Astronomy & Celestial Mechanics
the sky, computed
Concept

Primordial atmosphere — where it appears

An atmosphere of hydrogen and helium captured directly from the protoplanetary disc by a young planet, before the gas dispersed. Most rocky planets lost theirs, and how they lost it is recorded in the isotopes of the noble gases they kept.

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

The XUV energy that reached one astronomical unit, for three young Suns. The cumulative X-ray and extreme-ultraviolet energy delivered per square metre at the Earth's distance from the Sun, against age, for three histories that differ only in how long the young Sun stayed magnetically saturated: 20 Myr for a slow rotator, 100 Myr for a medium rotator, 300 Myr for a fast rotator. After saturation each declines to a common track by 1 Gyr, as rotation histories are observed to converge. By 4.5 Gyr the totals are 2.06·10¹⁵ J/m² for the slow rotator, 3.66·10¹⁵ J/m² for the medium rotator, 6.47·10¹⁵ J/m² for the fast rotator: the fast rotator delivered 3.1 times as much as the slow rotator, nearly all of it in the first few hundred million years. The Sun's own rotation at that age is not measured; it is inferred from the spread of rotation periods in young clusters, and all three histories are consistent with a Sun that ends up rotating as it does now.

The young Sun's spin decides what the Earth kept

The calculation that strips sub-Neptunes applies just as well to a planet with a trace of hydrogen. An Earth that captured a few hundredths of a per cent of its mass from the gas it formed in — several times the hydrogen now in its oceans — would have lost all of it, or kept most of it, depending on something nobody has measured — how fast the Sun was spinning in its first few hundred million years.

exoplanets · Radius valley The heaviest atom a hydrogen wind can carry, against the strength of the wind. The crossover mass — the heaviest atom an escaping hydrogen flow drags out with it — against the hydrogen flux at the base of the flow, on a logarithmic axis, for the Earth's gravity and gas at 1000 K. Atoms lighter than the crossover leave with the hydrogen; heavier ones stay. The crossover rises in proportion to the flux: lifting neon takes 9.7·10¹² hydrogen atoms per square centimetre per second, argon 1.8·10¹³, krypton 4.3·10¹³ and xenon 6.6·10¹³. The Earth loses about 3·10⁸ today, which lifts nothing heavier than hydrogen. Driven by a young Sun at its saturated X-ray and ultraviolet output, an energy-limited flow would reach 2.2·10¹³ on Mars, a crossover of 114; 2.3·10¹³ on Venus, a crossover of 50; 10¹³ on the Earth, a crossover of 21 — the smaller planet's weaker gravity both raises the flux per unit area and lowers the force holding the heavy atoms back.

The heaviest atom a hydrogen wind can lift

A planet losing hydrogen fast enough to blow off as a wind drags other gases with it, but only those lighter than a crossover mass set by how strong the wind is. Below it every gas leaves in proportion to its distance from the limit and its isotopes are sorted by the same amount per mass unit; above it nothing goes. The Earth's xenon is sorted and its krypton is not, which no wind of neutral atoms can arrange.

exoplanets · Radius valley An envelope worn down by a young star's ultraviolet. The mass of a primordial hydrogen envelope, as a fraction of the planet's mass, against age, for an Earth-mass planet in the middle of the eventual habitable zone of a 0.1 M☉ star, starting with 0.1%, 0.3%, 1%, 3% of its mass in hydrogen. The star contracts toward the main sequence and stays saturated in X-rays for 1.5 Gyr; the envelope inflates the planet, so it intercepts more of that light and loses mass faster than a bare rock would. The shaded span is the 75 Myr during which the planet receives more light than the runaway-greenhouse limit, when any exposed ocean would be steam. 0.1% is gone at 463 Myr; 0.3% is gone at 1.5 Gyr; 1% outlasts 5 Gyr; 3% outlasts 5 Gyr. An envelope that outlasts the shaded span has shielded the ocean through the whole of the runaway; one that also outlasts the planet's present age has left it a small gas-rich planet rather than a rocky one.

An envelope spent so an ocean could stay

A planet in the eventual habitable zone of a small red dwarf spends its first tens of millions of years too close to a star that is still contracting and still bright, with its ocean boiled into steam and the steam being split and lost. A wisp of hydrogen left over from the nebula — a few hundredths of a per cent of the planet's mass — would change that, because the star's ultraviolet would spend itself removing the hydrogen first. The envelope that shields the ocean and the envelope that never leaves bracket a range a factor of twenty wide, and the amounts a rocky planet is expected to capture fall inside it.

exoplanets · Habitable zone

Named alongside it

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

Energy-limited escapeXUV fluxPhotoevaporationTerrestrial planetsYoung sunAtmospheric escapeHabitable zoneHydrodynamic escapeIsotopic fractionationNebular gasNoble gasesPre-main-sequence

All concepts