Star-Planet Interaction Code

• Star-Planet Interaction (SPI) codes are simulation frameworks that model the complex exchanges between stars and planets using magnetic, tidal, and radiative mechanisms.
• They employ diverse methodologies, from full 3D MHD solvers and analytic radio-scaling laws to secular tidal evolution models, to generate accurate observables.
• Applications include predicting radio fluxes, spectral line profiles, and orbital evolution, enabling researchers to infer key stellar and planetary parameters.

A Star-Planet Interaction (SPI) code is a simulation or modeling framework designed to capture the multifaceted physical exchanges between host stars and their planets. These codes are used to investigate a range of astrophysical processes including magnetic, tidal, and radiative interactions, as well as their observable signatures (e.g., in light curves, spectral lines, radio emission, and secular orbital or rotational evolution). SPI codes span a diversity of architectures from analytic, fast scripts to full three-dimensional magnetohydrodynamic (MHD) solvers, and they often focus on specific physical regimes or measurable outcomes.

1. Categories and Core Objectives of SPI Codes

SPI codes are categorized according to the primary physical mechanisms and observational diagnostics they address:

• Magnetospheric/MHD SPI codes simulate the direct coupling of stellar winds and planetary magnetospheres, capturing bow shocks, magnetotails, Poynting flux, and associated auroral/radio signatures. Codes such as PLUTO, GAMERA, and FLASH implement the full MHD equations with user-defined inner and outer boundary conditions, supporting 2D, 2.5D, or full 3D setups, including planetary dipoles and evolving stellar winds (Strugarek et al., 2013, 2207.14658, Bagheri et al., 22 Apr 2024, Evangelista et al., 2019).
• Analytic and semi-analytic radio SPI codes (e.g., SIRIO, ExPRES) compute expected radio emission from magnetic interaction in the sub-Alfvénic regime, applying Poynting-flux scaling laws, magnetic geometry considerations, and radiative propagation models (including free–free absorption and beaming) (Chebly et al., 13 Nov 2025, Peña-Moñino et al., 28 Aug 2025).
• Spectroscopic/Photometric SPI codes (e.g., SOAP-T, SHELLSPEC) simulate light curves, radial velocities, and spectral profiles, often including the effects of starspots, transit anomalies, and the Rossiter-McLaughlin effect, as well as the interaction with circumstellar material (Oshagh et al., 2012, Budaj, 2011).
• Secular evolution and tidal interaction codes (e.g., ESPEM, PLATYPOS, tidal–chronology frameworks) focus on long-term angular momentum transfer, spin-orbit evolution, and planetary atmosphere evaporation driven by stellar irradiation (Benbakoura et al., 2018, Gallet et al., 2019, Ketzer et al., 2022).
• Specialized codes for wave–wave interaction in multi-planet systems extend standard MHD approaches to capture nonlinear wing–wing interactions (Alfvén wings) and their dynamical consequences (2207.14658).

Each category targets a distinct observational or theoretical SPI facet but shares a foundation in rigorous, physically motivated modeling.

2. Physical and Mathematical Models

SPI codes rely on a consistent set of physical equations, tailored to their regimes of applicability:

• Ideal MHD Equations: Governing mass, momentum, energy, and magnetic field evolution in a plasma environment, these are typically solved in conservative form:

$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0,$$

$$\frac{\partial (\rho \mathbf{v})}{\partial t} + \nabla \cdot [\rho \mathbf{v}\mathbf{v} + (p + \tfrac{1}{2}B^2)\mathbb{I} - \mathbf{B}\mathbf{B}] = \rho \mathbf{g} + \text{force terms},$$

$$\frac{\partial E}{\partial t} + \nabla \cdot [ (E + p + \tfrac{1}{2}B^2)\mathbf{v} - (\mathbf{v}\cdot \mathbf{B})\,\mathbf{B} ] = \rho \mathbf{g} \cdot \mathbf{v},$$

$$\frac{\partial \mathbf{B}}{\partial t} + \nabla \times (\mathbf{v} \times \mathbf{B}) = 0.$$

Supplementary source terms account for Coriolis/centrifugal forces, ion–neutral collisions, radiative losses, or planet-specific drag and Poynting-flux terms. Notably, neutral atmospheres are coupled via drag (ion–neutral collisions) in the wave–wing codes (2207.14658).

• Analytic Obstacles and Poynting Flux: In codes such as SIRIO and the ExPRES pipeline, key quantities include
  • Alfvén Mach number: $M_A = v_{\text{rel}} / v_A$, with $v_A = B_{\text{sw}}/\sqrt{4\pi\rho_{\text{sw}}}$
  • Poynting Flux: $$S_{\text{Alf}} = \tfrac{1}{2}(R_{\text{eff}}\alpha M_A B_{\text{sw}} \sin\Theta)^2 v_A$$
  • Radio power scaling law: $P_{\text{R}} = \beta S_{\text{Poynt}}$, typically with a conversion efficiency $\beta \approx 10^{-3}$
  • (Peña-Moñino et al., 28 Aug 2025, Chebly et al., 13 Nov 2025).
  • Multiple geometric regimes are supported: axisymmetric dipole, Parker spiral, hybrid-PFSS.
• Tidal/Orbital Evolution: ESPEM and tidal–chronology SPI codes integrate secular equations for the semi-major axis $a(t)$ and host-star spin $\Omega_\star$, incorporating both equilibrium and frequency-averaged dynamical tide dissipation, as well as wind braking torques. For instance, the secular evolution in ESPEM:

$$\frac{da}{dt} = - a^{1/2} \frac{2}{m_p M_\star} \sqrt{\frac{m_p + M_\star}{G}} \Gamma_{\text{tide}},$$

where $\Gamma_{\text{tide}}$ is derived from quality factors $Q'$ computed via ab initio prescriptions (Benbakoura et al., 2018, Rao et al., 2018, Gallet et al., 2019).

• Radiative Transfer and Spectral Synthesis: Codes such as SHELLSPEC and Guacho solve the formal radiative transfer equation through 1D, 2D, or 3D grids, including both LTE and velocity-dependent Doppler shifts:

$\frac{dI_\nu}{ds} = -\chi_\nu I_\nu + \eta_\nu.$

Microphysical modeling includes first-scattering, ionization, and emission lines, supporting the direct simulation of observed spectra and phase curves (Budaj, 2011, D'Angelo et al., 2019).

3. Numerical Implementation and Algorithmic Structure

• Grid Geometry and Discretization: High-fidelity MHD SPI codes use Cartesian, cylindrical, or spherical grids, often with nonuniform or logarithmic spacing to resolve both planetary and stellar scales. Spherical–polar coordinates are common for axisymmetric or full 3D treatments. Adaptive mesh refinement and parallelization strategies (MPI, OpenMP) are integral for efficiency (Bagheri et al., 22 Apr 2024, Strugarek et al., 2013, 2207.14658).
• Boundary Conditions: Inner boundaries can represent either the planetary surface or an ionospheric shell, enforcing reflecting or conducting conditions. Outer and side boundaries typically use outflow (zero-gradient) constraints; careful placement is needed for close-in orbits to preserve the uniform-wind assumption. Magnetic field boundary conditions may enforce fixed dipole or time-varying ZDI maps (Chebly et al., 13 Nov 2025, Bagheri et al., 22 Apr 2024).
• User Input and Model Configuration: Codes accept extensive parameter files (YAML, CSV, or driver scripts), specifying stellar/planetary properties, magnetospheric strengths, wind models, orbit configurations, and, when relevant, radiative source terms or evolutionary tracks (Chebly et al., 13 Nov 2025, Peña-Moñino et al., 28 Aug 2025, Benbakoura et al., 2018, Oshagh et al., 2012).

The following table summarizes major SPI code classes, selected algorithms, and key diagnostics:

Code/Framework	Core Physics	Key Outputs
PLUTO (2D/3D)	Full MHD (ideal/polytropic)	Poynting flux, torque, waves
SIRIO	Analytic wind+Poynting Flux	Predicted radio fluxes
ExPRES+AWSoM	3D MHD, radio beaming	Dynamic radio spectra
SOAP-T	Photometric/RV forward model	Light curves, RV, BIS
ESPEM	Secular tidal/spin evolution	$a(t), \Omega(t)$, fate
SHELLSPEC	3D radiative transfer	Synthetic spectra/images
FLASH	MHD with rigid boundaries	Magnetotail, wake structure

4. Major Applications and Validation Studies

SPI codes have been applied extensively to interpret and predict:

• Radio emission prospects: SIRIO has been benchmarked on systems such as Proxima Centauri, YZ Ceti, and GJ 1151, showing that sub-Alfvénic interaction regimes (PFSS geometry) produce radio fluxes sensitive to reconnection efficiency and wind absorption; these simulations span expected detections (GJ 1151, ~100 μJy) to low non-detections (Proxima b, μJy) (Peña-Moñino et al., 28 Aug 2025).
• Spectroscopic Signatures: Guacho reproduces Lyα and Mg line absorption in HD 209458b, allowing constraints on planetary magnetic fields ($<1\,$G, given line shapes) (D'Angelo et al., 2019).
• Orbital Evolution and Planet Survival: ESPEM demonstrates that a planet’s influence on stellar rotation depends on semi-major axis and competing torques, while analytic survival boundaries in the ($M_\star$, $m_p$, $a_{\text{ini}}$) parameter space have been derived for rapid estimation of spiral-in (Benbakoura et al., 2018, Gallet et al., 2019).
• Multi-planet Wave Interactions: Time-dependent MHD extensions to PLUTO reveal that conjunctions can nonlinearly intensify Poynting flux by ~20%, with dynamical evolution modulated by Alfvén-wing merging (2207.14658).

Empirical validation is achieved by matching light curves, line profiles, or secular decay rates to observations from Kepler, HST/COS, LOFAR, or ground-based RV measurements (Oshagh et al., 2012, D'Angelo et al., 2019, Peña-Moñino et al., 28 Aug 2025).

5. Parameter Constraints and Predictive Diagnostics

Advanced SPI codes enable parameter inference by confronting model predictions with observational non-detections or detections:

• Non-detection upper limits: If radio SPI is not detected, SIRIO can infer upper bounds on either the stellar mass-loss rate or planetary field strength for the system in question (Peña-Moñino et al., 28 Aug 2025).
• Direct field constraints: Reproducing observed radio or spectroscopic anomaly amplitudes allows inference of $B_{\star}$, $B_{\text{planet}}$, or wind density, guiding future observational campaigns.
• Efficiency dependence: Predictions are sensitive to parameter choices—magnetic topology (dipole/PFSS/Parker), free–free opacity, beaming solid angle, and conversion efficiency all critically affect expected fluxes (Chebly et al., 13 Nov 2025, Peña-Moñino et al., 28 Aug 2025).

6. Implementation, Extensibility, and Future Prospects

SPI code development continues to expand in flexibility and sophistication:

• Extensibility: Modular Python or C architectures allow users to adapt codes for new targets, magnetic maps, or physical processes (e.g., including explicit resistivity, more complex chemistry, coronal self-consistency) (Peña-Moñino et al., 28 Aug 2025, Chebly et al., 13 Nov 2025).
• Scalability: Effective parallelization (MPI, OpenMP) and vectorization support high-resolution parameter sweeps or long-term secular evolution over Gyr timescales (D'Angelo et al., 2019, Bagheri et al., 22 Apr 2024).
• Limitations and Frontiers: Assumptions such as constant ionospheric conductance, ideal MHD (lack of explicit resistivity), or uniform wind boundary conditions impose limits, particularly at the closest orbital separations ($<0.4$ au for Jupiter-like planets in GAMERA), or for multi-phase/kinetic plasma regimes (Bagheri et al., 22 Apr 2024).
• Future directions: Development is focused on 3D, time-dependent treatments, inclusion of multi-fluid effects, starspot–wind coupling, and full N-body + MHD hybrid schemes to model N-planet systems including wing–wing interactions (2207.14658, Chebly et al., 13 Nov 2025).

7. Representative Software and Research Groups

Several public SPI codes anchor the field:

• SIRIO: Python package for analytic radio-forecasting in the sub-Alfvénic regime; includes wind models, multiple magnetic geometries, and beaming/absorption calculation (Peña-Moñino et al., 28 Aug 2025).
• ExPRES: Radio beaming code coupled to MHD wind and ZDI magnetic maps for synthetic dynamic spectra (Chebly et al., 13 Nov 2025).
• PLUTO: General-purpose MHD framework extensible to multiple planetary and stellar configurations, including collisional coupling and nonlinear wave diagnostics (Strugarek et al., 2013, 2207.14658).
• GAMERA: 3D MHD code with explicit inertial/Coriolis terms and dipole or Earth/Jupiter ionospheric boundaries (Bagheri et al., 22 Apr 2024).
• SOAP-T, SHELLSPEC: Forward-modeling of transit photometry/RV and radiative transfer in optically thin circumstellar environments (Oshagh et al., 2012, Budaj, 2011).
• ESPEM: Fully coupled secular angular-momentum evolution toolkit with ab initio tidal and wind torques (Benbakoura et al., 2018).
• PLATYPOS: Planetary evaporation models using hydrodynamic, energy-limited, or radiative-recombination regimes (Ketzer et al., 2022).

The continued refinement and cross-validation of these codes remain essential for extracting robust physical constraints from observed star–planet systems and for guiding new observing strategies.