Assessing Zeeman Measurements of Magnetic Fields in Synthetic HI Observations
Zeeman observations provide the only direct probe of line-of-sight (LOS) magnetic fields in the interstellar medium. To evaluate their accuracy and limitations, we generate synthetic HI Zeeman spectra from magnetohydrodynamic simulations and idealized cloud models, and analyze the resulting Stokes I and V profiles using two complementary methods. Approach I uses the classical relation between Stokes V and dI/d{\nu} to estimate LOS-averaged magnetic fields, achieving an upper-limit relative error of 16% (half-width of 68.27% confidence interval) for a representative noise level of 0.014 K. Approach II applies Gaussian decomposition to Stokes I and V to estimate component-level magnetic fields, yielding a 13% relative error quantifying the same confidence range, reflecting the intrinsic uncertainty of such Zeeman estimates. Both approaches recover the original fields under uniform-field conditions and remain robust in turbulent environments. Approach I provides a simple and reliable LOS-averaged field estimate, while Approach II, although more complex, offers statistical insight into magnetic field variations along the LOS. We further show that joint fitting of Stokes I and V generally outperforms sequential fitting, particularly in the presence of attenuation. Increasing noise eight-fold produces a more modest rise in uncertainty, doubling to a 26% relative error, while substantial optical depth introduces only a minor additional contribution to the overall uncertainty. Applying these methods to FAST observations of the L1544 star-forming region, we confirm the previously reported LOS magnetic field strength, demonstrating the validity of Zeeman analysis in this benchmark core.