{"product_id":"sulphra-pixel-hoodie","title":"Sulphra – The [S II] 671.6\/673.1 nm Density Doublet Pixel Hoodie","description":"\u003cp\u003eSulphra, a two-faced porcelain oracle, breathes two unequal ribbons of red light into a balance that tips toward the brighter one.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eSingly 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°\u003csub\u003e5\/2\u003c\/sub\u003e and ²D°\u003csub\u003e3\/2\u003c\/sub\u003e levels down to the ⁴S°\u003csub\u003e3\/2\u003c\/sub\u003e 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eR = I(671.6) \/ I(673.1)\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003en\u003csub\u003ee\u003c\/sub\u003e → 0:  R → g(²D\u003csub\u003e5\/2\u003c\/sub\u003e)\/g(²D\u003csub\u003e3\/2\u003c\/sub\u003e) = 6\/4 ≈ 1.5      n\u003csub\u003ee\u003c\/sub\u003e → ∞:  R → (g A)\u003csub\u003e5\/2\u003c\/sub\u003e\/(g A)\u003csub\u003e3\/2\u003c\/sub\u003e ≈ 0.44\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eR: intensity ratio of the doublet (dimensionless)\u003c\/li\u003e\n\u003cli\u003eI: line intensity (W m⁻² sr⁻¹)\u003c\/li\u003e\n\u003cli\u003en\u003csub\u003ee\u003c\/sub\u003e: electron number density (cm⁻³)\u003c\/li\u003e\n\u003cli\u003eg: statistical weight 2J + 1 of the upper level\u003c\/li\u003e\n\u003cli\u003eA: Einstein spontaneous-emission coefficient of each line (s⁻¹)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eAt 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\u003csub\u003ee\u003c\/sub\u003e: gas more than ten million billion (10¹⁶) times thinner than air. Sources: Osterbrock \u0026amp; Ferland, \u003cem\u003eAstrophysics of Gaseous Nebulae and Active Galactic Nuclei\u003c\/em\u003e (2006); Sanders et al., \u003cem\u003eApJ\u003c\/em\u003e 816, 23 (2016); Kakkad et al., \u003cem\u003eA\u0026amp;A\u003c\/em\u003e 618, A6 (2018).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e 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.\u003c\/p\u003e\u003cp\u003eThe glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eAsk one tongue and you hear a colour. Ask both and compare, and I will tell you how crowded the dark is.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: 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.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eForbidden Transitions\u003c\/strong\u003e set with \u003ca href=\"\/products\/nebulia-pixel-hoodie\"\u003eNebulia\u003c\/a\u003e, \u003ca href=\"\/products\/coronix-pixel-hoodie\"\u003eCoronix\u003c\/a\u003e, \u003ca href=\"\/products\/flipwarden-pixel-hoodie\"\u003eFlipwarden\u003c\/a\u003e, \u003ca href=\"\/products\/viridael-pixel-hoodie\"\u003eViridael\u003c\/a\u003e, \u003ca href=\"\/products\/sanguora-pixel-hoodie\"\u003eSanguora\u003c\/a\u003e. Browse all \u003ca href=\"\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/collections\/astrophysics\"\u003eastrophysics \u0026amp; cosmology designs\u003c\/a\u003e, or the \u003ca href=\"\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"Black \/ S","offer_id":50964466827367,"sku":"32611904393364746608","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964466860135,"sku":"35020292875147891017","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964466892903,"sku":"13135463546790499486","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964466925671,"sku":"13373872655449288521","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964466958439,"sku":"64132118080329792959","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964466991207,"sku":"88439314632111916075","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964467023975,"sku":"77328200518484374728","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964467056743,"sku":"76089834310947899755","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H02_aabed8d2-2644-45a7-be4a-1bbbfceeb38e.png?v=1793678406","url":"https:\/\/pixelatedphysics.com\/products\/sulphra-pixel-hoodie","provider":"Pixelated Physics","version":"1.0","type":"link"}