Cosmic-Ray Drag and Damping of Compressive Turbulence
While it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected onc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | The Astrophysical Journal |
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| Online Access: | https://doi.org/10.3847/1538-4357/aceef9 |
| _version_ | 1827814346796826624 |
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| author | Chad Bustard S. Peng Oh |
| author_facet | Chad Bustard S. Peng Oh |
| author_sort | Chad Bustard |
| collection | DOAJ |
| description | While it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time ${t}_{\mathrm{damp}}\sim \rho {v}^{2}/{\dot{E}}_{\mathrm{CR}}\propto {E}_{\mathrm{CR}}^{-1}$ becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at ${\dot{E}}_{\mathrm{CR}}\sim \tilde{\epsilon }$ , where $\tilde{\epsilon }$ is the turbulent energy input rate. In that case, almost all of the energy in large-scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of E ≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large-scale motions, with kinetic energy reduced by up to 1 order of magnitude in realistic E _CR ∼ E _g scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large-scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e., $\tilde{\epsilon }\gg \rho {v}^{3}/L$ . |
| first_indexed | 2024-03-11T23:45:13Z |
| format | Article |
| id | doaj.art-a72b5615453f42cfb5a9c91b31efe197 |
| institution | Directory Open Access Journal |
| issn | 1538-4357 |
| language | English |
| last_indexed | 2024-03-11T23:45:13Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj.art-a72b5615453f42cfb5a9c91b31efe1972023-09-19T12:19:19ZengIOP PublishingThe Astrophysical Journal1538-43572023-01-0195516410.3847/1538-4357/aceef9Cosmic-Ray Drag and Damping of Compressive TurbulenceChad Bustard0https://orcid.org/0000-0002-8366-2143S. Peng Oh1https://orcid.org/0000-0002-1013-4657Kavli Institute for Theoretical Physics, University of California—Santa Barbara , Kohn Hall, Santa Barbara, CA 93107, USA ; bustard@ucsb.eduDepartment of Physics, University of California—Santa Barbara , Broida Hall, Santa Barbara, CA 93106, USAWhile it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time ${t}_{\mathrm{damp}}\sim \rho {v}^{2}/{\dot{E}}_{\mathrm{CR}}\propto {E}_{\mathrm{CR}}^{-1}$ becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at ${\dot{E}}_{\mathrm{CR}}\sim \tilde{\epsilon }$ , where $\tilde{\epsilon }$ is the turbulent energy input rate. In that case, almost all of the energy in large-scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of E ≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large-scale motions, with kinetic energy reduced by up to 1 order of magnitude in realistic E _CR ∼ E _g scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large-scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e., $\tilde{\epsilon }\gg \rho {v}^{3}/L$ .https://doi.org/10.3847/1538-4357/aceef9Cosmic raysMagnetohydrodynamicsPlasma astrophysicsCircumgalactic mediumInterstellar medium |
| spellingShingle | Chad Bustard S. Peng Oh Cosmic-Ray Drag and Damping of Compressive Turbulence The Astrophysical Journal Cosmic rays Magnetohydrodynamics Plasma astrophysics Circumgalactic medium Interstellar medium |
| title | Cosmic-Ray Drag and Damping of Compressive Turbulence |
| title_full | Cosmic-Ray Drag and Damping of Compressive Turbulence |
| title_fullStr | Cosmic-Ray Drag and Damping of Compressive Turbulence |
| title_full_unstemmed | Cosmic-Ray Drag and Damping of Compressive Turbulence |
| title_short | Cosmic-Ray Drag and Damping of Compressive Turbulence |
| title_sort | cosmic ray drag and damping of compressive turbulence |
| topic | Cosmic rays Magnetohydrodynamics Plasma astrophysics Circumgalactic medium Interstellar medium |
| url | https://doi.org/10.3847/1538-4357/aceef9 |
| work_keys_str_mv | AT chadbustard cosmicraydraganddampingofcompressiveturbulence AT spengoh cosmicraydraganddampingofcompressiveturbulence |