A wind measured by the wall it piles up

A massive star’s wind announces itself in its spectrum. Each ion in the outflow scatters the star’s ultraviolet light, and a blueshifted trough gives both the speed and, with a model, the rate. The wind of a Sun-like star offers nothing of the kind. The solar wind carries off about two hundred-trillionths of a solar mass a year, about ten million times less than a typical hot-star wind, and its column of gas is too thin to make any line that could be recognised against the star’s own. A spacecraft in the solar wind can measure it directly, which is why the number for the Sun is known so well. No spacecraft is going to be placed in the wind of another star.

The number matters a good deal, though. A wind removes almost no mass and nearly all the spin, so its rate at each age sets how a star brakes, and the entire method of dating stars by rotation rests on it. The wind’s pressure sets the size of a planet’s magnetosphere and how much of an atmosphere can be carried away. The young Sun’s wind may have stripped much of Mars. Each of these calculations has a term for the mass-loss rate of an active young star, and for a long time it could only be guessed from the Sun’s present value.

A way of measuring it was found in the 1990s, almost by accident, and it remains the only reliable route for a star like the Sun. It does not look at the wind at all. It looks at the place where the wind stops, an unimaginably thin boundary hundreds of astronomical units from the star, in the one spectral line strong enough to record it. The whole measurement rests on a piece of atomic bookkeeping that produces a feature at the edge of a line, and a long chain of inference that turns that feature into a rate.

Where a wind stops #

A wind expanding from a star thins with distance, and its pressure falls as the inverse square of the radius. Eventually that pressure falls to about the pressure of the interstellar medium the star is moving through, and the wind can go no further. Such a boundary was predicted for the Sun in the 1950s and 1960s and reached by Voyager 1 in 2012, at 121 astronomical units, and by Voyager 2 in 2018 at about 119. The bubble the wind has blown is the heliosphere, and around any other star it is called an astrosphere.

An astrosphere’s size is therefore a measure of its wind, given the surroundings. No telescope can see this bubble, as nothing in it emits to speak of. What makes it detectable is that the interstellar gas isn’t only plasma. Near the Sun, about half of it is neutral hydrogen, and neutral atoms pay no attention to magnetic fields or to the boundary between the plasmas. They drift straight across at the star’s speed through the interstellar medium.

Charge exchange and the wall #

The atoms do not drift through undisturbed. A neutral hydrogen atom close to a proton can hand over its electron without any significant change in either particle’s motion. The neutral atom has then become a fast or hot one, with the proton’s velocity, and the proton a slow one. In the region outside the boundary, where the interstellar plasma has been slowed and heated as it piles up against the obstacle, this happens repeatedly. A neutral population forms with the temperature and bulk speed of the slowed, compressed plasma, and it has a substantially greater density than the undisturbed gas outside. This is the hydrogen wall.

Vladimir Baranov and collaborators predicted this for the Sun in the late 1980s and early 1990s. Its properties suit the problem unusually well. The wall’s atoms have a temperature of around twenty or thirty thousand kelvin, much hotter than the interstellar hydrogen at about seven or eight thousand kelvin. Its column density is small, about $10^{14}$ to $10^{15}$ atoms per square centimetre, compared with about $10^{18}$ for the interstellar gas on the way to a star a few parsecs away. Yet because it is so hot, its Doppler-broadened absorption profile is much wider than that of the cool gas, so it reaches further into the wings.

The line in which it appears is the most sensitive one available. Hydrogen Lyman-α, at 121.6 nanometres, has a very high absorption strength, and it is emitted strongly in the chromosphere of any cool star. Its core is entirely absorbed by interstellar hydrogen along even the shortest sightlines. But its flanks survive, and that is what a space ultraviolet spectrograph on Hubble can measure.

So there is a feature that shows up where nothing should absorb. In 1996 Jeffrey Linsky and Brian Wood found extra absorption in the spectrum of α Centauri, in the flanks of Lyman-α, that the known interstellar gas could not explain. They identified the excess on the red side with the Sun’s own wall and the excess on the blue side with α Centauri’s. Light from another star passes through that star’s wall on its way out and through the Sun’s wall on its way in, and because of the geometry those two absorbers are displaced to opposite sides of the line. The red-side absorption is the Sun’s, the blue-side absorption the star’s. This is how a star’s wind began to be measured.

From a notch to a rate #

The feature’s depth depends on the wall’s column, and this is where the argument becomes a good deal less direct. There is no simple formula.

The conversion uses a computation for the particular star: its speed through the local interstellar medium, the direction of sight, and the assumed density of neutral hydrogen around it. For each star, a family of hydrodynamic models is run with different assumed wind strengths, and the Lyman-α absorption is computed along the line of sight for each. The model whose absorption matches the observed notch gives the mass-loss rate. Since the models are anchored to the Sun, where the wind and the wall can be compared with direct measurements, the method does in the end have a calibration of a sort.

That chain involves a good many steps, and each introduces uncertainty.

This is an awkward measurement, and it should be read as such. The conditions around any other star can’t be measured directly and are generally inferred from what the local gas looks like along other sightlines. Worse still, not all stars show the feature. Many stars have no detectable absorption from their astrospheres, for one of several possible reasons: their surroundings may be fully ionised, with no neutrals to pile up, or their absorption may fall behind the broad interstellar one. In any event, the sample of stars with a measured wind has been only about two or three dozen objects, and every one is within about 15 parsecs of the Sun. That is rather a small base for a subject with so many consumers.

A law with a wall of its own #

The first thing to ask of those measurements is how a wind’s rate depends on the star’s activity, because activity is what can be seen and a wind is what can’t. The natural proxy for activity is coronal X-ray flux per unit surface area.

For stars with up to about thirty times the Sun’s X-ray flux, Wood and his collaborators found a clear rise: the mass-loss rate per unit area scales as a little more than the first power of the flux. Beyond that, the relationship breaks down. The very active stars show less mass loss than the extrapolated line by an order of magnitude or more, even though they have enormous coronae. That break, called the wind dividing line, is the most surprising and most consequential result of the whole enterprise, and its existence is far from certain, resting on only a few objects such as ξ Boötis.

A plausible reason has been suggested in what the magnetic field does. On very active stars the X-ray emission and magnetic flux are concentrated in very strong, large polar spots, and a very strong dipole-dominated field might hold plasma in closed loops rather than let it escape. The wind would then be choked by the same field that makes the star so bright in X-rays. The same trend also appears indirectly in models that link the composition of the corona to what the wind carries off, though nothing about that link has been established. As an alternative, the sample’s few active stars could simply have unusual surroundings or an unusual geometry. Or the relation might show a very large scatter that the small sample has not revealed, in which case nothing can be said at all.

What it implies for the young Sun #

An X-ray flux falls as a star ages. Taking that together with the law gives a history of the solar wind, read off from other stars of various ages.

The peak’s presence has wide implications. If a law with no break were right, a young Sun’s rate would be enormous, as much as thousands of times today’s value in the first hundred million years. Its integrated mass loss could then be a few per cent of a solar mass, enough for a brighter early Sun and so a partial solution to the faint-young-Sun problem. With a break, the integrated loss over a lifetime is far smaller, too small for that purpose. The difference, therefore, turns on a few stars just beyond the dividing line.

The same history drives the shield a planet needs and what can be concluded from the hard-to-separate effects of wind and ultraviolet on atmospheric escape. Rotation evolution uses it as well, and the star’s early braking has been fitted to observed spin rates in young clusters, with a wind torque calibrated partly on such rates. There’s a certain circularity here that deserves notice, since these rates depend on the small sample of hydrogen walls, and a theory that uses them to fit rotation can’t then be taken as independent confirmation of them. The more worthwhile check would be something that is separately measured: for instance, whether rotation models using these rates predict the cluster sequences without their other parameters being retuned. The answer so far is mixed.

A second line of evidence #

Other ways of measuring these winds have appeared, and all are limited in ways of their own. Radio free-free emission from a wind should be visible if the mass loss is high, though for Sun-like stars this gives only upper limits, at around a hundred times the Sun’s rate or more. X-ray emission from charge exchange between a star’s wind and the neutral gas around it has been sought and hardly found. Planet-hosting stars offer a new possibility: the gas a close-in planet is losing is shaped by the wind it meets, so the cometary tail seen in Lyman-α during a transit depends on the wind’s pressure. For a particular planet, that is a measurement at a much closer distance from the star than the astrosphere. Each method has its own model dependence, and the comparison is just getting started.

There is one further method, based on what a star’s flares and coronal mass ejections do. On an active star, mass ejected in eruptions might carry as much as or more than the steady wind. The flares of the most active stars are frequent enough that, if each had a mass ejection on the solar pattern, the total mass loss would be greater than all that is otherwise observed, and it would exceed the star’s plausible energy budget too. That argues for something suppressing such ejections on these stars, which again points to a strong overlying field and links back to the dividing line. It is suggestive and indirect, as most evidence in this subject is.

The odd economy of the measurement #

The thing worth lingering over is how far removed the observation is from the object. A wind emanating from a star’s corona is measured from an absorption feature produced hundreds of astronomical units away, in neutral atoms that have never been in the wind. They were part of the interstellar medium, they took up the speed and temperature of slowed plasma by swapping electrons, and they sit in a place defined by a balance of pressures. Each element of the chain depends on physics quite remote from that of a corona. It is the sort of argument that would be easy to dismiss if a spacecraft had not flown through the Sun’s own version, and the Voyagers’ crossing of the heliopause did support the broad picture, at the only place it could be tested.

There is a further feature of the wall that is easy to overlook, which is how little of the wind’s energy it takes. The neutral atoms that make it up were never heated by the star, and the pressure balance that places it does not care about the details of the corona. So the method gives a mass-loss rate times a speed, in effect a momentum flux, and turning that into a rate of mass needs a wind speed assumed from the Solar System’s. A second odd feature is that this measurement is possible only for stars in a neutral, moderately dense part of the interstellar medium, close enough for their Lyman-α flanks to escape the interstellar column. So the sample isn’t representative in any simple sense. It selects on the Sun’s own neighbourhood, a structure of local clouds with a low column density. Further out, the interstellar absorption grows to swallow the flanks entirely, and even a strong wind could not be seen. It is a measurement limited not by the sensitivity of the instrument but by the very gas that makes it possible.

What the picture cannot show #

The line shapes in these figures come from a simple Gaussian intrinsic profile, a single absorber for the interstellar gas and another for the wall. A real analysis has to reconstruct the star’s unabsorbed line from its flanks, fit several interstellar clouds, and add the heliospheric absorption on the red side, and that has to be done without knowing what the original line looked like. The fit is therefore less certain than a figure with a clean separation suggests. Wall parameters are chosen to be typical, and the notch’s location and depth vary with the geometry of each sightline.

The size figure uses only a simple pressure balance, whereas real astrospheres are elongated by the star’s motion, with a long tail in the downwind direction, and the direction of view matters. The law’s points are rounded values and are drawn with none of their errors, and there is no statistical significance implied by the line. The history is a toy, taking a single power-law X-ray decline and a specific form for the fall past the break, where any number of different assumptions could be made. A real star’s activity at a given age has a wide range, as a young Sun’s rotation is itself not known. So the numbers there are only illustrations of how much depends on a single break.

Still open: whether the dividing line is real #

The wind dividing line rests on a handful of objects that are among the most active stars in the solar neighbourhood. Extending the sample is difficult as the Lyman-α flanks of more distant stars disappear into the interstellar absorption, and Hubble’s ultraviolet spectrographs have no announced successor, so the measurement faces a deadline. A careful re-examination of the existing sample, with hydrodynamic models that take the true surroundings and the magnetic geometry of each star into account, can address part of it. Spectropolarimetric maps of stellar fields now exist for many of these stars, and whether the ones falling below the line really are the ones with strong, dipole-dominated magnetic structures is a directly testable connection. If they are, the suppression has a cause. If not, the break might be a selection effect, and the history of the young Sun’s wind, and everything that follows from it, would have to be drawn differently.