Astronomy & Celestial Mechanics
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Exoplanets

The shield that is also a funnel

A magnetic field is supposed to protect an atmosphere from the stellar wind. Venus and Mars have no dynamo and Earth has one, and their measured ion escape rates lie within a factor of a few — with the magnetised planet losing the most, because a dipole's polar field lines are open and lead straight to space.

Assumes Atmospheric escape and Magnetosphere.

18 min read 10 figures Measuring the unreachableScales that defeat intuition

The claim is made routinely and it sounds obviously right: Mars lost its atmosphere because it lost its magnetic field, and the Earth kept its because it kept one. It appears in textbooks, in reviews of habitability, and in the design rationale for missions. It is also the kind of claim this collection exists to check, because it is a causal statement about two quantities that have both been measured.

The measurements do not support it.

The shield that does not shield. Above: measured ion escape rates for three planets against their surface magnetic field. Venus and Mars have no dynamo at all and Earth has one, and the three rates lie within a factor of 9 — with the magnetised planet losing the most. The intuition that a magnetosphere protects an atmosphere is not a small correction away from being right; the measurement does not support it. Below: why. A dipole's field lines are not all closed. Those emerging within a polar cap reconnect with the wind's own field and lead straight to space, and the cap's area is set by how far the magnetosphere reaches — a boundary at ten planetary radii still leaves 5.1 per cent of the surface open. So a magnetosphere is both a shield and a funnel: it deflects the wind from most of the planet and collects ions from the whole ionosphere into the polar wind, which is exactly what an instrument above the poles measures leaving. Whether the net is protection depends on quantities nobody can compute from the field strength alone, and the three points above are the state of the evidence.
Fig. 1 Above: measured ion escape rates for three planets against their surface field strength. Venus and Mars have no dynamo at all and the Earth has one, and the three rates lie within a factor of ten — with the magnetised planet losing the most. Below: why. A dipole’s polar field lines are open to the wind, and a magnetosphere reaching ten radii still leaves five per cent of the surface connected straight to space.

What is measured

Ion escape rates are measured directly, by spacecraft carrying instruments that count ions leaving.

For Mars the number is around ten to the twenty-fourth to ten to the twenty-fifth ions a second, from measurements over a full solar cycle. For Venus, similar. For the Earth, ten to the twenty-fifth to ten to the twenty-sixth — that is, at least as much and probably more.

Those measurements are not easy and the numbers carry uncertainties of a factor of a few, driven by the variability of the wind and by how much of the escaping flux the spacecraft’s orbit samples. But the ordering is not in doubt at the level the intuitive claim requires. If a magnetosphere reduced escape by orders of magnitude, that would be visible.

The Earth’s escape is dominated by the polar wind: a continuous outflow of ionospheric ions along open field lines over the polar caps, plus more energetic outflows during disturbed conditions. It is an outflow that exists because of the magnetosphere rather than in spite of it.

The shield that does not shield. Above: measured ion escape rates for three planets against their surface magnetic field. Venus and Mars have no dynamo at all and Earth has one, and the three rates lie within a factor of 9 — with the magnetised planet losing the most. The intuition that a magnetosphere protects an atmosphere is not a small correction away from being right; the measurement does not support it. Below: why. A dipole's field lines are not all closed. Those emerging within a polar cap reconnect with the wind's own field and lead straight to space, and the cap's area is set by how far the magnetosphere reaches — a boundary at ten planetary radii still leaves 5.1 per cent of the surface open. So a magnetosphere is both a shield and a funnel: it deflects the wind from most of the planet and collects ions from the whole ionosphere into the polar wind, which is exactly what an instrument above the poles measures leaving. Whether the net is protection depends on quantities nobody can compute from the field strength alone, and the three points above are the state of the evidence.
Fig. 2 The same three measurements without the polar-cap panel, which is worth having on its own because the top half is the entire empirical content of this essay. Three planets, two of them unmagnetised, one strongly so, and the rates within a factor of nine — with the magnetised one at the top. Everything else here is an attempt to explain that ordering. The figure asserts nothing about mechanisms; it reports ion counts from spacecraft instruments, and the claim it refutes is a claim about orders of magnitude.

The composition of what leaves is itself informative. The Earth loses oxygen ions in quantity, which is a heavy species that a purely thermal process could not remove at all — the criterion for thermal retention puts oxygen firmly on the retained side for a planet of this mass. So the escape being measured is not the atmosphere boiling off; it is ions being lifted electromagnetically, and the lifting is done along field lines that would not exist without the dipole.

There is a further asymmetry worth noting. Escape rises sharply during geomagnetic storms, by an order of magnitude or more, and storms are driven by the coupling between the wind and the magnetosphere. A planet with no field has no storms in that sense — its escape tracks the wind’s ram pressure smoothly, without the amplification that reconnection supplies.

Why an open field line matters

A dipole’s field lines do not all close. Those emerging within a cap around each magnetic pole reconnect with the interplanetary field and lead outward, and a particle on such a line is not confined by the field at all.

The area of that cap follows from geometry. A field line reaching the magnetopause at a given distance emerges at a colatitude whose sine is the square root of the reciprocal of that distance in planetary radii, so a magnetosphere reaching ten radii has caps of about eighteen degrees, covering some five per cent of the surface.

Five per cent sounds small. What matters is that the polar ionosphere is a reservoir of cold plasma sitting on a field line with a direct path to interplanetary space, and that ions in it are accelerated outward by an ambipolar electric field arising from the electrons’ greater mobility. The flux along those lines is substantial. There is a further consequence that runs the other way. A magnetosphere also collects: it gathers ionospheric plasma from a large area and channels it into a narrow region where it can be accelerated. An unmagnetised planet’s ions have to be picked up individually by the wind at the exobase, which is a less efficient process per unit area.

And a magnetosphere is an energy converter. The Dungey cycle takes the wind’s kinetic energy, stores it as magnetic energy in the tail, and releases it — some of it downward, into the ionosphere, where it heats the gas and drives outflow. An unmagnetised planet has no such machinery: the wind’s energy either goes past or is deposited directly, with no intermediate storage that can be released in concentrated bursts.

So the accounting has terms of both signs. The field excludes the wind from most of the planet, which reduces escape, and it collects, accelerates and energises ionospheric plasma along open lines, which increases it. Which dominates is a quantitative question, and the three measured planets say the two roughly cancel.

15 orders of magnitude between λ = 3 and λ = 40. The fraction of a Maxwellian gas that is moving fast enough to escape, against the Jeans parameter λ = GMm/kTR — the ratio of a molecule's gravitational binding energy to its thermal energy, and the only quantity this problem has. The curve is (1 + λ)e^−λ, and the reason it is drawn on a logarithmic axis spanning 15 decades is the whole argument: escape is not a threshold that a molecule is or is not over. The mean speed of a gas at any temperature a planet has is far below its escape speed — the tail is what leaves, and the tail is an exponential. So a gas at λ = 3 is gone in a geological instant, a gas at λ = 25 is there for the age of the universe, and there is no sharp line between: the conventional criterion of λ ≈ 36 is a place on a slope, chosen because it is where the loss time crosses the age of the solar system for a body of planetary size. A factor of two in the temperature is a factor of 10⁴ in the loss rate, which is why the exospheric temperature — the one the extreme ultraviolet sets, not the one the sunlight sets — is the only temperature that matters.
Fig. 3 The thermal channel the magnetic argument is usually confused with. The escaping fraction of a Maxwellian falls by fifteen orders of magnitude across the range drawn, and nothing in it refers to a magnetic field — the quantity is a ratio of gravitational to thermal energy and nothing else. Every planet in the comparison above is far to the right of anything that matters for its heavy species, so the escape being measured is not this process at all. Two mechanisms with the same name and no shared parameters is how the intuitive claim survives.

What an unmagnetised planet does instead

Venus and Mars are not undefended. Their ionospheres are conducting, the wind’s field cannot penetrate a conductor quickly, and the field drapes around them — producing an induced magnetosphere with a bow shock, a magnetic pileup region and a tail, on a scale of a planetary radius rather than ten. The physics is the same pressure balance a dipole strikes against the same wind, with an induced field in place of an intrinsic one.

The induced magnetosphere is a genuine obstacle. It deflects the bulk of the wind and it stands off the ionosphere at an altitude of a few hundred kilometres, which is above the bulk of the atmosphere.

What it does not do is prevent pickup. Neutral atoms in the extended exosphere are ionised by solar ultraviolet or by charge exchange, and once ionised they feel the wind’s motional electric field and are accelerated away. That process operates on the tenuous outer atmosphere and is limited by how much neutral gas is up there to be ionised.

The same wind strips a mini-Neptune inside 0.06 au and leaves a hot Jupiter intact. The fraction of a planet's hydrogen envelope removed in 5 billion years by an energy-limited wind, against orbital distance, at a heating efficiency of 0.15 and an extreme-ultraviolet fluence integrated over the star's own history — saturated at L_XUV/L_bol = 3.2·10⁻⁴ for the first 100 million years and declining as t to the power −1.23 after, which comes to 4.9·10¹⁵ J m⁻² at one astronomical unit and is some 7 times what today's flux would give over the same span. This is a different mechanism from the tail of a Maxwellian, not a correction to it. Close to a star the upper atmosphere absorbs more extreme ultraviolet than it can radiate away, expands, and flows off as a wind whose rate is set by the energy arriving — Ṁ = ηπR³F/GM — so the exponential in the Jeans parameter vanishes entirely and what remains is a ratio of radius cubed to mass, which is one over the density. That is why the three curves are ordered as they are. The hot Jupiter is dense enough to lose 0.0087 of itself even at 0.047 au, where HD 209458 b sits and where its escaping hydrogen makes a transit fifteen per cent deep in Lyman α against one and a half per cent in the optical — an exosphere filling and overflowing the Roche lobe, and still costing the planet almost nothing. The mini-Neptune loses its whole envelope anywhere inside 0.06 au, and what is left when it does is a bare core about 1.5 Earth radii across. That is one of the two standard accounts of the gap in the radius histogram, and this figure is what it looks like before any of the observations are brought in.
Fig. 4 The other escape channel, and the one that dominates for hot planets. A thermally driven outflow carries the atmosphere away as a bulk hydrodynamic wind rather than particle by particle, and its rate depends on the stellar ultraviolet flux and the planet’s gravity — not on any magnetic quantity.

So both planets lose ions and both do so at rates similar to the Earth’s, by different mechanisms. The mechanisms differ; the totals do not, and the totals are what an atmosphere’s history depends on.

The same wind strips a mini-Neptune inside 0.06 au and leaves a hot Jupiter intact. The fraction of a planet's hydrogen envelope removed in 1 billion years by an energy-limited wind, against orbital distance, at a heating efficiency of 0.15 and an extreme-ultraviolet fluence integrated over the star's own history — saturated at L_XUV/L_bol = 3.2·10⁻⁴ for the first 100 million years and declining as t to the power −1.23 after, which comes to 3.8·10¹⁵ J m⁻² at one astronomical unit and is some 26 times what today's flux would give over the same span. This is a different mechanism from the tail of a Maxwellian, not a correction to it. Close to a star the upper atmosphere absorbs more extreme ultraviolet than it can radiate away, expands, and flows off as a wind whose rate is set by the energy arriving — Ṁ = ηπR³F/GM — so the exponential in the Jeans parameter vanishes entirely and what remains is a ratio of radius cubed to mass, which is one over the density. That is why the three curves are ordered as they are. The hot Jupiter is dense enough to lose 0.0068 of itself even at 0.047 au, where HD 209458 b sits and where its escaping hydrogen makes a transit fifteen per cent deep in Lyman α against one and a half per cent in the optical — an exosphere filling and overflowing the Roche lobe, and still costing the planet almost nothing. The mini-Neptune loses its whole envelope anywhere inside 0.06 au, and what is left when it does is a bare core about 1.5 Earth radii across. That is one of the two standard accounts of the gap in the radius histogram, and this figure is what it looks like before any of the observations are brought in.
Fig. 5 The channel that does the damage, integrated over the first billion years rather than five. Almost all of the fluence is here — the star’s saturated phase lasts a hundred million years and the decay afterwards is steep — so a planet’s atmospheric history is decided in an epoch about which nothing magnetic is known for any of the three planets. Mars’s dynamo stopped around four billion years ago; the loss this curve describes was over before that, which is the chronological version of the essay’s argument.

The arithmetic that actually matters

Ten to the twenty-fifth ions a second sounds large and is not. Integrated over four billion years it amounts to a few times ten to the forty-second particles, which for oxygen is of order a hundredth of a bar on a planet the size of Mars.

That is the crucial number and it is the reason the whole framing is questionable. The measured present-day escape rates, extrapolated backwards at their current values, do not remove a substantial atmosphere from any of the three planets.

What could remove one is the same process operating when the Sun was young. A star’s extreme-ultraviolet output at an age of a hundred million years is a hundred times its present value, and escape rates driven by that radiation scale accordingly — so almost all of the loss happened in the first few hundred million years, when nothing about the present configuration applied. The scaling of escape with stellar activity is measured rather than assumed, at least in outline. Observations of hydrogen escaping from close-in giant planets around stars of different activity levels find escape rates rising with the star’s extreme-ultraviolet flux roughly as expected for an energy-limited outflow, with an efficiency of ten or twenty per cent. That relation, extrapolated to the young Sun, gives the front-loading described above.

That reframes the Martian question entirely. Mars did lose its atmosphere, the isotopic evidence for it is strong — argon and hydrogen on Mars are both enriched in their heavy isotopes in the way preferential escape of the light one produces — but the loss happened early, and whether Mars had a magnetic field then is exactly the period about which least is known.

What is known about the Martian field

Mars has crustal magnetisation: patches of strongly magnetised rock in the southern highlands, up to a few thousand nanotesla at satellite altitude, which is a fossil record of a field that existed when the rock cooled.

The northern lowlands, which are younger, are largely unmagnetised. The straightforward reading is that Mars had a dynamo, that it stopped some four billion years ago, and that surfaces formed afterwards recorded nothing.

So the sequence is that the dynamo stopped early, the Sun was still young and active, and the atmosphere was lost. The correlation is there and the causal claim is the one this essay is questioning, because at the time of the loss the escape would have been driven by an extreme-ultraviolet flux far above anything a magnetosphere is relevant to.

Pluto and Triton sit on the nitrogen line, and the Earth sits between helium and nitrogen. Escape speed against exospheric temperature, with a criterion line for each molecular species at v_esc = 6 v_th — the speed at which the Jeans loss time is comparable to the age of the solar system. Every line has slope one half, because the thermal speed goes as √T; a body above a line keeps that gas and a body below it does not. The horizontal axis is the temperature at the exobase, which for the Earth is near 1000 K rather than the 255 K of its equilibrium — the difference is extreme-ultraviolet heating, and using the wrong temperature puts the Earth above the hydrogen line, keeping an atmosphere it observably lost. Three readings are worth making. The Earth falls between helium and nitrogen and does exactly that: it loses helium as fast as radioactive decay supplies it, and keeps nitrogen for ever. Titan sits just above nitrogen and just above methane, which is why it has a thick nitrogen atmosphere and is slowly losing its methane. And Pluto and Triton sit on the nitrogen line, within 1 per cent — which is why both have atmospheres that are marginally bound and measurably escaping. Where it fails it fails in one direction only. Mercury, the Moon and the Galilean satellites all plot above lines for gases they do not have, because retention is necessary and not sufficient: a body also needs a source, and needs to survive the non-thermal losses this criterion says nothing about. Venus is the sharpest case — it sits above the hydrogen line and has still lost an ocean, because that hydrogen left by charge exchange with the solar wind rather than by moving fast enough.
Fig. 6 The condition that decides retention over the long run. A gas is retained if its thermal speed is well below the escape speed, and the boundary depends on the planet’s mass and the exosphere’s temperature — a criterion in which no magnetic quantity appears at all.

There is one place the crustal fields are informative in the present. Where they are strong they produce small local magnetospheres, and measurements over those regions find enhanced ion outflow rather than reduced — small closed regions surrounded by open ones is the worst of both arrangements.

That is a natural experiment and it is the closest thing to a controlled test the solar system offers. The same planet, the same wind, the same atmosphere, with and without a local field, measured by the same instrument; and the magnetised regions lose more. It is a small effect on a small area and it is in the opposite direction to the intuition.

Pluto and Triton sit on the nitrogen line, and the Earth sits between helium and nitrogen. Escape speed against exospheric temperature, with a criterion line for each molecular species at v_esc = 6 v_th — the speed at which the Jeans loss time is comparable to the age of the solar system. Every line has slope one half, because the thermal speed goes as √T; a body above a line keeps that gas and a body below it does not. The horizontal axis is the temperature at the exobase, which for the Earth is near 1000 K rather than the 255 K of its equilibrium — the difference is extreme-ultraviolet heating, and using the wrong temperature puts the Earth above the hydrogen line, keeping an atmosphere it observably lost. Three readings are worth making. The Earth falls between helium and nitrogen and does exactly that: it loses helium as fast as radioactive decay supplies it, and keeps nitrogen for ever. Titan sits just above nitrogen and just above methane, which is why it has a thick nitrogen atmosphere and is slowly losing its methane. And Pluto and Triton sit on the nitrogen line, within 1 per cent — which is why both have atmospheres that are marginally bound and measurably escaping. Where it fails it fails in one direction only. Mercury, the Moon and the Galilean satellites all plot above lines for gases they do not have, because retention is necessary and not sufficient: a body also needs a source, and needs to survive the non-thermal losses this criterion says nothing about. Venus is the sharpest case — it sits above the hydrogen line and has still lost an ocean, because that hydrogen left by charge exchange with the solar wind rather than by moving fast enough.
Fig. 7 The retention criterion with the marked masses shifted downward, which puts hydrogen and helium at the centre of the plot rather than at its edge. Those are the species every planet in the comparison loses, and they are lost by processes the criterion describes — so the one part of the picture where thermal escape genuinely operates is the part where every planet, magnetised or not, behaves the same way. Where the mechanism is understood the field does not enter; where the field might enter the mechanism is not thermal.

There is a mirror-image experiment at Venus, where the ionosphere’s own conductivity varies with solar activity. At high activity the ionosphere is dense enough to exclude the wind’s field entirely; at low activity the field penetrates and the escape changes character. That variation is measured over a solar cycle, so the natural experiment runs on a schedule set by the star’s own magnetic clock. Again the planet is its own control, and again the relationship between magnetic shielding and escape is not the simple one.

Pluto and Triton sit on the nitrogen line, and the Earth sits between helium and nitrogen. Escape speed against exospheric temperature, with a criterion line for each molecular species at v_esc = 7 v_th — the speed at which the Jeans loss time is comparable to the age of the solar system. Every line has slope one half, because the thermal speed goes as √T; a body above a line keeps that gas and a body below it does not. The horizontal axis is the temperature at the exobase, which for the Earth is near 1000 K rather than the 255 K of its equilibrium — the difference is extreme-ultraviolet heating, and using the wrong temperature puts the Earth above the hydrogen line, keeping an atmosphere it observably lost. Three readings are worth making. The Earth falls between helium and nitrogen and does exactly that: it loses helium as fast as radioactive decay supplies it, and keeps nitrogen for ever. Titan sits just above nitrogen and just above methane, which is why it has a thick nitrogen atmosphere and is slowly losing its methane. And Pluto and Triton sit on the nitrogen line, within 15 per cent — which is why both have atmospheres that are marginally bound and measurably escaping. Where it fails it fails in one direction only. Mercury, the Moon and the Galilean satellites all plot above lines for gases they do not have, because retention is necessary and not sufficient: a body also needs a source, and needs to survive the non-thermal losses this criterion says nothing about. Venus is the sharpest case — it sits above the hydrogen line and has still lost an ocean, because that hydrogen left by charge exchange with the solar wind rather than by moving fast enough.
Fig. 8 The same retention diagram at a slightly stricter criterion, and the narrow window the criterion has. Whether a planet keeps a species over the age of the solar system depends on the ratio of its escape energy to the thermal energy of the gas, and the usual rule of thumb is six — but the generator refuses anything much outside it, because the solar system itself pins the answer down: below five the criterion lets a 1,000 K exosphere hold gases nothing holds, above eight Pluto loses the nitrogen it has and above nine so does Titan. The rule is a fit to four worlds, and its width is that narrow.

What the isotopes say happened

The escape rates are a present-day measurement. The history is written somewhere else, and it is written in isotope ratios.

Escape is mass-selective: a lighter isotope has a higher thermal speed at the same temperature and is preferentially removed, so an atmosphere that has lost a large fraction of a species is enriched in that species’ heavy isotope. The enrichment is a logarithmic record of the fraction lost, and it does not depend on knowing the rate — the same trick by which an abundance ratio dates a population without needing the rate at which the enrichment ran.

Mars is enriched in argon-38 relative to argon-36 by about a third over the solar value, and in deuterium relative to hydrogen by a factor of five to six. Both say a large fraction of the original inventory is gone — for argon, something like two thirds; for water, most of an ocean’s worth. Venus is the extreme case: its deuterium-to-hydrogen ratio is a hundred and fifty times the terrestrial value, which is the strongest isotopic evidence anywhere for the loss of a large body of water. Venus has no magnetic field and never had one that anyone can detect, and it also retains ninety-two bars of carbon dioxide — an atmosphere ninety times the Earth’s, on a planet with no shield, closer to the Sun.

That last fact is the hardest one for the intuitive claim to accommodate. Whatever removed Venus’s water left its carbon dioxide entirely alone, over four billion years, with no magnetic protection of any kind.

Why this matters for planets elsewhere

The question is not academic, because it is being used to decide what is worth looking for.

Planets around M dwarfs sit in habitable zones a few hundredths of an astronomical unit from stars whose winds and flares are far more intense than the Sun’s, and whose active phases last billions of years rather than hundreds of millions — because a cool star spins down slowly and stays active, so the front-loading that spared the Earth does not apply. Whether such planets can retain atmospheres is the central question about the most numerous class of potentially habitable world. The argument from the solar system is that a magnetic field is not the deciding factor, and that the deciding factors are the planet’s gravity, the amount of gas it started with, its rate of volcanic resupply, and the star’s high-energy output history. That is a less satisfying answer than “look for a magnetosphere”, and it is the one the measurements support.

It also changes what an observing programme should prioritise. If magnetic fields decided the outcome, the goal would be to detect them, which is extraordinarily hard. If the star’s high-energy history decides it, the goal is to characterise stellar activity as a function of mass and age — which is difficult but tractable, and which surveys of thousands of stars are already doing. The two research programmes have almost nothing in common, and choosing between them is what the argument in this essay is for.

There is a third possibility that is gaining ground and that neither programme addresses well: that resupply matters more than retention. A planet with active volcanism replenishes its atmosphere continuously, and over four billion years a modest outgassing rate exceeds any plausible escape rate. On that reading the question is not what a planet loses but whether it keeps making more — which is a question about its interior, and about the same thermal history a dynamo depends on.

There is a genuine caveat and it should be stated. The three planets available differ in mass by a factor of ten, in orbital distance by a factor of two, and in atmospheric composition entirely, so attributing the similarity of their escape rates to the irrelevance of the field is a three-point argument with several confounds. It is the best available and it is not decisive.

The same wind strips a mini-Neptune inside 0.06 au and leaves a hot Jupiter intact. The fraction of a planet's hydrogen envelope removed in 5 billion years by an energy-limited wind, against orbital distance, at a heating efficiency of 0.15 and an extreme-ultraviolet fluence integrated over the star's own history — saturated at L_XUV/L_bol = 3.2·10⁻⁴ for the first 100 million years and declining as t to the power −1.23 after, which comes to 4.9·10¹⁵ J m⁻² at one astronomical unit and is some 7 times what today's flux would give over the same span. This is a different mechanism from the tail of a Maxwellian, not a correction to it. Close to a star the upper atmosphere absorbs more extreme ultraviolet than it can radiate away, expands, and flows off as a wind whose rate is set by the energy arriving — Ṁ = ηπR³F/GM — so the exponential in the Jeans parameter vanishes entirely and what remains is a ratio of radius cubed to mass, which is one over the density. That is why the three curves are ordered as they are. The hot Jupiter is dense enough to lose 0.0087 of itself even at 0.047 au, where HD 209458 b sits and where its escaping hydrogen makes a transit fifteen per cent deep in Lyman α against one and a half per cent in the optical — an exosphere filling and overflowing the Roche lobe, and still costing the planet almost nothing. The mini-Neptune loses its whole envelope anywhere inside 0.06 au, and what is left when it does is a bare core about 1.5 Earth radii across. That is one of the two standard accounts of the gap in the radius histogram, and this figure is what it looks like before any of the observations are brought in.
Fig. 9 The same integral over a range of orbital distance that includes the terrestrial planets rather than only the hot ones. Out at Venus’s and the Earth’s distance the curves are flat and near zero — the energy-limited wind removes essentially nothing from a planet of terrestrial mass at an astronomical unit, over the whole history — which is the quantitative statement that the loss from these planets was not hydrodynamic and had to happen by the ion channels the essay compares. The regime that strips a mini-Neptune leaves a terrestrial planet alone, and the argument about fields is confined to what is left.
The same wind strips a mini-Neptune inside 0.09 au and leaves a hot Jupiter intact. The fraction of a planet's hydrogen envelope removed in 5 billion years by an energy-limited wind, against orbital distance, at a heating efficiency of 0.3 and an extreme-ultraviolet fluence integrated over the star's own history — saturated at L_XUV/L_bol = 3.2·10⁻⁴ for the first 100 million years and declining as t to the power −1.23 after, which comes to 4.9·10¹⁵ J m⁻² at one astronomical unit and is some 7 times what today's flux would give over the same span. This is a different mechanism from the tail of a Maxwellian, not a correction to it. Close to a star the upper atmosphere absorbs more extreme ultraviolet than it can radiate away, expands, and flows off as a wind whose rate is set by the energy arriving — Ṁ = ηπR³F/GM — so the exponential in the Jeans parameter vanishes entirely and what remains is a ratio of radius cubed to mass, which is one over the density. That is why the three curves are ordered as they are. The hot Jupiter is dense enough to lose 0.017 of itself even at 0.047 au, where HD 209458 b sits and where its escaping hydrogen makes a transit fifteen per cent deep in Lyman α against one and a half per cent in the optical — an exosphere filling and overflowing the Roche lobe, and still costing the planet almost nothing. The mini-Neptune loses its whole envelope anywhere inside 0.09 au, and what is left when it does is a bare core about 1.5 Earth radii across. That is one of the two standard accounts of the gap in the radius histogram, and this figure is what it looks like before any of the observations are brought in.
Fig. 10 And the same loss at twice the efficiency of converting stellar ultraviolet into escaping gas. The rate is proportional to that efficiency and nobody measures it directly — it is inferred from the planets that survived, which makes the argument partly circular. Doubling it doubles the mass lost over five billion years, which is enough to move a planet across the radius valley, and that sensitivity is why the magnetic field’s role is hard to isolate from the star’s own output.

What a planet needs a field for instead

If the field is not shielding the atmosphere, it is worth asking what it is doing, because it plainly does something.

It shields the surface from energetic particles, which is a different question from shielding the atmosphere from the wind. A magnetosphere deflects solar energetic particles and galactic cosmic rays away from most of the planet, and the resulting surface radiation dose is far lower than it would otherwise be. For an atmosphere of a bar or more that hardly matters, since the atmosphere itself is a better shield than the field; for a thin atmosphere it matters a great deal. It also structures the upper atmosphere in ways that are chemically consequential. Energetic particle precipitation into the polar atmosphere produces nitrogen oxides that destroy ozone, and the effect is measurable in the terrestrial stratosphere after large solar events. So a field concentrates particle deposition into the polar regions rather than spreading it, which changes where the chemistry happens rather than how much of it there is.

And it is a diagnostic of the interior, which is the use astronomy actually makes of it. A dynamo requires a conducting fluid layer in convective motion, so a detected field says a planet has a liquid core and an energy source driving convection within it. That inference is what the Martian crustal magnetisation supports, and it is a statement about the planet’s thermal history rather than about its atmosphere.

What would settle it

Two kinds of measurement would help and both are being pursued.

More thorough accounting at the planets there are. Ion escape is one channel; neutral escape via photochemical processes and sputtering is another, and it is worse measured. If the neutral channels dominate at Mars — and there are indications they do for oxygen — then the ion rates that this essay has compared are not the quantity that matters. And observations of escape from exoplanets across a range of stellar activity. Transit observations in hydrogen and helium lines detect extended escaping envelopes, and the sample is now large enough to correlate escape with the star’s high-energy output. What it cannot do is correlate escape with the planet’s magnetic field, because no exoplanetary magnetic field has ever been measured.

That absence is the sharpest statement of where the subject is. The quantity at the centre of the argument is, for every planet outside the solar system, entirely unmeasured — and the three planets where it is measured say it does not matter much. A radio detection of an exoplanet’s own magnetosphere — the cyclotron emission a magnetised planet’s aurora should produce — would change that, and it has been searched for for twenty years without a confirmed result. Neither of those is a comfortable position, and together they are why the claim in the first paragraph is repeated so often and supported so little.

It is worth separating the two failures, because they are different in kind. The absence of exoplanetary field measurements is a gap that a technique may eventually close: the cyclotron emission a magnetised planet’s aurora produces falls at frequencies below the terrestrial ionospheric cut-off for a Jupiter-strength field at Jupiter’s rotation, which is why the searches have concentrated on hot Jupiters and why a detection is expected to be difficult rather than impossible.

The solar-system result is not a gap. It is a measurement, made repeatedly, by several spacecraft, at three planets, over a solar cycle — and it says the thing that was supposed to matter does not matter much. That is a stronger form of evidence than an absence, and it is treated as weaker, because it contradicts an argument that is easy to state and satisfying to hold.

The reason it is satisfying is that it has the shape of an explanation for something real. Mars did lose an atmosphere; Mars did lose a dynamo; and the two happened at roughly the same time. What the measurements say is that the coincidence is not causal in the direct way, and that the actual cause — a young star’s extreme-ultraviolet output, acting on a planet whose gravity was always too weak — is a story with no magnetic field in it and no obvious moral.

The practical importance of getting this right is that it decides what a habitability assessment should look at. If the field is the deciding factor, an unmagnetised planet is written off; if the star’s history and the planet’s gravity decide it, an unmagnetised planet of the right mass around a quiet star is a candidate. The second reading admits far more worlds, and it is the one the evidence supports. It also puts the observational effort where it can actually be spent, which is on measuring stellar ultraviolet histories rather than on a planetary quantity nobody can reach. That is a change of programme rather than a change of emphasis, and it follows from three measurements. Three is a small number of planets on which to rest it, and it is three more than the alternative has.

Where this goes next

Pluto and Triton sit on the nitrogen line, and the Earth sits between helium and nitrogen. Escape speed against exospheric temperature, with a criterion line for each molecular species at v_esc = 6 v_th — the speed at which the Jeans loss time is comparable to the age of the solar system. Every line has slope one half, because the thermal speed goes as √T; a body above a line keeps that gas and a body below it does not. The horizontal axis is the temperature at the exobase, which for the Earth is near 1000 K rather than the 255 K of its equilibrium — the difference is extreme-ultraviolet heating, and using the wrong temperature puts the Earth above the hydrogen line, keeping an atmosphere it observably lost. Three readings are worth making. The Earth falls between helium and nitrogen and does exactly that: it loses helium as fast as radioactive decay supplies it, and keeps nitrogen for ever. Titan sits just above nitrogen and just above methane, which is why it has a thick nitrogen atmosphere and is slowly losing its methane. And Pluto and Triton sit on the nitrogen line, within 1 per cent — which is why both have atmospheres that are marginally bound and measurably escaping. Where it fails it fails in one direction only. Mercury, the Moon and the Galilean satellites all plot above lines for gases they do not have, because retention is necessary and not sufficient: a body also needs a source, and needs to survive the non-thermal losses this criterion says nothing about. Venus is the sharpest case — it sits above the hydrogen line and has still lost an ocean, because that hydrogen left by charge exchange with the solar wind rather than by moving fast enough. The gas a planet cannot keep Escape is a statement about the tail of a distribution rather than about its mean, so the threshold is not a speed but a dimensionless number near thirty — and past that number the loss rate falls by twelve orders of magnitude. Then, for a hot Jupiter, the whole picture fails and the atmosphere leaves as a wind. A boundary that a sixty-fourfold gust moves by a factor of two. The standoff distance of a dipole magnetosphere against a wind, in planetary radii, against the wind's proton density, for three wind speeds. The boundary sits where magnetic pressure equals ram pressure — the only balance available, since the field exerts no force on neutral gas and the wind touches nothing. Because a dipole falls as the cube of distance its pressure falls as the sixth power, so the standoff goes as the ram pressure to the −1/6: at 450 km/s a density of 6 per cubic centimetre puts the nose at 9.3 radii — against a measured average of ten to eleven — and a sixty-fourfold compression moves it only to 4.7. That exponent is the reason a magnetosphere is a stable thing to have. It is also the reason the boundary's position is a poor measurement of the field: a factor of two in the distance is a factor of sixty-four in what caused it, so the standoff measures the wind badly and the planet's moment hardly at all. A boundary that hardly moves The magnetopause sits where the planet's magnetic pressure equals the solar wind's ram pressure. Because a dipole falls as the cube of distance, its pressure falls as the sixth power — so a sixty-fourfold gust in the wind moves the boundary by a factor of two, and a boundary that will not move is what makes a magnetosphere a stable thing to have. The habitable zone, and the radius inside which a day never ends. The conservative habitable zone — the runaway-greenhouse and maximum-greenhouse limits of Kopparapu's parameterisation — as a band in stellar mass against orbital distance, both logarithmic. For the Sun it runs from 0.99 to 1.71 AU, which is the published result and the check on the arithmetic here. The band moves inward far faster than the mass falls, because luminosity goes as roughly the fourth power of mass: a 0.2 M☉ star's zone is at 0.082–0.158 AU. The dashed line is the distance inside which a planet is tidally locked within 4.5 billion years, computed from τ = ω₀αmQa⁶/(3GM⋆²k₂R³) with an initial ten-hour spin, Q = 100 and k₂ = 0.3. It crosses the inner edge of the zone at 0.67 M☉ — so around every star below that, which is the great majority of stars, a planet in the habitable zone has one hemisphere in permanent daylight. The Earth is outside its own locking radius of 0.53 AU, and TRAPPIST-1e at 0.029 AU is inside its star's by a factor of 8. One number sets the zone The habitable zone is a band of stellar flux, so it scales as the square root of luminosity and moves inward far faster than mass falls. For most stars it lies inside the radius at which a planet is tidally locked.

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Atmospheric escapeExosphereHabitable zoneHydrodynamic escapeInduced magnetosphereIon pickupMagnetosphereOpen fluxPolar windSputteringStellar wind