A planet that borrows the wind's field

The Earth’s field holds the solar wind ten Earth radii away, at the place where the field’s magnetic pressure equals the wind’s dynamic pressure. Venus has almost no field — its interior does not run a dynamo, probably because the planet does not lose heat fast enough to keep its core convecting — and Mars lost its global field about four billion years ago, leaving only patches of magnetised crust. Neither has anything to push against the wind at ten planetary radii.

The wind still does not reach their atmospheres. Spacecraft orbiting both planets find a bow shock upstream, a region of compressed and slowed solar wind behind it, and then a sharp boundary a few hundred kilometres above the surface where the solar wind’s protons stop and the planet’s own ions begin. What stops the wind is the ionosphere: the layer of the upper atmosphere ionised by the Sun’s ultraviolet light, which is a good electrical conductor and a gas with pressure of its own.

That makes these planets’ magnetospheres a different kind of object from the Earth’s. The field that shapes them is not the planet’s but the wind’s, carried in and draped around the conducting obstacle, and the boundary is set by the ionosphere’s thermal pressure rather than by a magnetic one. The consequences differ in almost every respect, and they bear on how such planets lose their air.

A conductor in a moving field #

The interplanetary magnetic field is carried by the solar wind, frozen into the plasma because the plasma conducts so well. When the wind meets a conducting obstacle, the field cannot pass through it either: a changing field induces currents in the conductor that oppose the change, and in a good enough conductor those currents exclude the field almost entirely. So the field lines carried by the wind pile up against the dayside ionosphere, slowing and compressing, and drape around the planet like a cloth thrown over a ball, their ends still carried downstream by the wind on either side.

The draped field forms a magnetic barrier above the ionosphere, and the field strength in it rises until its magnetic pressure is comparable to the dynamic pressure the wind brought with it. The barrier deflects the wind round the planet, much as the Earth’s field does, and downstream the draped field lines are stretched into a two-lobed tail with a current sheet between them, oriented not by any planetary axis but by the direction the interplanetary field happened to have. When that field rotates, the whole tail rotates with it.

So Venus and Mars have magnetospheres, with a bow shock, a magnetosheath, a barrier and a tail, all on a much smaller scale than the Earth’s and all made of the wind’s own field. The planet’s only contribution is the conductor.

A boundary that moves by scale heights #

The inner edge of the barrier, where the solar wind’s pressure is finally taken up by the ionosphere’s, is the ionopause. Above it is wind plasma and draped field; below it, the planet’s own ionospheric plasma at much higher density and with very little field. The ionopause sits where the ionosphere’s thermal pressure — its density times the sum of its electron and ion temperatures — equals the pressure the wind exerts.

The contrast with the Earth is in how the boundary responds. A magnetopause balancing a dipole moves as the sixth root of the wind’s pressure, because the dipole’s pressure rises so steeply inward: a gust sixty-four times stronger moves it by a factor of two. An ionopause balancing an atmosphere moves logarithmically: each factor of $e$ in pressure moves it by one scale height, about a hundred kilometres. A gust ten times stronger drives it down by more than two hundred kilometres, which at Venus is most of the distance to the ionosphere’s peak.

That peak is a floor. The ionosphere’s pressure does not keep rising downward without limit, because below the peak the electron density falls again, into the neutral atmosphere where the ultraviolet light has been absorbed. When the wind’s pressure exceeds the peak pressure, there is no altitude at which the ionosphere can balance it.

When the wind wins #

What happens then is that the wind’s field is pushed into the ionosphere itself. The ionosphere becomes magnetised: the draped field penetrates its upper layers, forming horizontal field structures that persist after the pressure falls, and the ionospheric plasma is compressed and heated. Pioneer Venus, which orbited Venus through a full solar cycle, found the dayside ionosphere magnetised in this way whenever the solar wind’s pressure exceeded about the ionosphere’s peak thermal pressure.

The margin is small. At solar maximum, when the Sun’s ultraviolet output is highest and the ionosphere densest, the ionosphere at Venus out-pushes the median solar wind by less than a factor of two, and the wind wins for about a sixth of the time. At solar minimum the ionosphere is thinner, its peak pressure lower, and the wind wins most of the time. The Venus Express spacecraft, operating near solar minimum, found a planet whose ionosphere was magnetised far more often than Pioneer Venus had seen — the same planet, at a different point in the Sun’s cycle.

Mars is in a similar position: further from the Sun, so both the wind and the ultraviolet that makes the ionosphere are weaker, in roughly the same proportion. The margin is similar, and so is its dependence on the solar cycle. Mars adds one complication of its own — the remnant fields frozen into its southern crust, strong enough in places to form small local magnetospheres that rise above the ionosphere and deflect the wind. Seen in maps of where the ionosphere is magnetised, Mars is a patchwork of induced and intrinsic shielding.

How the boundary was found #

The first spacecraft to fly past Venus, Mariner 5 in 1967, found a bow shock much closer to the planet than one standing off a magnetic field would be, and a magnetometer reading that showed no planetary field at all: the obstacle had to be the atmosphere. Pioneer Venus, in orbit from 1978 to 1992, dipped into the ionosphere on every orbit and mapped the ionopause directly, finding it a few hundred kilometres up on the dayside, higher near the terminator, and lower whenever the solar wind’s pressure rose — the logarithmic response in the measurements, pass by pass. It also found the magnetised ionosphere, with thin flux ropes threading the plasma below the ionopause on days when the wind won.

Mars was harder, because its interaction is smaller and its crustal fields confuse it. A Soviet spacecraft, Phobos 2, measured escaping oxygen ions in 1989 before contact was lost; the Mars Global Surveyor found the crustal fields in 1997; and MAVEN, from 2014, carried the first complete set of instruments for the solar wind, the field, the ionosphere and the escaping ions together. The picture assembled from those missions is the one drawn here, and it is also the one predicted, in its essentials, before any of them flew: a conducting obstacle in a magnetised flow, borrowing the flow’s field.

A field that does not cover the atmosphere #

The difference that matters most for the long-term fate of these planets is not where the boundary sits but what lies above it. The Earth’s magnetopause stands tens of thousands of kilometres above its atmosphere; the exosphere, the tenuous outermost layer from which neutral atoms escape, lies far inside it, and an exospheric atom ionised by sunlight finds itself on a closed field line of the Earth’s field, trapped. At Venus and Mars the ionopause is a few hundred kilometres up, and the hydrogen and oxygen exospheres extend thousands of kilometres above it, into the region where the solar wind flows.

An atom from that extended exosphere — the tail of the velocity distribution that reaches heights where the gas is barely bound — ionised by ultraviolet light or by charge exchange with a wind proton, finds itself at rest in a plasma flowing past at four hundred kilometres a second through a magnetic field. It is picked up. The motional electric field of the flowing plasma, $\mathbf{E} = -\mathbf{v}\times\mathbf{B}$, accelerates the new ion; the magnetic field turns it; and the result, in the planet’s frame, is a cycloid: the ion repeatedly accelerates, turns, comes to rest and accelerates again, drifting downstream at the wind’s speed and reaching twice that speed at the top of each loop.

A plume to one side #

The size of the cycloid is set by the ion’s mass. A hydrogen ion’s loops are smaller than the planet; an oxygen ion’s are seven times larger at Mars. Pickup ions created near the planet therefore cannot simply be carried into a symmetric tail. They are flung out along the direction of the motional electric field, which points towards one side of the planet — the hemisphere where the electric field points away from the surface — and they leave in a plume on that side, on loops so wide that a single gyration takes them tens of thousands of kilometres from the planet.

The MAVEN spacecraft, orbiting Mars since 2014, has seen this plume directly: energetic oxygen ions streaming away in the direction of the solar wind’s electric field, with a strong asymmetry between the two hemispheres that rotates as the interplanetary field rotates. On the opposite side, where the electric field points into the planet, some picked-up ions are driven back into the atmosphere instead, where they deposit their energy and knock other atoms loose — a second, indirect escape process called sputtering.

The ions in the plume carry up to four times the energy per unit mass of the solar wind protons — an oxygen ion picked up at Mars reaches tens of kiloelectronvolts — far above anything the planet’s gravity can hold. Every ion that is picked up this way is lost.

What the plume is, and what it is not #

The pickup plume is one escape channel among several, and the totals are a separate argument: measured today, the ion escape rates of Venus, the Earth and Mars are within a factor of a few of one another, and none of them, extrapolated at its present value, removes a substantial atmosphere over the age of the solar system. What the plume adds to that argument is geometry. It says where the escaping ions go, how their direction is set, and why a spacecraft has to sample the right side of the planet to count them.

The direction is set by the interplanetary field, not by the planet. The motional electric field is perpendicular to both the wind’s velocity and its field, so as the field turns — and it turns continually, carried out from the rotating Sun along a spiral and twisted by every structure in the wind — the plume swings round the planet. A spacecraft in a fixed orbit sees the plume when the field happens to point it towards the spacecraft and misses it otherwise. The early estimates of Martian ion loss differed by an order of magnitude partly because they were made from orbits that sampled the plume at random; MAVEN’s coverage, with its orbit precessing around the planet and its measurements binned by the direction of the electric field, was designed to see it whole.

The mass dependence has a second consequence. Hydrogen, with loops smaller than the planet, behaves almost like a fluid carried along with the wind; oxygen, with loops seven times wider, behaves like a beam of individual particles. A fluid description of the interaction — magnetohydrodynamics, which treats the plasma as a single conducting liquid — cannot capture the oxygen at all, and the simulations that reproduce what MAVEN sees follow the heavy ions as particles. The interaction of the wind with Mars is one of the few places in the solar system where the size of a single gyration decides the shape of the whole system.

A tail that points where the field points #

Downstream of the planet the draped field forms the induced tail, and its orientation is again the wind’s rather than the planet’s. The field lines that piled up on the dayside are dragged past the flanks and stretched behind the planet, and the two halves of each draped line — one on each side — point in opposite directions, so a current sheet forms between them. The plane of that sheet contains the interplanetary field’s direction, and it turns as that direction turns.

Mars complicates the picture with its crustal fields, which reconnect with the draped field and add twists to the tail that rotate with the planet as well as with the wind. Venus does not, and its tail is the cleanest example in the solar system of a magnetosphere with no internal field at all — two lobes of borrowed field, reconfigured every few hours by changes in the wind. Comets show the same structure on a larger scale and more dramatically: a comet’s plasma tail occasionally disconnects and is swept away when the wind’s field reverses across the comet, a disconnection event visible from the Earth in photographs, and the same event has been seen at Venus in spacecraft data.

Why the logarithm matters #

The logarithmic response of an ionopause to the wind’s pressure is not only a curiosity of the figure. It makes the boundary sensitive in a way a magnetopause is not. A doubling of the wind’s pressure moves the Earth’s magnetopause inward by about eleven per cent; it moves the ionopause at Venus down by seventy kilometres, a large fraction of its height above the peak. The ionosphere’s response to the wind is correspondingly strong: compression, heating, and when the floor is reached, magnetisation. And because the ionosphere’s own pressure is set by the Sun’s ultraviolet light, which varies through the solar cycle, the boundary’s height and the frequency of magnetisation both track the cycle — a sensitivity that a planet with a dipole field, whose boundary depends only weakly on anything, does not show.

The standoff of the Earth’s field is robust because a dipole’s pressure rises as the inverse sixth power of distance, so a small inward motion buys a large increase in pressure. An atmosphere’s pressure rises only exponentially with depth, more slowly at first and then faster than any power, so a boundary held by an atmosphere moves easily until it reaches the floor and then cannot move at all. The difference between the two kinds of obstacle is the difference between a stiff spring and a soft one with a hard stop.

The same obstacle elsewhere #

The arrangement is not peculiar to two planets. A comet approaching the Sun — whose outgassing also pushes its orbit off the gravitational prediction — develops an ionosphere from that gas, and the solar wind piles up its field against it and drapes it into a tail that rotates with the interplanetary field — the plasma tail that points straight away from the Sun. Titan, Saturn’s large moon, orbits mostly inside Saturn’s magnetosphere, and Saturn’s rotating plasma flows past it as the solar wind flows past Venus, draping Saturn’s field around Titan’s ionosphere. Pluto, with its thin nitrogen atmosphere far from the Sun, was found by New Horizons to have a small interaction region of the same general kind. Wherever a conducting atmosphere meets a flowing magnetised plasma, the same physics builds the same object.

Exoplanets close to their stars face winds far denser than the solar wind, and many are losing atmosphere by a thermal outflow that dwarfs any ion process; and for an unmagnetised rocky planet in that position the induced magnetosphere and its pickup losses may decide whether any atmosphere survives. Whether those planets have fields, and how much their fields help, is not yet something any observation can determine.

What the pressure balance leaves out #

The figures balance the wind’s dynamic pressure against the ionosphere’s thermal pressure at the subsolar point, with the ionosphere’s pressure falling on a single scale height. The real balance is more complicated in each part. The wind’s pressure is transferred through the magnetic barrier, so it is the barrier’s magnetic pressure that the ionosphere meets, and that is somewhat less than the full dynamic pressure; away from the subsolar point the pressure falls with the cosine squared of the angle from the Sun, and the ionopause rises towards the terminator. The ionosphere’s temperature rises with height, so its pressure falls more slowly than a constant scale height suggests. The scale heights and peak pressures used here are illustrative of the measured ones, not fitted to a particular orbit.

The pickup picture treats each ion as created at rest in a uniform flow. Near the planet the flow is slowed and deflected in the magnetosheath and the field is draped, so real pickup ions near the ionopause start in a more complicated field, and the clean cycloid applies only to ions created upstream or far from the planet.

Still open: how much the field protected the Earth #

The comparison of escape rates among Venus, the Earth and Mars has reopened an old question: whether a magnetic field protects a planet’s atmosphere at all, or merely changes how it leaks. The answer is not the same at every stage of a planet’s life. Under the young Sun’s intense wind, an unmagnetised planet’s pickup losses may have been far larger than a magnetised one’s polar outflow; today they are comparable. Disentangling those regimes needs measurements at all three planets through the full range of solar conditions, and models that follow each escape channel back to the young Sun — and the outcome bears on which of the many rocky planets around other stars could have held on to the atmospheres they started with.