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]

Near A Black Hole

In the heart of the Milky Way galaxy is a supermassive black hole with about 4 million times the mass of our Sun. Data gathered over the past 17 years (between 1995 and 2012) by the Keck Observatory in Hawaii has revealed the presence of a star with the shortest known orbital period around the supermassive black hole. To compensate for the distorting effects of the Earth’s atmosphere, a combination of speckle imaging (1995 to 2005) and adaptive optics (2004 to 2012) observations were used. Named S0-102, this star orbits the supermassive black hole with a period of just 11.5 years. The previous record holder was S0-2 which has an orbital period of 16 years.

The gravitational potential in this region of the galaxy is dominated by the supermassive black hole and effects arising from the curvature of space time due to the strong gravitational field are expected. Deviations in the orbits of S0-102 and S0-2 from pure Keplerian orbits are likely to be detected in future. These 2 stars will be useful for testing Einstein’s General Theory of Relativity. Furthermore, the wavelength of light being emitted by S0-102 and S0-2 is expected to be gravitationally redshifted to a detectable amount. The gravitational redshift will be largest when the star is at closest approach to the supermassive black hole.

Paraterraforming: Creating Habitable Worlds

It’s really incumbent upon us as life’s agents to extend life to another planet. I think that being a multi-planet species will significantly increase the richness and scope of the human experience.

- Elon Musk, founder of SpaceX, interview in Ad Astra, 2006

The quality of a civilization is measured not by what it has to do, but by what it wants to do.

- Bruce Murray, research scientist, Exploring Space, 1991

Terraforming is the process of modifying a planet, moon or any other suitable object in order to make it habitable for humans. The word terraforming literally means “Earth-shaping”. Mars is often regarded as the first candidate for terraforming because it is the most Earth-like planet in the Solar System. Early in its history, Mars is believed to be a lot more like Earth with a significantly thicker atmosphere and abundant liquid water on its surface. Today, transforming Mars into an Earth-like world through terraforming will require thickening its atmosphere, warming up the planet and keeping the atmospheric constituents from escaping into space. Such an endeavour will require numerous technological breakthroughs and demand huge economic resources. Furthermore, terraforming Mars is a gradual process which is expected to occur over a timescale that is likely to exceed a human lifespan and the lack of gratification in return for investment will deter initial investors. For these reasons, paraterraforming serves as an attractive intermediate step before full terraforming is achieved.

Figure 1: Artist’s impression of a terraformed Mars.

 Figure 2: Artist’s impression of a terraformed Venus.

Paraterraforming involves the construction of a pressurised habitat in the form of an air-tight roof over a particular area on a planet where an Earth-like environment is completely enclosed within the habitat. A modular, “pay-as-you-go” approach of expansion is possible for paraterraforming and this allows it to appropriately meet increasing demand. As the population increases, more pressurised habitats can be constructed over the surface of a planet until most of the planet’s surface is covered or until full terraforming of the planet is eventually achieved.

A typical habitat can consists of an ultra-strong membrane that is primarily supported by the air pressure contained within it. The membrane acts as a roof over the surface of the planet, allowing sunlight in and preventing the atmosphere from escaping. At regular intervals, tension cables or support towers can anchor the membrane to the surface of the planet. To support a more Earth-like hydrological cycle, the membrane needs to be at least a few kilometres above the planet’s surface so as to provide sufficient altitude for clouds to form. A higher membrane height is also advantages for aerial transport within the habitat. To deal with the occasional meteor strike, the membrane should be designed to be capable of self-repairing.

An object that is somewhat less massive than Mars will be unsuitable for terraforming since its gravity will be too weak to hold on to an Earth-like atmosphere for long. Therefore, one key advantage of paraterraforming over terraforming is that paraterraforming can be done on objects much less massive than Mars since the atmosphere is contained by the overlying membrane rather than by gravity. As a result, even small objects such as asteroids can be paraterraformed since an Earth-like atmosphere can be contained around an asteroid by a membrane which completely envelops the asteroid. This creates a habitable environment which fully encompasses the asteroid. A paraterraformed asteroid will be rather interesting as a habitat due to its very low gravity environment.

Paraterraforming also allows the creation of Earth-like habitable environments on worlds that are too cold to support life. Such places include asteroids beyond the orbit of Mars, the satellites of the gas giant planets, comets and Kuiper Belt Objects (KBOs). The paraterraforming membranes that are used to envelope such objects can be designed to provide the necessary super-greenhouse effect to create Earth-like habitable environments at large distances from the Sun. Many of these objects are small enough that a single membrane is sufficient to completely envelope such an object. A paraterraformed comet completely enveloped within a membrane that provides a strong greenhouse effect will melt and eventually settle as a sphere of water with denser rocky material gravitationally settling in its core.

Failed-Detonation Supernova

Type Ia supernovae are known to originate from the thermonuclear explosions of carbon-oxygen (C-O) white dwarf stars. A common pathway for the production of a type Ia supernova begins with a C-O white dwarf accreting matter from a nearby companion star. As the mass of the white dwarf grows towards the Chandrasekhar mass-limit, unstable thermonuclear burning will eventually ignite at some position within the white dwarf. This sets off a buoyancy-driven deflagration flame which rises and burns its way towards the surface of the white dwarf.

In a conventional type Ia supernova, the deflagration flame will transition to a detonation flame as it enters the lower density outer layers of the white dwarf. The detonation flame then consumes the entire white dwarf and the energy release from thermonuclear burning causes the whole star to explode violently as a type Ia supernova. The difference between a deflagration flame and a detonation flame is that the latter propagates faster than the local speed of sound in the white dwarf. As a result, a detonation flame is able to consume the entire white dwarf since the material in front of the detonation flame is unable to “see” the approaching flame front.

However, it is possible to have a failed-detonation scenario where the deflagration flame fails to transition to a detonation flame. This may explain a peculiar subset of type Ia supernovae that are characterised by low ejecta velocities, low luminosities and low ejecta masses. A failed-detonation type Ia supernova occurs when enough mass is burnt during the deflagration phase such that the conditions necessary for the deflagration flame to transition to a detonation flame cannot be achieved and the white dwarf fails to detonate. In this scenario, thermonuclear burning during the deflagration phase delivers energy to the white dwarf, causing the star to expand and then contract. Because too much energy is delivered to the white dwarf, it is unable to attain high enough densities and temperatures to launch a detonation flame during maximum contraction.

For a failed-detonation type Ia supernova, the white dwarf will remain intact as the deflagration is too weak to completely unbind it. However, the white dwarf will now have a lower mass as the failed-detonation event is expected to produce a few tenths of a solar mass of ejecta. The thermonuclear fusion processes occurring within the deflagration flame results in ejecta that is rich in intermediate-mass elements (magnesium, silicon and sulphur) and iron-group elements (iron, cobalt and nickel). A significant proportion of the heavy elements are expected to fall back to the white dwarf and gravitationally settle to form an iron/heavy-core at its centre. The end result is an iron/heavy-core C-O white dwarf.

Due to the highly asymmetric nature of the outburst, the white dwarf will receive a kick velocity of a few 100 km/s. Even so, the large orbital velocities found in most binary star systems suggest that even a kick velocity of a few 100 km/s may be insufficient to unbind the binary. However, for binary systems consisting of a white dwarf accreting matter from an evolved star such as a red giant, the natal kick velocity is likely to unbind the system because of the large binary separation between the white dwarf and the red giant. It is also possible for the natal kick from the asymmetric outburst to launch the white dwarf towards its companion star and this should produce very interesting results.

Reference:

George Jordan IV, et al., 2012, “Failed-Detonation Supernovae: Sub-Luminous Low-Velocity Ia Supernovae and Their Remnant-Kicked Iron-Core White Dwarfs”, arXiv:1208.5069v1 [astro-ph.HE]

Plutonium-238 for Deep Space Exploration

A radioisotope thermoelectric generator (RTG) is a type of power generator which converts heat produced from the decay of a suitable radioactive material into electricity. Plutonium-238 is normally employed in RTGs because it has a long half-life of 87.7 years and is a very powerful alpha emitter that does not emit other forms of more penetrating radiation. Alpha radiation can be easily blocked by something as thin as a sheet of paper. RTGs are commonly used to power spacecraft that travel to places in the Solar System where solar cells are not practical and where the mission duration is too long for batteries or fuel cells to be used. One kilogram of plutonium-238 produces 560 watts of power in the form of heat. Examples of spacecraft powered by RTGs include the Cassini spacecraft in orbit around Saturn, the Curiosity rover on Mars and the New Horizons spacecraft on its way to Pluto and beyond. All these missions are made possible by the availability of Plutonium-238.

Figure 1: Artist’s impression of NASA’s Curiosity rover on the surface of Mars.

Figure 2: Artist’s impression of NASA’s Cassini spacecraft in orbit around Saturn.

The United States ceased producing plutonium-238 in 1988 and since 1993, all plutonium-238 used to power spacecraft for deep space exploration were purchased from Russia whose own supply is already running low. Production of plutonium-238 needs to be restarted soon in order to produce sufficient quantities to support future deep space exploration missions. In the past, plutonium-238 is produced from neptunium-237 extracted from spent nuclear fuel taken out from uranium-fuelled light water reactors (LWRs). When neptunium-237 is extracted, it is bombarded with neutrons to get neptunium-238 which beta decays into plutonium-238. Plutonium-238 cannot be directly extracted from spent nuclear fuel because the presence of uranium-238 in LWRs also leads to the production of other isotopes of plutonium from neutron absorptions. Spent nuclear fuel from LWRs typically contains slightly over 1 percent of plutonium-238 out of the total amount of plutonium produced. Since isotopes are chemically identical, it is almost impossible to separate out plutonium-238 and this makes it necessary to extract neptunium-237 out of the spent fuel to produce plutonium-238.

Figure 3: The series of neutron absorptions and beta decays leading to the production of plutonium-238 in a LFTR.

In a previous article titled “NuclearPower for Lunar Settlements”, a radically different type of nuclear reactor is described. This type of reactor is known as a liquid fluoride thorium reactor (LFTR) and it is basically a reactor where the nuclear fuel is in the form of a fluoride-based molten salt mixture. The operation of a LFTR is attractive for the production of plutonium-238 because almost all of the plutonium it produces is plutonium-238 and allows for the direct chemical extraction of plutonium-238. This is because uranium-238 is not present to produce other isotopes of plutonium. Since the nuclear fuel in a LFTR is fluid in nature, the plutonium-238 can be extracted using a small adjacent chemical plant while the LFTR continues running with no downtime incurred. In a LFTR, fissile uranium-232 that is bred from thorium-232 is used to generate energy through the fission process. For every 1000 kg of naturally occurring thorium that is fed into a LFTR, 15 kg of plutonium-238 is produced as the end product. In comparison, NASA’s Curiosity rover uses 4.8 kg of plutonium-238 while the Cassini spacecraft uses 33 kg of plutonium-238.

On Chariots of Fire

there was a time

we roared to the heavens on fire

and reached for another world

on a voyage of mythological proportions

slipping the bounds of Mother Earth

we leapt far enough

and saw ourselves for the first time

“My God!” we cried

we landed our vessels

and left footprints on an alien world

our ambitions were clear

as we sought new destinations

but the burdens of our world

held down the triumphs we had

the decades

they came and went

but the words echoed through time

that one small step!

that giant leap!

kept the dream alive

poised for flight

we dare once again

to reach for the heavens

on chariots of fire

Written by Xuan Yang Koh on Sunday, 26 August 2012, and this is dedicated to Neil A. Armstrong (1930 - 2012) and the Apollo Program.

Nuclear Power for Lunar Settlements

The Moon is often regarded as the next logical step in the expansion of human activities into space and it also contains resources which can be exploited for such purposes. Energy is required for these activities and to sustain human settlements on the lunar surface. A lunar settlement will have the same basic needs as any community on Earth, but it will have a number of unique constraints. The absence of coal, natural gas, petroleum, an atmosphere and any lakes or rivers severely limits the number of options available to provide power for a lunar settlement. Solar energy will be a tough option because a night on the Moon lasts 2 weeks and storing 2 weeks worth of energy will be a problem. Only lunar settlements at the poles of the Moon can benefit from solar energy as collectors can be erected on top of strategic mountain peaks at the poles where the Sun rarely sets.

It seems that nuclear energy is the only feasible option to power lunar settlements and to support the expansion of activities on the Moon. However, almost all commercial nuclear reactors used around the world today are uranium-fuelled light water reactors (LWRs) and the numerous disadvantages associated with such reactors make them unsuitable to power lunar settlements. As a result, a different type of reactor known as a liquid fluoride thorium reactor (LFTR) comes in as an attractive choice as it does not have the problems associated with uranium-fuelled LWRs.

In LWRs, U235 is the primary fissile material that is burnt to produce energy. LWRs use solid fuel rods that are arranged into fuel assemblies within the reactor core. The uranium in the fuel rods is enriched with 3 percent U235 and the rest is U238. Some fission energy is also generated from the fissioning of Pu239. Pu239 is produced when U238 absorbs a neutron. LWRs use ordinary water as both the coolant and moderator in the reactor core. Water boils at 100 degrees Centigrade at atmospheric pressure and this is insufficient to carry away the heat that is generated from the fission process in the reactor core. Therefore, water in a LWR needs to be pressurised up to over 150 times atmospheric pressure in order to bring up its boiling temperature for it to become an effective coolant. As a result, a LWR has to be designed as a pressure vessel and it has to be placed within a massive containment building to keep the high pressure steam from escaping in the event of an accident.

Named after the Norse god of thunder, thorium is a silvery-white metal that is slightly denser than lead. It is about 4 times more abundant than uranium in the Earth’s crust and it frequently occurs as a by-product from the mining of rare earth metals. All thorium in nature is found as Th232 which alpha decays with a very long half-life of 14.05 billion years. Within the Earth, the decay of radioactive uranium (U235 and U238), thorium (Th232) and potassium (K40) is responsible for generating most of Earth’s internal heat. Like on Earth, the Moon also contains abundant surface deposits of thorium which can be exploited to power LFTRs.

Figure 1: Global map of elemental thorium on the Moon. Credit: NASA.

A LFTR is a type of molten salt reactor (MSR) where the nuclear fuel is in the form of a fluoride-based molten salt mixture. In such a reactor, U233 is the fissile material while Th232 is the fertile material. The production of nuclear energy originates from the fissioning of U233. When a U233 nuclei absorbs a neutron, it fissions and produces an average of just over 2 neutrons. One neutron continues the chain reaction by causing another U233 nucleus to fission while the excess neutrons are used to create more U233 from Th232. U233 is created by exposing Th232 to neutrons. In this process, Th232 absorbs a neutron to become Th233 and after a couple of beta decays, U233 is produced. In such a fuel cycle, slightly more fissionable U233 is produced than consumed. Therefore, in the operation of a LFTR, all Th232 can be converted into fissionable U233 to produce energy.

A typical design for a LFTR consists of a core which contains fissile U233 and an outer blanket which contains fertile Th232. In the outer blanket, Th232 absorbs neutrons produced from the fissioning of U233 in the core and transforms into U233. The U233 that is produced in the outer blanket can be chemically separated continuously using a small adjacent chemical plant and then fed into the core as fission fuel. Since molten salts are used, a LFTR can operate at atmospheric pressure or lower. The heat produced during the fissioning of U233 in the reactor core mostly comes from the kinetic energy of the resulting fission fragments. The heated molten salt mixture is pumped from the core to a primary heat exchanger. Here, heat is transferred to a second loop of molten salt mixture which is pumped through an intermediary heat exchanger where it heats a working fluid. A typical working fluid is water which is heated to drive a turbogenerator to generate electricity.

Figure 2: Layout of a molten salt reactor (MSR). Credit: Generation IV International Forum (GIF).

To get a LFTR running, an initial load of fissile material will be required. Besides U233, U235 can also be used as the initial start-up material. Since a LFTR breeds slightly more U233 than it consumes, the excess U233 can be used to start-up new LFTRs. The technologies required to construct a LFTR were largely addressed successfully during the 1960s and 1970s. In fact, most of the technologies were tested in the Molten-Salt Reactor Experiment (MSRE) led by American physicist Alvin Weinberg at Oak Ridge National Laboratory (ORNL). The centrepiece of the MSRE was a fluoride-based molten salt reactor which employed U233 as the fissile material. The reactor went critical in 1965 and it operated until 1969 which at that time set the record for the longest continuous operation of a nuclear reactor.

Figure 3: Energy extraction comparison between a uranium-fuelled LWR and a LFTR.

Advantages of LFTRs over LWRs:

• For LFTRs, no reprocessing of naturally occurring Th232 is required since all of the Th232 can be converted into U233 and be burnt in the reactor to generate energy. Whereas for LWRs, fissile U235 makes up only 0.71 percent of naturally occurring uranium and it has to be enriched to about 3 percent through a complex process of isotope separation before being used as nuclear fuel. In LFTRs, all of the U233 can be burnt to generate energy. However, in LWRs, only a small fraction of the fuel in the fuel rods is burnt before the fuel rods become spent and must be replaced. As a result, LFTRs can produce up to a factor of three hundred times as much electrical power per unit mass of raw fuel ore than LWRs.
• Since LFTRs are basically tubs of molten salt, fuel fabrication is not needed at all. In the case for LWRs, the enriched uranium fuel needs to be fabricated into solid fuel rods before being inserted into the reactor. This is an expensive and lengthy process which imposes a much higher operational cost for LWRs. The simplicity of LFTRs is a huge plus point for powering lunar settlements since the facilities for enrichment and fuel fabrication are entirely unnecessary.
• Comparatively, LFTRs produce many times less radioactive fission products than LWRs. Furthermore, the fission products from LFTRs decay to background levels in less than 300 years but those from LWRs take over 10,000 years. This makes it much easier to have a repository to store nuclear waste from LFTRs. However, a lot of the “nuclear waste” from LFTRs have novel applications and are likely to be extracted for use rather then be tucked away in a repository.
• LFTRs offer much greater resistance to proliferation than LWRs. Although U233 in LFTRs is a fissile material, it is not an attractive bomb-making material since it contains small amounts of U232 which decays into products that emit highly energetic gamma radiation. Also, virtually all of the plutonium produced in LFTRs is Pu238 which is not a fissile material and cannot be employed in bomb-making. In comparison, the technology involved in the enrichment of U235 for LWRs can be extended to produce highly enriched weapons grade U235 for bomb-making. Additionally, fissionable Pu239 produced in LWRs from the absorption of fast neutrons by U238 is also a conventional bomb-making material.
• Unlike LWRs, LFTRs are not pressurized and do not need to be designed as a pressure vessel. This allows LFTRs to take on a much lighter design which makes them more feasible for space applications as it is a lot less costly to deliver a lighter reactor. Since LFTRs are not pressurized, they cannot explode or fail from overpressure which is a huge safety advantage over LWRs.
• During any fission process, large amounts of xenon and krypton gases are produced. In LWRs, these gases build up to high pressures within the cladding of the solid fuel rods and it can pose a serious problem during a heating transient or an accident. In LFTRs, these gases are continuously removed from the molten salt mixture and there are no confine spaces where these gases can build up to high pressures.
• The fluoride-based molten salt mixture employed in LFTRs is chemically stable and impervious to radiation. In LWRs, an overheating anomaly can dissociate water to produce combustible hydrogen gas which can accumulate and lead to an explosion as seen during the Fukushima-Daiichi nuclear accident. Since water is not present in the core of a LFTR, a hydrogen explosion is impossible for such a nuclear reactor. Finally, a fluoride-based molten salt mixture has a slightly higher volumetric heat capacity than water and this allows it to absorb more heat during heating transients.
• LFTRs can operate with overall thermal to electrical efficiencies that exceed 50 percent. In comparison, LWRs have overall efficiencies of only 30 to 35 percent.
• LFTRs do not experience downtime during refuelling since the nuclear fuel is in the form of a fluoride-based molten salt mixture and new fuel can be continuously fed into the reactor. This allows LFTR to produce power continuously. In comparison, LWRs will experience downtime during refuelling since the reactor must be shut down before the spent fuel rods can be taken out and replaced by new ones.
• The reactor core of a LFTR is fail safe since it contains a freeze plug at the bottom which has to be actively cooled using a small electric fan. If the cooling fails because of a power outage or an emergency, the freeze plug melts and the fuel gravitationally drains from the reactor core into a passively cooled storage facility which rapidly shuts down the reactor. Since the drained fuel does not require active cooling to keep it from overheating, an incident like the Fukushima-Daiichi nuclear accident is impossible to occur for a LFTR. Once the power outage or emergency is over, the drained fuel can be fed back to the reactor core and it is business as usual for the LFTR.
• Unlike a LWR, it is impossible for a LFTR to experience a nuclear meltdown since the fuel in the reactor core is already molten in normal operation.

With a LFTR, a lunar settlement can be entirely self-sufficient. Energy produced from a LFTR can be used to power a wide range of activities which include dissociating water to produce rocket fuel, growing food on the Moon even during the 2 week lunar night, processing lunar material, HVAC (heating, ventilation and air conditioning), life support systems, lighting, communications and the recycling of water, air and waste products. In fact, to power any settlement on any planet or moon in the Solar System, nuclear power generation systems, especially LFTRs, will be well suited for such purposes. This is because nuclear systems can provide power during the night, are not affected by the Sun’s proximity or orientation, can operate in dusty environments, are compact, have a high specific power, can be scaled to very high power levels, can potentially have very long lifetimes and can serve as a source of heat in addition to electricity generation.

Figure 4: This is a split image of Shackleton with elevation map (left) and shaded-relief image (right). Shackleton is a 21 kilometre diameter crater located adjacent to the lunar South Pole. Its interior is permanently shadowed and large deposits of frozen water are known to exist within it. Credit: NASA/Zuber, M.T. et al., Nature, 2012.

If the LFTR is such an attractive means of provide power to lunar settlements, they should also be very useful here on Earth as a cheap, clean, safe and reliable means of energy generation. In July 2001, the Generation IV International Forum which consists of a dozen or so governments was established to explore the feasibility and performance capabilities of the next generation nuclear energy systems. Listed are a number of competing technologies. Most of them are advances to existing technologies and only the molten salt reactor (MSR) is truly different from the rest. The LFTR is a type of MSR and its huge benefits have fuelled a renewed interest worldwide. There is sufficient easily accessible thorium on Earth to provide carbon-free energy to meet the world’s energy needs for many thousands of years. To sum up, LFTRs can deliver what fusion promises but without the numerous difficulties that plague conventional uranium-fuelled reactors.

Winds on Hot Jupiters

Hot Jupiters are a class of Jupiter-mass exoplanets that are characterised by high surface temperatures as they orbit very close to their parent stars. Most hot Jupiters have near-circular orbits with near-zero orbital eccentricities. A perfectly circular orbit is one where the orbital eccentricity is zero. There exist a fraction of hot Jupiters that have non-circular orbits with orbital eccentricities exceeding 0.1. One of the most extreme cases is the exoplanet HD80606b which has an orbital eccentricity of 0.93. Due to its large orbital eccentricity, the amount of flux HD80606b receives from its parent star varies by a factor of over 800.

Superrotation is a common phenomenon in atmospheric circulation models of hot Jupiters. Planetary scale waves in the atmosphere of a hot Jupiters converges angular momentum from the mid-latitudes towards the equator to generate an equatorial superrotating jet. The presence of an equatorial superrotating jet causes an eastward displacement of the hottest spot on the planet from the substellar point. Hot Jupiters in near-circular orbits are expected to be synchronously rotating where the same hemisphere of the planet perpetually facing its parent star like how the same hemisphere of the Moon always faces the Earth. This is due to the fact that the rotational and orbital periods of a synchronously rotating planet are equal. Things are different for hot Jupiters on non-circular eccentric orbits since they are expected to be pseudo-synchronously rotating where the same hemisphere of the planet does not perpetually face its parent star because the planet’s rotational and orbital periods are not equal. Instead, the same hemisphere of an eccentric hot Jupiter approximately faces its parent star only at closest approach during each orbit.

Figure I: Simulations of a hot Jupiter with an orbit-averaged stellar flux of 185691 W/m² where the orbital eccentricity is increased from zero (top row) to 0.75 (bottom row). Illustrated here are plots of the orbit-averaged zonal wind speeds (left column) and the wind and temperature profiles at 30 millibars in the atmosphere during closest approach (right column). The vertical bars in the right column denote the substellar longitude. (Credit: Tiffany Kataria, et al., 2012)

Models of atmospheric circulation of eccentric hot Jupiters have shown that at closest approach to their parent stars, dayside temperatures, day-night temperature differences and wind speeds all increase with increasing orbital eccentricity. In Figure I shown above, an orbit-averaged stellar flux of 185691 W/m² is employed for a hot Jupiter to model the effects of increasing orbital eccentricity on atmospheric circulation. As orbital eccentricity varies from 0 to 0.75, the peak temperatures at closest approach increase from 1000 to 1300 degrees Kelvin at the 30 millibar level in the atmosphere. Since the day-night temperature difference increases with increasing orbital eccentricity, the peak wind speed within the equatorial superrotating jet strengthens from 2500 m/s for a circular orbit to 5000 m/s for an orbital eccentricity of 0.75.

A larger orbital eccentricity also results in a shorter rotational period for the hot Jupiter which translates to an increase in rotational rate and a smaller Rossby radius of deformation. This is because the Rossby radius is inversely proportional to the square root of rotational rate. As a result, a hot Jupiter with a larger orbital eccentricity is expected to have a narrower equatorial superrotating jet since the width of the superrotating jet is directly proportional to the Rossby radius of deformation. In Figure I shown above, an orbital eccentricity of zero gives an average jet width of 100 degrees latitude while an orbital eccentricity of 0.75 gives an average jet width of 40 degrees latitude. Apart from the effects of orbital eccentricity, an increase in the orbit-averaged stellar flux shown below in Figure II also leads to strengthening and narrowing of the equatorial superrotating jet. A planet with a higher orbit-averaged stellar flux orbits its parent star at a smaller distance, resulting in a faster rotation rate and a narrower equatorial superrotating jet.

Figure II: Simulations of a hot Jupiter with an orbital eccentricity of 0.25. From top to bottom, the rows illustrate an increase in the orbit-averaged stellar flux. Shown here are plots of the orbit-averaged zonal wind speeds (left column) and the wind and temperature profiles at 30 millibars in the atmosphere during closest approach (right column). The vertical bars in the right column denote the substellar longitude. (Credit: Tiffany Kataria, et al., 2012)

Reference:

Tiffany Kataria, et al., 2012, “Three-dimensional atmospheric circulation of hot Jupiters on highly eccentric orbits”, arXiv:1208.3795v1 [astro-ph.EP]