Energetic particles accelerated via turbulent magnetic reconnection in protoplanetary discs -- I: ionisation rates

Abstract

Ionisation controls the chemistry, thermal balance, and magnetic coupling in protoplanetary discs. However, standard ionisation vectors such as stellar UV, X-rays, Galactic Cosmic Rays (GCRs) might not be efficient enough, as UV/X-rays are attenuated rapidly with depth, while GCRs are modulated. Turbulence-induced magnetic reconnection in disc atmospheric layers offers a physically motivated, in-situ source of energetic particles (EPs) that has never been considered. We quantify the ionisation and heating produced by EPs accelerated by turbulent reconnection, identify where they dominate over X-rays and GCRs, and determine energetic thresholds for their relevance. We provide scalable diagnostics tied to the local energy budget. We adopt a Fermi-like acceleration model with parameters linked to a turbulent reconnection geometry trigger by the magneto-rotational instability, yielding a steady-state energy distribution of the EP forming a power-law of index $p=2.5$. We propagate electrons and protons through the disc and compute primary and secondary ionisation and associated heating on a fiducial T Tauri disc model background. The non-thermal normalisation is set by the fraction of local viscous accretion energy dissipation channelled to EPs, parametrised by $κ$. For $κ\gtrsim 0.4\%$, EPs ionisation overpass standard sources like X-rays and GCRs in the disc atmosphere and intermediate/deep layers out to radii of a few tens of AU. Even at $κ\sim 0.025\%$, EPs contribute at the few-percent level, thus are chemically and dynamically relevant. EP-induced heating complements UV/X-ray heating in the atmosphere and persists deeper. These results identify EPs accelerated by turbulence-induced magnetic reconnection as a rather robust, disc-internal ionisation channel that should be included in thermo-chemical and dynamical models of protoplanetary discs.

Figures (10)

• Figure 1: Left: schematic radial cut from $R\sim0.1$ to $\sim 50$ AU presenting our scenario qualitatively. The disc is vertically stratified into a neutral mid-plane (blue; MRI-stable), where energetic particles (EPs) arriving from above travel quasi-ballistically (CSDA-like) along near-vertical paths, and an ionised atmosphere (yellow; low-$\beta_p$ MRI-active), where sub-Alfvénic turbulence ($M_A<1$) triggers turbulent magnetic reconnection that injects EPs, which then stream downward (black arrows). In the bottom-left part, a patchy variant of the ionised atmospheric layer is sketched, with a lower covering area and possible lateral growth (black arrows). In the ionised turbulent layer, EP transport could be treated as stochastic. The inner star–disc interaction zone treated in 2023MNRAS.519.5673B2024MNRAS.530.3669B is indicated at $R\lesssim0.3$. Right: radial cut from $R\sim0.07$ to $\sim 600$ AU displaying the disc chemical and turbulent structure used in this work based on the ProDiMo model. The top panel shows the total hydrogen number density $n_{\rm H,tot}$ (colour) with vertical column-density contours $N=10^{15},10^{19},10^{21},10^{24}\,\mathrm{cm^{-2}}$ (black dashed). The red dashed line marks the ionised–atomic transition ($\mathrm{H^+/H}$) defining the boarder between the region where $\mathrm{H^+}$ dominates and the region where $\mathrm{H}$ dominates. Analogously, the orange dashed line delimit the atomic–molecular transition ($\mathrm{H/H_2}$). The bottom panel displays the Alfvénic Mach number $M_A\equiv v_{\rm turb}/V_A$ (colour). The red curve traces $M_A=1$. The sub-Alfvénic region ($M_A<1$) identifies where fast, turbulence-enabled reconnection, thus EP acceleration is expected. The solid red lines delimit the region where EP are efficiently accelerated, i.e. to energy more than 10 MeV. The white region is the so called "dead zone", where MRI is inefficient (see criterion Eq. \ref{['eq:effectiveviscosityThi']}), there is no turbulence, $M_A$ is set to 0.
• Figure 2: Sketch of MRI-driven turbulence and embedded turbulent magnetic reconnection. Left: eddies at the injection scale $L$ in a sub-Alfvénic regime characterised by the Alfvénic Mach number $M_A$. Right: the reconnection layer produced by the turbulence, with length $L_r=L$ and thickness $\Delta_r$. The turbulence parameters {$L,M_A$} set the reconnection, geometry parameters {$L_r,\Delta_r$}, speed $V_{\rm rec}\sim V_A M_A^2$ and the EP acceleration parameters used in this work.
• Figure 3: Non-thermal–to–thermal energy density ratio, $U_{\rm nt}/U_{\rm th}$ for $\kappa=0.1$. The red contour encloses regions where the local maximum particle energy exceeds $10~\mathrm{MeV}$ (efficient acceleration sites capable of supplying ionising EPs). The black contour marks a vertical column density $N=10^{19} \mathrm{cm^{-2}}$ (approximate disc surface).
• Figure 4: Particle energy distributions at $R=1$ AU for $\kappa=0.1$. The dashed curves show the thermal Maxwellian based on ProDiMo density and temperature for $Z/R=0.25\text{–}0.35$. The solid curves show the non-thermal distribution produced by magnetic-reconnection acceleration.
• Figure 5: Ionisation rates as function of the disc vertical column density at $R=1$ AU for $\kappa=0.1$. The lines in “viridis” colour scale are the contribution to the ionisation rate coming from EPs accelerated in region at different $Z/R$. The thick orange line is the total ionisation rate corresponding to the weighted sum (Eq. \ref{['eq:totalionisationrate']}) of each local contribution. The black line is the ionisation rate from the stellar X-rays.