An analytical model for the magnetic field in the thick shell of Galactic bubbles with uniform initial conditions

¹ Université Libre de Bruxelles, Science Faculty CP230, 1050 Brussels, Belgium
² Institut für Astroteilchenphysik, Karlsruher Institut für Technologie, Karlsruhe 76344, Germany
³ Institutt for fysikk, Norwegian University of Science and Technology (NTNU), Trondheim, Norway

^★ Corresponding author; vincent.pelgrims@ulb.be

Received: 9 November 2024
Accepted: 19 February 2025

Abstract

Bubbles and super-bubbles are ubiquitous in the interstellar medium and influence their local magnetic field. Starting from the assumption that bubbles result from violent explosions that sweep matter away in a thick shell, we derived the analytical equations for the divergence-free, regular magnetic field in the shell. The explosion velocity field is assumed to be radial but not necessarily spherical, making it possible to model various-shaped bubbles. Assuming an explosion center, the magnetic field at the present time is fully determined by the initial uniform magnetic field, the present-time geometry of the bubble shell, and a radial vector field that encodes the explosion-induced displacement of matter, from its original location to its present-time location. We presented the main characteristics of our magnetic-field model using a simple linear model for the radial displacements. Next, we used our analytical prescription, informed by a three-dimensional dust density map, to estimate the expected contribution of the shell of the Local Bubble, the super-bubbles in which the Sun resides, to the integrated Faraday rotation measures and synchrotron emission and to compare these to full-sky observational data. We found that, while the contribution to the former is minimal, the contribution to the latter is very significant at Galactic latitudes |b| > 45°. Our results underline the need to take the Local Bubble into account in large-scale Galactic magnetic field studies.