Too Hot for Gas Giant Planets

The minimum temperature of protoplanetary disks around stars located in massive dense star clusters can exceed the temperature necessary for water ice to condense (~ 150 to 170 degrees Kelvin). Massive dense star clusters tend to form in single bursts of intense star formation where temperatures can remain too hot for water ice to condense on a timescale that is comparable to the planet formation timescale. This can inhibit the formation of gas giant planets as they only form in environments where the temperature is cool enough for water ice to condense. Irradiation experienced by a protoplanetary disk in a dense cluster environment is made up of flux from the stars in the cluster and flux from the central star. The minimum temperature of the protoplanetary disk is determined by the total flux it receives from stars in the cluster and if this component of flux is strong enough, it will result in a protoplanetary disk that is too hot for water ice to condense.

A protoplanetary core with about 10 Earth-mass is required for the formation of a gas giant planet. This is because only an object that massive is able to initiate the runaway accretion of hydrogen and helium from the protoplanetary disk to form a gas giant planet. In a typical protoplanetary disk where the temperature is cool enough for water ice to condense, the mass of all condensables is a factor of a few times higher than the mass of all rocky material. If the temperature is too high for water ice to condense, the protoplanetary disk will lack the surface mass density required for sufficient material to accrete and form a 10 Earth-mass protoplanetary core. Since the presence of a large amount of condensables is an essential requirement for gas giant planets to form, protoplanetary disks that are too hot for water to condense are expected to form only rocky terrestrial planets where they too are likely to be devoid of water. As a result, stars that form in massive dense star clusters may be devoid of gas giant planets and habitable planets.

There are a number of places which can have cluster environments that are massive and dense enough to keep temperatures above the water ice condensation temperature. Examples of such places include nuclear star clusters and the cores of globular clusters. The formation of stars in such environments is an exception rather than the norm. Searches for planets around stars in these places should turn up a paucity of gas giant planets if temperatures during their formative periods were high enough to prevent the condensation of water ice in protoplanetary disks around the clusters' stars. In fact, searches for gas giant planets around stars in the dense core of a globular cluster named 47 Tucanae turned up zero planets even though 10 to 15 of them were expected based on the known abundance of gas giant planets discovered around stars nearer the Sun. Lastly, in the cores of galaxies, accretion of material by supermassive black holes can put out enormous amounts of energy which can inhibit the formation of gas giant planets in protoplanetary disks around stars located up to great distances away.

4 Classes of Habitable Worlds

Over the past several years, the search for planets around other stars show that most stars harbor planets and terrestrial planets are indeed very abundant. This leads to the idea of defining the types of planets where life can exist. Since our Earth is the only viable example of a planet that is habitable, planets with environments that can potentially support the kind of life on Earth are investigated. For this reason, the kind of life that is considered here uses carbon-based molecules with liquid water as a solvent and has one or more sources of energy to support it. Speculative forms of life based on other substrates such as liquid ammonia or even plasma ions are not considered due to the absence of any such examples. With regards to detecting the signatures of life on an exoplanet or exomoon, a biosphere which significantly modifies the planetary environment is much easier to detect and characteristic. On the other hand, a subsurface biosphere is unlikely to modify its planetary environment in an observable way, making the detection of such biospheres extremely difficult.

Class I habitable worlds consists of Earth-like planets where liquid water and sunlight are available on the planet's surface. Here, life derives its energy from sunlight either directly through photosynthesis or indirectly by consuming things that do. Due to the abundance of energy, complex multi-cellular life can evolve and thrive on the planet's surface. Sun-like stars which comprise of F, G and K-type stars are the most suitable stars around which class I habitable worlds can exist.

Low mass red dwarf stars can also harbor class I habitable planets even though a significant fraction of such planets are probably tidally-locked. This is because atmospheric and oceanic circulation can be sufficient to distribute heat between the permanent day and night hemispheres to prevent temperature extremes from building up. Class I habitable planets can also exist within the habitable zones around white dwarfs or brown dwarfs. However, as the white dwarf or brown dwarf cools, the habitable zone will shrink and eventually leave the class I habitable planet out in the cold, beyond the outer edge of the habitable zone. This can turn a class I habitable planet into a class III habitable planet.

Figure: Artist’s impression of a class I habitable world.

Class II habitable worlds consists of planets where life can exist but the planet evolves differently from the Earth. This class of habitable worlds includes planets that initially harbored Earth-like conditions but had evolved to be unable to sustain surface liquid water. In this case, life could have migrated to whatever limited pockets of habitable environments that still remain. Venus and Mars are potentials candidates for class II habitable worlds. For Venus, life could have established itself in the cool upper atmosphere, and for Mars, life could have migrated down into deep subsurface aquifers.

Figure: Mars, a potential class II habitable world.

Class III habitable worlds consists of planetary bodies with subsurface oceans of liquid water that directly interact with a silicate core. On such a world, the surface temperature is too low for liquid water to exist on the surface and the subsurface ocean lies beneath a surface layer of ice. An example of a potential class III habitable world is Jupiter's moon Europa which may be the only place in the Solar System with a global subsurface ocean of liquid water that is in contact with a silicate core. The ocean on Europa is kept warm through tidal heating and it is expected to contain a factor of a few times more liquid water than all oceans on Earth combined. The benefit of being in direct contact with a silicate core at the bottom of the ocean is that interactions with silicates and hydrothermal activity can provide the ocean with materials that are essential for life. A class III habitable world can transform into a class I habitable world if the temperature on its surface exceeds 273 degrees Kelvin, allowing surface liquid water to exist.

Class IV habitable worlds consists of water-rich worlds with liquid water oceans existing above a layer of solid ice. Here, the water layer is thick enough that pressures at the bottom are sufficiently large for water to exist as high pressure forms of solid ice (ice polymorphs). In the solar system, examples of potential class IV habitable worlds include Jupiter's moons Ganymede and Callisto, and Saturn's moon Titan. For each of these 3 moons, their liquid water oceans are sandwiched between a thick overlying layer of normal ice and a bottom layer of high pressure ice.

Class IV habitable worlds also include "ocean planets" where the surface temperature is high enough for liquid water to exist, resulting in a deep surface ocean overlying a layer of high pressure ice. Such "ocean planets" have no analogues in the Solar System. For some "ocean planets", volcanic and tectonic activity can create undersea mountains that may be sufficiently high enough to penetrate above the layer of high pressure ice. This allows the ocean to have some interaction with silicates, thereby blurring the distinction between a class I and a class IV habitable world.

Figure: Artist’s impression of a class III or class IV habitable world where a liquid water ocean exists beneath the surface.

Potentially Habitable Planets around Gliese 667C

Gliese 667C is a low mass red dwarf star located at a distance of 22 light years away. It is one-third as massive as the Sun and has 1.4 percent the Sun's luminosity. Observations using the High Accuracy Radial Velocity Planet Searcher (HARPS) spectrograph mounted on the European Southern Observatory's (ESO) La Silla telescope have revealed the presence of multiple planets around Gliese 667C. HARPS detect planets by measuring the Doppler shifts in a star's spectrum caused by small gravitational tugs on the star by the possible presence of one or more planets orbiting the star.

The 6 Keplerian signals detected by HARPS for Gliese 667C is consistent with a system of up to 6 planets with orbital periods of 7.2, 28.1, 30.8, 38.8, 53.2 and 91.3 days. The 7.2 and 28.1 days signals correspond to the orbital periods of two previously known planets around the star. It should be noted that the signal with a period of 53.2 days may not be from a planet since this period also corresponds to the 2nd harmonic of the star's rotation. The five planets detected by HARPS with orbital period, distance and mass in parenthesis are:
Gliese 667Cb (7.2 days, 0.049 AU, 5.4 M_Earth),
Gliese 667Cc (28.1 days, 0.123 AU, 4.8 M_Earth),
Gliese 667Cd (30.8 days, 0.130 AU, 3.1 M_Earth),
Gliese 667Ce (38.8 days, 0.152 AU, 2.4 M_Earth), and
Gliese 667Cf (91.3 days, 0.268 AU, 5.4 M_Earth).

With only 1.4 percent the Sun's luminosity, the habitable zone around Gliese 667C is expected to be located much closer to the star. Here, the habitable zone is defined as the region around the star where temperatures are suitable for liquid water to exist on the surface of a rocky planet. As a result, the three planets with orbital periods of 28.1 days (Gliese 667Cc), 30.8 days (Gliese 667Cd) and 38.8 days (Gliese 667Ce) all happen to reside in the centre section of the habitable zone of Gliese 667C. Although the outermost planet Gliese 667Cf is just within the outer edge of the habitable zone, its eccentric orbit means that it actually spends most of its time beyond the habitable zone, possibly making it too cold to be considered potentially habitable. With 3 potentially habitable planets, Gliese 667C makes a particularly interesting target for follow-up observations that can determine the habitability of these telluric worlds.

Reference:

Philip C. Gregory (2012), “Evidence for Multiple Planets in the Habitable Zone of Gliese 667C: A Bayesian Re-analysis of the HARPS Data”, arXiv:1212.4058

Ocean Planets

An ocean planet is a class of planet whose entire surface is covered by an ocean of liquid water that is much deeper than the oceans on Earth. Up to half or more of the mass of an ocean planet can be in the form of water. In comparison, only 0.02 percent of the Earth’s mass is made up of water. This gives an ocean planet a lower bulk density than a rocky planet like the Earth, resulting in a larger diameter for a given mass in comparison to a rocky planet. A planet such as the Earth which formed close to its parent star tends to acquire much lower water content due to the scarcity of volatiles at close distances. In order to have such an enormous amount of water, an ocean planet will have to form in the cooler outer regions of the protoplanetary disk where it can acquire a water-rich cometary-like bulk composition. The planet subsequently migrates inwards into the habitable zone where it is warm enough for an ocean of liquid water to exist on the planet’s surface for it to become an ocean planet.

For a bulk composition by mass comprising of 1/2 water, 1/3 silicates and 1/6 metals, a 6 Earth-mass ocean planet will have 2 times the Earth’s diameter and 1.54 times the Earth’s surface gravity. In comparison, a rocky planet of the same mass with an Earth-like bulk composition by mass of 2/3 silicates and 1/3 metals will have 1.63 times the Earth’s diameter and 2.24 times the Earth’s surface gravity. With the given bulk composition, this 6 Earth-mass ocean planet is expected to have an interior structure which comprises of a thick water layer extending to a depth of 4800 km, followed by a silicate mantle from 4800 km to 8400 km and a metallic core from 8400 km down to the planet’s centre at 12800 km.

Only the uppermost portion of the thick water layer of this 6 Earth-mass ocean planet can exist as a liquid water ocean with thousands of kilometres of high pressure ice separating it from the silicate mantle beneath. This is due to the fact that at a certain depth beneath the surface, hydrostatic pressure becomes large enough for a high pressure phase of ice known as ice VI to exist. As a result, it is reasonable to consider how deep this liquid water ocean may be. Assuming an isothermal profile and surface temperatures of 0, 7 and 30 degrees Centigrade, the resulting ocean depths are estimated to be 40, 45 and 65 km respectively. Assuming an adiabatic profile and surface temperatures of 0, 7 and 30 degrees Centigrade, the resulting ocean depths are estimated to be 60, 72 and 133 km respectively. For both isothermal and adiabatic cases, a higher ocean surface temperature corresponds to a larger ocean depth. In reality, the ocean depth for a given surface temperature will be somewhere between the limits defined by the isothermal and adiabatic cases.

On an ocean planet, thousands of kilometres of high pressure solid ice separates the surface ocean from the silicate mantle. This inhibits interaction between liquid water and silicates which limits the availability of elements necessary for life (iron, magnesium, potassium, sodium, etc). However, such elements can still be delivered to the ocean by micrometeorites or be already present as dissolved material in the ocean. Although ocean planets have no analogues in the Solar System, searches for planets around other stars have revealed a number of planets that may turn out to be ocean planets.

Stellar Disruption from Accumulated Tidal Heating

Sagittarius A* is a 4 million solar mass supermassive black hole located in the centre of the galaxy. A disk of young stars surrounds Sagittarius A* and within the inner radius of this disk is a group of stars known as the S-stars. The S-stars are the closest stars known to orbit the supermassive black hole and they are young main sequence stars that are each several times more massive than the Sun. With new instruments, more stars with lower masses are expected to be found orbiting even closer to Sagittarius A*.

Figure: An infrared image of the galactic centre.

Stars orbiting sufficiently close to Sagittarius A* can accumulate tidal heating from multiple close approaches with the supermassive black hole. The amount of accumulated tidal heating can eventually disrupt the star even though its closest approach is a few times the tidal disruption distance which is the distance within which the gravity of the supermassive black hole becomes sufficiently strong to unbind the star. With each close approach, the star experiences tidal heating which causes the deposition and accumulation of heat in the star’s interior. As a result of this added source of energy, the star expands and becomes more bloated which reduces the binding energy of the star. Furthermore, tidal heating becomes stronger as the size of the star increases. This results in a runaway process and after a sufficient number of close approaches; the star becomes unbound, leading to its disruption.

Massive stars are more susceptible to eventual disruption by accumulate tidal heating. This is because the tidal disruption distance is larger for a massive star than for a low mass star. As a result, a low mass star can get closer to Sagittarius A* before being subjected to tidal disruption. Such a mechanism may explain the lack of high mass stars existing very close to Sagittarius A*. In light of new instruments that can detect lower mass stars, it can be conceived that there could be an increase in the fraction of low mass stars closer to Sagittarius A* since low mass stars can approach closer to the supermassive black hole without being disrupted by accumulate tidal heating.

Reference:

Gongjie Li & Abraham Loeb (2012), “Accumulated Tidal Heating of Stars Over Multiple Pericenter Passages Near SgrA*”, arXiv:1209.1104 [astro-ph.GA]

Keeping Hot Jupiters Inflated

Hot Jupiters are a class of extrasolar planets with similar characteristics as Jupiter but have high surface temperatures as they orbit very close to their parent stars. While Jupiter takes almost 12 years to orbit the Sun, many of these hot Jupiters take only a few days to orbit their parent stars. The discovery of a number of hot Jupiters with up to twice the radius of Jupiter is puzzling because as these planets age, they are expected to cool and contract to around the radius of Jupiter within the age of several million years. It seems that some process is at work to stall the contraction of these planets or to re-inflate them. A number of models such as intense stellar irradiation and tidal heating have been proposed to explain the observed radii of these inflated hot Jupiters. Nevertheless, these models are inadequate to fully account for the large radii of these planets.

Figure: Size comparison of WASP-17b (right) with Jupiter (left). Although WASP-17b is less than half the mass of Jupiter, it has an inflated radius that is about twice Jupiter’s radius.

A mechanism known as Ohmic heating was proposed by Batygin & Stevenson (2010) to explain the larger-than-expected radii of these hot Jupiters. Ohmic heating occurs when strong stellar irradiation partially ionizes the planet’s atmosphere and drives a surface wind which blows across the planet’s magnetic field. This induces a current which travels inwards into the deeper regions of the planet where the current is deposited as heat. Wu & Lithwick (2012) further proposed that Ohmic heating can stall the cooling contraction of hot Jupiters but cannot significantly re-inflate the radii of hot Jupiters that have already contracted.

For a hot Jupiter starting off in a state of high entropy where it has not previously cooled and contracted significantly, Ohmic heating can allow the planet to persist in a state of perpetual youth by keeping the planet inflated for billions of years. In the same radiation environment, a less massive planet can be kept inflated at a larger planetary radius than a more massive planet. With Ohmic heating, the radii at which contraction is stalled is consistent with the observed radii of most inflated hot Jupiters.

Inward orbital migration can transport a Jovian planet into a close-in orbit around its parent star a few million to a few billion years after the planet’s formation. For such a hot Jupiter, it is expected to have previously cooled and contracted significantly before being subjected to strong stellar irradiation and Ohmic heating. In this case, Ohmic heating becomes inefficient as it is unable to penetrate beyond the shallower layers of the planet since higher pressures are reached at shallower depths within the planet. As a result, the more the planet has contracted, the more inefficient Ohmic heating is in re-inflating the planet.

References:

1. Konstantin Batygin and David J. Stevenson (2010), “Inflating Hot Jupiters With Ohmic Dissipation”, arXiv:1002.3650 [astro-ph.EP]

2. Yanqin Wu and Yoram Lithwick (2012), “Ohmic Heating Suspends, not Reverses, the Cooling Contraction of Hot Jupiters”, arXiv:1202.0026 [astro-ph.EP]

Close-In Super-Earths

Results from Kepler and HARPS (High Accuracy Radial-Velocity Planetary Search) have shown that most Sun-like stars harbour close-in super-Earths. These planets have sizes between 2 to 5 Earth radii and orbital periods of less than 100 days, hence the term close-in super-Earths. The existence of such planets around most Sun-like stars suggests that the dominant mode of planet formation may not have occurred for our Solar System since it has no planet interior to Mercury’s 88 day orbit.

The population of close-in super-Earths is characterised by orbital periods ranging from days to weeks, mass ratios on the order of 1/10,000th to 1/100,000th the mass of the parent star and nearly circular orbits that are co-planar to within a few degrees for the known multi-planetary systems. Such characteristics resemble the satellite systems of our Solar System’s giant planets - Jupiter, Saturn and Uranus. This could mean that the formation process of close-in super-Earths may be more akin to the formation of satellite systems around the giant planets. Based on the characteristics of close-in super-Earths around Sun-like stars, red dwarf stars and brown dwarfs are correspondingly expected to be accompanied by close-in super-Earths and Earths. For red dwarf stars, many of these close-in super-Earths and Earths can be situated within the circumstellar habitable zone where a planet with sufficient atmospheric pressure can maintain liquid water on its surface.

Close-in super-Earths around Sun-like stars can form in situ from circumstellar disks of solids and gas extending interior to 0.5 AU and inward orbital migration is not required. The need for inward orbital migration was partly motivated by the minimum mass solar nebula (MMSN) which contains too little material inward of 0.5 AU to form close-in super-Earths. Since close-in super-Earths are the norm and our Solar System is probably the exception, the MMSN may not be the right approach to explain the formation of these worlds.

Instead, a minimum mass extrasolar nebula (MMEN) computed based on the super-Earths detected by Kepler is used to explain the formation of close-in super-Earths. With the MMEN, there exists sufficient material inward of 0.5 AU to form close-in super-Earths in the observed abundance around Sun-like stars. These planets form quickly, with a formation timescale that is orders of magnitude less than the circumstellar disk lifetime. Close-in super-Earths are expected to remain where they form because the largest velocity dispersion they can attain by mutual planet-planet scattering is much less than the escape velocity from the star.

Reference:

E. Chiang and G. Laughlin (2012), “The Minimum-Mass Extrasolar Nebula: In-Situ Formation of Close-In Super-Earths”, arXiv:1211.1673v1 [astro-ph.EP]

Contemplating Habitable Exomoons

With hundreds of known exoplanets and thousands more that will soon be confirmed, it is a natural consequence that moons will also exist around many of these exoplanets. Such a moon is known as an exomoon. The search for exomoons is already well underway for the Kepler space telescope and the first detected exomoon is expected to be roughly Earth-sized. A large number of Neptune-sized to Jupiter-sized exoplanets are known to orbit their host stars at the right distance where any Earth-sized exomoons orbiting such exoplanets could be potentially habitable.

This is an artist’s impression of Kepler-47c which is a Neptune-sized planet that orbits a binary star at a comfortable distance where an Earth-sized moon can be potentially habitable. (Credit: NASA/JPL-Caltech/T. Pyle)

Exomoons are attractive with regards to habitability for a number of reasons. An exomoon is expected to be tidally locked to its host planet and this ensures that exomoons in the stellar irradiation habitable zone (IHZ) have days that are shorter than their stellar year. This is advantageous for the habitability of Earth-sized exomoons in the IHZ of M-dwarf stars since an Earth-sized planet orbiting independently within the IHZ of an M-dwarf star is expected to be tidally locked to the star where the same hemisphere of the planet perpetually faces the star. Neptune-sized and Jupiter-sized exoplanets are likely to maintain their original spin-orbit misalignment than smaller planets. For this reason, an Earth-sized exomoon orbiting in the equatorial plane of such a planet is more likely to experience seasons than a single Earth-sized planet orbiting independently at the same distance from the star. Given the large number of Neptune-sized and Jupiter-sized exoplanets orbiting within the “Goldilocks” distance from their host stars, there is a possibility that habitable exomoons may outnumber habitable exoplanets.

Besides illumination from its host star, the habitability of an exomoon also depends on illumination from the host planet, tidal heating, constraints from orbital stability and eclipses when passing through the shadow of the host planet. There is an outer and inner limit to the range of distance where a habitable exomoon can orbit its host planet. The outer limit is defined by the host planet’s sphere of gravitational influence, beyond which the orbit of the exomoon becomes unstable to perturbations from the host star. The inner limit is defined by the minimum distance an exomoon can be from its host planet before tidal heating becomes significant enough to trigger a runaway greenhouse effect.

For a given planet-moon system, the distance between the outer and inner limit shrinks when the planet-moon system is moved from the IHZ of a G-dwarf star to a K-dwarf star and finally to an M-dwarf star. Our Sun is a G-dwarf star while M-dwarf stars are the smallest and most abundant class of stars. The range of habitable orbits ultimately vanishes for M-dwarf stars below 0.2 times the Sun’s mass. In the solar system, there is no moon with a mass that is in the range for habitable exomoons and the most massive moon, Ganymede, is only 0.025 times the Earth’s mass. As a result, it is unclear if exomoons as massive as Mars (0.107 times the Earth’s mass) or 10 times the mass of Ganymede can easily exist. However, given the unexpected diversity of known exoplanets, it is hard to not expect the existence of Earth-mass exomoons.

Reference:

René Heller and Rory Barnes (2012), “Constraints on the Habitability of Extrasolar Moons”, arXiv:1210.5172 [astro-ph.EP]

Assembling Extremely Massive Stars

Young and dense star clusters such as R136 in the Large Magellanic Cloud (LMC) and NGC 3603 in the Milky Way are known to contain the most massive stars known with masses that well exceed 100 times the Sun’s mass. These massive stars are thought to have formed through multiple stellar collisions in the dense environments found in such star clusters. An extremely high-mass star may also lead to the formation of an intermediate-mass black hole (IMBH) with 100 to 1000 times the Sun’s mass if the stellar collision rate is high enough to overcome the extraordinary mass-loss rate that such a massive star experiences. This process of multiple stellar collisions occurring in the heart of a dense star cluster is known as core-collapse.

To form extremely massive stars, the process of core-collapse in a dense star cluster has to take place early and quickly enough as the main-sequence lifetime of such stars is only a few million years. One way for this to happen is by the merging of a number of sub-clusters into one single star cluster. This is because the process of core-collapse takes place earlier and quicker in a sub-cluster than in a larger cluster. The merging of sub-clusters into one single star cluster creates an environment where the growth of extremely massive stars through multiple stellar collisions can take place much more efficiently. However, the merger of sub-clusters does not always lead to the efficient formation of extremely massive stars.

If the sub-clusters merge after each one has already experienced core-collapse (“late-assembling” case), multiple stellar collisions will result in the formation of a number of very massive stars instead of a single extremely massive star and the growth of very massive stars comes to a halt after the sub-clusters have merged. In this case, the most massive stars are expected to have around 200 to 400 times the Sun’s mass. Furthermore, very massive stars in each sub-cluster tend to form massive binaries. As the sub-clusters merge, many of these massive binaries in each sub-cluster will gravitationally interact with one another, causing some of the massive stars to collide and others to be ejected from the cluster.

The formation of extremely massive stars through multiple stellar collisions occurs most efficiently when the sub-clusters merge into a single cluster before core-collapse occurs (“early-assembling” case). In this case, the stellar collision rate is efficient enough to form a few or a single extremely massive star with around 1000 times the Sun’s mass. Such a massive star can collapse directly to form an IMBH.

An image from Hubble showing the star cluster R136 and its surroundings. (Credit: NASA and ESA)

R136 in the LMC is a dense cluster which contains some of the most massive stars known and it is more consistent with the “late-assembling” case. It consists of 5 very massive stars, each with over 100 times the Sun’s mass. The most massive member is R136a1 which is estimated to have 320 times the Sun’s mass at birth and has lost about 50 solar masses over the past million years or so. R136 has no evidence for any extremely massive star with 1000 times the Sun’s mass.

Reference:

M. S. Fujii and S. Portegies Zwart (2012), “The Growth of Massive Stars via Stellar Collisions in Ensemble Star Clusters”, arXiv:1210.3732 [astro-ph.GA]