Point a camera at the sword of Orion and leave the shutter open. What comes back is red — huge, ragged, luminous, fourteen hundred light-years off. You might read it the way you read dust in a sunbeam: gas, lit by a star. It is not. Nearly every hydrogen atom out there has had its electron torn off, and the red is what happens when an electron finds its way back.
The cloud also has an edge — not a shell, and not a place where the gas stops, because the gas runs on for light-years. An edge where the ionization stops, startlingly abrupt, with nothing in it.
A budget, and where it closes
A hot star pours out ultraviolet. Any photon above 13.6 electron-volts can strip the electron off a hydrogen atom, and, crucially, it is spent doing it. One photon, one atom, photon gone. Meanwhile, inside that volume, free electrons keep blundering into protons and sticking, and each time one does the star must spend another photon to take that atom back.
So there is a budget. The star emits so many ionizing photons a second; the sphere suffers so many recombinations a second, and that rate climbs as the radius cubed. Where the two match, the boundary stops moving.
Bengt Strömgren wrote this down in 1939; the radius has carried his name since. It is one line of arithmetic — the photon budget over the density squared, cube-rooted — and for a hot young B star in gas at five hundred atoms per cubic centimetre it returns 0.554 parsecs, under two light-years. Nothing in it describes a surface, because there isn’t one. The radius is the answer to a counting problem.
Inches, not feet
The strange part is how sharp it is.
Inside the sphere, hydrogen is ionized down to a whisper of neutral atoms, so an ultraviolet photon has almost nothing to hit and crosses light-years untouched. But absorption depends on the neutral atoms in a photon’s path, so the moment neutrals become common the gas goes opaque. The transition is one mean free path thick — here, hundreds of billions of kilometres, which sounds vast until you set it beside a radius five thousand times larger. Shrink the whole bubble to a mile across and its wall is inches thick, not feet — and it holds itself that sharp, because a photon slipping past the front runs straight into a thickening bank of neutrals.
The recombinations that pay for themselves
Here is the part I did not expect, and it turns out to be the whole thing.
Not every recombination costs the star a photon. When a free electron drops straight onto the ground state, the atom emits on the way down a photon of at least 13.6 electron-volts — which is precisely an ionizing photon. It strips the next atom it meets. That recombination undid itself; it never reaches the bill.
The ones that do cost the star are those where the electron is caught in a high orbit and walks down by stages, shedding a smaller photon at each step. Astronomers use a recombination rate that counts only these, the only events that permanently remove an ionizing photon from circulation.
One of those steps — third orbit down to second — emits at 656 nanometres. Red.
So the red is not incidental to the calculation. It is the calculation, made visible. Every red photon marks one recombination that actually cost the star something to undo — which is why astronomers treat a nebula as a photon counter. Measure its total red and you have measured the star’s ultraviolet, otherwise swallowed whole. The ledger is legible from fourteen hundred light-years because the ledger is the light.
Not that kind of edge
No. 95 found the ionosphere to be a running difference between sunlight and recombination — a mirror with no boundary at all, only a density. This is its inverse: almost nothing but a boundary. No. 126’s crystal found the temperature where two rates crossed; this finds a place. And unlike No. 51’s magnetosphere, which ends where two pressures balance, nothing here is shoving. Nothing at the Strömgren radius knows it is at the Strömgren radius. The condition is met by the whole volume at once, and the edge appears where the total runs out.
Then it starts pushing
Having found its radius by counting, the bubble turns crude. Ionized gas at ten thousand kelvin, with two particles per hydrogen atom instead of one, is wildly over-pressured against the cold cloud around it. So it expands, driving a shock ahead of itself, hunting now for the radius where pressures balance rather than photons. The count sets the starting line; what it starts is a piston, and the piston is what eventually takes the nursery apart.
Meanwhile every atom inside cycles. At a bright nebula’s densities an atom is stripped and re-formed once a decade or so, and these clouds last hundreds of thousands of years. The thing in your photograph is not a cloud of glowing gas. It is a few thousand rounds of the same argument, per atom, and the light is the receipts.
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One loop I’m watching
Next: in 1834 a young engineer on horseback chased a heap of water down a Scottish canal for two miles, and it never changed shape. Two ways a wave has of falling apart, cancelling each other exactly — which is why a message crosses an ocean of glass tonight and arrives still legible.