Velocity centroid gradients for absorbing media

We explore how the velocity gradient technique (VGT) can be applied to absorbing media in the case of$^{13}$CO 2-1 emission. The VGT is a new way to trace magnetic fields in the plane of the sky using only spectroscopic observations. We apply the VGT to magnetohydrodynamic turbulence simulations that have been post-processed to include $^{13}$CO 2-1 emission and we calculate the velocity centroid gradients. We find that the velocity centroid gradients trace the projected magnetic field in media with different $^{13}$CO abundances, densities and optical depths. Our study opens up the possibility of using velocity centroid gradients to trace magnetic fields in molecular clouds using 13CO emission.