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\begin{document}

\title{The Tractrix Magnetopause: A Novel Physics-Based Functional Form for the
Magnetopause Shape}



\author[1]{C. J. O'Brien}%
\author[2]{Michael R Collier}%
\author[1]{Brian Walsh}%
\author[3]{David Gary Sibeck}%
\author[4]{E. Taylor}%
\affil[1]{Boston University}%
\affil[2]{NASA Goddard SFC}%
\affil[3]{GSFC}%
\affil[4]{Howard University}%


\vspace{-1em}



  
  \date{May 18, 2024}


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\begin{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 model\selectlanguage{ngerman}â\textbackslash{}euro\selectlanguage{english}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.%
\end{abstract}\selectlanguage{ngerman}%



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