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Alfvén wave propagation in the partially ionized lower solar atmosphere: a test of the single-fluid approximation

Roberto Soler

Abstract

Alfvén waves are widely believed to play an important role in the transport of energy from the solar photosphere to the corona through the partially ionized chromosphere. In previous work, the properties of torsional Alfvén waves were theoretically studied using a multi-fluid model. Here, we compare those multi-fluid results with those obtained using the single-fluid magnetohydrodynamic approximation, as a way to assess the performance of the latter in the context of Alfvénic waves in the lower solar atmosphere. We consider a broadband photospheric driver that excites torsional Alfvén waves with frequencies ranging from 0.1 mHz to 300 mHz. These waves propagate upwards to the corona along a magnetic flux tube expanding with height. For both models, we compare the energy flux, chromospheric reflection, transmission and absorption coefficients, and the associated heating rates. In general, the results are almost identical in the two models, with the exception of two minor differences: (1) the net energy flux reaching the corona is approximately 5% larger in the single-fluid model, mainly owing to the higher reflectivity found in the multi-fluid model for wave frequencies exceeding 10 mHz; and (2) in a narrow region around 500 km above the photosphere, the single-fluid model underestimates the plasma heating rate due to ion-neutral damping by about a factor of two compared with the multi-fluid model. Both discrepancies arise from the approximate treatment of the ion-neutral drift in the single-fluid model and are expected to have a very limited impact on practical applications.

Alfvén wave propagation in the partially ionized lower solar atmosphere: a test of the single-fluid approximation

Abstract

Alfvén waves are widely believed to play an important role in the transport of energy from the solar photosphere to the corona through the partially ionized chromosphere. In previous work, the properties of torsional Alfvén waves were theoretically studied using a multi-fluid model. Here, we compare those multi-fluid results with those obtained using the single-fluid magnetohydrodynamic approximation, as a way to assess the performance of the latter in the context of Alfvénic waves in the lower solar atmosphere. We consider a broadband photospheric driver that excites torsional Alfvén waves with frequencies ranging from 0.1 mHz to 300 mHz. These waves propagate upwards to the corona along a magnetic flux tube expanding with height. For both models, we compare the energy flux, chromospheric reflection, transmission and absorption coefficients, and the associated heating rates. In general, the results are almost identical in the two models, with the exception of two minor differences: (1) the net energy flux reaching the corona is approximately 5% larger in the single-fluid model, mainly owing to the higher reflectivity found in the multi-fluid model for wave frequencies exceeding 10 mHz; and (2) in a narrow region around 500 km above the photosphere, the single-fluid model underestimates the plasma heating rate due to ion-neutral damping by about a factor of two compared with the multi-fluid model. Both discrepancies arise from the approximate treatment of the ion-neutral drift in the single-fluid model and are expected to have a very limited impact on practical applications.
Paper Structure (8 sections, 21 equations, 7 figures)

This paper contains 8 sections, 21 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Model, basic equations, and method
  3. Background atmosphere
  4. From multi-fluid equations to the single-fluid approximation
  5. Governing equations for torsional Alfvén waves
  6. Numerical method
  7. Comparing single-fluid and multi-fluid results
  8. Discussion

Figures (7)

  • Figure 1: Equilibrium magnetic flux tube model embedded in the background atmosphere. The red and blue lines outline some selected magnetic field lines that cross the photosphere at 40 km and 70 km from the tube axis, respectively. The color gradient illustrates the density stratification from the photosphere (brown) to the low corona (yellow). The transition region height is marked by a horizontal, semi-transparent plane. For visualization purposes, the horizontal and vertical directions are not to scale.
  • Figure 2: Dependence on height above the photosphere of the collision frequencies involving neutrals (top) and the Ohmic and ambipolar diffusion coefficients (bottom) according to the assumed background atmospheric model. The ambipolar coefficient displayed in this plot has been computed using the magnetic field strength at the axis of the flux tube.
  • Figure 3: Dependence on height above the photosphere of the horizontally averaged net energy flux in the single-fluid and multi-fluid models (top) and percentage difference of the single-fluid flux with respect to the multi-fluid flux (bottom).
  • Figure 4: Percentage contributions of the Ohmic term and the ambipolar term to the horizontally averaged net energy flux as functions of height above the photosphere. The horizontal red dashed lines denotes no contribution. Results in the single-fluid model.
  • Figure 5: Coefficients of reflectivity, transmissivity, and absorption as functions of the wave frequency in the single-fluid and multi-fluid models. Note that both axes are in log-scale.
  • ...and 2 more figures