The role of ambipolar heating in the energy balance of solar prominences

Abstract

Solar prominence threads are typically located around magnetic dips, where cold and dense plasma is suspended against gravity in the hot corona thanks to the upward magnetic force. Because prominences are partially ionized, ambipolar diffusion can deposit part of the energy of their non-force-free magnetic field into the plasma. This ambipolar heating may therefore play a role in the energy balance of prominences. In this proof-of-concept work, we explore the effect of ambipolar diffusion in one-dimensional models that satisfy both mechanical equilibrium and energy balance. The magnetic configuration is based on the classic Kippenhahn-Schlüter model, incorporating a sheared magnetic field. The temperature profile along the magnetic field is computed numerically by balancing radiative losses, thermal conduction, and ambipolar heating. The resulting models consistently consist of a cold, dense, partially ionized thread with prominence core conditions, a very thin prominence-corona transition region, and an extended, hot, fully ionized region with coronal conditions. In addition to providing heating that partly compensates for radiative losses, ambipolar diffusion also gives rise to stationary flows associated with the gravitational drainage of neutrals in the partially ionized region. We investigate how the length of the cold threads depends on the central temperature, central pressure, magnetic field strength, and shear angle, and show that thread lengths compatible with observations are obtained for realistic values of these parameters. Therefore, we demonstrate that ambipolar diffusion plays a relevant role in this simple configuration, indicating that this effect should be incorporated into more elaborate multi-dimensional models and simulations.

Figures (11)

• Figure 1: Ionization fractions of hydrogen and helium for $p=5\times10^{-3}$ Pa as functions of the temperature, $T$.
• Figure 2: Visualization in 3D of the magnetic dip obtained for the reference model with $T_{0}=$ 8,000 K, $p_{0}=5\times 10^{-3}$ Pa, $B_{0}=10$ G, and $\phi=88^{\circ}$. The color gradient denotes the variation of the density along the magnetic field line. Note that the axes are not to scale.
• Figure 3: Equilibrium profiles along the magnetic field line for the reference model: a) temperature, b) mean atomic weight, c) $z$-component of the magnetic field, d) pressure, e) density, f) ambipolar diffusion coefficient, g) $y$-component of the velocity, h) $z$-component of the velocity, and i) ambipolar heating rate. Results for $T_{0}=8000$ K, $p_{0}=5\times 10^{-3}$ Pa, $B_{0}=10$ G and $\phi=88^{\circ}$. The vertical red dashed lines mark the location of the cool and dense prominence thread of length $a \approx 2.56$ Mm, being this the distance between the two lines.
• Figure 4: Close-up views of some quantities of the reference model around the cold thread and the PCTR: a) Mass fractions of protons (ionized hydrogen), singly ionized helium, and doubly ionized helium. b) Ambipolar diffusion coefficient. Only half the domain with $s \geq0$ is displayed due to the symmetry of the profiles. The discontinuous derivatives of the ambipolar diffusion coefficient are caused by the first-order interpolation used to implement the hydrogen ionization degree from the tabulated values in heinzel2015fast.
• Figure 5: Mechanical equilibrium along the magnetic field line for the reference model: a) longitudinal and b) vertical components of the forces. Only a region around the cold thread, the PCTR, and the beginning of the coronal part is displayed.