Inferring physical parameters of solar filaments from simultaneous longitudinal and transverse oscillations

TL;DR

This work applies Bayesian inference to solar prominence seismology, combining longitudinal oscillations described by the pendulum model with transverse kink oscillations to jointly constrain the magnetic-field strength $B$, flux-tube length $L$, and twist $\phi$ of the supporting flux rope. By deriving a posterior for $B$ from $P_l$ and using it as a prior for $L$ from transverse modes, the authors obtain full posterior distributions that reveal very long flux tubes (roughly $100$–$1000$ Mm) and small twist numbers (not more than a few turns). The approach, validated by grid integration and MCMC, highlights the value of Bayesian methods for propagating observational uncertainties into prominence parameter estimates and demonstrates that simultaneous wave diagnostics can substantially inform magnetic-structure geometry. These results have implications for improving constraints in solar-filament models and guiding future multi-modal observations.

Abstract

Context. Different modes of oscillations are frequently observed in solar prominences/filaments, and prominence seismology helps estimate important physical parameters like the magnetic field strength. Although the simultaneous detection of longitudinal and transverse oscillations in the same filament is not common, such rare observations provide a unique opportunity to constrain the physical parameters of interest. Aims. In this study, we aim to estimate the physical parameters of prominences undergoing simultaneous longitudinal and transverse oscillations. Methods. We apply Bayesian seismology techniques to observations of longitudinal and transverse filament oscillations to infer the magnetic field strength, the length, and the number of twists in the flux tube holding the prominence plasma. We first use the observations of longitudinal oscillations and the pendulum model to infer the posterior probability density for the magnetic field strength. The obtained marginal posterior of the magnetic field, combined with the observations of the transverse oscillations, is then used to estimate the probable values of the length of the magnetic flux tube that supports the filament material using Bayesian inference. This estimated length is used to compute the number of twists in the flux tube. Results. For the prominences under study, we find that the length of the flux tubes supporting the quiescent prominences can be very large (from 100 to 1000 Mm) and the number of twists in the flux tube are not more than three. Conclusions. Our results demonstrate that Bayesian analysis offers valuable methods to perform parameter inference in the context of prominence seismology.

Figures (4)

• Figure 1: Joint posterior distribution of magnetic field strength and electron density and marginal probability distribution of magnetic field. Panel (A) shows the joint probability distribution of magnetic field strength and electron number density inferred for the average longitudinal oscillation period $P_l = 58 \pm 15$ min reported by 2018ApJS..236...35L, assuming uniform priors on electron density, $\mathcal{U}(n_{\rm e},[\mathrm{cm}^{-3}]; 10^{9}, 10^{11})$, and magnetic field strength, $\mathcal{U}(B,[\mathrm{G}]; 1, 70)$, evaluated on a two-dimensional grid with $N_{n_{\rm e}} = 990$ and $N_B = 1380$ points. Panel (B) presents the marginal probability distribution of the magnetic field obtained from direct numerical integration (solid line) and from the emcee MCMC sampling (pink histograms), using a two-dimensional parameter space with approximately 15 walkers, 50 000 steps per walker, and a burn-in phase discarding the first 20% of the iterations.
• Figure 2: Marginal posterior distributions of the magnetic field. Marginal probability distributions inferred using uniform (violet dot–dashed), gamma (orange dashed), and Gaussian (teal dotted) magnetic-field priors from longitudinal oscillations in panels (A) 2020AA...633A..12M and (B) 2025MNRAS.542.1308P, with all distributions normalised to their maximum values. The direct solutions assume uniform priors on the electron number density, $\mathcal{U}(n_{\rm e},[\mathrm{cm}^{-3}]; 10^{9}, 10^{11})$. For the magnetic field, the priors $\mathcal{U}(B,[\mathrm{G}]; 1, 70)$, $\gamma(B; 3.6, 0.2)$, and $\mathcal{G}(B,[\mathrm{G}]; 22.6, 11.9)$ are used for panel (A), while $\mathcal{U}(B,[\mathrm{G}]; 1, 70)$, $\mathcal{G}(B,[\mathrm{G}]; 5.1, 0.5)$, and $\gamma(B; 100, 20)$ are adopted for panel (B).
• Figure 3: Joint and marginal posterior distributions of flux-tube parameters. The top-left panel shows the joint posterior distribution of magnetic field strength and flux-tube length, the top-right panel shows the joint distribution of density and flux-tube length, the bottom-left panel shows the marginal distribution of the magnetic field, and the bottom-right panel shows the marginal distribution of the flux-tube length, assuming uniform priors for all parameters and using the observational constraints of 2020AA...633A..12M. The prior on the magnetic field is taken from the posterior obtained in Sect. \ref{['sec:longitudinal_oscillations']} using the uniform prior ($B_u$). Purple curves denote marginal posterior distributions obtained via Bayesian inference, while pink histograms correspond to results from the emcee MCMC algorithm with the same dimensionality, number of walkers, steps, and burn-in phase as in Fig. \ref{['figure:longitudinal_general']}. The bottom panels are not normalised \ref{['figure:longitudinal_general']}.
• Figure 4: Marginal probability distributions of the flux-tube length. Marginal probability distributions inferred using uniform (violet dot–dashed), gamma (orange dashed), and Gaussian (teal dotted) magnetic-field priors from longitudinal oscillations in panels (A) 2020AA...633A..12M and (B) 2025MNRAS.542.1308P, with all distributions normalised to their maximum values.