Astronomy & Celestial Mechanics
the sky, computed
Concept

Supermassive black hole — where it appears

A black hole of a million to ten billion solar masses at the centre of a galaxy. Most are not accreting and are detected only through the motions of nearby stars or through the flare produced when a star wanders close enough to be pulled apart.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

S2's orbit, and the mass it implies. The orbit of S2 about the centre of the Milky Way, drawn from its measured elements: a semi-major axis of 0.1251 arcseconds, which at 8.28 kpc is 1036 AU, an eccentricity of 0.8843, and a period of 16.05 years watched round twice. Kepler's third law in solar units — a³/P² — gives 4.31 million solar masses, by exactly the calculation that weighs a planetary system. At periapsis the star is 120 AU from the focus, 1407 Schwarzschild radii, and the mean density inside that radius is 5.3e+15 M☉ per cubic parsec — a million times the densest star cluster known. That density, not the mass, is the argument: there is no configuration of stars that would fit.

The mass at the centre that is not stars

One star at the centre of the Milky Way has been watched round a complete orbit. Its semi-major axis and its period give four million solar masses by Kepler's third law — and the volume that mass occupies is small enough to rule out every alternative to a black hole.

galaxies · Galactic nuclei Two lengths that cross at 1.1·10⁸ solar masses, above which nothing is seen. The radius at which a star of 1 solar radius and 1 solar mass is pulled apart by a black hole, and the hole's own horizon, both against the hole's mass and both on logarithmic axes. The tidal radius is the star's own radius times the cube root of the mass ratio, so it climbs with a slope of one third; the horizon is proportional to the mass, so it climbs with a slope of one. Two lines of different slope cross once, and this pair crosses at 1.14·10⁸ solar masses. Below that the star is torn apart outside the horizon, half of it is thrown out and half falls back, and the fallback is visible for months. Above it the star crosses the horizon while it is still a star, is swallowed whole, and produces no flare at all. The consequence is the reason these events are worth watching: a flare that is seen is an upper limit on the mass of the hole that made it, obtained without resolving anything, and it is the only such limit available for a hole that is not currently accreting.

A flare that puts a ceiling on a mass

A star torn apart by a black hole lights up for a year. The tidal radius grows as the cube root of the hole's mass and the horizon grows as the mass itself, so above about a hundred million suns the star is swallowed whole and nothing is seen — which makes the existence of a flare a measurement.

galaxies · Tidal disruption The horizon and the orbit that cannot come back, against the hole's spin. Two radii round a rotating black hole, in gravitational radii GM/c², against its spin a from −1 (an orbit against the rotation) to +1 (with it), for orbits in the equatorial plane. The lower curve is the horizon, 1 + √(1 − a²), which is the same whichever way the orbit goes. The upper one is the marginally bound orbit, 2 − a + 2√(1 − a): the closest a body falling in from far away can pass and still escape back out. For a hole with no spin the horizon is at 2 and the marginally bound orbit at 4 — twice as far out. With maximal spin the marginally bound orbit comes in to 1.09 for a prograde orbit (a = 0.998) and moves out to 5.83 for a retrograde one. A star whose tidal radius lies inside this curve is swallowed whole, so the curve, not the horizon, is the line a disruption flare is measured against — and it moves by a factor of 5.3 with the spin.

The line a star is swallowed at is not the horizon

A star torn apart by a black hole makes a flare, and a star swallowed whole makes nothing, so the heaviest hole that can produce a flare is a measurement. That ceiling is set not at the horizon but at the closest orbit from which infalling matter can still come back out — twice as far out for a hole that does not spin, and moved by a factor of five by the hole's rotation.

galaxies · Tidal disruption

Named alongside it

The objects these essays reach for when they reach for this one.

AccretionEvent horizonM sigma relationSchwarzschild radiusTidal radiusAccretion discActive galactic nucleusBlack hole spinEddington limitEffective potentialGravitational radiusHills mass

All concepts