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.