Spectrum
Methods and data
Absorption model
Blackbody radiation at temperature T passes through a helium atmosphere with uniform temperature and density. The gas temperature equals the blackbody temperature. The temperature range is 4,000–9,000 K, and the He number density is 10²⁰–10²¹ cm⁻³.
F(λ) = Bλ(T) exp[−Σ Nᵢ σᵢ(λ,T,nHe)]
Bλ is the blackbody spectral intensity, σᵢ is the absorption cross section of each component, and Nᵢ is its column density along the line of sight. The model omits depth-dependent temperature and density, re-emission, ionization equilibrium, and molecule formation.
Relative amounts and line widths
One internal amount unit corresponds to column densities of 10¹⁶ cm⁻² for Na I, 10¹⁶ for Ca, 10¹⁵ for Li I, and 10¹⁷ for C₂. Atomic populations are in the ground state, with Ca I and Ca II fixed at a 1:1 ratio. Column densities are set independently of the He number density.
The displayed widths are full widths at half maximum (FWHM) of the line cores, not the extent of the broad Na wings or entire C₂ bands. Wavelengths are in vacuum.
Absorption data and limits
- Na: Allard et al. 2023 / CDS Na–He unified profiles are interpolated in temperature and density. The line core and its join to the tabulated profile (30–100 cm⁻¹) use numerical approximations. Absorption profiles cover temperatures up to 10,000 K; displayed core widths use the 6,000 K coefficients above 6,000 K.
- Ca I: Blouin et al. 2019, Fig. 3 provides digitized line widths. These apply to line cores at He number densities up to 10²¹ cm⁻³. Above 6,000 K, the 6,000 K coefficients are used.
- Ca II H and K: Hammond 1975, Eqs. 6–10 supplies line widths measured at 4,400–6,080 K and He number densities of 1.6–3.1×10²¹ cm⁻³. Density is extrapolated linearly to the slider range; temperatures outside the measured range use power-law extrapolation. The width coefficients have an accuracy of about ±30%.
- Li: Allard et al. 2014, Eqs. 4–5 supplies widths in the low-density impact approximation for 500–4,000 K. Temperatures above 4,000 K are extrapolated.
- C₂: ExoMol 8states Swan transitions provide intensities under local thermodynamic equilibrium and thermal widths. The pressure shift is ΔE = 0.2ρHe eV, with ρHe in g/cm³. Collisional broadening is omitted. The transmission table covers 3,000–6,000 K; above 6,000 K, the 6,000 K values are used.
For Ca and Li, natural, pressure, and thermal broadening are combined in a pseudo-Voigt profile. Extending the line-core approximation into the far wings introduces uncertainty in wing absorption. Line positions and strengths are based on the NIST tables for Ca I, Ca II, Li I.
C₂ transmission is computed at 0.002 nm spacing, averaged into 0.1 nm bins, and interpolated. Pressure shifts are approximated by shifting the table; natural broadening is omitted. Unresolved line structure, overlap with other species, and interpolation introduce numerical errors.
Line-width coefficients and sources · Na data processing · C₂ data processing · C₂ numerical validation
Displayed color
The spectrum is multiplied by the CIE 1931 2° color-matching functions and integrated from 360 to 830 nm using the trapezoidal rule at 0.02 nm spacing to obtain XYZ. After conversion to linear sRGB, the largest component is normalized to 1 and the sRGB transfer function is applied. Negative RGB components are clipped to zero. Displayed colors have normalized brightness; visual adaptation and Earth’s atmosphere are not modeled. The fill beneath the spectrum approximates wavelength colors.
Color-matching function data · Data license
Color search
The largest linear RGB component of each target and candidate is normalized to 1. Displayed sRGB colors are converted to OKLab for color comparison, with hue differences weighted more heavily. The selected candidate is applied to the controls. The search includes the current settings and sweeps the full Na range in internal steps of 0.01. Results are candidates within this model, not guaranteed global optima or physical conditions of real stars.