A New Method of Measuring Magnetic Field Strength in Highly Structured Protostellar Envelopes

Abstract

Magnetic fields play a fundamental role in protostellar collapse and disk formation, yet direct measurements of magnetic field strength in deeply embedded protostellar envelopes remain difficult. We present a new method to estimate both the vertical and total magnetic field strength in collapsing, pseudodisk- or sheetlet-dominated protostellar envelopes, derived directly from the magnetohydrodynamic momentum equation. The method relates the magnetic field strength to two observationally accessible quantities: the projected gravitational acceleration toward the center of collapse and the face-on column density of the pseudodisk, and two dimensionless parameters, $a_{b, R}$ and $\gamma_{zR}$, which characterize magnetic contribution to the force balance and the field geometry, respectively, through $|B_z|=(2\pi a_{b,R}\gamma_{zR}g_R\Sigma)^{1/2}$. Using non-ideal magnetohydrodynamic simulations, we verify the assumptions underlying the method, justify the adopted approximations, and calibrate the two key dimensionless parameters. We provide canonical estimates of these two parameters, and show that they exhibit only weak spatial and temporal variations, allowing robust field strength estimates even when detailed gas kinematics or high-resolution polarization information is unavailable. We show that the method is applicable in both turbulent and non-turbulent envelopes and is insensitive to the ambipolar diffusion coefficient, making it robust against uncertainties in the local turbulence strength and ionization rate. We apply the method to the Class 0 source L1157, using column-density and gravitational-acceleration estimates from the literature to estimate the magnetic field strength for L1157. Our result is broadly consistent with previous estimates from independent methods, demonstrating the utility of this approach for constraining magnetic fields in embedded protostellar systems.