Stark Width of a Line at Given Plasma Conditions

Computes the Stark width (and shift) of a line at a given temperature and electron density, from the Stark broadening parameters returned by starkb_lines().

Usage

stark_width(
  stark,
  wavelength,
  temperature,
  density = 1e+17,
  perturber = "electron",
  tolerance = 0.5
)

Arguments

stark: A tibble returned by starkb_lines().
wavelength: The wavelength of the line, in nm.
temperature: The temperature, in K (a vector is allowed).
density: The perturber (electron) density, in cm\(^{-3}\). Default is \(10^{17}\).
perturber: The perturber. Default is "electron".
tolerance: The largest allowed difference between wavelength and the tabulated wavelength, in nm. Default is 0.5.

Value

A tibble with one row per temperature and columns wavelength (the requested wavelength, nm), tabulated_wavelength, upper, lower, perturber, temperature, density, width (FWHM, nm) and shift (nm).

Details

The transition whose wavelength is closest to wavelength is used; its wavelength must lie within tolerance nm. STARK-B often tabulates a multiplet at its mean wavelength \(\lambda_m\); the width and shift of a line of the multiplet at \(\lambda\) are then \(w_\lambda = w_m \lambda^2 / \lambda_m^2\) (and likewise for the shift), as the database recommends. This scaling is applied to every match. Within the impact approximation, the width and shift are proportional to the perturber density, so the tabulated values at the density closest to density are scaled linearly to density. Between the tabulated temperatures, the width is interpolated linearly in \(\log w\) against \(\log T\), and the shift linearly against \(\log T\); temperatures outside the tabulated range give an error.

Examples

# A table in the format of starkb_lines(), for illustration
stark <- data.frame(
  species = "X II", wavelength = 500, upper = "u", lower = "l",
  perturber = "electron", temperature = c(5000, 10000, 20000),
  density = 1e17, width = c(0.020, 0.014, 0.010), shift = 0, source = ""
)
stark_width(stark, wavelength = 500, temperature = 8000, density = 5e16)
#> # A tibble: 1 × 9
#>   wavelength tabulated_wavelength upper lower perturber temperature density
#>        <dbl>                <dbl> <chr> <chr> <chr>           <dbl>   <dbl>
#> 1        500                  500 u     l     electron         8000    5e16
#> # ℹ 2 more variables: width <dbl>, shift <dbl>