Sulphra

Sulphra, a two-faced porcelain oracle, breathes two unequal ribbons of red light into a balance that tips toward the brighter one.

The Physics

Singly ionised sulphur, S⁺ (S II), emits a forbidden red doublet at 671.6 nm and 673.1 nm (air 6716.44 / 6730.82 Å) from the ²D°_5/2 and ²D°_3/2 levels down to the ⁴S°_3/2 ground level. The two upper levels lie at almost the same energy, so temperature hardly matters, but they have different radiative rates. That makes the line ratio a gauge of electron density.

R = I(671.6) / I(673.1)

n_e → 0: R → g(²D_5/2)/g(²D_3/2) = 6/4 ≈ 1.5 n_e → ∞: R → (g A)_5/2/(g A)_3/2 ≈ 0.44

• R: intensity ratio of the doublet (dimensionless)
• I: line intensity (W m⁻² sr⁻¹)
• n_e: electron number density (cm⁻³)
• g: statistical weight 2J + 1 of the upper level
• A: Einstein spontaneous-emission coefficient of each line (s⁻¹)

At low density every collisional excitation radiates, so R follows the collision strengths (proportional to g). At high density the levels reach Boltzmann populations and R follows gA. In between, roughly 50 to 2000 cm⁻³, R measures n_e: gas more than ten million billion (10¹⁶) times thinner than air. Sources: Osterbrock & Ferland, Astrophysics of Gaseous Nebulae and Active Galactic Nuclei (2006); Sanders et al., ApJ 816, 23 (2016); Kakkad et al., A&A 618, A6 (2018).

Honest caveat: The limiting ratios (about 1.45 to 1.5 and 0.44) depend on the atomic data adopted and weakly on temperature, so density values carry real systematic uncertainty.

The glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.

In character

Ask one tongue and you hear a colour. Ask both and compare, and I will tell you how crowded the dark is.

On the hoodie

Front: two red bars of unequal height under a tiny scale. Back: Sulphra in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “TWO LINES. ONE DENSITY.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.

Part of the Forbidden Transitions set with Nebulia, Coronix, Flipwarden, Viridael, Sanguora. Browse all physics hoodies, more astrophysics & cosmology designs, or the Deep Cuts.