The Tractrix Magnetopause: A Novel Physics-Based Functional Form for the
Magnetopause Shape
Abstract
A new model for the shape of the magnetopause is presented using a
closed-form analytic function known as a tractrix. This shape is derived
from several physics-based underpinnings, eliminating the need for
fitting ad-hoc functional forms that, while convenient, are not
physically motivated. One feature of the magnetopause predicted by this
model is that the magnetotail flares outward until it reaches a constant
width, a feature that has significant observational evidence but is
seldom represented in functional forms of the magnetopause shape. To
optimize the parameters of this model, a dataset of over 13,000
magnetopause crossings from THEMIS/ARTEMIS, Cluster, Geotail, Interball,
and several other spacecraft is utilized. Using a Bayesian approach
combined with a Markov Chain Monte Carlo (MCMC) method to estimate the
posterior probability distribution in parameter space, the maximum
likelihood parameters for the model that optimize its performance on
this dataset are determined. The modelâ\euro™s performance is compared
to that of other popular models of the magnetopause with a focus on
their relative performance, and is shown to outperform models that
assume the tail flares outward to infinity at far distances. The
optimized model more accurately predicts magnetopause position along the
tail than other popular static analytic magnetopause models, while still
being easy to implement for a variety of applications.