[Paper Review] The structure of sunspot penumbrae IV. MHS equilibrium for penumbral flux tubes and the origin of dark core penumbral filaments and penumbral grains

J. M. Borrero|ArXiv.org|Apr 24, 2007

Solar and Space Plasma Dynamics31 references16 citations

TL;DR

This study investigates magnetohydrostatic (MHS) equilibrium in horizontal sunspot penumbral flux tubes with circular cross-sections, showing that force balance is achieved when the magnetic field has a transverse component. The resulting thermodynamic structure reproduces dark core penumbral filaments and penumbral grains due to high density and low temperature in the tube's upper region, consistent with spectropolarimetric observations and the Evershed flow concentrated in dark lanes.

ABSTRACT

We study the magnetohydrostatic equilibrium of magnetic flux tubes with circular cross sections embedded in a magnetic surrounding atmosphere. We solve the static momentum equation in 2.5D to obtain the thermodynamics that are consistent with a prescribed velocity and magnetic fields. We show that force balance is roughly satisfied if the flux tube's magnetic field is aligned with its axis. Equilibrium is guaranteed if this magnetic field possesses a transverse component. Several forms of this transverse field are investigated. The resulting magnetic field configurations are critically reviewed in terms of the results from spectropolarimetric observations. The thermodynamic structure that allows the flux tube to be in mechanical equilibrium is also calculated. We show that the inferred pressure, density and temperature stratification reproduce intensity features similar to dark core penumbral filaments and penumbral grains.

Motivation & Objective

• To investigate the magnetohydrostatic equilibrium of horizontal flux tubes with circular cross-sections in sunspot penumbrae beyond the thin-flux tube approximation.
• To determine whether such flux tubes can achieve mechanical equilibrium under realistic solar conditions, particularly in the photosphere where tube radius is comparable to pressure scale height.
• To reproduce observed intensity features such as dark core penumbral filaments and penumbral grains through calculated thermodynamic structures.
• To compare the resulting magnetic and thermodynamic configurations with spectropolarimetric observations, especially regarding field inclination, velocity gradients, and Evershed flow.

Proposed method

• Solving the 2.5D static momentum equation in cylindrical coordinates to determine pressure, density, and temperature distributions consistent with prescribed velocity and magnetic fields.
• Assuming a potential magnetic field in the external atmosphere and applying boundary conditions at the flux tube interface to derive plausible internal magnetic field configurations.
• Using a general form for the flux tube's magnetic field with a transverse component to satisfy force balance and enable equilibrium.
• Calculating thermodynamic stratification (P, ρ, T) from the momentum equation under force balance, assuming no energy equation or dynamic evolution.
• Simulating continuum intensity using the Radiative Transfer Equation to compare model output with observed penumbral features.
• Applying observational constraints such as Evershed flow (v = v₀ eₓ inside tube, v = 0 outside) and field inclination gradients from spectropolarimetry.

Experimental results

Research questions

• RQ1 Can horizontal flux tubes with circular cross-sections achieve magnetohydrostatic equilibrium in the penumbra when the thin-flux tube approximation does not apply?
• RQ2 What magnetic field configuration within the flux tube ensures force balance, particularly in the presence of transverse field components?
• RQ3 Does the resulting thermodynamic structure reproduce the observed dark core penumbral filaments and penumbral grains?
• RQ4 How do the simulated intensity profiles and velocity gradients compare with high-resolution spectropolarimetric observations?
• RQ5 Why is the lower boundary of the flux tube invisible in the model, and how does this compare with observational evidence?

Key findings

• Force balance in flux tubes is only approximately satisfied when the magnetic field is aligned with the tube axis; equilibrium is significantly improved when a transverse magnetic field component is present.
• The thermodynamic structure resulting from transverse field configurations produces high density and low temperature in the upper half of the flux tube, reproducing the dark core penumbral filaments.
• The model reproduces the Evershed flow concentrated in the dark lanes of filaments, with higher opacity at the tube center enhancing the darkening effect.
• Simulated intensity profiles match observed continuum features, with the flux tube's upper region forming the τ₅ = 1 level inside the tube, making the lower boundary invisible to spectropolarimetry.
• The model predicts weak flows on the bright sides of filaments, consistent with observations by Bellot Rubio et al. (2005).
• The model is prone to Rayleigh-Taylor instabilities due to high-density plasma above low-density regions, and the role of horizontal magnetic fields in stabilization remains unclear.