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Assessing Zeeman Measurements of Magnetic Fields in Synthetic HI Observations

Duo Xu, Peter Martin, Stella Offner, Robert Gutermuth, Michael Grudic, Joshua Speagle

Abstract

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/dν 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.

Assessing Zeeman Measurements of Magnetic Fields in Synthetic HI Observations

Abstract

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/dν 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.
Paper Structure (62 sections, 20 equations, 52 figures)

This paper contains 62 sections, 20 equations, 52 figures.

Table of Contents

  1. Introduction
  2. MHD Simulations and Synthetic Observations of Zeeman HI Spectra
  3. Magnetohydrodynamics Simulations
  4. The HI Gas
  5. Physical conditions along the LOS shaping spectra
  6. Radiative Transfer: POLARIS
  7. Adding Noise to the Model Spectra
  8. The importance of optical depth
  9. Two Approaches to Analyzing Zeeman HI Spectra
  10. Zeeman Analysis Approach I: Fitting Stokes $V$ with $dI/d\nu$.
  11. Zeeman Analysis Approach II: Gaussian Decomposition
  12. Models for $I$ and $V$
  13. Number of Gaussian Components
  14. Sequential Fitting Strategy
  15. Joint Fitting Strategy
  16. ...and 47 more sections

Figures (52)

  • Figure 1: HI and H$_2$ column density maps (upper left and right), HI integrated intensity map $W$ (lower left), and the ratio of $C\,W$ to HI column density (_ CWN $r_{\mathrm {CWN}}$ -- see text) (lower right). Subregions SR2, SR3, and SR4 have a box size of 0.125 pc, which at a distance of 140 pc subtends 3. LSR1 is 16 times larger in size.
  • Figure 2: LOS profiles of physical properties directly relevant to the Stokes $I$ and $V$ spectra for the four selected subregions: HI number density $n_{\mathrm{HI}}$, excitation temperature $T_{\mathrm{ex}}$, LOS velocity $v_z$, and LOS magnetic field strength $B_z$. Also shown for context, though not observable, the 3D velocity magnitude $v_{\mathrm{3D}}$ and 3D magnetic field magnitude $B_{\mathrm{3D}}$. To assess whether the small-shift approximation remains valid at the voxel level we plot the ratio of the Zeeman-induced frequency shift $\Delta \nu$ to the local velocity dispersion $\sigma$ (valid: see text). We also plot $T_{\mathrm{ex}} \cdot \tau_{\mathrm{HI,\, Center}}$ (see text). Each quantity has been suitably scaled to use the common value scale on the y axis.
  • Figure 3: Synthetic Stokes $V$ spectrum of the SR2 subregion with different noise levels added. The first column shows spectra at the native velocity intervals of 0.04 km s$^{-1}$. The second column shows the same spectra resampled to 0.1 km s$^{-1}$ channels. The third column presents the Hanning-smoothed versions of the resampled spectra. For comparison, the red line shows the FAST spectrum from 2022Natur.601...49C, which has a noise level of 0.006 K after Hanning smoothing for 0.1 km s$^{-1}$ channels, close to an injected noise level of 0.014 K in the left column.
  • Figure 4: Maps of HI integrated intensity $W$ viewing from the $+z$ direction (upper left -- same as Fig. \ref{['fig.column_density_full_4panel']} lower left) and $-z$ direction (upper right); the ratio of the $+z$ to $-z$$W$ maps (lower left); and _ CWN $r_{\mathrm {CWN}}$ viewed from the $-z$ direction (lower right -- c.f., Fig. \ref{['fig.column_density_full_4panel']} lower right, which shares the same denominator).
  • Figure 5: Schematic illustration of the five-layer cloud structure. Note that layer 5 (aka L5) and L1 have the same properties, as do L4 and L2, but they produce quite different contributions to the $I$ and $V$ spectra because of attenuation (see Figure \ref{['fig.5_Layer_GPB']}). Not encoded here is that L2 and L4 are half as thick as the other three, so that individual layers span 12.5% (orange, pink) or 25% (blue, green, brown) of the total spatial extent (see Figure \ref{['fig.f_sim_5_layers']}).
  • ...and 47 more figures