# Velocity centroid gradients for absorbing media

## TL;DR

This paper demonstrates that velocity centroid gradients can effectively trace magnetic fields in absorbing media like $^{13}$CO 2-1 emission, expanding the applicability of the VGT method to molecular cloud studies.

## Contribution

The study extends the velocity gradient technique to absorbing media, showing its effectiveness with $^{13}$CO 2-1 emission in various conditions.

## Key findings

- Velocity centroid gradients trace magnetic fields across different $^{13}$CO conditions.
- The method is effective in media with varying densities and optical depths.
- Application to simulations suggests potential for observational studies.

## Abstract

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.