A Radially Resolved Magnetic Field Threading the Disk of TW Hya

We present a new approach to detecting and characterizing a magnetic field in protoplanetary disks through the differential broadening of unpolarized molecular emission from CN. To demonstrate this technique, we apply it to new ALMA observations of the full complement of hyperfine components from the $N=1-0$ transition, achieving a spatial and spectral resolution of ${\approx}\,0.5^{\prime\prime}$ and $80~{\rm m\,s^{-1}}$, respectively. By fitting a model that incorporates the velocity structure of the disk, the potential non-LTE excitation of the molecule, and the Zeeman effect, we recover a radially resolved magnetic field with a strength of ${\sim}10~{\rm mG}$ between 60 and 120~au. The morphology of the field is also inferred through azimuthal variations in the line broadening, revealing a predominantly poloidal field at 60~au, sharply transitioning to one within the disk plane outside of the gap at 82~au. The signal-to-noise ratio of the data meant that the planar component was unable to be decomposed into toroidal and radial components. Lower limits on the local gas density ($n({\rm H_2}) \gtrsim 10^8~{\rm cm^{-3}}$) from the excitation analysis of the CN emission correspond to a lower limit between 0.1 and 0.01 for the plasma $\beta$.