Astronomy & Celestial Mechanics
the sky, computed
Concept

Black hole mass — where it appears

The mass of the black hole at a galaxy's centre, measured from the orbits of stars or gas close to it or estimated from the speed and distance of the gas it lights. It sets the Eddington luminosity and correlates with the host galaxy's bulge.

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

A single-epoch mass, good to a factor of 2.6. The error budget of a black-hole mass obtained from one spectrum, as probability densities in the logarithm of the ratio of the estimate to the truth. Four independent widths go in. The radius comes from the luminosity through a relation with 0.19 dex of scatter about it. The line width has to be measured on a profile that is blended with narrow lines and with iron, and it enters the mass squared, so 0.12 dex. The luminosity was not measured at the epoch the relation was calibrated for and the object has varied since, which is 0.053 dex. And the term this figure exists for is orientation: the virial factor is one number fitted to a sample, every individual object has its own according to how its broad-line region is inclined, and the spread of that is 0.35 dex — the largest of the four by some margin. In quadrature the total is 0.42 dex — a factor of 2.6 — and the drawn total's half-width is checked against that combination rather than assumed. The bracket at the foot is a different kind of error and is not in the quadrature: the absolute calibration of the virial factor, uncertain by about a factor of 3, which moves every quasar mass ever published by the same 0.24 dex and widens nothing.

The factor that multiplies every quasar mass

A reverberation lag and a line width give a length times a velocity squared, which is a mass multiplied by an unknown number of order one. That number is fixed by making a few dozen nearby active galaxies lie on a correlation measured in quiescent ones — so every black-hole mass at redshift two rests on a fit performed at redshift zero.

galaxies · Quasars Three arrangements of gas, three velocity–delay maps. The response of a broad emission line to a flash of the continuum, as the density of emitting gas in delay (up, days) and line-of-sight velocity (across, km/s; positive is receding), for gas between 10 and 30 light-days from a hundred-million-solar-mass black hole in three kinematic states, 6,000 clouds each. Left: a rotating disc inclined at 30° with orbits tilted up to 15° from its plane — an ellipse symmetric in velocity, with the fastest gas, nearest the hole, responding soonest. Middle: gas falling in at the free-fall speed — the near side is moving away from the observer and responds first, so the red side leads and the blue side lags, by 27 days on average beyond 1,500 km/s. Right: the same gas flowing out — the mirror image, the blue side leading and the red lagging by 27 days. The three maps are as different as maps can be; their projections onto either axis alone are not.

A delay that tells which way the gas is moving

A broad emission line echoes the continuum after a delay, and the delay is a radius. Measure it separately in the line's blue wing and its red wing and it becomes a map — symmetric for gas in orbit, lagging on the blue side for gas falling in, on the red side for gas blown out — and the one route to the geometry factor for an individual black hole.

galaxies · Quasars

Named alongside it

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

Broad line regionReverberation mappingTransfer functionVirial factorEddington ratioInflowLight-travel timeM sigma relationOutflowRadius luminosity relationSingle epoch massVelocity delay map

All concepts