Jarrod R Hurley & Michael M Shara. American Scientist. Volume 90, Issue 2. Mar/Apr 2002.

The existence of planets outside our solar system has been a delicate matter in astronomy ever since the 16th-century philosopher Giordano Bruno was burned at the stake for (among other things) proposing that the universe holds an infinite number of other worlds. People are no longer set aflame in the public square for proposing the existence of extrasolar planets, but the field remains contentious. To date more than 70 planets have been found in orbit around other stars, generating a considerable amount of excitement in the astronomical community. Perhaps even more intriguing is the discovery of a few dozen extrasolar planets that are not affiliated with any star at all. These so-called “freefloating planets” are among the most controversial objects yet found in the search for other worlds.

The problem is that astronomers don’t all agree on what it means to be a planet. Some of the objects found orbiting other stars are in fact much larger than any of the giant planets in our own solar system, weighing in at more than 10 times the mass of Jupiter (although most are less than 3 or 4 Jupiter masses). This approaches the size threshold of another type of substellar object known as a brown dwarf, often described as a “failed star” because it’s too small to ignite the fusion of hydrogen in its core. Brown dwarfs are intermediate in size between planets and true stars, and the boundary lines at the upper and lower limits of brown dwarfdom are still a little fuzzy. (To further confuse the issue, it was recently reported that brown dwarfs may themselves harbor planets! See also “The Discovery of Brown Dwarfs,” November-December 1997).

On the other hand, some of the free-floating planets appear to be no larger than Jupiter, but their very existence challenges the traditional notions of what a planet ia substellar object that orbits the star around which it formed. Many people are reluctant to call the free-floating objects “planets,” and for now many scientists just call them free-floaters.

Beyond the politics of nomenclature, part of the challenge of understanding free-floaters involves trying to explain their origins. If these objects were formed like stars by the gravitational collapse of a dusty cloud of gas, then a certain number of them might be born alongside the stars in a newborn stellar cluster or association. If, however, the free-floaters were formed in the protoplanetary disk that surrounds a nascent star, then it raises the question of how the orphaned planet came to be found so far from its parent star.

Our research addresses this latter possibility. We specialize in the study of globular clusters (of stars), understanding what they are and how they evolve using both observational methods and computer simulations. Although this may seem to be far afield from the study of extrasolar planets, it turns out that dense stellar clusters may be fertile grounds to look for these objects because of the dynamic interactions between the stars inside the clusters. Here we consider the recent discoveries of free-floating planets and, at the risk of igniting a public pyre, show that they might not be so surprising after all.

Enter the Free-Floaters

Free-floaters are interesting and important objects beyond the fact that they are currently an astronomical novelty item. The number and variety of bodies in our galaxy that are smaller than a star-less than about 0.08 solar masses (or 80 Jupiter masses)-is simply not known. They are expected to come in a range of sizes-from the relatively large objects such as brown dwarfs and giant gaseous planets to rocky planets like the Earth and smaller bodies like the moons and the asteroids in our solar system. A quantitative measure of their existence is important not only in our search for habitable worlds and extraterrestrial life, but also to address fundamental questions in astrophysics and cosmology, such as the relative numbers and sizes of newborn stars in a cluster (the initial-mass function) and the identity of normal (baryonic) dark matter in the universe.

Motivated by such questions, teams of astronomers launched a celestial hunt for other worlds in the early 1990s. The trail has led to a series of surprising discoveries beginning with the very first detection of an extrasolar planet in 1991. It so happened that this object was orbiting an exotic variety of “dead” star-a pulsar, which is a rapidly spinning neutron star that emits powerful radio waves. No one expected pulsars to have planets because the supernova event that produces a neutron star was supposed to have obliterated or otherwise vanquished any surrounding planets.

Extrasolar planets were eventually found in orbit around conventional stars in 1995, but these too were peculiar systems. Many proved to have Jupiter-sized planets with very tight orbits (of less than 5 days). These hot Jupiters didn’t conform to the contemporary models of planetary-system formation, which placed such gas giants at great distances from the central star with orbital periods more like that of our own Jupiter-nearly 12 years.

With all the surprises that these other “solar systems” held for astronomers, perhaps it should have been expected that the free-floating worlds would provide their share of upsets as well. Oddly, in view of the clamor that now surrounds the free-floaters, their first discovery in 1998 was reported with little or no fanfare. Buried in the middle of an article on young brown dwarfs by Motohide Tamura, of the National Astronomical Observatory of Japan, and his colleagues was a casual note that some of the objects they observed were below the brown-dwarf boundary (about 13 Jupiter masses), and so in the “giant planet mass regime.” Thirteen Jupiter masses is the threshold at which an object begins to fuse deuterium (an isotope of hydrogen) and so is sometimes considered to be the lower limit of “brown dwarfdom.” Because the Japanese scientists were so modest about their discovery, it did not actually become widely known for a couple of years (see “Free-Floating Planets,” May-June 2000).

Tamura and his colleagues found these planet-sized bodies during a search for low-mass young stellar objects in the Chamaeleon I molecular clouds, a rich star-forming region (see also “Protostars,” July-August 2001). In retrospect it’s not surprising that the first free-floaters were found in one of these regions. Because young “planets” still retain some of the heat generated during the accretionary process that forms them, their warm glow can be recognized with the same infrared detectors that astronomers use to observe brown dwarfs and very young stars.

Similar investigations of low-mass objects in star-forming regions eventually led to more discoveries in 2000. In the spring of that year a British pair, Philip Lucas and Patrick Roche, reported perhaps 13 free-floating candidates in the heart of the Orion Nebula (M42), a star-forming region 1,500 light-years away. According to the authors, several of these objects were below 13 Jupiter masses. Like Tamura’s studies, the identity of these objects hinges partly on their age. If they are very young, perhaps only a million years old, then their brightness (luminosity) corresponds to objects the size of giant planets.

Some astronomers questioned the Lucas and Roche discoveries, arguing that these objects are intrinsically brighter than they appear, actually lying behind the Orion Nebula, and so only look like young planets because they are dimmed by the dust in the nebula. If so, the objects would actually have the masses of brown dwarfs. Others questioned whether these objects should be called planets at all. Alan Boss of the Carnegie Institution believes that mass should not be the defining characteristic of a planet, but rather how it was formed-within a protoplanetary disk around a young star. Boss has suggested a mechanism in which planet– sized objects are made in much the same way that stars are formed. Such objects would not be planets, but rather “sub-brown dwarfs.”

Shortly after the Lucas and Roche discoveries, a second group of astronomers reported the detection of free-floaters in another part of the Orion constellation. Maria Rosa Zapatero Osorio, now at the California Institute of Technology in Pasadena, and her colleagues discovered 18 faint, red free– floaters in long-exposure images of a cluster near the star Sigma Orionis. The region is only about 1,000 light-years from Earth and is home to a nest of newborn stars, perhaps only 1 million to 5 million years old. Situated among the young stars are a number of objects with very cool temperatures, about 1,700 to 2,200 kelvins. (By comparison, the temperature of the Sun’s atmosphere is about 5,800 kelvins.) Because of their young age and relatively cool temperatures, the astronomers calculate that these objects must be quite “small,” perhaps 5 to 15 Jupiter masses. And they tread carefully in identifying these objects, referring to them as “young, isolated planetary mass objects” in the title of their paper.

More recently, Lucas, Koche and colleagues came back in the autumn of 2001 with results they say confirm their earlier observations that the free– floaters do indeed lie within the Orion Nebula, and so must be planet-sized objects. Their spectroscopic studies of the Orion free-floaters indicate the presence of water, suggesting that the objects are young (about one million years old) and of low mass. At this point they believe they have found about 15 planetary mass free-floaters. Hoping to sidestep some of the naming controversy, they coined a new term for planet-sized objects that do not orbit a star: “planetars.”

The common thread in all of these reports is the discovery of the free– floaters within groups of newborn stars. The stars within these groups eventually disperse with time, either because they are not gravitationally bound to one another (loose associations), or because they are small enough (so-called open clusters) to be decimated by galactic tides on a timescale of a few billion years. Except for those paired with other stars in multiple-star systems, these field stars will eventually wander alone through the galaxy, much as our sun does. It seems reasonable to assume then that any planet-sized free floaters formed within the open cluster will also disperse with the tides. Once freed from their birthplace, these wanderers must be very cold, dark and lonely worlds, and they would be exceedingly difficult to detect.

Floaters in Globulars?

There is another place where the free– floaters might be found-within the very dense stellar confines of a globular cluster. Unlike the young associations in a stellar nursery, globular clusters consist of stars that are gravitationally bound to one another. And rather than being only a few million years old, the globular clusters are ancient objects, some more than 10 billion years old. Given the differing properties of these two environments, it may seem odd that both could provide fertile hunting grounds for free-floaters. Yet this may well be the case.

The first search for planets in a globular cluster did not consider the free– floaters at all. In July 1999 Ronald Gilliland and his colleagues observed nearly 34,000 stars in the globular cluster 47 Tucanae (Tuc) using the Wide Field Planetary Camera 2 on the Hubble Space Telescope. Globular cluster 47 Tuc is one of the largest and densest in our galaxy, containing perhaps several million stars. The core is so densely packed that nearly 3,000 stars reside within every cubic light-year. (Some globulars have a core density approaching 3 million stars per cubic light-year!) By comparison there is only a single star inside a one-light-year cube centered on our sun, and the nearest star is more than four light– years away. Because 47 Tuc is very old, Gilliland’s team hoped that their search would shed some light on the planetary systems of ancient stars.

The Space Telescope was aimed to detect the transit (crossing) of hot Jupiters in front of their parent stars. Such transits can be detected because the star dims slightly as the planet crosses in front of it. Theoretical considerations, based on the frequency of hot Jupiters in the solar neighborhood, suggested that the hunt in 47 Tuc should uncover about 20 hot Jupiters, roughly one for every 1,700 stars. When it was all said and done, however, they actually found zero planets.

So what is going on? There are a couple of explanations. One possibility depends on the apparent relation between the chemical composition of a star and its predilection for hot Jupiters. In the search for extrasolar planets in the solar neighborhood, astronomers have discovered that metal-rich stars (those with a relatively high abundance of elements heavier than helium) are at least 10 times more likely to have planets with short orbital periods than are the metal-poor stars. The reason for the relation is being explored by astronomers, but here we need only point out that the ancient stars in 47 Tuc are generally poor in metals (about one-fifth of solar levels) because they were formed early in the Galaxy’s history, before the heavier chemical elements had been synthesized in great abundance. Interestingly, an extrasolar planet in orbit around a pulsar was found in the low-metallicity globular cluster M4. (See also “The Formation and Evolution of the Milky Way,” November-December 2001).

Yet another possibility is that the dense cluster environment somehow inhibits the formation of planets or perhaps limits the orbital migration of the gas giants toward their parent stars. It may also be that planetary systems do form within the globular cluster, but are soon disrupted by stellar collisions with neighboring stars owing to the density of the cluster. If so, the planets in these colliding systems might be set free of their parent stars. Since Gilliland’s team was looking only for transiting events of hot Jupiters, they would not have spotted these free-floaters.

A report in the summer of 2001 had originally described some candidates for free-floating planets in the globular cluster M22 using the technique of gravitational microlensing. It turned out, however, that cosmic rays had hit the camera and fooled the astronomers into believing they had discovered the planets.

Where Have All the Planets Gone?

What should we make of the null detection of extrasolar planets in the globular duster 47 Tuc? We must first appreciate that the life of a planet inside a globular cluster must be very different from one circling a star in a less dense neighborhood. The encounters and outright collisions between the stars in these densely populated regions must have profound consequences on the integrity of the planetary systems. With the 47 Tuc results in mind, a number of astrophysicists, including ourselves, have attempted to model the fate of planetary systems in these environments.

First we must create a reasonable facsimile of a globular cluster. This turns out to be a tricky proposition. Although there are various ways to construct a computer model of a stellar cluster, our approach attempts to follow the behavior of each star in a so-called N-body simulation. The enormous number of stars in a globular cluster makes this a major computational challenge. In practice we simply cannot consider the interactions of millions of stars, and our current simulations involve on the order of 104 stars. Even this number of stars requires special-purpose hardware specifically designed for the task. The latest incarnation of these computers is the GRAPE-6 (GRAvity PipE), a powerful machine-capable of 1.0 teraflops (Tflops, one trillion floating point operations per second)-developed by Jun Makino and his team at the University of Tokyo. (A 0.5 Tflops prototype GRAPE-6 board was used to generate the results presented here.

In addition to special hardware, sophisticated software is needed to model the processes inside a stellar cluster. For the past 30 years, the state-of-theart N-body algorithms have been provided by the work of Sverre Aarseth of the Institute of Astronomy in Cambridge, England. He and his colleagues have generated a succession of N-body codes of increasing efficiency and realism. Aarseth’s NBODY4 code, which was used in our simulations, was developed to run on the GRAPE machines. (The logic of the system is shown on page 144.)

The first step is to set up the initial conditions inside the globular cluster. This includes such variables as the initial mass function, the stellar metallicity, the number of binary star systems and their orbital characteristics, the number of planets and the stellar density distribution. The masses, positions and velocities of the cluster stars are also constrained by the requirement that the cluster begins in virial equilibrium-a general property of gravitationally bound systems, which states that the absolute value of the potential energy is twice the value of the kinetic energy within the system. These considerations define a “zero-age” cluster, in which all star formation has ceased and all residual gas has been removed.

Once the system has been described, it’s “just” a matter of letting the particles (stars and planets) interact according to Newtonian physics-calculating the force on each particle and correcting its position and velocity with the next increment of time-while also taking account of the evolution of the stars and binaries.

All of this takes place in the context of various astrophysical processes, which are included in the computation during the integration, or evolution of the system. For example, we also consider the evolution of the cluster itself, which involves core collapse (the progressive increase in the density of the central core) while the cluster loses stars (evaporates) due to tidal forces in the Galaxy. We believe this integration scheme gives us a good idea of how real globular clusters with hundreds of thousands or millions of stars might behave.

We ran three simulations in which we followed the evolution of 22,000 cluster stars (10 percent were binary-star systems), plus 2,000 to 3,000 planets the size of Jupiter. The simulations differed from one another slightly in their metallicity and the orbital separations between the planets and their parent stars. Each simulation was allowed to evolve to an age of 4.5 billion years-the age of our solar system.

The planets, each in orbit around a star at the beginning of the simulation, experienced a variety of fates. After 4 billion years-when only about 25 percent of the cluster’s original mass remained-about 10 percent of the planets had been liberated from their parent stars, and about 13 percent of these still remained in the cluster. Nearly 66 percent of the planets escaped the cluster still attached to their parent stars, about 1 percent were swallowed by their parent stars, and nearly 4 percent were exchanged into orbit around another star.

The results also show that planets in wide orbits-about 50 Astronomical Units (AU) away from their parent stars (one AU is equal to the average distance between the Sun and the Earth)-are about 10 times more likely to be separated than planets only 1 AU away. Although planets are preferentially liberated in the dense core, nearly half are freed with a velocity less than the cluster’s escape velocity. This means that most of the free-floaters become orphaned deep within the cluster and then slowly diffuse to the outer regions of the cluster. Within the cluster, the average position of the free-floating planets lies just outside the half-mass radius (within which half the cluster’s mass lies). And the planets take about 200 million years to move from the core to outside the half-mass radius.

Most of the planetary systems that escape the globular cluster do so because the galactic tidal field strips away the stars in the outer parts of the cluster. A smaller number of stars and planets are ejected from the cluster when they attain escape velocity through an encounter with another star, but most encounters are more likely to result in the liberation of a planet rather than ejection from the cluster.

These results are intriguing because they do suggest that a good number of Jupiter-sized, free-floating objects should still be found in a typical globular cluster, even after billion of years of stellar billiards.

It is still too early to assess the significance of the 47 Tuc results. It’s been suggested that future surveys for planetary systems should be conducted in clusters less dense than 47 Tuc, such as a metal-rich open cluster. At the moment it’s not clear whether the lack of hot Jupiters in 47 Tuc is due to the low metallicity of the cluster or the dynamic interactions inside it.

As we expand the number of parameters in our N-body simulations, we should be able to create more realistic models, such as the inclusion of multiple planets per star. The full 1.0 Tflops GRAPE-6 hardware is now available, and it will allow us to simulate about 100,000 particles in a reasonable period of time-and so reach the realm of real globular clusters.