Vulcanoids

Asteroids are the most abundant minor objects in the Solar System and most of them are distributed within the main asteroid belt between Mars and Jupiter, and in the two groups of Trojan asteroids located 60 degrees ahead of and behind Jupiter in its orbit around the Sun. Asteroids in these regions of the Solar System can reside stably over billions of years. Apart from these regions, are there other regions of the Solar System where long-lived stable belts of asteroids can possibly exist? In this article, I will describe the possibility of a long-lived stable belt of asteroids existing close to the Sun, in a region of space that is interior to Mercury’s orbit around the Sun.

Mercury is the closest planet to the Sun and it orbits the Sun at an average distance of 57.9 million kilometres or 0.387 AU, where 1.0 AU is basically the mean distance of the Earth from the Sun. The asteroids that belong to this hypothesized belt of asteroids that exists interior to Mercury’s orbit are referred to as the Vulcanoids. The Vulcanoids are a population of intra-Mercurial asteroids that exist in a region between 0.09 AU and 0.20 AU from the Sun. The inner edge of the Vulcanoid belt is approximately 0.09 AU from the Sun as any asteroid orbiting closer to the Sun than this will have an unstable orbit due to perturbation by the intense radiation of the Sun. On the other hand, the outer edge of the Vulcanoid belt is approximately 0.20 AU from the Sun as any asteroid located outside this boundary will be perturbed by Mercury’s gravity.

As the asteroids in the hypothesized Vulcanoid belt orbit the Sun at high velocities in a relatively small volume that is entirely interior to Mercury’s orbit, evolution through the mutual collisions of asteroids will be much more frequent than in the main asteroid belt between Mars and Jupiter. Models of the collisional processes have shown that for the Vulcanoid belt, only a few hundred asteroids larger than one kilometre in size could have survived until the current epoch. Because collisional evolution of asteroids proceeds fastest at smaller distances from the Sun, it has been proposed that a favourable location to search for existing Vulcanoids is near the outer edge of the Vulcanoid belt.

It is estimated that the region between 0.16 AU and 0.18 AU is most likely to contain surviving kilometre-sized Vulcanoids since objects near 0.20 AU from the Sun can get perturbed by the gravity of Venus. The closeness of the Vulcanoids to the Sun makes them extremely challenging to observe from the Earth. However, this closeness is expected to cause the Vulcanoids to be hot enough to give off a significant amount of infrared emission, making infrared detection methods the best choice for detecting the elusive Vulcanoids. To date, no Vulcanoids has yet been discovered and the Vulcanoid belt remains merely as a hypothesis.

Steppenwolf Planet

During the formation of planetary systems around stars, gravitational interactions with gas giant planets can cause some planets or planetesimals to enter hyperbolic orbits and get ejected into interstellar space. These objects will wander the dark and vast expenses of interstellar space as rouge planets. Several months ago, I wrote an article about the possibilities that a wandering planet in interstellar space can have a dense and high pressure atmosphere of hydrogen gas which can create a greenhouse effect that is strong enough such that liquid water can be maintained on the planet’s surface by the planet’s geothermal heat flux alone, making the planet potentially habitable. In this article, I explore the possibilities in which a planet wandering in interstellar space can be potentially habitable from an alternative mechanism that was recently published in a paper entitled “The Steppenwolf: A Proposal for a Habitable Planet in Interstellar Space”. This paper explores whether an Earth-like planet wandering in interstellar space can be potentially habitable by sustaining a subglacial ocean of liquid water.

In this case, an Earthlike planet means that the planet has a total mass and a water mass fraction that is within one order of magnitude of the Earth’s, and the planet also has approximately the same composition as the Earth. A rouge Earth-like planet wandering in interstellar space and harboring a subglacial ocean of liquid water is referred to in the paper as a Steppenwolf planet. Such a planet will have a layer of ice on top of a subglacial ocean of liquid water where the radiogenic geothermal heat flux from the interior of the planet prevents the liquid water from freezing solid. Furthermore, the overlying layer of ice acts an insulating layer which prevents the radiogenic geothermal heat flux from escaping too quickly into space, thereby trapping sufficient heat energy to sustain the subglacial ocean of liquid water.

The radiogenic geothermal heat flux is produced from the decay of radioisotopes in the interior of the planet and it is estimated to be sufficient to keep the subglacial ocean of liquid water from freezing for the duration of a few billion years. For instance, the Earth has a current average geothermal heat flux of 0.087 watts per square meter of the Earth’s surface and since this geothermal heat flux decays with time, the Earth is estimated to have a geothermal heat flux of twice the current value at around 3 billion years ago. After a few billion years, the decline in the amount of radioisotopes makes the rate of radiogenic heating insufficient to provide enough warmth to keep the subglacial ocean of liquid water from freezing. Hence, a Steppenwolf planet will have a habitable lifetime that is comparable to planets that are found in the traditional habitable zones of Sun-like stars.

The steady-state thickness of the layer of ice on a Steppenwolf planet depends on the amount of radiogenic geothermal heat flux being radiated by the planet. A greater heat flux will allow for a thinner steady-state layer of ice to exist above the subglacial ocean of liquid water while a lower heat flux will result in a thicker layer of ice. If the heat flux is too low, the resulting steady-state thickness of the layer of ice will be greater than the depth of the ocean and no subglacial ocean of liquid water will be possible in this case. In addition, volcanoes on continents or islands that rise above the layer of ice on a Steppenwolf planet can emit significant quantities of carbon dioxide, leading to the eventual formation of a thick cryo-atmospheric layer of carbon dioxide. Such a layer of carbon dioxide can raise the temperature at the top surface of the layer of ice and enable a significantly reduced thickness for the steady-state layer of ice overlying the subglacial ocean of liquid water.

Without a cryo-atmospheric layer of carbon dioxide, a Steppenwolf planet with the same radioisotope composition, age and water mass fraction as the Earth will have to be at least 3.5 times more massive than Earth in order to sustain a subglacial ocean of liquid water. In contrast, a Steppenwolf planet with ten times the water mass fraction of the Earth and with a thick cryo-atmospheric layer of carbon dioxide will require a mass of only 0.3 times the mass of the Earth for it to sustain a subglacial ocean of liquid water. The transport of heat up the layer of ice on a Steppenwolf planet can be assumed to be conductive in nature since any transport of heat by convecting ice is expected to occur only in the lower and warmer regions of the ice layer where it will be capped by an overlying lid of stagnant conducting ice.

Steppenwolf planets will be very challenging to detect as they wander through the dark and immense voids of interstellar space and produce no light of their own. However, if a Steppenwolf planet were to loiter close enough to our Sun, it could make its presence know by detecting the sunlight being reflected off its surface. For instance, a planned wide-field survey telescope known as the Large Synoptic Survey Telescope (LSST) will be able to detect a Steppenwolf planet out to a maximum distance of around 1000 astronomical units where one astronomical unit is the average distance of the Earth from our Sun. It should be known that only surveys that observe large regions of the sky continuously will be likely to discover any Steppenwolf planets because such planets can be anywhere in the sky. Finally, the discovery of any potentially habitable Steppenwolf planets will be rather exciting because it can mean that potentially habitable worlds are truly ubiquitous in the universe.

Hot Rock

Kepler-10b is the name of the first confirmed rocky planet that was discovered by NASA’s Kepler space telescope. The star around which Kepler-10b orbits is an old Sun-like star designated Kepler-10. This star has an estimated age of 12 billion years and it is located at a distance of 560 light years away. Kepler-10b orbits its host star at a distance of only 3.45 stellar radii, taking just 20 hours to complete one orbit! This means that Kepler-10b transits in front of its host star once every 20 hours. During each transit event which lasts for a duration of 1.81 hours, Kepler-10b induces a 152 parts-per-million dimming of its host star. Being so near to its host star, Kepler-10b is certainly tidally locked where the same hemisphere of the planet is perpetually locked to face its parent star. Therefore, one hemisphere of Kepler-10b is in perpetual daylight while the other hemisphere experiences eternal night. The equilibrium temperature on the dayside hemisphere of Kepler-10b is estimated to be over 1833 degrees Kelvin, which makes it hot enough to melt iron.

The diameter of Kepler-10b is measured to be 1.4 times the diameter of the Earth and the mass of Kepler-10b is estimated from radial velocity measurements to be 4.6 times the mass of the Earth. This gives Kepler-10b an estimated mean volumetric density of 8.8 metric tons per cubic meter, making it on average 1.6 times denser that the Earth. Within two standard deviations of its derived mass and diameter, Kepler-10b is unequivocally a high density rocky planet with a large fraction of its mass being in the form of iron. The official paper announcing the discovery of Kepler-10b is entitled “Kepler's First Rocky Planet: Kepler-10b” and it can be obtained from http://arxiv.org/abs/1102.0605.

As Kepler-10b orbits its host star, the observed amount of reflected starlight from the planet will vary because the planet will present different proportions of its illuminated hemisphere during different phases in its orbit. The amount of reflected starlight from the planet will be the lowest when the planet is directly in front of the star because a distant observer will be looking entirely at just the night side of the planet and none of the day side of the planet will be visible. On the contrary, the amount of reflected starlight from the planet will be the highest when the planet is almost directly behind the star because almost all of the illuminated day side of the planet will be visible. However, the amount of reflected starlight from the planet will be zero when the planet is directly behind the star as the planet will be blocked by the star.

NASA’s Kepler space telescope observed a 7.6 parts-per-million phase curve amplitude for the total photometric output centred on the host star of Kepler-10b each time the planet makes one orbit around its host star. Furthermore, as Kepler-10b passes directly behind its host star, a 5.8 parts-per-million dip in the total photometric output is observed. This gives Kepler-10b an estimated effective geometric albedo of 0.61 which makes the planet unusually reflective because the only objects in our Solar System with such a high albedo are the planet Venus with its reflective layer of photochemically induced hazes and Saturn’s moon Enceladeus with its global coat of fresh ice. One explanation for the high albedo of Kepler-10b is a reflective layer of silicate clouds that cover the entire day side of the planet. Because Kepler-10b is such a hot world, the silicate clouds are basically clouds that are comprised of tiny suspended droplets of molten rock.

Puffy Planet

A remarkable property of gas giant planets and brown dwarfs is that even though their individual masses can range from less than half the mass of Jupiter up to over 80 times the mass of Jupiter, they all have roughly the same diameters as Jupiter as their sizes do not increase with mass. This is because the volumetric size of a gas giant planet is governed by Coulomb pressure while the volumetric size of a brown dwarf is governed by electron degeneracy pressure and both of these forces neatly compensate for gravitational compression, giving approximately the same diameter as Jupiter for objects ranging in mass from gas giant planets to brown dwarfs. A significant number of extrasolar planets are known with diameters that are much larger than the diameter of Jupiter, making these planets larger than what is theoretically expected for them. Attempts have been made to explain the anomalously large diameters of these extrasolar planets by a number of proposed heating mechanisms that can potentially deliver enough thermal energy into the interiors of these planets to inflate them to their observed diameters.

The largest extrasolar planet currently known is a transiting planet called WASP-17b. This planet has 49 percent the mass of Jupiter and its orbit around its host star happens to be orientated in such a way that the planet is observed to periodically pass in front its host star. WASP-17b is located at a distance of 7.7 million kilometres from the centre of its host star and it takes 3.74 Earth-days to make one orbit around its host star. The host star of the WASP-17b is a spectral type F6V star with 1.3 times the mass of our Sun, an estimated surface temperature of 6650 degrees Kelvin and a luminosity that is over 4 times greater than our Sun’s luminosity. Looking from WASP-17b, its host star will appear almost two thousand times brighter than our Sun as seen from the Earth.

Measuring the fraction of starlight blocked by WASP-17b as it passes in front of its host star gives the planet an estimated size that is twice the diameter of Jupiter. Such a diameter also means that WASP-17b is up to 0.2 Jupiter diameters larger than the next largest planet and up to 0.7 Jupiter diameters larger than the theoretical diameter predicted using the standard cooling theory of irradiated gas giant planets. With twice the diameter of Jupiter and just under half the mass of Jupiter, WASP-17b has a density of just 6 percent the mean density of Jupiter or 8 percent the density of water, making it the least dense planet known. For such an inflated and low density planet, the surface gravity of WASP-17b is less than one-third the surface gravity of the Earth even though WASP-17b has slightly less than half the mass of Jupiter which already translates to 155 times the mass of the Earth.

The orbit of WASP-17b around its host star is slight non-circular with a very small non-zero orbital eccentricity. This means that WASP-17b is a little nearer to its host star than at other times. It has been suggested that a planet can be inflated to twice the diameter of Jupiter or more during a transient phase of heating caused by tidal circularization from a highly eccentric orbit to an almost circular one. In this scenario, the planet can persist in an inflated state for over a billion years after its orbit has circularized considerably. However, such a planet is expected to cool and contract significantly prior to complete orbital circularization where its orbit is still noticeably non-circular. Therefore, under the scenario of transient heating, the near-zero orbital eccentricity of WASP-17b and its highly inflated size means that a transient phase of tidal heating from orbital circularization alone is insufficient to have inflated the planet to its current observed size.

An enhanced atmospheric opacity for WASP-17b will enable its internal heat to be radiated off at a much lower rate and this can slow the contraction of the planet from a previous transient phase of tidal heating. However, even this is still insufficient to account for the current inflated diameter of WASP-17b. Ongoing tidal heating can still occur for WASP-17b if its orbit is being kept non-circular by interaction with another planet in the system. However, this is unlikely to be the primary source of heating to account for the inflated diameter of WASP-17b because its orbital eccentricity is too small for sufficient tidal heating to occur. Finally, the kinetic energy from the strong winds generated in the atmosphere by the large day-night temperature contrasts of the tidally-locked WASP-17b can be transported into the deep interior of planet and be deposited as thermal energy. However, a means to convert the kinetic energy into thermal energy will still be necessary and turbulent dissipation is one of the proposed mechanisms. To conclude, no current theory is able to account for the remarkable inflated diameter of WASP-17b.

New Worlds

NASA’s Kepler is a space telescope which hunts for planets around other stars by using a method called transit photometry. A transiting extrasolar planet is one which periodically blocks a small fraction of the light from its parent star as it passes in front. Transits only occur when a planet’s orbit around its parent star happens to be orientated almost edge-on with respect to our line of sight. Transit photometry works from observing the amount by which a star dims as a planet passes in front of it to determine the size of the planet. For the same star, a larger planet will occult a greater fraction of the star’s light as compared to a smaller planet. An Earth-size planet transiting a Sun-like star is expected to cause a mere 84 parts-per-million decrease in the star’s brightness and the incredible precision of Kepler’s photometer makes its suited for detecting such planets. Furthermore, by measuring the time between two successive transits, the orbital period and the distance of the planet from its host star can be determined.

The ‘Holy Grail’ for NASA’s Kepler mission is the eventual discovery of Earth-size planets orbiting in the habitable zones of Sun-like stars. However, this will require at least around 3 years of data collection by the space telescope, including a large amount of follow-up observations before these types of planets can emerge from the data. In the mean time, Kepler is already revolutionizing our understanding of extrasolar planets when on 1 February 2011, the Kepler mission team released data for 156453 stars that were observed by the Kepler space telescope from 2 May 2009 to 16 September 2009. During this period of observations, 1235 planetary candidates were detected and these planetary candidates are associated with 997 host stars. These planetary candidates are classified into five classes with 68 Earth-size candidates (less than 1.25 Earth-radii), 288 super-Earth size candidates (between 1.25 to 2 Earth-radii), 662 Neptune-size candidates (between 2 to 6 Earth-radii), 165 Jupiter-size candidates (between 6 to 15 Earth-radii) and 19 super-Jupiter size candidates (between 15 to 22 Earth-radii). For comparison, the radius of Neptune is about 4 Earth-radii and the radius of Jupiter is about 11 Earth-radii.

The planetary candidates in this first 4 months of data released by the Kepler mission team are strictly candidates only as each one of these planetary candidates will require rigorous follow-up observations in order for them to be confirmed as true planets. However, well over 90 percent of the 1235 planetary candidates are expected to be eventually confirmed as true planets due to the extremely meticulous vetting process through which these planetary candidates were extracted from the raw data in order to weed out events that are masquerading as transiting planets. The current set of data is restricted to planetary candidates with orbital periods of less than 125 Earth-days because planets with longer orbital periods will require more time by Kepler for multiple transits to be recorded.

It is interesting to note that out of the 68 Earth-size planetary candidates; around 2 dozen of them are actually somewhat smaller in size than the Earth. Furthermore, 54 of the 1235 planetary candidates are located within the habitable zones of their host stars and they have sizes ranging from Earth-size to larger than that of Jupiter. The habitable zone is basically defined as a region around a star where a rocky planet with an Earth-like atmosphere can have a surface temperature that lies between the freezing point and the boiling point of water. Of the 54 planetary candidates that are located within the habitable zones of their host stars, 5 of them are less than twice the size of the Earth while 2 of them are significantly larger than the size of Jupiter. Additionally, of the 5 approximately Earth-size planetary candidates, one of them is actually smaller than the Earth. Finally, it is also conceivable to expect the presence of potentially habitable Earth-size moons around some of the larger planets.

Of the 997 host stars that contain the 1235 planetary candidates, 170 of the host stars have two or more transiting planetary candidates. Of these 170 host stars, there are 115 stars with 2 transiting planetary candidates, 45 stars with 3 transiting planetary candidates, 8 stars with 4 transiting planetary candidates, one star with 5 transiting planetary candidates and finally, a single star with a staggering 6 transiting planetary candidates! In a recent press conference held on 2 February 2011, the 6 transiting planetary candidates orbiting that single star are no longer just planetary candidates as all 6 of them have been announced to be true planets orbiting the same star which has been named Kepler-11. The 6 planets are named Kepler-11b, 11c, 11d, 11e, 11f and 11g in order of increasing distance from Kepler-11. Since the size of a planet’s orbit is generally much larger than the physical size of its host star, being able to observe 6 planets transiting the same star means that the planetary system of Kepler-11 has to be remarkably flat where the orbital planes of all 6 planets have to be almost perfectly coplanar.

The planetary system of 6 transiting planets around the star Kepler-11 is an extraordinary and unprecedented discovery. The planets Kepler-11b, 11c, 11d, 11e, 11f and 11g have orbital periods of 10.30 days, 13.03 days, 22.69 days, 32.00 days, 46.69 days and 118.38 days respectively, sizes of 1.97 Earth-radii, 3.15 Earth-radii, 3.43 Earth-radii, 4.52 Earth-radii, 2.61 Earth-radii and 3.66 Earth-radii respectively and orbital distances of 13.6 million kilometres, 15.9 million kilometres, 23.8 million kilometres, 29.0 million kilometres, 37.4 million kilometres and 69.1 million kilometres respectively from their parent star Kepler-11. With so many transiting planets for a single star, observing more than one planet transiting the star at the same time is a rather frequent occurrence and on one occasion, the Kepler space telescope was observing three planets transiting the star Kepler-11 at the same time!

All the 6 planets around Kepler-11 have orbits that are almost perfectly circular and one of the most striking features is how close the orbits of the 5 inner planets are to one another. In fact, the inner 5 planets are all closer to their parent star than the planet Mercury is from our Sun and each of the 5 planets are not particularly small either as they have diameters ranging from two to over four times the diameter of the Earth. Dynamically, the inner 5 planets of the star Kepler-11 have one of the most densely packed configurations for any system of planetary orbits ever discovered. The 6th planet orbits significantly further from the star Kepler-11 than the inner 5 planets, but its orbit is still smaller than Venus’ orbit around our Sun!

The transits of a single planet around its host star are strictly periodic. However, for stars with more than one transiting planets, gravitational interactions among planets will cause the orbits of the individual planets to speed up and slow down by small amounts, leading to deviations from perfectly periodic transit timings. Such transit timing variations are strongest for stars with multiple transiting planets whose orbits are particularly close to one another, like in the case for the closely packed inner 5 transiting planets around the star Kepler-11. Hence, analysis of the transit timing variations have allowed the masses of the inner 5 planets around the star Kepler-11 to be estimated and this is the second time transit timing variation measurements have ever been employed to measure the masses of extrasolar planets.

Typically, the mass of an extrasolar planet is determined via radial velocity measurements by observing the Doppler shifts in the star’s spectral lines as the star wobbles back and forth periodically due to the gravitational tug of the orbiting planet. A large number of planets detected by Kepler will be very low mass planets and determining the masses of these planets by radial velocity measurements will not always be possible due to the incredibly small radial velocity amplitudes expected for such planets. Therefore, stars with multiple transiting planets offer a unique opportunity where any low mass transiting planets in such planetary systems can have their masses estimated from observations of transit timing variations which enables much smaller planetary masses to be measured as compared to radial velocity measurements. Knowledge about both the size and the mass of a planet allows the internal composition of the planet to be constrained.

The official paper detailing the release of the 1235 planetary candidates by the Kepler mission team is entitled “Characteristics of planetary candidates observed by Kepler, II - Analysis of the first four months of data” and it can be obtained from http://arxiv.org/abs/1102.0541. Additionally, the official paper on the 170 host stars with multiple transiting planets is entitled “Architecture and Dynamics of Kepler's Candidate Multiple Transiting Planet Systems” and it can be found at http://arxiv.org/abs/1102.0543v1. Finally, the paper confirming the planetary system of 6 transiting planets around the star Kepler-11 is entitled “A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11” and it can be found at http://arxiv.org/abs/1102.0291.

Galaxy Defined

What constitutes a galaxy? Over the past several years, the discovery of a number of very small galaxies has motivated some astronomers to reconsider the definition of a galaxy since there is currently no widely accepted standard definition for a galaxy. The tiniest galaxies have masses and sizes that are known to overlap with the largest globular clusters. Basically, a globular cluster is a gravitationally bound spherical collection of stars which can contain anywhere from a few thousand to several million stars. In comparison, a large galaxy such as the Milky Way galaxy contains hundreds of billions of stars, measures approximately 100000 light years in diameter and has a total mass that is around one trillion times the mass of our Sun. There are about 150 or so globular clusters that are currently known to orbit the Milky Way galaxy.

In recent years, the discovery of objects called Ultra Compact Dwarfs has shown that these objects have properties which blur the distinction between the smallest galaxies and the largest globular clusters. Ultra Compact Dwarfs generally contain on the order of one million to a hundred million times the mass of our Sun and they typically have sizes of around several tens of light years across. In the Local Group, Omega Centauri is the largest globular cluster in the Milky Way galaxy while Mayall II is the largest globular cluster in the neighbouring Andromeda galaxy. Omega Centauri is estimated to contain a total of 5 million times the mass of our Sun and Mayall II is believed to be twice as massive as Omega Centauri. These are among the largest globular clusters known and they clearly show properties which overlap with Ultra Compact Dwarfs. It has also been suggested that Omega Centauri and Mayall II may even be the remaining cores of tidally disrupted dwarf galaxies. Furthermore, the smallest ultra-faint Dwarf Spheroidal Galaxies also have properties which overlap with the largest globular clusters.

A number of requirements are discussed here that can help in distinguishing a small dwarf galaxy from a large globular cluster. To start off, the minimum requirement for a galaxy is that it has to be gravitationally bound and it must contain stars. This means that streams of stars and material that were ejected from the collision of galaxies and masses of starless ‘dark galaxies’ cannot be classified as galaxies. However, these requirements will still include all globular clusters and Ultra Compact Dwarfs as galaxies. Hence, a number of additional requirements and their implications will be discussed to better distinguish objects that have properties which are intermediate between the largest globular clusters and the smallest galaxies.

A gravitationally bound stellar system that is in a dynamically stable state will have stars whose orbits are determined by the mean gravitational field of the system rather than by encounters between individual stars. If a galaxy is defined as a dynamically stable gravitationally bound stellar system with a two-body relaxation timescale that is longer than the age of the universe, then Ultra Compact Dwarfs can be classified as galaxies but not globular clusters. In gravitationally bound stellar systems with deep gravitational potential wells, gases enriched with heavy elements created by nucleosynthesis processes from one or more episodes of star formation will remain gravitationally bound to the system. These enriched gases can be available for subsequent episodes of star formation, leading to populations of stars with different abundances of heavier elements. If a galaxy is required to have multiple populations of stars, then almost all Ultra Compact Dwarfs and the most massive globular clusters can be classified as galaxies.

The Milky Way galaxy is embedded within a massive halo of non-baryonic dark matter. If the presence of a massive dark matter halo is required for a stellar system to be classified as a galaxy, then globular clusters, Ultra Compact Dwarfs and some Dwarf Spheroidal Galaxies cannot be classified as galaxies. A known characteristic of all large galaxies such as the Milky Way galaxy and the Andromeda galaxy is that they all have systems of globular clusters and smaller satellite galaxies in orbit around them. If a system of globular clusters is required, then Ultra Compact Dwarfs and some dwarf galaxies will be unable to meet this requirement to be classified as galaxies. Finally, size can also be a requirement for defining what constitutes a galaxy. Ultra Compact Dwarfs generally have sizes of up to just over 100 light years across, while the smallest ultra-faint Dwarf Spheroidal Galaxies have sizes that are as small as 300 light years across. If a minimum size of 300 light years is a requirement for a galaxy, then all Ultra Compact Dwarfs and globular clusters cannot be classified as galaxies.

Gravitational Recoil

Supermassive black holes are the most massive type of black holes and they can contain between hundreds of thousands to billions of times the mass of our Sun. Almost all galaxies are known to harbour supermassive black holes within their cores. For example, the Milky Way Galaxy contains a supermassive black hole at its centre called Sagittarius A* and this behemoth packs around 4 million times the mass of our Sun. From time to time, galaxies are known to collide and eventually merge with one another. When two galaxies collide, the two supermassive black holes that are located in each of their galactic cores can eventually come close enough to each other to form a gravitationally bound binary pair.

As two supermassive black holes orbit around each other, the emission of gravitational waves will cause them to loose angular momentum and spiral towards each other, leading to an increasingly tighter orbit. The rate at which angular momentum is lost through the emission of gravitational waves increases dramatically as the two supermassive black holes get closer to each other, leading to a final inspiral that is followed by an eventual coalescence of the two supermassive black holes. During the final inspiral of the two supermassive black holes, the anisotropic emission of gravitational waves is able to impart a large gravitational wave recoil velocity to the final supermassive black hole. The final supermassive black hole can have a gravitational wave recoil velocity that is as large as 4000 kilometres per second.

A large gravitational wave recoil velocity can displace the supermassive black hole arbitrarily far from the core of its host galaxy, or even completely eject the supermassive black hole from its host galaxy if the gravitational wave recoil velocity is larger than the escape velocity of its host galaxy. In reality, the majority of coalescenced supermassive black holes will have gravitational wave recoil velocities that will be significantly less than the escape velocities of typical galaxies. Following a merger, the resultant supermassive black hole will be displaced at some maximum distance from the core of its host galaxy as a result of the gravitational wave recoil.

The supermassive black hole will oscillate a number of times through the core of its host galaxy with decaying amplitudes as it transfers its ‘excess’ kinetic energy gained from the gravitational wave recoil to the surrounding stars. This has the effect of reducing the density distribution of stars in the region of the host galaxy’s core that is near the supermassive black hole. The time required for the amplitude of the oscillatory motion of a ‘kicked’ supermassive black hole to eventually decay down to roughly the core radius of its host galaxy is on the order of a few hundred million years or less. For dwarf galaxies and globular clusters, the gravitational wave recoil velocities are more likely to completely eject most coalesced black holes from these systems due to their much lower escape velocities as compared to typical galaxies.

A supermassive black hole that is displaced from the core of its host galaxy is expected to carry with it an entourage of stars that remains gravitationally bound to the supermassive black hole as a densely packed cluster of stars. Such a cluster of stars is referred to as hypercompact stellar system and it differs from all the other types of star clusters by having an exceptionally high internal velocity distribution due to the deep gravitational potential well of the central supermassive black hole. The total mass of all the stars in a hypercompact stellar system is expected to be on the order of one percent of the mass of the supermassive black hole itself, making the cluster similar in size and luminosity to globular clusters. However, in extreme cases, the size and luminosity of a hypercompact stellar system can approach that of ultra-compact dwarf galaxies.

Although hypercompact stellar systems share similarities with globular clusters, they differ from globular clusters in two fundamental aspects which can help in the identification of these unique clusters. Firstly, hypercompact stellar systems have much higher velocity dispersions than globular clusters as the stars in hypercompact stellar systems have velocities that are on the order of a hundred to a thousand kilometres per second. This is comparable to the velocity imparted to a post-merger supermassive black hole from the gravitational wave recoil. Secondly, the stars in hypercompact stellar systems come from the cores of galaxies and they will exhibit higher metallicities than the stars in globular clusters. This is due to the multiple episodes of stellar evolution that occur in galaxies which enable subsequent generations of stars to be made up of a far higher proportion of elements that are heavier than hydrogen and helium as compared to the stars in globular clusters.

Fiery World

Well over 500 extrasolar planets have been discovered so far and this number of set to increase ever more rapidly. A large fraction of these extrasolar planets are known to transit their host stars and transiting extrasolar planets allow much more to be known about them than would have been otherwise. An extrasolar planet which passes in front and transits its host star is also likely to pass behind and get occulted by its host star. The occultation of the planet as it goes behind its host star allows the total thermal emission and total reflected light from the planet to be measured, thereby allowing the temperature of the planet to be determined. A recently published paper entitled “Thermal Emission from WASP-33b, the Hottest Known Planet” describes observations of the thermal emission from an extrasolar planet called WASP-33b and this planet is the first known to orbit an A-type star.

WASP-33b orbits its host star at a distance of just 3.82 million kilometres, making it 15.2 times closer to its host star than the planet Mercury is from our Sun. At such a close distance, WASP-33b takes just 1.22 Earth days to complete one orbit around its host star. The host star of WASP-33b is a spectral class A5 star that has 1.44 times the diameter of the Sun, 1.50 times the mass of the Sun, almost 6 times the luminosity of the Sun and a surface temperature of 7430 degrees Kelvin. WASP-33b is expected to be tidally locked whereby one hemisphere is locked to perpetually face its host star while the other hemisphere faces away from its host star. The mass of WASP-33b is deduced to be less than 4.1 times the mass of Jupiter while the diameter of WASP-33b is estimated to be almost 1.5 times the diameter of Jupiter.

Assuming an albedo of zero and uniform heat redistribution to the night-side, the equilibrium temperature of WASP-33b is estimated to be around 2700 degrees Kelvin. In comparison, the planet WASP-12b which was previously the hottest known extrasolar planet has an estimated equilibrium temperature of 2500 degrees Kelvin. Furthermore, the hottest temperature measured for WASP-33b stands at a blistering 3466 degrees Kelvin, making it the hottest temperature ever recorded for an extrasolar planet. At this temperature, metals such as iron, gold and aluminium will not be able to condense into a liquid from their gaseous forms. This huge temperature suggests that the heat transport from the day-side of the planet to its night-side is inefficient and this enables a very high temperature to persist on the planet’s day-side.

The sub-stellar point on the tidally locked WASP-33b is basically a spot on the planet where its host star is always directly overhead. On this blazingly hot spot, the host star of WASP-33b will appear around ten thousand times brighter than our Sun would appear on a clear day on the Earth. The amount of irradiation received by WASP-33b is so enormous that the total amount of energy incident on an effective area of just one square meter on the sub-stellar point on WASP-33b for a period of one year will equal the amount of energy released in a 90 kiloton nuclear explosion.

Ringworld

From a thousand miles above the Earth - from, say, a space station in a two-hour orbit - the Earth is a great sphere. The kingdoms of the world revolve below. Details disappear around the horizon's curve; other, hidden features rotate into view. At night, glowing cities outline the continents.

But from a thousand miles above the Ringworld, the world is flat, and the kingdoms thereof are all there at once. The rim wall was of the same stuff as the Ringworld floor. Louis had walked on it, in places where eroded landscape let it show through. It had been greyish, translucent, and terribly slippery. Here the surface had been roughened for traction. But the pressure suit and backpack made Chmeee and Louis top-heavy. They moved with care. That first step would be a beauty.

At the bottom of a thousand miles of glassy cliff were broken layers of cloud, and seas: bodies of water from ten thousand to a couple of million square miles in area, spread more or less uniformly across the land, and linked by networks of rivers. As Louis raised his eyes, the seas grew smaller with distance ... smaller and a little hazy ... too small to see, until sea and fertile land and desert and cloud all blended into a blue knife-edge against black space.

To left and right it was the same, until the eye found a blue band swooping up from the infinity beyond the horizon. The Arch rose and narrowed and curved over and above itself, baby blue checked with midnight blue, to where a narrow ribbon of Arch lost itself behind a shrunken sun.

This part of the Ringworld had just passed its maximum distance from the sun… but a Sol-type star could still burn your eyes out. Louis blinked and shook his head, his eyes and mind dazzled. Those distances could grab your mind and hold it, leave you looking into infinity for hours or days. You could lose your soul to those distances. What was one man when set against an artefact so huge?

- Larry Niven, 1980

The Ringworld is a hoop-shape megastructure that is constructed around a star and its dimensions are so vast that it makes the physical sizes of entire planets seem insignificant in comparison. From afar, the Ringworld will appear as a circular ribbon-like structure which completely encircles a star. The Ringworld spins in order to generate artificial gravity from centrifugal forces to establish a habitable environment across its entire inner surface. In this article, I will be describing a hypothetical Ringworld which exists around a Sun-like star.

Spanning a diameter of 300 million kilometres, a circumference of 942.48 million kilometres and a width of 2 million kilometres, the Ringworld features a habitable Earth-like environment which spans an immense area of 1880 trillion square kilometres over its entire inner surface. This unimaginably huge area is almost 3.7 million times the total surface area of the Earth! This is like having 3.7 million Earths all mapped flat and joined edge to edge. With an average thickness of 40 kilometres and with an average density that is similar to the Earth’s crust, the Ringworld is estimated to have a total mass of about 33000 times the mass of the Earth or about 10 percent the mass of our Sun.

Rim walls that are over a thousand kilometres high are found along the edges at the inner surface of the Ringworld. These walls keep the atmosphere within the inner surface of the Ringworld by preventing the atmosphere from slipping off the edge into space. The Ringworld is so huge that journeying from one rim wall to the other will mean covering a distance that is equal to circling the Earth 50 times. Additionally, circumnavigating the entire Ringworld will mean covering a vastly greater distance that is equal to circling the Earth 23500 times. Travelling at a speed of one kilometre per second, it will take almost 30 years to completely circumnavigate the Ringworld!

The enormous size of the Ringworld allows equal scale maps of entire worlds to be reconstructed on its surface. If all the continents of the Earth were reconstructed to scale in one of the Ringworld’s many great oceans, the entire archipelago of continents will span only one percent the width of the Ringworld. To generate an Earth-like gravity on the inner surface of the Ringworld, the entire megastructure will have to spin at a rate of once every 777000 seconds. At this spin rate, the rim of the structure will be travelling at a speed of 1210 kilometres per second.

Interior to the Ringworld and located at a closer distance to the central sun, an enormous ring of equally spaced rectangular shades block the sun at regular intervals to provide a day-night cycle along the habitable inner surface of the Ringworld. During the day on the inner surface of the Ringworld, the sun always appears directly overhead and night arrives following an eclipse of the sun by one of the rectangular shades.

Between the Ringworld and its sun, a series of climate control shades are positioned into another ring which has the same spin rate as the Ringworld itself such that each climate control shade remains fixed over the same region of the Ringworld’s inner surface. These climate control shades block out various fractions of the Ringworld’s sun and create cold spots on the Ringworld’s inner surface which allow temperature gradients to be generated. These temperature gradients drive large scale atmospheric and oceanic circulations. Sufficient cooling by large enough climate control shades also lead to the creation of ice caps.

Olympus Mons

Olympus Mons is a large shield volcano mountain that is located on the planet Mars and it has a morphology similar to the large volcanoes that make up the Hawaiian Islands. Rising to a height of 22 kilometres above the surrounding plains or 21 kilometres above the standard topographic datum of Mars, Olympus Mons is the tallest mountain known in the Solar System. This makes Olympus Mons stand at just under three times the height of Mount Everest. The base of Olympus Mons measures over 600 kilometres across and the outer edge of the mountain is rimmed by an immense cliff which rises up to 8 kilometres above the surrounding terrain.

Due to the sheer size of Olympus Mons and from the fact that the average slope of the volcano’s flank is only 5 degrees, the entire vertical profile of Olympus Mons will not be visible to an observer who is standing at a great distance away on the surrounding plains as the curvature of the planet Mars would obscure the mountain’s summit. Similarly, an observer standing on the summit of Olympus Mons will be unable to view the surrounding plains as the slopes of the volcano would extend well beyond the horizon. However, the immense cliffs which surround almost the entire base of Olympus Mons will definitely make an impressive sight.

Olympus Mons is located on the northwestern edge of the Tharsis Bulge which also has some of the largest volcano mountains known in the Solar System. To the southeast of Olympus Mons are the mountains Arsia Mons, Pavonis Mons and Ascraeus Mons. Like Olympus Mons, these mountains are also immense shield volcanoes that rise to impressive heights, greatly dwarfing even the prominence of Mount Everest. The Tharsis Bulge, on which these colossal mountains are located, covers millions of square kilometres in area and the height of Everest’s summit is merely comparable to the surface elevation of the massive plateau above the standard topographic datum of Mars.

The extraordinary size of Olympus Mons is due to the fact that unlike the Earth, Mars does not have plate tectonics and this enables the crust of Mars to remain stationary over a hotspot. By doing so, magma coming out of the hotspot continuously builds the volcano in the same location and allows Olympus Mons to become so large. A unique observational aspect of Olympus Mons is that it is sufficiently high enough to penetrate above the frequent Martian dust storms that can occasionally be large enough to engulf the entire planet. This was the first observational hint of the incredible height of Olympus Mons, long before the first spacecraft arrived in orbit around Mars.

The atmospheric pressure on the top of Olympus Mons is about 70 Pascal and this is about 11 to 12 percent of the atmospheric pressure at the standard topographic datum of Mars which has a value of 610 Pascal. In comparison, the atmospheric pressure on the top of Mount Everest is about 31400 Pascal while the atmospheric pressure at sea level on the Earth is 101325 Pascal. To put this into an Earthly perspective, the atmospheric pressure on the top of Olympus Mons is like being at an altitude of 50.5 kilometres above sea level while the atmospheric pressure at the standard topographic datum of Mars is like being at an altitude of 34.5 kilometres above sea level.

Orographic clouds that are made up of particles of water ice have long been known to be associated with Olympus Mons and with the other great volcano mountains on Mars. These clouds form when air masses are forced from a lower elevation to a higher elevation as they move up the slopes of these great mountains. The air masses cool as they rise and the moisture content carried within them condenses into particles of water ice, forming orographic clouds.