Astronomy & Celestial Mechanics
the sky, computed
Concept

Stellar population — where it appears

A group of stars treated as one object with an age, a composition and a mass function, from which its integrated light is computed. The word covers a globular cluster and a whole galaxy alike, and what makes the abstraction work is that integrated light depends on the distribution rather than on the individuals.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

One population, three integrals, two ends. The same mass function weighted three ways, each normalised so that the area under it is one, against mass on a logarithmic axis — so a share of the page is a share of the total. The light is a zero-age population's, every star still on the main sequence, which is the only age at which the top of the range is present at all. The steep curve on the left is the number of stars, which peaks at 0.08 M☉ and falls away because the function is steeper than m⁻¹; the middle one is the mass they carry; the one on the right is the light they emit, computed from this file's own main-sequence relation and peaking at 55.0 M☉ — 682 times further up the axis. The population that is counted and the population that is seen are two different populations. Above 8 M☉ there are 0.63% of the stars, 21% of the mass and 99% of the light. The slopes are α = 1.3 above 0.08 M☉, α = 2.3 above 0.5 M☉, and the low-mass end is where the honesty runs out: it has never been measured in another galaxy, and every mass inferred from a luminosity assumes it.

Most stars are small, and most of the light is not

The mass function is steep and the mass–luminosity relation is steeper, so counting stars and measuring their output are integrals of the same function dominated by opposite ends of it. Every mass inferred from a brightness passes through that mismatch.

stars · Initial mass function The mass-to-light ratio of NGC 3198, radius by radius. The dynamical mass inside each radius divided by the light inside it, in solar units. Inside two disc scale lengths it is nearly flat at about 2.2 — a galaxy made of stars, weighing what stars weigh. Outside the disc the light stops and the mass does not, so the ratio climbs to 10 by 30 kpc with no sign of turning over. The curve is not fitted: it is the rotation curve's enclosed mass divided by the light profile's enclosed light, both drawn elsewhere in this collection.

The mass that is not the light

A galaxy's mass-to-light ratio is not a number, it is a curve, and it rises without turning over. What stellar populations can plausibly weigh sets a ceiling; the dynamics sit far above it, and the gap is a shape rather than a discrepancy.

galaxies · Dark matter Two populations, and the valley between them. 420 model galaxies, 42 per cent of them drawn from a tight red sequence tilted by -0.08 magnitudes of colour per magnitude of brightness, the rest from a broad blue cloud. Only 3.3 per cent land in the band of width 0.20 magnitudes midway between the two sequences, against 17 per cent in the same band laid on the blue cloud and 27 per cent on the red sequence. The bimodality is the strongest statement the galaxy census makes: a galaxy is usually forming stars or has stopped, rarely in between, and since colour tracks the age of the newest stars, the emptiness of the middle is a statement about a timescale — whatever ends star formation does it in a few hundred million years, not a few billion.

Two colours, and almost nothing between

Plot a few hundred thousand galaxies by colour and brightness and they do not fill the plane. They pile into a tight red sequence and a broad blue cloud with a near-empty gap between, and an empty gap is a statement about how fast something happens.

galaxies · Galaxy populations A high end that is 2.5 in slope steeper than the one stars were born with. The mass function a star count measures against the one stars were born with, for a population that has been forming stars steadily for 10 billion years. Below about a solar mass nothing has had time to die, so the two coincide exactly. Above it the fraction still alive is the main-sequence lifetime divided by the age, and since the lifetime falls as the two-and-a-half power of the mass, the present-day function is steeper than the initial one by exactly that exponent. A count of massive stars in an old population therefore under-represents them by orders of magnitude, and reading it as an initial mass function gives a slope far too steep. The correction is large, it is calculable, and it depends on the star-formation history — which is usually the thing the mass function was going to be used to constrain.

A mass function corrected by an age

Counting stars by mass gives the stars that are alive. What every argument needs is the stars that were born, and the two differ by the fraction of each mass still on the main sequence — which is a lifetime divided by an age, and which for massive stars in an old population is a very small number.

stars · Initial mass function The count theory predicts, and the inference it costs. The galaxy stellar mass function: galaxies per cubic megaparsec per dex of stellar mass, both axes logarithmic. Two Schechter components share a characteristic mass of 10^10.66 M☉ — one of slope -0.35 carrying the quenched galaxies at the knee, one of slope -1.47 carrying the star-forming ones below it — and the dashed line is the single component a luminosity function is usually fitted with. Integrated over the range drawn it gives 0.0487 galaxies per cubic megaparsec holding 2.22·10⁸ solar masses of stars, of which 51 per cent sits above the knee. This function is not measured. What is measured is a luminosity function; turning one into the other needs a mass-to-light ratio for every galaxy in the sample, and that ratio is not a constant — it runs by a factor of about five from the bluest galaxies to the reddest, so the conversion moves the red end of the distribution further than the blue end and changes the SHAPE rather than the units. A stellar mass function is a luminosity function plus a stellar population model, and the second half is where its disagreements live.

The count theory predicts, and the inference it costs

A luminosity function is measured. A stellar mass function is inferred, one galaxy at a time, through a ratio that runs by a factor of six from the bluest galaxies to the reddest — so the conversion changes the shape and not merely the units.

galaxies · Luminosity function

Named alongside it

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

Initial mass functionMass-to-light ratioCompletenessQuenchingStar formation historyBaryonBimodalityBlue cloudBrown dwarfColour magnitude diagramDark matterDynamical mass

All concepts