PS700 Colloquia Spring 2006
Christopher Rees 3rd Year Physics
Disc-Planet Interactions during Planet formation
Professor Richard Nelson
Queen Mary University London
Colloquium on “Disc-Planet Interactions during Planet formation” given on the
8 February 2006 by Professor Richard Nelson from Queen Mary University
London.
Professor Nelson’s colloquium addressed the following topics:
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The Discoveries of planets over the past nine years.
Observational techniques used to discover these planets.
Planet formation.
Protoplanets in laminar protostellar discs.
Protoplanets in turbulent discs.
Effect of Jupiter like planet migration.
Using observational techniques over 170 exoplanets have been discovered so
far orbiting distant stars. Of these planets we find that 145 are in planetary
systems. A planetary system consists of various non-stellar objects orbiting a
star such as planets, moons, asteroids, meteoroids, comets, and cosmic dust.
Collectively, one or more stars and their planetary systems form a star system.
An example of such a star system this is our very own solar system.
Of these new extra solar planets, found around distant stars, 5 were
discovered by the “transit observational method”. The transit method detects
the periodic dimming of the starlight as the planet passes between star and
observer. The diagram below shows that the brightness is affected as the
planet transits its host star and hence how here on earth we can detect this
dip in luminosity.
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http://www.star.ucl.ac.uk/~rhdt/diploma/lecture_2/
3 of the 170 discovered planets used the micro-lensing technique.
Microlensing involves the gravitational field of foreground star focusing light
from background stars. If a lensing star has a planet in orbit around it, then
the light curve from it may be distorted. This can be shown more easily in the
diagram below where the apparent brightness of a star increases caused by a
lensing star with an orbiting planet.
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Discoveries of other planets used the radial velocity method. The radial
velocity technique measures the orbital motion of the star as it and its planet
system orbit about a common centre of mass.
A star's gravity can be strong enough to keep a planet in orbit, but the planet
is pulling on the star too, and this tug causes the star to “wobble”. The
planetary systems discovered so far are at such great distances that it is
impossible to image the planet itself with current technology. However the
movement of the star is an alternative way to detect the presence of the
companion planet.
Shown below is a diagram that explains how we detect this “wobble” of a
distant star. We do this by measuring the red and blue shift in the visible
spectrum of light. The planet exerts its gravitational effect on the star and
hence the variance caused can be calculated.
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http://www.star.ucl.ac.uk/~rhdt/diploma/lecture_2/
www.spectrashift.com/ basics.shtml
The current discoveries of extra-solar planets show that few have masses
greater than ten times the mass of Jupiter. The discoveries indicate that lower
mass planets are more common.
If we look at the orbital period of planets we see that planets with larger orbital
periods are more common place orbiting distant stars. This is broadly
predicted by the migration theory of planets. However the rise in the discovery
of planets with short periods seems to suggest a mechanism which would
stop migration of planets.
Zucker and Mazeh in 2001 suggested a higher incidence of massive planets
at longer periods and thus a “possible correlation between the masses and
periods of the extrasolar planets”4. This then leads on to suggesting that
heavier objects migrate more slowly? Thus hot planets with the size of
Neptune are now being discovered orbiting close in around distant stars. We
also see from observations that planets with eccentric orbits are the “rule” in
other solar systems.
Some of the very recent discoveries listed by Professor Nelson are as follows:
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HD149026 has a period=2.88days, a radius=0.77 Jupiter radius, its
mass=0.36 Jupiter mass and its core mass=70 Earth core mass
GJ876 is known to have 2 planets in 2:1 resonance effect. The velocity
residuals show periodic variation suggesting a 3rd planet with mass ~
7.5 Earth masses.
In order for planets such as the ones listed above to form, there must be a
collision of dust to form clumps. These in turn must settle into to the disc midplane. In this plane there is then a continued growth towards the kilometre
size clomps. After this there is a runaway growth of bodies, with “oligarchic”
growth occurring when stirring affect in the disc mid-plane is increased
(“runaway growth ends when the largest protoplanets dominate the dynamics
of the planetesimal disk; the subsequent self-limiting accretion mode is
referred to as oligarchic growth''5). There are then two possibilities for the
future of this growth:
1. A giant planet cores forms, this occurs because of the continued
oligarchic growth. Gas then accretes onto the rock and ice core,
forming a giant planet or as we see in our own solar system a gas giant
such as Jupiter.
2. A terrestrial planet can be formed, caused by giant impacts from space
after oligarchic growth is exhausted. Thus the creation of planets with
similar properties of that of Earth or Mars.
We see through observations and spectroscopy that metal rich stars have
higher probability of harbouring planets. This suggests and supports the core
instability model. The following diagram shows how a star, which has a higher
metal content, has a greater chance of having planets orbiting it (in this case
we have the amount of iron relative to the sun).
“On the Mass-Period Correlation of the Extrasolar Planets”, Shay Zucker and Tsevi Mazeh, The
Astrophysical Journal, volume 568, part 2 (2002), pages L113–L116
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http://www.spaceref.com/news/viewsr.html?pid=8370
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For the above example 378 planetary systems were imaged and 61 planets
were found to exist. First “the spectrum of each star was analyzed by
simulating the transfer of light through the atmosphere of the star using a local
thermodynamic equilibrium (LTE) model”. After grouping the stars according
to iron abundance, each group of stars was examined for the presence of
planets using the Doppler technique, discussed earlier. All the observed
“metal rich” stars were found as predicted to have planets orbiting them. The
number above each bar indicates the number of planetary systems in each
group of iron content. It was thus concluded that stars with large amounts of
iron are more likely to harbour planets, than iron-poor stars
As discussed earlier there is evidence that planets themselves migrate
inwards towards the host star, this migration could be caused by a number of
possible reasons.
This migration leads to the existence of planets similar in size to Jupiter, but
with much higher surface temperatures and with short orbital periods around
their host star. This suggests a migration inwards towards the centre of a
solar system for “hot Jupiter”. It is unlikely such planets could have formed so
close in, due to the huge gravitational effects of the star.
It is not only giant planets that we see orbiting close in around their host stars.
Neptune size planets have been observed orbiting with similar short periods.
These short orbital period planets have temperatures in excess of 1500k with
an average distance from the star being 0.1AU. Further evidence is seen from
“dust sublimates” where transition appears to occur straight from gas/dust
clouds into a solid where there is no evidence of a liquid phase. As said
before it is highly unlikely planets formed this close in around their host star so
it is more likely that they formed further out and migrated inwards.
The likely origin for this is as follows: two planets form on well-separated
orbits. Then differential migration causes orbits to converge and thus trapping
the planets in resonance. This can be the same for low mass planets where
spiral waves can cause resonance and hence inwards migration. The
gravitational interaction between planet and spiral waves causes exchange of
“Planetary Companions around Two Solar-Type Stars: HD 195019 and HD 217107”, Debra A.
Fischer, Geoffrey W. Marcy, R. Paul Butler, Steven S. Vogt, and Kevin Apps, Publications of the
Astronomical Society of the Pacific, volume 111 (1999), pages 50–56
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angular momentum. This leads to the fact that low mass planets can be
theorised to migrate rapidly.
Gas accretion onto solid core requires roughly 7 million years. Hence it is
more difficult to form gas giant like planets and even more so in closer orbits
where the gravitational tidal forces from the star are stronger. Reducing dust
opacity speeds up gas “accretion but the migration is always more rapid”7.
Even with this increased gas accretion we still see “hot Jupiter’s” orbiting
close in around distant stars.
This leads onto a theorem for the migration of planets. Hence from this
theorem we can denote migration of the planets as “type I or II migration”.
Type I migration is usual relevant to low mass planets where the mass is less
than 10 earth mass. The torque from the interaction with the planetary disc,
the spinning star and the mass loss from the planetoid means that there is a
momentum exchange. Thus this results in a very quick process for migration
type I and inwards migration towards the host star.
However we see that migration does not move the planet into “hot Jupiter” like
orbits, a prime example of this is Earth where we are just the right distance
from the Sun, not too hot, not too cold. Thus there must be something
stopping type 1 migration. Professor Nelson suggests the following reasons:
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MHD turbulence
A strong magnetic field in the planetary system
Planet-Planet scattering affect
Eccentric discs
Planet enters cavity due to transition from dead zone
For High Mass Planets there must be another form of migration in order to
account for the “hot Jupiter’s” observed orbiting distant stars
When planets grow to a roughly Jovian mass (denotes from the Roman
mythology referring to Jupiter) they open gaps in the discs. These openings
can have two affects:
(i)
(ii)
The waves they excite become shock waves inside the disc plane
The planets tidal torques then exceeds the viscous torques.
Thus the inward migration of a Jovian size planet occurs on a viscous
evolution time scale of disc. This migration timescale usual occurs within a
few 10^5 years.
From observations it appears that Jovian mass planets remain on circular
orbits, however heavier mass planets appear to continue their migration
inwards or form eccentric orbits.
This “Eccentric Evolution” disc interaction can cause both growth and
damping effect inside the planetary disc plane. However as we have seen
planets with a mass close to a Jovian mass can have their migration inwards
stopped. Type II migration is applied to masses in excess of 1 Jovian mass
and as such there are certain ways to stop it. We see from observations that
not all Jupiter size planets orbit close in around their host star. For example in
“Models of accreting gas giant protoplanets in protostellar disks”, J. C. B. Papaloizou and R. P. Nelson,
Astronomy and Astrophysics 433, 247-265 (2005)
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our own solar system we see that the gas giants are further out and they
rocky metallic planets are in closer orbits to the sun, thus there must be some
conditions sometimes stopping type II migration.
Professor Nelson during his colloquia suggested that the following possible
effects that would stop type II migration:
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A fortuitous disc removal can mean that planets form much later on in a
solar system time scale. Hence there would be fewer gaps in the discs
for a planet to move into and hence migration would effectively be
stopped.
“Roche lobe overflow”. Roche-lobe overflow occurs in a binary system
when a star fills its Roche-lobe (often by expanding during the later
stages of stellar evolution). Models show that in systems such as this,
any material that passes beyond the Roche-lobe of the star will flow
onto the binary companion, often by way of an accretion disk. This
would stop type II migration but only works for a planetoid close in
around the host star.
A magnetic aspheric cavity will stop type II migration, however once
again will only work close in around the host star.
If in a solar system simulation the viscosity effect is switched off we see
that type II migration is halted.
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Planets with a magneto rotational instability will lead to vigorous turbulence in
the discs. The necessary ingredients for a condition such as this are as
follows:
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A weak magnetic field.
dΩ/dR < 0
Sufficient ionisation =
In a dust free disc we see roughly 50% of matter in a turbulent state. However
in a dusty in environment we see about 3% of matter in a turbulent state. So it
seems that the dusty environment actually prevents turbulence in the discs.
Professor Nelson went on to show some turbulent disc models showing
planetary systems with small magnetic fields applying and the effects this had
on the amount of turbulence in the discs.
Thus this leads onto the Torque experienced by the planets in orbit around a
star. The Torque distribution can be calculated using the following:
_
T  T  
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T
Finally Professor Nelson discussed terrestrial planet Formation, during giant
planet migration. There can be a number of factors leading to terrestrial planet
formation. During the colloquia an N body simulation was shown, which
examined the effect that gas giant planet migration has on the formation of
terrestrial planets. “The models incorporated a 0.5 Jupiter mass planet
undergoing type II migration through an inner protoplanet--planetesimal disk,
where gas drag had been included”8. Initial conditions in the inner disc under
go different stages of oligarchic growth in order for terrestrial planets to have a
chance of forming. Or a giant planet migrates through the inner planet forming
a disc around the host star possibly allowing a terrestrial planet to form.
In conclusion only in the last decade has the search for extra solar planets
become a science fact and not science fiction. Since then over170 planets
have been found orbiting different stars. Using different observational
techniques astronomers and astrophysicists have calculated these planets
sizes, orbits and atmospheric conditions. We have seen planets roughly the
same size as our own orbiting much further out and much closer in from its
host star than us, but who knows with further observations a planet such as
earth may be found. We have seen that the way a solar system forms is not
random and that planet migration is common place. Under type I migration
low mass planets under go rapid migration towards the star around which they
orbit. Higher mass planets under go a slower migration under the conditions in
type II migration. Turbulence affects within the solar system and discs modify
type I migration and may prevent large scale inward migration for some
planets.
These migration effects though can be stopped leading to non-decaying orbits
and the possible chance of a habitable planet the right distance from a star to
create life.
Professor Nelson’s talk over ran at the end and sadly there was no chance for
formal questions.
“Oligarchic and giant impact growth of terrestrial planets in the presence of gas giant planet
migration”, to be published in Astronomy and Astrophysics, Martyn J. Fogg, Richard P. Nelson (Queen
Mary, University of London).
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