Astronomy & Celestial Mechanics
the sky, computed
Concept

Main-sequence lifetime — where it appears

How long a star burns hydrogen in its core, the fuel divided by the burn rate, and steeply shorter for heavy stars because consumption rises faster. It runs from ten billion years at a solar mass to a few million at fifty, which is why every massive star seen anywhere formed recently.

Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.

How long a star lasts, against its mass. Main-sequence lifetime against mass, on logarithmic axes. Fuel grows in proportion to mass and consumption grows as its three-and-a-half power, so the lifetime falls steeply — a star of thirty solar masses lives for a few million years.

Why the biggest stars die first, and take the galaxy with them

A star thirty times the Sun's mass has thirty times the fuel and burns it forty thousand times faster. It lasts a few million years, and everything heavier than iron exists because of it.

stars · Stellar lifetimes 14 radial orders of the Sun, at 135.1 μHz apart. The p-mode spectrum of the Sun — 1 solar mass in 1 solar radius — from the asymptotic relation with its second-order term, drawn as 14 radial orders of ℓ = 0, 1 and 2 under a Gaussian envelope centred on ν_max = 3,090 μHz. Two numbers are marked and they do very different work. The large separation, 135.1 μHz, is the spacing between consecutive ℓ = 0 modes and fixes the mean density. The small separation, 9.00 μHz, is 2.7 pixels on this axis — it fixes the age, and it is why the échelle diagram exists rather than being a convenience. The vertical axis is the measurement: each mode moves the surface by about 20.0 cm s⁻¹ at the peak, and brightens it by a few parts per million, which is why this was impossible before a decade-long velocity series. Each mode is one line: its true width is set by its lifetime and is far below a pixel here.

The interior read from a comb of frequencies

A star's surface moves by about twenty centimetres a second, in thousands of overlapping sound modes at once. Two numbers off that spectrum give a mass and a radius with almost no stellar model in the chain, and a third gives an age.

stars · Asteroseismology 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 A free parameter worth 42 per cent of an age. The main-sequence lifetime of a star against its mass, for four values of the convective overshoot parameter. A convective core has a boundary where buoyancy vanishes, and a rising blob arriving there still has momentum, so it penetrates into the stable region above and mixes fresh hydrogen into the core. How far it penetrates is not computed — it is a parameter, quoted in pressure scale heights, and the values in current use range from zero to about a third. A larger core is a larger fuel supply, so the lifetime rises and the turn-off at a given age is more massive. Across the plausible range the lifetime of a two-solar-mass star changes by 42 per cent, and an age read off a cluster's turn-off changes by the same amount. That is larger than the quoted uncertainty on almost every cluster age in the literature.

A convective boundary with no theory to fix it

A convective core has an edge where buoyancy vanishes. A blob arriving there still has momentum, so it carries on, mixing fresh hydrogen into the core and extending the star's life. How far it carries on is a fitted parameter, and across its plausible range every stellar age changes by nearly half.

stars · Stellar evolution The habitable zone of a 1 M☉ star, sweeping outwards. The inner and outer edges of the liquid-water zone against time, for a 1 solar-mass star whose main sequence lasts 10.0 Gyr. The star brightens as it burns hydrogen — a heavier core needs a hotter centre to hold the star up — so both edges move outward by a factor of 1.63 across the whole main sequence, and the band drawn here sweeps past any fixed orbit rather than containing it. Two quite different zones can be read off. The instantaneous zone at the age of the present-day Sun is 0.99 to 1.71 AU, which is the band a survey means by "in the habitable zone". The continuously habitable zone over the 10.0 Gyr drawn is the overlap of every instant in it — outside the inner edge at the end and inside the outer edge at the beginning — which is 1.37 to 1.44 AU, 10 per cent of the instantaneous width. The horizontal line is an orbit at 1 AU. It leaves the zone at 4.72 Gyr, when the inner edge overtakes it. None of these edges is a measurement: both come from one-dimensional climate models, and the inner one in particular is where a runaway greenhouse begins in a model whose clouds are prescribed.

The band moves and the orbit does not

A star brightens as it burns, so the distance at which water can be liquid sweeps outwards by a factor of one and a half across a main sequence. The band a survey quotes is an instant; the band a planet needs is the overlap of every instant, and for the Sun it is a tenth as wide and does not contain the Earth.

exoplanets · Habitable zone How long a star lives on the main sequence, down to the smallest stars. Main-sequence lifetime against mass, on logarithmic axes, as the hydrogen a star burns divided by its luminosity, scaled so that the Sun lives ten billion years. The dashed line assumes every star burns a tenth of its hydrogen, as the Sun does; the solid line lets stars below about a third of a solar mass, which are convective throughout, burn nearly all of it. The horizontal line is the age of the universe, 13.8 billion years: every star lighter than 0.90 solar masses that has ever formed is still on the main sequence. A star of a tenth of a solar mass lives about 8 trillion years — 597 times the present age of the universe — and its life so far is a few thousandths of one per cent of it.

A lifetime that is still a forecast

No star lighter than nine-tenths of the Sun has ever died, because none has had time. The smallest are convective to their centres, burn almost all their hydrogen rather than a tenth of it, and will shine for trillions of years. Most of the stars in the Galaxy therefore have a life history no observation has tested, and only one in thirteen stars ever born has finished.

stars · Stellar lifetimes Four clocks for a 1 M☉ dwarf, and the best of them. The fractional age uncertainty each method reaches for an isolated 1 solar-mass main-sequence star, against its age, logarithmic, for isochrones, rotation, oscillations and chemical clock, with representative published precisions. Rotation is best while the star is young, once its spin has forgotten its start and before its braking weakens; isochrones and oscillations improve with age as the star moves further on the diagram. The combination (heavy line) is 14 per cent at 1 Gyr, 9 at 3 and 4 at 8. It is better than ten per cent (dashed) from 2.6 to 9.4 Gyr.

Four clocks and the stars none of them reads

An isolated dwarf star can be dated four ways — by its position on the Hertzsprung–Russell diagram, by how fast it spins, by its oscillations, and by the ratio of two elements its galaxy made at different rates. Each clock has an age range where it works and masses it cannot read. Laid side by side for a Sun-like star they cover most of its life to ten per cent or so. For a star of eight-tenths of the Sun's mass only one clock is left, it works only while the star is young, and the commonest stars in the Galaxy's disc are dated one at a time no better than fifteen per cent at any age.

stars · The HR diagram

Named alongside it

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

Initial mass functionAsteroseismologyConvectionEclipsing binaryThe HR diagramIsochroneMain-sequenceStellar ageStellar evolutionBlack holeCarbonate silicate cycleClimate model

All concepts