Resonant Scattering of the He I 1.0833$μ$m Triplet in H II Regions: Emission Spectra

TL;DR

This study analyzes resonant scattering of the He I $1.0833\,\mu\mathrm{m}$ triplet in H II regions using Monte Carlo radiative transfer that fully treats the three-line multiplet with Voigt profiles and partial redistribution. It shows that resonant trapping at large $\tau_{\rm tot}$ produces unusually broad, blue-shifted, and occasionally multi-peaked emission, with dust further attenuating the flux and shaping the spectrum. The work provides diagnostic predictions for well-studied regions (e.g., M17-B, NGC 3603, and M51's NE-Strip) and a method to derive the He$^+$/H$^+$ ratio from the $1.0833\,\mu\mathrm{m}$ line after correcting for trapping and dust. Observations with high-resolution near-infrared spectrographs can test these predictions, constraining nebular conditions and improving abundance determinations in star-forming environments.

Abstract

Resonant scattering of He I 1.0833$μ$m triplet photons by metastable He 2 $^3$S$_1$ is studied for optical depths characteristic of H II regions. Regions with large He 2 $^3$S$_1$ column densities are predicted to have unusually broad, multi-peaked 1.0833$μ$m emission profiles, with the centroid blue-shifted by up to $\sim$14 km/s relative to other lines. The feature FWHM can exceed 100 km/s for some regions. Resonant trapping enhances dust absorption and reduces the He I 1.0833$μ$m emission. Care must be taken when using the He I 1.0833$μ$m/H I 1.0941$μ$m (Pa$γ$) ratio to estimate the He$^+$/H$^+$ ratio. Predicted spectra are computed for examples, including M-17B and NGC3603 in the Galaxy, and a star-forming region in M51. Observations of the 1.0833$μ$m triplet with spectrometers such as NIRSPEC, CARMENES, or X-Shooter can confirm the predicted effects of resonant scattering in H II regions, and constrain the nebular conditions.

Figures (15)

• Figure 1: Energy levels of He1 below 23.5 eV. Permitted transitions are shown as solid lines, with the $1.0833\micron$ triplet shown in red. Dashed lines indicate forbidden transitions. Dotted lines show the principal paths for collisional depopulation of $2\,^3{\rm S}_1$ by electrons.
• Figure 2: H2 region cross-section. $\xi$ is the fraction of the volume where He is mainly He$^+$.
• Figure 3: Number of scatterings for spherical geometry for (a) single resonance line (e.g., Lyman $\alpha$), for two values of the damping constant $a$. (b) He1 $1.0833\micron$ triplet, for two values of $b$. The approximations (\ref{['eq:nsca1']}) and (\ref{['eq:nsca3']}) are shown as dashed red curves.
• Figure 4: Escape probability $\beta\equiv 1/(1+\langle N_s\rangle)$ as a function of optical depth. (a) Single resonant line, for spherical geometry, and $a=1.37\times10^{-4}$ (appropriate for He1 1.0833$\micron$) and $a=4.72\times10^{-4}$ (appropriate for H1 Ly$\alpha$). Also shown: $\beta$ calculated using Eq. (\ref{['eq:nsca1']}), and the escape probability $\beta_{\rm BSS02}$ estimated by Benjamin+Skillman+Smits_2002. (b) Full three-line treatment for the He1 $1.0833\micron$ triplet for spherical geometry, for two values of $b$. Also shown: $\beta$ calculated using Eq. (\ref{['eq:nsca3']}), and $\beta_{\rm BSS02}$.
• Figure 5: $\langle L_{\rm path}\rangle/R$, where $\langle L_{\rm path}\rangle$ is average path length traveled by photons before escaping from a sphere of radius $R$. (a) Results for a single line (e.g., Ly$\alpha$) for two values of $a$. The dashed line is an empirical fit (Eq. \ref{['eq:Lfita']}). (b) Results for the He1 $1.0833\micron$ triplet for 4 values of $b$. The dashed line is an empirical fit (Eq. \ref{['eq:Lfit']}).