Fluorescent [O I] Line Diagnostic for the Incident Ultraviolet Radiation Field

The face-on [O I] 1.316 μm line intensity multiplet (4s³S⁰₁ – 3p³P_0,1,2) is shown as a function of incident radiation in Habing (G₀) units. I^obs(1.316 μm) is the observed line intensity in units erg cm^-2 s^-1 sr^-1 and i is the angle between an edge-on PDR and the line of sight. For a strictly edge-on PDR **(i=0)** additional constraints need to be added for the depth of the PDR along the line of sight. Lines are shown for PDRs of constant density **n = 10³** (red), **n = 10⁴** (green), and **n = 10⁵** (blue) cm^-3.
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Explanation

This diagram and the instructions below will help you take into account viewing inclination angle when interpreting measured [O I] 1.316 μm emission lines from a PDR.

How the diagram was computed

A plane-parallel geometry for the PDR is assumed. All [O I] levels are included for which atomic data is available in the line list of van Hoof, P.A.M., 2018, Galaxies, 6, 63. Radiation pumping is considered to occur from the lowest fine-structure levels of [O I] (³P_0,1,2) to higher levels. The ultraviolet continuum radiation has the shape of a Draine field. Self-shielding in the pumping lines is handled using an FGK approximation separately for each line (Federman, Glassgold, & Kwan, 1979, AJ, 227, 466). As the pumping lines become optically thick, an escape probability is used to diminish the radiative de-excitation to ground (e.g., Tielens & Hollenbach 1985, ApJ, 291, 722). The radiative cascade is calculated starting from the highest level and working downward to lower levels accounting for the direct UV pumping and entry into each level by radiative de-excitation from above. The distribution with depth into the PDR of the ground-state [O I] level populations is taken from the full PDR model. The final emitted [O I] line intensity is the result of the integrated emissivity along a line perpendicular to the PDR face.

Directions for Use

Measure the sum of the [O I] 1.316μm multiplet line emission (4s³S⁰₁ – 3p³P_0,1,2) . There are 3 lines in the multiplet, and likely unresolved in JWST observations. Units need to be erg cm^-2 s^-1 sr^-1.
Multiply the observed intensity by sin(i) where i is the angle between the face of the PDR and the line of sight. The face is the surface facing the illuminating star. A face-on PDR has i = 90 (sin(i) = 1) and a strictly edge-on PDR has i = 0 (sin(i) = 0). This plot works only for i > 0.
For example, the value of i has been estimated for the Orion Bar to be ~4 degrees from the width of the ionized gas lines at the ionization front (Pellegrini et al 2009, Salgado et al. 2016, Peeters et al. 2024).
The product of the observed line intensity times sin(i) gives an estimate for the emission emitted from the face of the PDR.
Read off the G₀ incident on the face of the PDR from the plot. Density curves are plotted for 10³, 10⁴, and 10⁵ cm^-3, but the spread in G₀ is only about a factor of 2 for a range in density of 10². If the density is unknown then use the 10⁴ curve.