The Effects of Cosmic Ray Protons on Galactic Nonthermal Filaments

Technical Summary: The Effects of Cosmic Ray Protons on Galactic Nonthermal Filaments

Problem Statement
The Galactic Center (GC) hosts a population of nonthermal filaments (NTFs) extending tens of parsecs in length, illuminated by synchrotron radiation from cosmic rays (CRs). The physical origin of these structures remains unresolved. Two primary injection mechanisms are proposed: (1) NTFs are fueled by jets from pulsar wind nebulae, resulting in a lepton-dominated population; or (2) NTFs are fueled by accelerated particles from interstellar shocks, resulting in a proton-dominated population (with a proton-to-lepton ratio of roughly 100:1). While the Galactic CR population exhibits a power-law energy distribution consistent with NTF observations, the specific causal connection between the injection source and the filament morphology is unclear. Furthermore, the poloidal magnetic field topology within the Central Molecular Zone (CMZ) is complex, with many filaments appearing non-linear, suggesting the potential role of interstellar turbulence. This study aims to distinguish between the lepton-dominated and proton-dominated scenarios by simulating CR propagation, heating, and plasma flow under varying Galactic Center conditions.

Methodology
The authors employed the magnetohydrodynamics (MHD) code Athena++, modified to include radiative and collisional loss terms, to simulate CR propagation in a 1D flux tube representing a filament. The simulation models a uniform background medium perturbed by the injection of CR energy at the filament's midpoint.

• Physical Processes: The model incorporates diffusion (scattering off Alfvén waves) and streaming (convection at the Alfvén speed). Loss mechanisms for leptons include synchrotron radiation, inverse Compton scattering, Coulomb losses, and bremsstrahlung. Secondary production is modeled where primary protons interact with ambient protons to generate secondary electrons and positrons.
• Parameters: The study varies key parameters including magnetic field strength ($B$), plasma density ($n_p$), the CR diffusion coefficient ($\kappa$), and the total injected energy ($E_{\pm}$).
• Simulation Sets: Each parameter set was simulated twice: once with leptons only and once with a proton-lepton mixture (scaling the total injection rate by 100 to account for the proton-to-lepton ratio). The fiducial parameters adopted were $B = 200\,\mu\text{G}$, $n_p = 100\,\text{cm}^{-3}$, and $\kappa = 1 \times 10^{26}\,\text{cm}^2\,\text{s}^{-1}$.
• Analysis: The authors analyzed the spatial energy density profiles, induced gas flows, heating rates, and the resulting synchrotron luminosity and spectral indices over time (up to 40 kyr).

Key Results

1. Indistinguishability of Injection Mechanisms: The simulations revealed few observable differences between the proton-dominated and lepton-dominated cases. While proton injection drives stronger gas flows and provides more heating due to the higher total energy density, these effects remain below detectable thresholds. Even at the lowest densities considered, induced velocities ($\sim 2.5\,\text{km s}^{-1}$) and heating rates are negligible compared to radiative cooling and typical thermal line widths.
2. Propagation Constraints: The observed plateaued, uniform surface brightness of NTFs suggests a diffusion coefficient significantly lower than the typical Galactic value ($\kappa \sim 10^{28}\,\text{cm}^2\,\text{s}^{-1}$). The authors find that a lower diffusion coefficient ($\kappa \sim 10^{26}\,\text{cm}^2\,\text{s}^{-1}$) is necessary to reproduce the observed luminosity profiles.
3. Filament Length and Age: The simulations indicate that without a mechanism to truncate propagation, filaments would continue to expand indefinitely. The length of an NTF is therefore dependent on its age. Radiative and collisional losses, even when combined with secondary production, do not create a steady-state length because secondary leptons are born further from the injection site and diffuse similarly to primary particles.
4. Spectral Index Variability: The study explored mechanisms for the observed variation in synchrotron spectral indices (ranging from -2 to +0.5).
   • Energy-dependent diffusion: If diffusivity scales with energy ($\kappa \propto \gamma^q$), the spectral index varies along the filament, generally hardening away from the injection site.
   • Synchrotron aging: High-energy particles lose energy faster, leading to spectral steepening over time.
   • Secondary production: Steepens the spectrum at late times.
   • Despite these mechanisms, the authors note that no single combination of these effects fully explains the jagged, asymmetric spectral index variations observed in real NTFs.

Significance and Conclusions
The primary contribution of this work is the demonstration that the presence of a large population of cosmic ray protons does not produce distinct, observable signatures in filament morphology, flow, or heating that would allow astronomers to distinguish between pulsar-driven (lepton) and shock-driven (proton) origins based on current 1D MHD simulations.

Consequently, the authors argue that the inability to distinguish between these two standard injection models, combined with the observed structural imperfections of NTFs (kinks, splits, and non-linear alignments), motivates the consideration of a third formation mechanism. The paper proposes that NTFs may arise from intermittent structures in Galactic Center turbulence. In this scenario, inhomogeneous MHD turbulence could amplify magnetic fields and stretch eddies into thin filaments, creating the observed structures without requiring a specific, localized CR injection source. The authors conclude that future work should focus on simulating these turbulent effects to better understand the origin of NTFs.