Following the coronal temperature profiles of stars

Title: Temperature and density profiles in the corona of main sequence stars induced by stochastic heating in the chromosphere

Authors: Luca Barbieri, Lapo Casetti, Andrea Verdini, and Simone Landi

First Author’s Institution: Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, FI, Italy

Status: Submitted to Astronomy & Astrophysics [open access]

One open question in heliophysics is how the Sun maintains its peculiar temperature profile in its outermost atmosphere, called the corona. In the corona, the temperature increases with distance from the Sun’s surface, a phenomenon called a temperature inversion. This inversion leads to an ambient coronal temperature of millions of degrees Kelvin (K), or about 1000 times hotter than the solar surface. These features inform the coronal heating problem. 

Recent work by today’s leading author suggests that this problem may be solved by random (or stochastic), impulsive disturbances to the region below the corona called the chromosphere. Such disturbances are observed on the Sun in the extreme ultraviolet (EUV) and in Hydrogen-alpha. In today’s paper, the authors use the same framework that they used for the Sun to investigate the possible temperature and density profiles of other main-sequence stars less than 1.5 times the mass of the Sun (M_☉).

The Model

There are two components of the authors’ model. The first is a magnetic loop in the corona that contains a material where particles do not interact through collisions frequently; this is called a collisionless coronal loop. This loop is in contact with the second component of the model: the chromosphere, which acts as a source of reference temperature T_b that is increased by random increments and at random intervals. Actually, these intervals are so brief and frequent that the chromosphere is never able to “relax” fully to the reference temperature!

These increases in temperature are responsible for energizing coronal particles where the loop is in contact with the chromosphere. Because the coronal loop material is collisionless, the spatial distribution of particles of a given energy is only going to depend on their velocity and the star’s gravity– the faster a particle moves, the more kinetic energy it has to work against the star’s gravity. This is called velocity filtration and it results in higher-energy particles reaching larger heights in the stellar atmosphere than lower-energy particles.

A few fundamental parameters of the coronal profile start to become apparent: how much the chromosphere’s temperature increases to energize the corona, how much time the chromosphere spends at an increased temperature, and the gravitational force at a given height in the corona (the specific gravity). A relatively complicated physical problem is reduced to just a few variables! Equipped with simplified equations, the authors seek the values that can replicate a sun-like coronal profile, as shown in Figure 1.

Because velocity filtration only allows the fastest particles to reach large heights, particles higher in the corona are going to have a higher kinetic temperature– velocity filtration naturally produces a temperature inversion. By extension, if the surface gravity is sufficiently large, then slow particles are efficiently contained low in the corona and there is an extreme stratification of particle velocities with height. This produces a temperature profile considered sun-like and is demonstrated in the left panel of Figure 1.

What is considered a “sufficiently large” surface gravity depends on the coronal loop size and the chromospheric temperature. As such, the authors parameterize whether the temperature profile is sun-like or not based on the temperature at the top of the loop if a.) the interval between heating events is random and b.) there is no interval between heating events (i.e., the chromosphere is always being heated). If the ratio between Case a and Case b (denoted by X) is 1, then the model produces a sun-like profile.

The application

Using well-established scaling laws between quantities like stellar mass and stellar radius or temperature, the authors’ model can predict the coronal profile of a given main-sequence star using just the star’s mass (see Figure 2). What they find is that as long as the loop’s height is at least ~1% of the star’s radius, then essentially all stars less massive than 1.5M_☉ are expected to have a sun-like corona.  The smaller the star is, the more this percentage decreases, making it easier for small stars to have sun-like coronae. This is true down to about 0.5M_☉, where the mass-radius scaling law significantly changes, which impacts the specific gravity scaling.

Measuring the coronal temperature profiles of stars is difficult. Different spectral lines are formed at different temperatures and hence different coronal heights. However, without being able to spatially resolve stars beyond our solar system, we cannot tell the exact height that a temperature occurs at, only that the temperature does occur. This makes it difficult to confirm whether these models accurately represent what is actually happening on other stars. 

Thankfully, the Sun is close enough that we can easily spatially resolve it and (less easily) make in-situ measurements of these quantities. The fact that this model is largely consistent with solar observations is exceptionally promising for its application to sun-like stars. This is important for understanding things like stellar winds– persistent outflows of stellar material– which have important impacts on the chemistry and sustainability of atmospheres of planets. It will be exciting to see how the authors improve these models in the future and what explorations of the associated stellar wind reveal about both the star and its surrounding environment.

Astrobite edited by Annelia Anderson

Featured image adapted from Figure 3 in the paper and NASA’s Solar Dynamics Observatory AIA instrument