Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium
We investigate the transport of spectrally resolved cosmic-ray (CR) protons with kinetic energies between 1 and 100 GeV within the multiphase, dynamic interstellar medium (ISM), using a two-moment CR fluid solver applied to a TIGRESS MHD simulation with conditions similar to the solar neighborhood....
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IOP Publishing
2025-01-01
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| Online Access: | https://doi.org/10.3847/1538-4357/adea68 |
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| author | Lucia Armillotta Eve C. Ostriker Nora B. Linzer |
| author_facet | Lucia Armillotta Eve C. Ostriker Nora B. Linzer |
| author_sort | Lucia Armillotta |
| collection | DOAJ |
| description | We investigate the transport of spectrally resolved cosmic-ray (CR) protons with kinetic energies between 1 and 100 GeV within the multiphase, dynamic interstellar medium (ISM), using a two-moment CR fluid solver applied to a TIGRESS MHD simulation with conditions similar to the solar neighborhood. Our CR transport prescription incorporates space- and momentum-dependent CR scattering coefficients σ = κ ^−1 , computed from the local balance between streaming-driven Alfvèn wave growth and damping processes. We find that advection combines with momentum-dependent diffusion to produce a CR distribution function f ( p ) ∝ p ^− ^γ with γ ≈ 4.6 that agrees with observations, steepened from an injected power-law slope γ _inj = 4.3. The CR pressure is uniform in the highly diffusive, mostly neutral midplane region, but decreases exponentially in the ionized extraplanar region where scattering is efficient. To interpret these numerical results, we develop a two-zone analytic model that captures and links the two (physically and spatially) distinct regimes of CR transport in the multiphase, dynamic ISM. At low momenta, CR transport is dominated by gas advection, while at high momenta, both advection and diffusion contribute. At high momentum, the analytic prediction for the spectral slope approaches γ = (4/3) γ _inj − 1, and the predicted scaling of grammage with momentum is $X\propto {p}^{1-{\gamma }_{{\rm{inj}}}/3}$ , consistent with the simulations. These results support a physical picture in which CRs are confined within the neutral midplane by the surrounding ionized gas, with their escape regulated by both the CR scattering rate in the ionized extraplanar gas and the velocity and Alfvén speed of that gas, at effective speed ${v}_{{\rm{c}},{\rm{eff}}}\approx (1/2){[{\kappa }_{\parallel }\,d(v+{v}_{{\rm{A}},{\rm{i}}})/dz]}^{1/2}$ . |
| format | Article |
| id | doaj-art-ec8ac0bf430a4fb8b0955cb87360d2ea |
| institution | DOAJ |
| issn | 1538-4357 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | The Astrophysical Journal |
| spelling | doaj-art-ec8ac0bf430a4fb8b0955cb87360d2ea2025-08-20T02:58:11ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-01989214010.3847/1538-4357/adea68Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar MediumLucia Armillotta0https://orcid.org/0000-0002-5708-1927Eve C. Ostriker1https://orcid.org/0000-0002-0509-9113Nora B. Linzer2https://orcid.org/0000-0001-8840-2538INAF Arcetri Astrophysical Observatory , Largo Enrico Fermi 5, Firenze, 50125, Italy ; lucia.armillotta@inaf.it; Department of Astrophysical Sciences, Princeton University , Princeton, NJ 08544, USADepartment of Astrophysical Sciences, Princeton University , Princeton, NJ 08544, USADepartment of Astrophysical Sciences, Princeton University , Princeton, NJ 08544, USAWe investigate the transport of spectrally resolved cosmic-ray (CR) protons with kinetic energies between 1 and 100 GeV within the multiphase, dynamic interstellar medium (ISM), using a two-moment CR fluid solver applied to a TIGRESS MHD simulation with conditions similar to the solar neighborhood. Our CR transport prescription incorporates space- and momentum-dependent CR scattering coefficients σ = κ ^−1 , computed from the local balance between streaming-driven Alfvèn wave growth and damping processes. We find that advection combines with momentum-dependent diffusion to produce a CR distribution function f ( p ) ∝ p ^− ^γ with γ ≈ 4.6 that agrees with observations, steepened from an injected power-law slope γ _inj = 4.3. The CR pressure is uniform in the highly diffusive, mostly neutral midplane region, but decreases exponentially in the ionized extraplanar region where scattering is efficient. To interpret these numerical results, we develop a two-zone analytic model that captures and links the two (physically and spatially) distinct regimes of CR transport in the multiphase, dynamic ISM. At low momenta, CR transport is dominated by gas advection, while at high momenta, both advection and diffusion contribute. At high momentum, the analytic prediction for the spectral slope approaches γ = (4/3) γ _inj − 1, and the predicted scaling of grammage with momentum is $X\propto {p}^{1-{\gamma }_{{\rm{inj}}}/3}$ , consistent with the simulations. These results support a physical picture in which CRs are confined within the neutral midplane by the surrounding ionized gas, with their escape regulated by both the CR scattering rate in the ionized extraplanar gas and the velocity and Alfvén speed of that gas, at effective speed ${v}_{{\rm{c}},{\rm{eff}}}\approx (1/2){[{\kappa }_{\parallel }\,d(v+{v}_{{\rm{A}},{\rm{i}}})/dz]}^{1/2}$ .https://doi.org/10.3847/1538-4357/adea68Cosmic raysMagnetohydrodynamicsInterstellar medium |
| spellingShingle | Lucia Armillotta Eve C. Ostriker Nora B. Linzer Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium The Astrophysical Journal Cosmic rays Magnetohydrodynamics Interstellar medium |
| title | Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium |
| title_full | Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium |
| title_fullStr | Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium |
| title_full_unstemmed | Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium |
| title_short | Energy-dependent Transport of Cosmic Rays in the Multiphase, Dynamic Interstellar Medium |
| title_sort | energy dependent transport of cosmic rays in the multiphase dynamic interstellar medium |
| topic | Cosmic rays Magnetohydrodynamics Interstellar medium |
| url | https://doi.org/10.3847/1538-4357/adea68 |
| work_keys_str_mv | AT luciaarmillotta energydependenttransportofcosmicraysinthemultiphasedynamicinterstellarmedium AT evecostriker energydependenttransportofcosmicraysinthemultiphasedynamicinterstellarmedium AT norablinzer energydependenttransportofcosmicraysinthemultiphasedynamicinterstellarmedium |