Denser Sampling of the Rosette Nebula with Faraday Rotation Measurements: Improved Estimates of Magnetic Fields in HII Regions

We report Faraday rotation measurements of 11 extragalactic radio sources with lines of sight through the Rosette Nebula, a prominent HII region associated with the star cluster NGC 2244. It is also a prototypical example of a "stellar bubble" produced by the winds of the stars in NGC 2244. The goal of these measurements is to better determine the strength and structure of the magnetic field in the nebula. We calculate the rotation measure (RM) through two methods, a least-squares fit to $\chi$( $\lambda^2$) and Rotation Measure Synthesis. In conjunction with our results from Savage et al. (2013), we find an excess RM due to the shell of the nebula of +40 to +1200 rad m$^{-2}$ above a background RM of +147 rad m$^{-2}$. We discuss two forms of a simple shell model intended to reproduce the magnitude of the observed RM as a function of distance from the center of the Rosette Nebula. The models represent different physical situations for the magnetic field within the shell of the nebula. The first assumes that there is an increase in the magnetic field strength and plasma density at the outer radius of the HII region, such as would be produced by a strong magnetohydrodynamic shock wave. The second model assumes that any increase in the RM is due solely to an increase in the density, and the Galactic magnetic field is unaffected in the shell. We employ a Bayesian analysis to distinguish between the two forms of the model.