Astronomy & Celestial Mechanics
the sky, computed
Concept

Disc evolution — where it appears

The draining of a protoplanetary disc onto its star over a few million years, with the accretion rate decaying as roughly the inverse of the age. The heat it releases fades with it, so every condensation front sweeps inward while planets are still growing.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

The ice line at 2.7 AU, and the 3.4-fold jump in solid material across it. Two temperature thresholds turned into radii, against stellar mass, both axes logarithmic. The shaded band is the habitable zone, where water can be liquid on a planet's surface. The heavy line is the snow line of the disc the planets formed in — the distance at which a passively heated disc, whose temperature falls as the inverse square root of radius, reaches 170 K and water freezes. For a solar-luminosity star it sits at 2.71 AU, just outside the asteroid belt, and it is 1.6 times further out than the outer edge of the habitable zone; around a 0.15 solar-mass star both have moved inwards and the ratio is 5.5. What makes the line matter is what happens as it is crossed. Water is by far the most abundant condensable material after hydrogen and helium, so freezing it raises the surface density of solids by roughly 3.4 times in one step. Everything about the architecture of a planetary system follows from that step: a core massive enough to capture gas can be assembled outside the line and not inside it, which is why the solar system has small rocky planets in and giant ones out, and why a giant planet found at 0.05 AU is a statement about migration rather than about formation. The line is drawn where a mature disc puts it; a young, accreting disc is hotter and its line is several times further out, sweeping inwards as the disc drains.

The line beyond which ice counts as rock

A disc of gas around a young star gets colder outwards, and at about a hundred and seventy kelvin water stops being vapour and becomes a building material. Crossing that one line multiplies the solid mass available by roughly three and a half, in a single step, and the architecture of every planetary system is downstream of it.

exoplanets · The snow line The solid mass available, as a staircase of 5 fronts. The share of the condensable material that is solid, against distance from a 1 solar-mass star, on a logarithmic radius axis. Each riser is one species freezing out, at the radius where the disc's temperature — falling as the inverse square root of the distance — reaches that species' condensation point. silicates and iron at 1400 K and 0.04 AU; water ice at 170 K and 2.71 AU; carbon dioxide at 70 K and 16.00 AU; methane and ammonia at 30 K and 87.11 AU; carbon monoxide at 20 K and 196.00 AU. Inside every front the solid surface density is 22 per cent of what is available, which is the refractories alone; water alone contributes 53 per cent, more than twice everything else combined, which is why one of these steps is called the snow line and the others are not. A body's composition is decided by which pair of risers it formed between, and the steps are narrow because a vapour pressure is exponential in the inverse temperature.

There is not one line, there is a staircase

Water freezing is the biggest step in a protoplanetary disc and it is one of five. Each condensable species has its own temperature and therefore its own radius, and what a body is made of is decided not by which side of a line it formed on but by which pair of risers it formed between.

exoplanets · The snow line The ice line sweeps from 6.4 to 2.7 AU while the disc drains. The radius at which a disc around a 1 solar-mass star reaches 170 K, against the disc's age, both axes logarithmic. The temperature is the fourth root of the sum of two fluxes: starlight, which does not change, and the disc's own accretion, which releases gravitational energy at a rate set by how fast material is flowing inward. The accretion rate decays as the disc drains — taken here as 5e-5 solar masses a year falling off as t^(−3/2) beyond 0.1 million years — so the viscous term fades and the line sweeps in. It starts at 6.38 AU and ends at 2.73, the passive value the closed form gives. A body at three astronomical units formed dry if it formed early and icy if it formed late, so a composition dates a formation rather than locating one, and the dating is only as good as the accretion history assumed.

A composition that dates a formation rather than placing it

The ice line in a young disc starts six astronomical units out and sweeps inward to under three as the disc drains. A body at four astronomical units therefore formed dry or wet depending only on when — so what it is made of is a clock, and reading it as a map is the mistake the moving line makes easy.

exoplanets · The snow line

Named alongside it

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

Condensation sequenceEquilibrium temperaturePlanetesimalProtoplanetary discThe snow lineSolid surface densityVolatile deliveryAccretion rateCore accretionFormation timeGiant planet formationIsolation mass

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