Observatory · the fall
Spaghettification
Fall feet first into a black hole and your feet are pulled harder than your head. Far out the difference is nothing; it grows a thousandfold every time the distance shrinks tenfold, and somewhere it wins. Whether that happens outside the event horizon, where the universe could watch, or inside it, where no one ever will, depends on one thing only: how heavy the hole is. And the answer runs the wrong way round.
The fall
Fig. I. A body falling feet first, drawn out by the tidal pull.
- Distance
- Head to feet
- Feels like
- Your own watch
- Horizon
- Torn apart at
- So
The body is two metres, falling from rest far away; "torn apart" is taken as a hundred times its own weight pulling head and feet apart, far more than a body holds. For a black hole of ten Suns that point lies thousands of kilometres out, and everything after it happens in plain view. For Sagittarius A*, at the centre of our galaxy, you would cross the horizon feeling a ten-thousandth of a g, and have about half a minute on your own watch before the end; for M87*, nearly twelve hours. Your watch is the only one that counts in there: seen from far away, as the clock shows, you never cross at all, but slow, redden and fade at the edge.
Torn first, or the horizon first
Fig. II. Where tearing begins and where the horizon lies, against the black hole's mass.
Both distances against the mass, on log scales. The horizon grows in step with the mass: ten times heavier, ten times wider. The tearing point grows only with its cube root: ten times heavier, barely more than twice as far out. So the lines cross. Below about 4,600 solar masses you are torn apart outside the horizon; above it, inside. The dotted line is the mass on the slider above; drag it and watch which line is on top.
A star torn apart
Fig. III. A star drawn into a stream by a supermassive black hole.
The same stretch works on stars. A star holds itself together by its own gravity; inside the tidal radius, R*(M/M*)1/3, the hole's stretch across it is stronger, and every part of it goes its own way. The part that was nearer the hole is slightly more tightly bound and falls back; the far part is flung out. About half the star returns, wraps round and heats up, and for months the hole outshines its galaxy: a tidal disruption event. For a star like the Sun passing Sagittarius A*, the tidal radius is about 113 million kilometres, nine times the horizon, so the show is visible. Above about a hundred million solar masses the horizon is wider than the tidal radius, and a Sun-like star is swallowed whole, without a flash.
Who worked it out
Where it already matters
Flares from quiet galaxies. Sky surveys now catch tidal disruption events many times a year: a galaxy whose central hole had been dark brightens for weeks to months and fades in the way the fall-back of the stream predicts. ASASSN-14li in 2014 was one of the first studied closely.
The same stretch at home. The Moon pulls on the Earth in exactly this way, only very gently: the tide is the same stretch, working on the oceans and the rock. Comet Shoemaker–Levy 9 was pulled into a string of fragments by Jupiter in 1992 and hit it in 1994; Saturn's rings lie inside the distance where a moon could not hold together.
The word. Stephen Hawking used it in A Brief History of Time (1988). Astronomers also say "the noodle effect".