# Coronal Loop Scaling Laws for Various Forms of Parallel Heat Conduction

## TL;DR

This paper investigates how different regimes of thermal conduction affect the scaling laws of coronal loops, revealing that turbulence-dominated conduction leads to fundamentally different relationships than traditional collision-dominated models.

## Contribution

It introduces new scaling laws for coronal loops considering turbulence and free-streaming conduction, expanding beyond classical collision-dominated assumptions.

## Key findings

- Turbulence-dominated conduction results in different loop scaling laws.
- Scaling laws depend primarily on low-temperature conditions in turbulence regimes.
- Regimes of temperature and density determine the applicable conduction-based scaling laws.

## Abstract

The solar atmosphere is dominated by loops of magnetic flux which connect the multi-million-degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops is determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and hence the form of the loop scaling law provides insight into the key physics that controls the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here we examine the impact of different regimes of thermal conduction -- collision-dominated, turbulence-dominated, and free-streaming -- on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in temperature and density space in which each of the applicable scaling laws prevail.