🔭 astrophysics

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

This proof-of-concept study demonstrates that ambipolar heating, arising from the partial ionization of solar prominence plasma, can effectively balance radiative losses and sustain cold, dense threads within a one-dimensional Kippenhahn-Schlüter magnetic model, suggesting its critical role should be incorporated into more complex multi-dimensional simulations.

Original authors: Llorenç Melis, Roberto Soler

Published 2026-03-18

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CC BY 4.0

Original authors: Llorenç Melis, Roberto Soler

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Sun's atmosphere as a giant, super-hot oven (the corona). Floating inside this oven are strange, cold, and dense clouds of gas called solar prominences. It's like having a block of ice hovering inside a blast furnace without melting. The question scientists have asked for decades is: How does this ice stay frozen?

Usually, we think of heat flowing from hot to cold. So, why doesn't the cold prominence just evaporate instantly? And what keeps it from falling down due to gravity?

This paper by Melis and Soler investigates a hidden "heater" that might be keeping these solar clouds in a delicate balance. Here is the story in simple terms.

1. The Setup: A Magnetic Hammock

Think of a solar prominence as a heavy blanket of gas. Gravity wants to pull it down, but it doesn't fall. Why? Because it's sitting in a magnetic hammock. The Sun's magnetic field lines curve upward, creating a dip or a "bowl" that holds the heavy gas up against gravity.

However, this gas isn't a perfect fluid. It's partially ionized, which is a fancy way of saying it's a mix of:

Electrically charged particles (like tiny magnets that follow the magnetic field lines).
Neutral particles (like regular gas that doesn't care about magnets).

2. The Problem: The Ice is Melting

Even with the magnetic hammock holding it up, the cold gas is constantly losing heat. It's like a campfire in the rain; the rain (radiative cooling) is constantly trying to put the fire out. To stay in equilibrium, the prominence needs a heat source to replace the lost energy, otherwise, it would collapse or evaporate.

Scientists have tried to find this heat source. Some thought it was waves crashing, others thought it was light from the Sun. But this paper asks: What if the magnetic field itself is generating the heat?

3. The Solution: The "Friction Heater" (Ambipolar Diffusion)

Here is the core idea of the paper, explained with an analogy:

Imagine a crowded dance floor.

The charged particles are dancers who are holding hands with the magnetic field lines. They are forced to move in perfect sync with the music (the magnetic field).
The neutral particles are dancers who are just dancing to their own rhythm. They don't hold hands with the magnetic field.

Because the magnetic field lines are curved and twisted (like a slinky), the charged dancers are forced to move in a specific way. But the neutral dancers want to move differently. As they try to move past each other, they bump and rub against one another.

In physics, this rubbing is called collisions. Just like rubbing your hands together creates warmth, these collisions between charged and neutral particles create friction. This friction generates heat.

The authors call this Ambipolar Heating. It's the heat generated by the "friction" of the two types of gas particles trying to move in different directions.

4. The Experiment: Building a Digital Model

The scientists built a computer model (a "proof-of-concept") to see if this friction heater is strong enough to save the prominence.

They created a 1D model (like a single thread of the prominence).
They balanced the forces: Gravity pulling down vs. Magnetic force holding up.
They balanced the energy: Heat lost to space vs. Heat gained from friction.

The Results:

It Works: The friction heater provides enough energy to offset a significant chunk of the cooling. In some cases, it covers up to 90% of the heat loss!
The Structure: The model creates a structure that looks exactly like real observations:
- A cold, dense core (the prominence thread).
- A thin, sharp transition zone where the temperature jumps from cold to hot.
- A hot, extended outer region (the corona).
The Drain: The friction doesn't just heat the gas; it also causes a slow "drainage." Imagine the neutral particles slowly sliding down the magnetic hammock due to gravity, creating a gentle, steady flow of material.

5. Why Does This Matter?

This paper is a "proof of concept." It shows that you don't need a mysterious, external explosion to heat a prominence. The magnetic field of the prominence itself, interacting with its own partially ionized gas, creates enough internal friction to keep the energy balance working.

The Takeaway:
Solar prominences are like complex machines where the magnetic field acts as a scaffold, and the "friction" between different types of gas particles acts as a built-in heater. This discovery suggests that to truly understand how these solar clouds survive, we must include this "friction heating" in our future, more complex 3D simulations.

In short: The Sun's magnetic field isn't just a cage; it's also a heater, keeping the cold clouds from freezing or melting away.

1. Problem Statement

Solar prominences are cool, dense plasma structures suspended in the hot solar corona. While their mechanical equilibrium (balance between gravity and magnetic forces) is well-understood via the classic Kippenhahn-Schlüter (K-S) model, their energy balance remains an open problem.

The Challenge: Prominences are partially ionized. Standard radiative equilibrium models often predict temperatures lower than those observed in prominence cores. While radiative heating from the photosphere and corona is significant, it is often insufficient to balance net radiative losses.
The Gap: Previous studies have explored heating via MHD waves or arbitrary parametrized heating, but the specific role of ambipolar diffusion (the dissipation of currents due to ion-neutral collisions in partially ionized plasma) as a self-consistent heating mechanism in prominence energy balance has not been thoroughly investigated.

2. Methodology

The authors developed a one-dimensional (1D) self-consistent equilibrium model that simultaneously satisfies mechanical equilibrium and energy balance, incorporating ambipolar diffusion.

Physical Framework:
- Governing Equations: Used single-fluid Magnetohydrodynamics (MHD) equations for partially ionized plasmas, including continuity, momentum, induction, and energy equations.
- Composition: Modeled a plasma of Hydrogen and Helium (10% He abundance). Ionization fractions were calculated using non-LTE data for Hydrogen and the Saha equation (LTE) for Helium.
- Ambipolar Diffusion: Included the ambipolar diffusion coefficient ( $\eta_A$ ), which depends on ion-neutral collision frequencies. Ohmic and Hall effects were neglected as $\eta_A$ is dominant in prominence conditions.
Mechanical Equilibrium:
- Adopted a modified Kippenhahn-Schlüter (K-S) configuration with a sheared magnetic field ( $B_x, B_y, B_z$ ).
- The magnetic field creates a "dip" where gravity is balanced by magnetic tension.
- Unlike the static classic K-S model, the inclusion of ambipolar diffusion introduces stationary flows (gravitational drainage of neutrals) in the equilibrium state.
Energy Balance:
- Solved the energy equation where the heat-loss function ( $L$ $L$ ) includes:
  1. Ambipolar Heating ( $Q_A$ ): Generated by the dissipation of perpendicular currents ( $J_\perp$ ) associated with the non-force-free magnetic field.
  2. Radiative Cooling ( $L_{rad}$ ): Approximated using an optically-thin cooling curve modified for low temperatures.
  3. Thermal Conduction: Calculated considering parallel conductivity of charged particles and isotropic conductivity of neutrals.
Numerical Strategy:
- Employed an iterative scheme to solve the circular dependency: the heating rate depends on the magnetic field and temperature, while the temperature profile depends on the heating rate.
- The process iterates until the $L_2$ relative error of the temperature profile converges ( $< 10^{-7}$ ).
- Boundary conditions: Fixed central temperature ( $T_0$ ) and pressure ( $p_0$ ), with zero gradient at the center.

3. Key Contributions

Self-Consistent Coupling: This is the first work to couple the mechanical force balance (K-S model) with the energy balance equation while explicitly including ambipolar diffusion as the heating source, rather than an external or arbitrary source.
Stationary Flows: The model demonstrates that ambipolar diffusion naturally drives stationary flows in equilibrium, specifically a gravitational drainage flow of neutral particles, which compensates for converging flows along the field lines.
Parameter Survey: A systematic exploration of how thread length depends on central temperature ( $T_0$ ), pressure ( $p_0$ ), magnetic field strength ( $B_0$ ), and shear angle ( $\phi$ ).

4. Key Results

Structure of the Models: The resulting models consistently exhibit three distinct regions:
1. Cold Core: A dense, partially ionized thread ( $T \approx 8,000$ K) where ambipolar heating is active.
2. Prominence-Corona Transition Region (PCTR): A very thin region with a sharp temperature rise and rapid ionization of H and He.
3. Coronal Region: An extended, hot, fully ionized region where ambipolar heating vanishes.
Heating Efficiency:
- Ambipolar heating is confined to the partially ionized region.
- In the cool core, ambipolar heating partially compensates for radiative losses (up to ~90% for low pressures/high temperatures, but typically ~10-50% for realistic parameters).
- In the PCTR and corona, radiative losses are balanced primarily by thermal conduction.
Drainage Flows: The model predicts vertical drainage velocities ( $v_z$ ) of neutral hydrogen and helium due to gravity. Calculated values ( $v_z \approx -14$ m/s at the center) align with previous theoretical studies and indirect observational evidence.
Parameter Dependence (Thread Length $a$ ):
- Temperature ( $T_0$ ): Higher $T_0$ leads to shorter threads (increased radiative losses).
- Pressure ( $p_0$ ): Higher $p_0$ leads to shorter threads (heating rate decreases faster than cooling rate as density increases).
- Magnetic Field ( $B_0$ ): Stronger fields lead to shorter threads, with a critical minimum $B_0$ required for equilibrium existence.
- Shear Angle ( $\phi$ ): Large shear angles (approaching $90^\circ$ ) are crucial for obtaining realistic thread lengths (2–30 Mm). Small shear angles result in unrealistically short threads (<0.2 Mm).
Critical Limits: Equilibrium solutions cease to exist if parameters fall below critical thresholds (e.g., if $p_0$ is too low for a given $T_0$ , or $B_0$ is too weak), causing the thread length to diverge asymptotically.

5. Significance and Conclusions

Relevance of Ambipolar Heating: The study demonstrates that ambipolar diffusion is a non-negligible heating source in solar prominences. It provides a physical mechanism to partially offset radiative cooling without relying on external wave heating or arbitrary parameters.
Implications for Modeling: The results suggest that future multi-dimensional MHD simulations of prominences must include ambipolar diffusion to accurately capture the energy balance and thermal structure of prominence threads.
Limitations & Future Work:
- The model is 1D and stationary, ignoring dynamic evolution, shocks, and 3D geometries (e.g., cylindrical threads).
- Radiative cooling was approximated; future work will incorporate full non-LTE radiative transfer tables (e.g., from Gunár et al. 2025) for higher accuracy.
- Stability analysis of these new equilibrium configurations is a necessary next step.

In summary, Melis and Soler provide a proof-of-concept that ambipolar heating is a viable and necessary component in the energy budget of solar prominences, capable of sustaining cold, dense threads against radiative cooling in a self-consistent magnetic configuration.