Astronomy & Celestial Mechanics
the sky, computed
Concept

Innermost stable orbit — where it appears

The smallest radius at which a circular orbit around a black hole is stable, six gravitational radii for a non-rotating hole and less for a rotating one. It fixes an accretion disc's inner edge, and so the disc's peak temperature and radiative efficiency.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as multicolour blackbody — the same set of essays touches all of them, so they are one junction rather than several.

The temperature of a disc around a stellar black hole. Effective temperature against radius, in units of the inner edge, for a stellar black hole of 10 solar masses accreting 10⁻⁸ solar masses a year. Two features are structural. The profile turns over rather than rising all the way in: the factor (1 − √(r_in/r)) is the statement that no torque acts across the inner edge, so nothing is dissipated there and the peak sits at 49/36 of it, measured here at 1.361. And outside a few inner radii the run is exactly r^−3/4, drawn as the dashed line, which is what makes a disc's spectrum broad: every decade of radius contributes at a temperature a factor of 5.6 lower. The peak is 3.46·10⁶ K here, so the disc radiates in X-rays, and integrating the whole profile gives 4.72·10³⁰ W — which is GMṀ/2r_in to a per cent, half the binding energy released and no more, because the other half is still going round.

The disc that has to throw angular momentum away

Matter cannot simply fall onto a compact object. At the energy it arrives with, it has far too much angular momentum, and the only way in is for some of it to be carried outwards — which is what a disc is for.

stars · Accretion A spectrum belonging to no temperature at all. The disc's summed emission, with the individual annuli drawn faintly beneath it. Each ring is a blackbody at its own temperature, and each is drawn at the area it actually has — the outer rings are cool and enormous, the inner ones hot and small. The sum has three parts and only the two ends belong to a temperature: a Rayleigh–Jeans rise of slope 2 from the outermost ring, a Wien cutoff at the hottest, and between them a stretch of slope 0.316, against the 1/3 that comes out of integrating ν²T(r)r dr with T ∝ r^−3/4. That middle section is the observational signature of a disc: no single blackbody produces it, no photosphere produces it, and its width rather than its peak is what says how far in the disc goes. What the figure cannot show is that a real disc's innermost rings are neither thin nor blackbodies, which is where the model's clean edges stop.

A spectrum that is a stack of temperatures

An accretion disc is not hot. Its inner edge is, its outer edge is not, and the temperature runs continuously between them as a power of radius — so what leaves the disc is the sum of a great many blackbodies at different temperatures, which is a spectrum with no temperature in it and a slope no single body can produce.

stars · Accretion

Named alongside it

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

Accretion discEddington limitMulticolour blackbodyRadiative efficiencyAccretion rateAngular momentum transportDisc truncationEffective temperatureMagnetorotational instabilityQuasarReverberation mappingSpecific angular momentum

All concepts