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What is a "Typical" Solar System?

by John G. Cramer

Alternate View Column AV-155
Keywords: extrasolar, planets, no-Jupiter, systems
Published in the December-2010 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 7/16/2010 and is copyrighted ©2010 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


Much of science fiction is set on and around planets that are orbiting stars other than our Sun.  How are the planets arranged in other star systems?  The usual assumption is that we can take our own Solar System as a model.  By this logic, each star should have a set of inner planets, with perhaps one or two that are Earth-like and habitable, an asteroid belt, and a set of outer gas giants, perhaps some with rings like those of Saturn.

There are, of course, variations.  One alternate scenario is a Jupiter-like gas giant that is close enough to the parent star to have an Earth-like planet as a moon.  The rebel base on the moon Yavin-4 in Star Wars 4: A New Hope and the moon Pandora in Avatar are examples of habitable moons of gas giant planets.  Another is a pair of habitable planets orbiting each other as they orbit the parent star, as in Ursula Le Guin’s The Disposessed.  Nevertheless, for most of SF our Solar System is the model.

But is our Solar System really a typical star systems?  The Nice Model described in a recent AV column (see AV-151) suggests that during its evolution, our own Solar System was subjected to a major rearrangement.  A 2:1 orbital resonance occurred between Jupiter and Saturn that produced the Late Heavy Bombardment of the inner solar system and the orbit-swapping of Neptune and Uranus as they were flung out to larger orbits.  This violent and chaotic behavior of the gas giants in our Solar System might just as well have produced configurations of planets that are very different from the present one.  Further, the Nice scenario depends directly on the fact that our Solar System has four gas giants.  Is that typical?

Let me begin with some planetary astronomy basics.  Because of Newtonian physics, planetary orbits have the geometric shape of an ellipse, with the parent star located at one focus of the ellipse.  The size of the orbit of a planet is characterized by its semi-major axis, represented by the symbol a.   The semi-major axis a is half of the width of the ellipse along its long axis.  Astronomers like to describe orbital sizes by using Earth’s orbit as the standard.  Thus, the orbit of the Earth is exactly one astronomical unit (a = 1.0 AU), and the orbit of Jupiter has a = 5.2 AU.

During the past decade, astronomers have been able to detect over 400 extrasolar planets of relatively nearby stars.  These planets orbiting other stars have been detected mainly using the Doppler radial velocity technique, in which the “wobble” of a star induced by a close-orbiting planet is observed.  The overwhelming majority of the planets detected have been short orbital-period gas giants with masses comparable to those of Jupiter or Saturn.  This dominance of gas giants is to be expected, of course, because the Doppler radial velocity technique is strongly biased toward the detection of planets with large masses and short orbital periods.  If a planet has a mass less that 35 Earth-masses or an a greater than 7.5 AU, the wobble induced in the parent star will be too small to be observed, and the Doppler radial velocity technique will not detect the planet.

It is important to note that most of the stars studied with this technique do not show any indication of the presence planets.  The detection of planets in some systems and not in others raises the question of how common gas giants really are in the star systems of our Galaxy.  Astronomers have carefully examined this question using all available data and have concluded that between 24% and 50% of all stars have gas giants in orbits with a less than 20 AU (i.e. inside the orbit of Uranus).  Thus, the majority of all stars do not have Jupiter-like gas giants at a = 5 to 20 AU orbits that would affect the inner, possibly Earth-like, planets.  Possibly this is because the density of pre-planetary matter is too low in many cases to support the runaway formation of gas giants in the early stages of planet formation.

How then are the planetary systems configured in these more typical star systems, around half of which have no gas giants in Jupiter-like orbits?  Andrew W. Mann and Eric Gaidos (U. Hawaii) and B. Scott Gaudi (Ohio State U.) have used computer simulations to address this question.  They have numerically studied the evolution of one-solar-mass star systems using 230 different sets of starting conditions.  They followed the disk of gas and matter around a new star as it developed planets from proto-planets (which they call “oligarchs”) and the smaller “planetesimal” chunks of orbiting matter until stable orbits are reached.  The calculations spanned a system time period of about 5 billion years.  The planet-formation scenario used consisted of three phases: (1) the runaway accretion of protoplanets from the primordial disk of planetesimals; (2) the slower growth of oligarchs from these protoplanets as they consume neighboring planetesimals and each other; and (3) the chaotic or giant impact phase that is reached when the mass in residual planetesimals is less than that in the protoplanets and the oligarchs’ orbits began to cross and resonate.  The phase 3 behavior resembles the Nice Scenario (described in AV-151) but is somewhat less violent because the oligarch masses are smaller.

The calculations are focused on planet formation beyond the “ice line”, an adjustable parameter of the calculations (varied from a = 2.7 to 5 AU) corresponding to the orbital radius at which ambient water is a solid, increasing the probability of planet formation.  The calculations also vary the starting oligarch number (2 to 12) and oligarch spacing, as well as the initial oligarch masses (0.44 to 3.63 Earth-masses) and the mass of ice initially resident in the disk (10 to 35 Earth-masses).  Some 230 different simulations were run for 5 billion years (model time), enabling certain conclusions and generalizations to be proposed, based on the results.

One conclusion that one can draw from the calculations is that “oligarch swapping” is common, and the closest-in oligarch at the start of the process does not always end up as the innermost planet.  When only two oligarchs are present, each has about a 50% chance of ending up as the inner planet.  Sometimes, particularly when more than two initial oligarchs are present, one or more of them may be ejected from the system.  The inner oligarch in all cases migrates inward from the ice line, typically becoming the most massive planet of the system and moving inward by more than 3 AU, most often settling in an orbit between 1.2 and 1.9 AU.  In our Solar System that would be roughly at the orbit of Mars (1.6 AU).  A massive planet so close to the small inner planets (not included in the planet-formation simulation) would be expected to cause disruption of orbits.

The role of inner planets was investigated in two sets of runs by putting analogs of Venus and Earth with appropriate masses in orbits at 0.7 and 1.0 AU and observing the effects and orbit stability.  It was found that while the presence of these inner planets had little effect on outer planet formation beyond the ice line, the effect of the outer planets on the inner ones was significant.  In all 10 runs of one simulation, the “Earth” and “Venus” analogs collided after 15 to 70 million years, leaving a single planet of a few Earth-masses in an orbit around 0.8 AU.  The conclusion from this is that in the most probable scenario, in which no gas giants form, planetary systems with multiple inner planets are unlikely.  With no gas giants you would get only one crack at having an Earth-like planet.

The authors concluded by considering the future testability of their results.  They considered the chances that existing planet-detection techniques and proposed space missions might detect planets of the masses and orbits predicted by their calculations.  In particular, they consider ground-based Doppler and microlensing detection and the space missions Kepler and the space interferometry mission SIM-Lite.  They concluded that the Doppler technique could detect none of the predicted planets. Microlensing studies at large ground-based telescopes might be able to detect the half of the predicted planets having orbits with a less than 6 AU.  The Kepler and SIM-lite missions are less sensitive, but might detect roughly a third of the predicted planets with a less than 2.5 AU.  In other words, we can expect the predictions of the calculations to be tested in the next few years, primarily with ground-based microlensing techniques.


From the point of view of science fiction, the message of these calculations is a bit dismaying.  Our own Solar System is not a model that we expect to find repeated elsewhere in the galaxy.  It is the unlikely product of gas giant formation followed by a resonant period of chaotic Late Heavy Bombardment that happened to place Jupiter at 5.2 AU.  This was far enough out to leave the inner system relatively unperturbed, so that Venus, Earth, and Mars could form and have stable orbits in the inner region.

The more likely scenario is that no gas giants form.  Instead, a set of outer planets with masses less than that of Uranus form, the largest of which, with 10 or so Earth-masses, orbits at about 1.5 AU.  This probably leaves room for only one inner planet, which may or may not have a mass, orbit, and water and heavy metal content appropriate to be Earth-like and to support life.  The universe is a difficult and hostile place for life, and only a multiple series of lucky accidents prepared the Earth as a cradle for life.

We would be well advised to take better care of our Cradle.  


References:

Detection of Extrasolar Planets:

“The Keck Planet Search: Detectability and the Minimum Mass and Orbital Period Distribution of Extrasolar Planets”, A. Cumming, R. P. Butler, G. W. Marcy, S. S. Vogt, J. T. Wright, and D. A. Fischer, Publications of the Astronomical Society of the Pacific 120, 531–554 (2008).

See also The Catalog of Nearby Exoplanets,  http://www.exoplanets.org

Computer Simulations of Outer Planet Formation:

“The Invisible Majority: Evolution and Detection of Outer Planetary Systems without Gas Giants”, A. W. Mann, E. Gaidos , and B. S. Gaudi; arXiv e-print:1007.2881v1.


SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .

AV Columns Online: Electronic reprints of about 177 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at: http://www.npl.washington.edu/av.


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