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
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