Astronomy & Celestial Mechanics
the sky, computed
Concept

Isophote — where it appears

A contour of equal surface brightness on an image of an extended object. A galaxy's size is usually quoted at an isophote rather than at an edge, so the size depends on the threshold chosen and on how far that threshold is dimmed by redshift.

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

What distance does, and does not, do to a galaxy. Three quantities against distance, each relative to its value at 5 Mpc, on logarithmic axes so that a power law is a straight line and its exponent is the slope. Flux falls with slope −2 and angular size with slope −1, both of which are ordinary. Their ratio has slope zero: a galaxy of surface brightness 23.5 magnitudes per square arcsecond has that surface brightness at every distance, and a sky of 22 is brighter than it at every distance too. The contrast against the sky — the quantity that decides whether the thing is detectable at all — is -1.5 magnitudes wherever it is put.

The brightness distance cannot touch

Flux falls as the inverse square of distance and so does solid angle, so their ratio does not fall at all. A galaxy's surface brightness is the same number wherever it is put, which means whole populations can be undetectable at any distance whatever.

galaxies · Surface brightness The same disc measured smaller at every redshift. The isophotal radius, at a limit of 26.5 magnitudes per square arcsecond, of three exponential discs that do not change at all — central surface brightnesses 20.5, 21.65, 23, the same scale length throughout — against the redshift they are placed at. Surface brightness falls as (1+z)⁴, three magnitudes at z = 1 and six at z = 3, before anything about the galaxy evolves or any band shift is accounted for, so every isophote moves inward. The discs vanish from an isophotal catalogue entirely at z = 2.98, 2.05, 1.24. The dashed line is the half-light radius, 1.68 scale lengths, which is defined by the galaxy's own light and does not move. Galaxies at high redshift are genuinely smaller than their present-day counterparts; how much smaller depends on which of these two kinds of radius is quoted, and the isophotal kind would report a shrinkage for galaxies that have none.

A radius that is a measurement of the threshold

A galaxy has no edge. Its light fades exponentially for as far as anyone can measure, so every size ever quoted for one is the radius at which the fading crossed some line that somebody drew. Drawn at a fixed surface brightness, the line measures how bright the galaxy's centre is as much as how big the galaxy is — and at high redshift it measures the expansion of the universe as well.

galaxies · Surface brightness

Named alongside it

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

Low-surface brightness galaxySelection effectSurface brightnessAngular-diameter distanceDetection limitExponential discFreeman's lawThe half-light radiusInverse square lawIsophotal radiusMalmquist biasPetrosian radius

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