Below E_br, the CR spectrum inside the cloud is harder (softer) than in the ISM if the ISM spectrum is steeper (harder) than ∝ p^{-0.42}.
• At energies below 0.58 MeV, the CR spectrum inside the cloud is attenuated by up to three orders of magnitude compared to the ISM.
• The ionization rate for H2 molecules in a typical diffuse cloud (N_H ≈ 3×10^21 cm⁻²) drops from 3.59×10⁻¹⁶ s⁻¹ (unmodified max spectrum) to 2.61×10⁻¹⁷ s⁻¹ when propagation effects are included.
• The minimum-spectrum ionization rate drops from 3.49×10⁻¹⁷ s⁻¹ to 1.05×10⁻¹⁷ s⁻¹, indicating a strong suppression of ionization at low energies.
• The gamma-ray luminosity of the cloud is not significantly reduced because the threshold for neutral pion production (≈280 MeV) lies above the break energy.