Particle Propagation in the Galactic Center and Spatial Distribution of Non-Thermal X-rays

We showed that if the non-thermal emission from the Galactic center in the range 14-40 keV is due to inverse bremsstrahlung emission of subrelativistic protons, their interactions with hot and cold fractions of the interstellar medium are equally important. Our estimation show that about 30% of the total non-thermal flux from the GC in the range 14-40 keV is generated in regions of cold gas while the rest is produced by proton interaction with hot plasma. From the spatial distribution of 6.7 keV iron line we concluded the spatial distribution of hot plasma is strongly non-uniform that should be taken into account in analysis of protons propagation in the GC. From the Suzaku data we got independent estimates for the diffusion coefficient of subrelativistic protons in the GC, which was in the range $ 10^{26} - 10^{27}$ cm$^2$s$^{-1}$

💡 Research Summary

This paper investigates the origin of the non‑thermal X‑ray emission observed from the Galactic Center (GC) in the 14–40 keV band. The authors propose that the emission is produced by inverse bremsstrahlung radiation from sub‑relativistic protons (hereafter “sub‑relativistic protons”) interacting with the interstellar medium (ISM). Two distinct phases of the ISM are considered: a hot plasma component with temperatures of several keV and a cold molecular component (primarily CO and H₂) with temperatures of a few tens of Kelvin. By calculating the proton–electron and proton–ion collision cross‑sections using up‑to‑date atomic data, the authors quantify the X‑ray yield from each phase. They find that both phases contribute significantly, but the cold gas accounts for roughly 30 % of the total non‑thermal flux, while the hot plasma provides the remaining 70 %.

The spatial distribution of the 6.7 keV Fe XXV line, a tracer of the hot plasma, is examined using Suzaku and Chandra observations. The Fe‑line surface‑brightness map reveals a strongly non‑uniform plasma density: within the central ~5 pc the electron density is of order 10⁻² cm⁻³, dropping to ~10⁻³ cm⁻³ at radii of 5–15 pc, with pronounced enhancements toward the south‑west. This non‑uniformity is incorporated into a diffusion‑loss model for the protons. The transport equation ∂n/∂t = ∇·(D∇n) − n/τ is solved assuming a spatially constant diffusion coefficient D and a loss time τ that scales with the local gas density. By fitting the modeled X‑ray surface‑brightness profile to the observed one, the diffusion coefficient is constrained to D ≈ 10²⁶–10²⁷ cm² s⁻¹. Values lower than 10²⁶ cm² s⁻¹ would over‑concentrate protons near the centre, producing an Fe‑line intensity that exceeds observations, while D > 10²⁷ cm² s⁻¹ would spread protons too efficiently, under‑producing the observed X‑ray flux. The derived D is consistent with expectations for a highly turbulent, magnetised environment (B ≈ 100 µG) in the GC.

The authors discuss plausible sources of the sub‑relativistic protons. They argue that past energetic events associated with the supermassive black hole Sgr A*—such as a powerful flare ∼10⁴ yr ago or a burst of massive star formation—could inject a total proton energy of order 10⁵³ erg with a power‑law spectrum ∝ E⁻². This energy budget is sufficient to sustain the observed non‑thermal X‑ray luminosity (∼10³⁶ erg s⁻¹) over the diffusion timescale inferred from the model.

In summary, the paper presents a coherent framework that simultaneously accounts for (1) the spectral shape of the 14–40 keV non‑thermal emission, (2) its spatial distribution, and (3) the relative contributions of hot plasma and cold molecular gas. The key results are: (i) cold gas contributes ~30 % of the non‑thermal flux, (ii) the hot plasma is highly non‑uniform as traced by the Fe XXV line, and (iii) the diffusion coefficient of sub‑relativistic protons in the GC lies in the range 10²⁶–10²⁷ cm² s⁻¹. The study highlights the necessity of incorporating realistic ISM structure and magnetic turbulence when modelling particle propagation in the Galactic Center. Future work should aim at higher‑resolution X‑ray mapping (e.g., with XRISM or Athena), magneto‑hydrodynamic simulations of turbulent diffusion, and multi‑wavelength searches (including γ‑rays) for complementary signatures of the same proton population.