# An Improved Analytical Model of the Local Interstellar Magnetic Field: The Extension to Compressibility

## TL;DR

This paper extends an existing analytical model of the local interstellar magnetic field near the heliopause from incompressible to compressible flow, incorporating isothermal and adiabatic conditions, and validates it against MHD simulations.

## Contribution

It introduces a compressible extension of a previous magnetic field model, providing exact expressions and approximations for density and flow velocity, and compares results with MHD simulations.

## Key findings

- The extended model accurately describes magnetic draping in compressible flows.
- Analytical solutions align well with self-consistent MHD simulation results.
- The model enhances understanding of interstellar magnetic field behavior near the heliopause.

## Abstract

A previously published analytical magnetohydrodynamic model for the local interstellar magnetic field in the vicinity of the heliopause (R\"oken et al. 2015) is extended from incompressible to compressible, yet predominantly subsonic flow, considering both isothermal and adiabatic equations of state. Exact expressions and suitable approximations for the density and the flow velocity are derived and discussed. In addition to the stationary induction equation, these expressions also satisfy the momentum balance equation along stream lines. The practical usefulness of the corresponding, still exact analytical magnetic field solution is assessed by comparing it quantitatively to results from a fully self-consistent magnetohydrodynamic simulation of the interstellar magnetic field draping around the heliopause.