Publications Topics:

Books

ASP Conference Series

Monograph Publications

IAU Publications

Books of Note

Purchase through the AstroShop

Journals

Publications of the ASP (PASP)

Magazines

Mercury Magazine

Archive

Guidelines for Authors

Order Mercury Issues

Mercury Advertising Rates

Newletters

The Universe in the Classroom

ASP E-mail Newsletters

Special Features

Astronomy Beat

Contact Us

Mercury, January/February 1999 Table of Contents

Can a star swallow a planet? The extrasolar planets discovered over the past two years display an odd range of characteristics - from their masses to the size and shape of their orbits. And they just may offer us clues to stellar diets.

Eric Sandquist
Northwestern University

The discovery of a Jupiter-like planet circling the star 51 Pegasi on an orbit considerably smaller than that of Mercury was a surprise to astronomers. Planets like Jupiter, it was thought, could not form that close to a star because the high temperatures there would have prevented "icy" and "rocky" solids from condensing out of the gas. Without a solid core, a giant planet would not be able to form quickly enough to capture a large amount of gas before the star sucked it up or drove it out of the system. The 51 Peg discovery meant that either our ideas about giant planet formation were seriously flawed or the planet had to have been moved from its birthplace by some means. Not surprisingly, the second (simpler, and less damaging) idea of "planet migration" is currently in vogue. But if planets can move so close to stars, can they also be caught and eaten?

A comparison of the orbits of planets known to circle stars like the Sun. The Sun is shown to scale in the lower panel. Illustration courtesy of author.

The work that my collaborators -- Ronald Taam at Northwestern University, Doug Lin at the University of California at Santa Cruz, and Andreas Burkert at the Max-Planck-Institute for Astronomy in Heidelberg -- and I have been doing relates to whether it is possible to determine if a star has eaten a planet by looking at the chemical composition of the star's surface. To understand how realistic this scenario might be, we must first look at what the know extrasolar planets tell us.

What's for Dinner?

Looking at the newly discovered planetary systems with an open mind, we see that none of them bear an obvious resemblance to our own. The planets that have been detected display an odd range of characteristics -- from their masses to the size and shape of their orbits. Of the eleven confirmed as of this writing, only the planet circling 47 Ursae Majoris reasonably conforms to the expectations astronomers had based on the Solar System. Even so, that planet is at least 2.4 times more massive than Jupiter and occupies an orbit slightly larger than that of Mars.

There is some evidence that the remaining extrasolar planets split into two subgroups, though there is still a chance that we may be misled by the small size of the sample. One subset -- those around the stars 70 Virginis, 16 Cygni B, 14 Herculis, HD 114762, and Gliese 876 -- is notable for the large eccentricity of the planet orbits. In our solar system, Pluto has the largest eccentricity at 0.25 with Mercury a close second at 0.21. Even so, these eccentricities are probably the result of unusual circumstances -- Pluto's orbit may be the result of being a captured comet-like object, whereas Mercury's is the result of interaction with the Sun. None of the gas giants in our solar system has an eccentricity of more than 0.06. In contrast, the eccentricities of these five extrasolar planets range between 0.35 and 0.63.

Another subset - composed of the planets orbiting 51 Pegasi, Rho Cancri, Tau Bootis, Upsilon Andromedae, and Rho Coronae Borealis - have low eccentricity orbits that are considerably smaller than that of Mercury. These five planets all have masses greater than that of Saturn, and have managed to survive very close to their host stars. In fact, the three planets with the smallest orbits circle at distances of only about ten times their parent stars' radii.

How did these planets get there?

From the Freezer...

The collapse of the gas cloud that will eventually form a planetary system fairly quickly creates the star and a rotating disk of gas. Though the gas cloud may start out with very little initial rotation, this is magnified during the collapse in the same way an ice skater in a spin can pull in his arms and spin faster. At some point the centrifugal force due to the rotational motion can balance gravity. When this happens, the gas can settle down onto relatively stable orbits. Nothing prevents the cloud from collapsing along its axis of rotation, however, so the gas forms a flattened disk.

Where temperatures in the gas disk are low enough, the heavy elements or "metals" (the astronomer's catchall term for elements with atomic masses larger than helium) can condense out of the gas to form dust-grain size particles. Over time, these particles collide and stick to form larger and larger bodies. As they grow more massive, these "planetessimals" begin to be able to use their mutual gravitational attraction to accelerate the process. When a planetessimal reaches a critical mass of around fifteen Earth masses, its gravity is great enough to draw in and retain nearby gas, and if it collects enough gas, the planetessimal becomes a giant planet.

In this way it is expected that giant planets tend to get more than their fair share of heavy elements - the Sun has less than 2% of its mass in heavy elements, while Jupiter may have as much as 10%, with much of that concentrated in the core it needed to form.

Tidal interaction between a planet and a star. If the planet orbits in synchronism with the rotation of the star, a tidal bulge develops at the surface of the star on a line between the planet and the center of the star. If the planet orbits more quickly than the star rotates, the tidal bulge lags the planet's motion. This results in a small net pull backwards on the planet, stealing its orbital energy and causing its orbit to decay. Illustration courtesy of author.

...to the Frying Pan

While the gas disk is still in existence around the star, it exerts a drag on the planets orbiting within it. The gravity of a planet distorts the orbits of the gas near it, causing a slight buildup of gas. Because gas just inside a planet's orbit moves more quickly than the planet, the gas buildup is always in front of the planet in its orbit. As a result, the gravitational interaction between the two tends to pull back on the gass and pull forward on the planet. Similarly, the gas just outside the planet's orbit moves more slowly than the planet, so that the planet tends to be pulled back by that gas. The balance of the pulls of the mass interior and exterior to the planet's orbit tends to be biased in favor of the exterior because there is slightly more mass there. The net result is that energy the planet needs to stay in orbit at its current distance is stolen, causing the planet to begin a slow spiral towards the star over the course of millions of years. This is one way in which a planet can migrate.

When a Jupiter-sized planet moves to within about ten stellar radii of the star, the tidal interaction between the star and the planet becomes important. Just as the Moon causes tides in the Earth's oceans, the migrating planet creates tidal bulges in the gas on the star's surface. The induced tidal bulges can result in an increase or decrease in orbital distance, depending on whether the object with the tides (Earth or the star) is rotating faster or slower than the orbital motion of the body causing the tides (the Moon or the planet). The Earth rotates faster than the Moon orbits, so the tides on the Earth tend to lead the Moon in its orbit -- the combination of rotation and friction carry the bulge a bit forward of where it would be if Earth didn't rotate. The gravitational attraction between the nearer tidal bulge and the Moon gives energy to the Moon at the expense of Earth's rotation, since a component of the gravity pulls the Moon forward in its orbit and speeds it up. Thus, the centrifugal force on the Moon increases slightly above the gravitational forces, pushing the Moon slowly away from the Earth.

When the gas disk is present, the star will also be rotating faster than the orbiting planet. As a result, the tidal bulge on the star will lead the planet, tending to give the planet additional speed and slowing its migration. However, the disk dissipates about 10 million years after the star forms. When the disk evaporates, the planet's inward progress stops, at least temporarily. Processes similar to ones described here are believed to result in the presence of planets close to their host stars.

After approximately 100 million years, stars like the Sun are observed to lose the spin they gained during their formation -- probably because magnetic fields transfer the spin to the gas in their stellar winds. Once a star is rotating more slowly than the nearby planet orbits, the tidal interaction between the two drags the planet towards the star's surface again. But what would be the observable consequences of the consumption of the planet?

Into the Blender

We know that at least twelve stars, including the Sun, harbor planets. Though their orbits make the planets appear to belong to different classes, the majority of their host stars seem to share at least one common characteristic that may tell us what we should be looking for. Spectroscopic observations of the host stars by Guillermo Gonzalez of the University of Washington indicate that all but two of the eleven stars measured to date have abundances of metals that are larger than the average for G dwarfs in the neighborhood of the Sun, which is itself classified as spectral type G2. In addition, three of the host stars are among the most metal-rich stars known. We question again whether this will still be true when a larger sample of planets has been gathered. But in the meantime, it is natural to ask whether this observed characteristic is because planets can only form out of gas that is inherently rich in metals, or whether the atmospheres of the host stars are being contaminated by a process that is related to the presence of planets.

The first is a real possibility, according to current theories of planet formation. The terrestrial planets obviously required a certain level of heavy element enrichment in the gas from which they formed. However, the terrestrial planets contain only a small fraction of the heavy elements that are inferred to exist in our own solar system. The gas giants have somewhere upwards of seventy Earth masses of heavy elements combined, and the Sun contains about 6000 Earth masses of heavy elements. Clearly it is almost impossible to account for the entire heavy element content of a star like the Sun by simply throwing planets into it. However, you don't have to contaminate the whole star…

During the early stages of its formation, the gravitational energy released by the contracting protostar is so large that it has to be carried to the surface by convection, the most efficient means of transport available to it. Convection occurs in a heated pot of water that hasn't reached the boiling point -- heat from the bottom of the pot is brought to the top by the water's circulatory motion. (Throw in some frozen peas and you can watch them circulate.) As a result of convection within the protostar, the gas is kept very well mixed. To attempt to enrich the metal abundance of the forming star during this phase would be futile since any added material would be quickly diluted with the entire mass.

Schematic cross sections of a heated pot of water and the Sun. In both cases, heat from below causes expansion (of water in the pot, and gas in the Sun), which increases buoyancy and causes material to move upward. Cooling results in compression and loss of buoyancy. The circulation causes very efficient mixing of the material. Illustration courtesy of author.

If metal-rich material were added at the surface of the star when the gas was not mixing so violently, less would be needed to make it appear that the star is rich in metals, since abundance measurements can only be made of surface material. Indeed, as a protostar slowly contracts and heats with time, the gas at its center becomes less and less opaque. As this happens, radiation is able to carry thermal energy away from the center more efficiently than convection, and the mixing motions subside in the core. And as the protostar contracts further, this radiative region ex-pands outward. For stars like the Sun, this continues until only the outermost few percent of the star's mass still undergoes convection.

Therefore, if a star consumes a planet when the star has only a small convection zone at its surface, it can fool us into thinking that it has a high abundance of metals throughout. In this way, the formation of a planet could end up altering the chemical appearance of the star around which it formed.

Dig In!

To test this idea, we have run simulations to see if a planet could be dissolved in a star's convection zone. In our first calculation, we placed a planet like Jupiter (according to radius and mass distribution) on a circular orbit at the surface of a Sun-like star. When a planet reaches a star's surface, its orbit decays primarily due to a kind of air resistance resulting from the impact of stellar gas on the planet's leading side. On average, Jupiter is considerably denser than the gas at the stellar surface. Initially then, Jupiter is only slightly distorted, but mass is slowly stripped off due to the high velocities (about 400 km/s) at which the stellar gas is hitting the planet.

After one orbit around the star, the planet in our simulation lost 11% of its initial mass and sank by about 3% of the star's radius. The density of the impacting stellar gas increases as the planet plunges further in, so that the mass loss and orbital decay accelerate. Before the planet made it through another orbit, all its mass had been stripped away through a combination of heating by shock waves and ablation by the stellar material. Jupiter, core and all, would be melted away before it had completely passed through the Sun's convection zone. And in our simulation, the whole process - from the time the planet hit the star's surface to its disintegration - took about 5 hours.

The progressive ablation of a Jupiter-like planet moving through the envelope of a star like the Sun. Stellar material enters from the left. Image courtesy of author.

But what of stars with masses different from the Sun's? On the one hand, stars of lower mass than the Sun are less likely to show enhancements because their convection zones are more massive and would dilute any metals from added planets. On the other hand, stars of slightly higher mass have less massive convective zones - the only question is whether a planet can be dissolved in it. To check, we ran two additional simulations with a star about 20% more massive than the Sun - the first using a Jupiter-like planet, the other using a Saturn-like one. In both cases the planet survived passage through the base of the convection zone, losing about 30% of its mass in the zone, to dissolve deeper in the star.

In these cases, we need to know how the heavy elements are distributed in the planet in order to know how much enrichment to expect. If the core holds all of the heavy elements, we would be unable to see any evidence of the planet's death.

The Secret Ingredient

Because Jupiter is made up of mostly hydrogen and helium, we have a reasonable idea of what Jupiter's internal structure is like, simply from how those two elements behave under pressure. The heavy elements, being traces, are more difficult to gauge because they don't significantly affect the structure of the planet. Direct measurements of chemical composition can only reach material very near the planet's visible surface: The Galileo spacecraft's atmosphere probe plunged only about 150 km into Jupiter's atmosphere before being crippled, and the impacting fragments of Comet Shoemaker-Levy 9 dredged up material from similar depths.

Jupiter's core is expected to be very metal-rich according to the theory of its formation. However, we are unable to directly measure its core mass or that of any giant planet in the Solar System, for that matter. The only reason we can infer anything about the actual mass distribution of the giant planets is that they rotate fairly fast. The rotation causes them to distort into flattened spheroids (for Saturn, this oblateness is noticeable in photographs). As a result, the gravitational field of the planet is not spherically symmetric, and the planet does not act simply like a point-mass - mass closer to the surface affects the trajectories of probes like Voyagers 1 and 2 relatively more than does mass deeper in the planet. These deviations of the gravitational field from that of a spherical assembly of mass tell us about the internal structure of the planet.

Still, this measure is insensitive to the mass closer to the center of the planet. The most recent models indicate that the core of Jupiter is somewhere between two and twelve Earth masses, whereas on theoretical grounds it is expected that about fifteen Earth masses were needed for Jupiter to form. While Jupiter was forming, it is possible that heat being released by accreting gas melted the outer parts of the core so that some of the heavy elements were mixed into the gas. Depending on whether those heavy elements could condense out again later, melted core material could still be floating around in Jupiter's envelope today.

Divining a planet's interior. Note in this 1981 Voyager 2 image how Saturn is noticeably flattened. This distortion is caused by the planet's rapid rotation, and it is what allows us to infer its structure from its gravitational field. Image courtesy of NASA.

The best models of Jupiter indicate that there is a total of around thirty Earth masses of heavy elements contained throughout the planet. Our simulations predict that a Jupiter-like planet swallowed by a main-sequence star like the Sun could increase the abundance of heavy elements at the star's surface by up to 26%. The heavy element enrichment of a more massive star's surface by a Jupiter-like planet (which did not completely dissolve in the convection zone) could range up to 50% if the planet's heavy elements were uniformly distributed. The enhancement is larger since the added metals aren't as heavily diluted. For a Saturn-like planet that carries fewer heavy elements, the maximum enrichment could be 14%, so that its consumption would probably not contaminate the star enough to be recognized.

Thus, examinations of the chemical makeup of stars like the Sun provide us with some hope of telling whether the star had a planet like Jupiter, even if the star has already finished its meal.

ERIC SANDQUIST is a postdoctoral researcher at Northwestern University in Evanston, Illinois. He frequently wonders if there is a psychological reason why much of his work has involved astronomical objects crashing together. His email address is erics@apollo.astro.nwu.edu.