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Resistive MHD Simulations of Stellar Wind-Magnetosphere Coupling in TRAPPIST-1e

J. J. González-Avilés, N. Baltazar Pérez-Negrón, A. Segura

Abstract

Close-in terrestrial exoplanets around M dwarfs reside in dense, magnetized winds, where non-ideal plasma coupling can strongly affect how electromagnetic energy is redistributed within the dayside interaction region. We present three-dimensional resistive magnetohydrodynamic simulations of the TRAPPIST-1 wind interacting with a dipolar TRAPPIST-1e magnetosphere for three stellar-wind forcing cases and four prescribed magnetic diffusivities, $η=(0,\ 538.018,\ 5.38018\times10^{8},\ 5.38018\times10^{12})$ cm$^{2}$ s$^{-1}$. Energy transport is diagnosed using maps of the total energy density, the magnitude of the total Poynting flux, and the divergence of the total Poynting flux. We further estimate a radio-power proxy from the volume integral of $\nabla\cdot \mathbf{S}_{\rm total}$ over the dayside bow-shock and magnetopause layers. Across all cases, increasing prescribed $η$ broadens the coupling layer and shifts the dominant energy-conversion regions from thin, patchy boundary arcs to thicker, more spatially extended structures, with an increasing relative contribution from the magnetopause. The inferred radio-power proxy increases by several orders of magnitude across the explored scan. However, because the estimated numerical magnetic diffusivity in the strongest-gradient regions is $η_{\rm num}\sim10^{15}$-$10^{16}$ cm$^{2}$ s$^{-1}$, the present $η$ scan is best interpreted as a controlled sensitivity study rather than as a direct constraint on the physical diffusivity of the TRAPPIST-1e environment. For the adopted planetary fields ($B_{\rm eq}=0.32$-$1.28$ G), the maximum cyclotron frequencies are $ν_{c,\max}\approx1.8$-$7.2$ MHz, below the ground-based window, implying that meaningful radio constraints on TRAPPIST-1e magnetism will require space-based observations below 10 MHz or substantially stronger planetary fields than those assumed here.

Resistive MHD Simulations of Stellar Wind-Magnetosphere Coupling in TRAPPIST-1e

Abstract

Close-in terrestrial exoplanets around M dwarfs reside in dense, magnetized winds, where non-ideal plasma coupling can strongly affect how electromagnetic energy is redistributed within the dayside interaction region. We present three-dimensional resistive magnetohydrodynamic simulations of the TRAPPIST-1 wind interacting with a dipolar TRAPPIST-1e magnetosphere for three stellar-wind forcing cases and four prescribed magnetic diffusivities, cm s. Energy transport is diagnosed using maps of the total energy density, the magnitude of the total Poynting flux, and the divergence of the total Poynting flux. We further estimate a radio-power proxy from the volume integral of over the dayside bow-shock and magnetopause layers. Across all cases, increasing prescribed broadens the coupling layer and shifts the dominant energy-conversion regions from thin, patchy boundary arcs to thicker, more spatially extended structures, with an increasing relative contribution from the magnetopause. The inferred radio-power proxy increases by several orders of magnitude across the explored scan. However, because the estimated numerical magnetic diffusivity in the strongest-gradient regions is - cm s, the present scan is best interpreted as a controlled sensitivity study rather than as a direct constraint on the physical diffusivity of the TRAPPIST-1e environment. For the adopted planetary fields (- G), the maximum cyclotron frequencies are - MHz, below the ground-based window, implying that meaningful radio constraints on TRAPPIST-1e magnetism will require space-based observations below 10 MHz or substantially stronger planetary fields than those assumed here.

Paper Structure

This paper contains 11 sections, 13 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Model and methods
  3. Numerical methods
  4. Initial conditions and boundary conditions
  5. Simulation cases
  6. Results of the numerical simulations
  7. Case #1
  8. Case #2
  9. Case #3
  10. Estimation of radio emission
  11. Discussion and Conclusions

Figures (6)

  • Figure 1: Case #1. Equatorial-plane maps of mass density $\rho$ (panels a and d; g cm$^{-3}$) and dynamic pressure $p_{\rm dyn}$ (panels b and e; dyn cm$^{-2}$), together with meridional-plane maps of $\rho$ (panels c and f). Black curves show the magnetic field lines. The top row corresponds to $\eta=0$ cm$^{2}$ s$^{-1}$, and the bottom row to $\eta=5.38018\times10^{12}$ cm$^{2}$ s$^{-1}$.
  • Figure 2: Case #2. Equatorial-plane maps of mass density $\rho$ (panels a and d; g cm$^{-3}$) and dynamic pressure $p_{\rm dyn}$ (panels b and e; dyn cm$^{-2}$), with magnetic field lines overplotted in black. Panels c and f show meridional-plane maps of $\rho$ at $x=1.5\,R_{\rm p}$. The top row corresponds to $\eta=0$ cm$^{2}$ s$^{-1}$, and the bottom row to $\eta=5.38018\times10^{12}$ cm$^{2}$ s$^{-1}$.
  • Figure 3: Case #3. Equatorial-plane maps of mass density $\rho$ (panels a and d; g cm$^{-3}$) and dynamic pressure $p_{\rm dyn}$ (panels b and e; dyn cm$^{-2}$), with magnetic field lines overplotted in black. Panels c and f show meridional-plane maps of $\rho$ at $x=1.5~R_{\rm p}$. The top row corresponds to $\eta=0$ cm$^{2}$ s$^{-1}$, and the bottom row to $\eta=5.38018\times10^{12}$ cm$^{2}$ s$^{-1}$.
  • Figure 4: Contributions to the peak $P_{R}$ from the bow shock and magnetopause at $\eta=5.38018\times10^{8}$ cm$^{2}$ s$^{-1}$ for Case #1 (panel a), Case #2 (top of panel b), and Case #3 (bottom of panel b). The volumetric renderings show $\nabla\cdot\mathbf{S}_{\rm total}$ in erg cm$^{-3}$ s$^{-1}$.
  • Figure 5: Integrated radio-power proxy in the bow shock (panel a), magnetopause (panel b), and total (panel c) for Cases #1--#3 as a function of the four magnetic diffusivity values. Both axes are logarithmic.
  • ...and 1 more figures