Trillion Years

Red dwarf stars are by far the most common stars in the galaxy and they have masses ranging from 0.08 to 0.4 times the mass of the Sun. 0.08 times the mass of the Sun is just about the lowest possible mass a star can have and still be able to sustain hydrogen fusion within its core. The least massive red dwarf stars shine at only 0.01 percent the luminosity of the Sun while the most massive ones do not exceed 10 percent the luminosity of the Sun.

Assuming that the lifespan of a star is the total duration in which it is able to sustain nuclear fusion reactions, the lowest mass red dwarf stars can have lifespans that exceed 10 trillion years. In comparison, the current age of the universe is a mere 13.7 billion years and the estimated lifespan of the Sun is just 12 billion years. At the current age of 13.7 billion years, all the red dwarf stars in the universe have only just begun their seemingly eternal existence.

One reason why red dwarf stars have such incredibly long lifespans when compared to more massive stars is because red dwarf stars have fully convective interiors and this means than almost all of the hydrogen within such stars is available for sustaining nuclear fusion within the cores of these stars. A more massive star such as the Sun has a mostly radiative interior and this means that only the hydrogen within the core of the Sun is available for nuclear fusion due to the absence of any convective mixing between the matter in the core with the matter in the overlying layers. The other reason for the longevity of red dwarf stars is that such stars burn their hydrogen via nuclear fusion at a much smaller rate than more massive stars.

In this article, we shall follow the evolution of a red dwarf star that has 0.1 times the mass of the Sun. It takes an estimated 2 billion years for this red dwarf star to contract from an initial cool cloud of hydrogen and helium to the point where is able to sustain hydrogen fusion within its core. At the onset of stable hydrogen fusion within its core, the newly formed red dwarf star will have a surface temperature of 2200 Kelvin and shine at 0.04 percent the luminosity of the Sun. Since the red dwarf star has a fully convective interior, almost all of its hydrogen is available to sustain the fusion reactions within its core. With 0.1 times the mass of the Sun, this red dwarf star is estimated to have a nuclear burning lifespan of over 6 trillion years. In fact, the current age of the universe is not even a quarter of a percent of the multi-trillion year lifespan of this red dwarf star.

At age zero, the mass of the red dwarf star is three quarters hydrogen and one quarter helium. Over the subsequent trillions of years, the red dwarf star will fuse hydrogen into helium within its core, gradually converting more of its fraction by mass into helium. The steady rise in the helium mass fraction of the red dwarf star increases the rate at which energy is being generated by nuclear fusion in the core of the star, causing the surface temperature and the overall luminosity of the star to also increase.

After 3.1 trillion years, the red dwarf star’s fraction of mass that is helium surpasses the fraction of mass that is hydrogen. At this point, the red dwarfs star will have a surface temperature of 2500 Kelvin and shine at 0.1 percent the luminosity of the Sun. As the red dwarf star crosses the age of 5.7 trillion years, over 85 percent of its mass will now be in the form of helium and this is the point where radiative transport of energy replaces convection in the core of the star. At this stage, the red dwarfs star will have a surface temperature of 3500 Kelvin and shine at 0.3 percent the luminosity of the Sun.

The creation of the radiative core within the red dwarfs star signifies the closing stages of its near eternal lifespan as the evolution of the star begins to accelerate. The core of the red dwarf star increases in mass via the buildup of helium as the remaining hydrogen undergoes fusion into helium in a shell surrounding the core which gradually moves outward through the star. During this process, the surface temperature and luminosity of the red dwarf star continues to increase until it eventually reached a maximum surface temperature of 5800 Kelvin and shines with just under one percent the luminosity of the Sun. In fact, the surface temperature of the red dwarf star is now slightly greater than the surface temperature of the Sun even though its overall luminosity is much lower due to its vastly smaller size compared to the Sun. At this stage, the red dwarf star is a far cry compared to what it initially was.

After the red dwarf star attains its maximum surface temperature, it beings to turn around and evolves towards a lower surface temperature and a lower luminosity. At this point, the red dwarf star is still producing energy by burning hydrogen into helium in a shell surrounding a large and inert helium core. The rate at which energy is being generated by the fusion of hydrogen into helium in the shell gradually diminishes and it is eventually extinguished at 540 billion years after the red dwarf star first develops its radiative core. At this point in time, the red dwarf star has a surface temperature of 1700 Kelvin and shines with 0.0005 percent the luminosity of the Sun, 80 times dimmer than its luminosity at birth. Since the onset of the radiative core occurs 5.7 trillion years into the lifespan of the red dwarf star, the total duration of nuclear burning within the star adds up to just over 6 trillion years.

The red dwarf star now ends its life as a low mass helium white dwarf star with a final mass fraction where 99 percent of it is helium with the remaining 1 percent being hydrogen. This final mass fraction shows the extraordinary efficiency in which the red dwarf star generates energy by burning its hydrogen into helium through nuclear fusion. In comparison, the Sun burns only 10 percent of its hydrogen throughout its entire lifespan.

A 6 trillion year lifespan is not the longest a red dwarf star can possibly have. In fact, a red dwarf star with 0.08 times the mass of the Sun has an estimated lifespan of 12 trillion years, making it twice as long as a red dwarf star with 0.1 times the mass of the Sun. In this incredibly distant future universe, the red dwarf star with 0.1 times the mass of the Sun has finally evolved into a white dwarf star. After many trillions of years of further cooling, this white dwarf star will eventually become a black dwarf where its surface temperature gets ever nearer to absolute zero.

Given that red dwarf stars make up the vast majority of stars in a galaxy and that these stars can live for trillions of years, most of the stellar evolution that will occur has yet to occur. In the far future universe, red dwarf stars will play an increasingly important role in contributing to the total luminosity of a galaxy as the rate of star formation decreases and as the more massive stars in the galaxy age and fade away. This is because the gradual increase in the luminosities of red dwarf stars nearly compensates the loss in luminosity as the rate of star formation declines and as the more massive stars fade away. This ultimately causes the total luminosity of the galaxy to remain fairly constant over trillions of years.

Intergalactic Wanderer

Hypervelocity stars are stars with sufficiently large velocities that they are no longer gravitationally bound to the galaxy. While ordinary stars have velocities on the order of 100 kilometers per second, hypervelocity stars have velocities on the order of 1000 kilometers per second. At such velocities, hypervelocity stars will escape their home galaxy forever and become lone wanderers of intergalactic space. In February 2010, I wrote and posted a short article about hypervelocity stars, including possible mechanisms that can lead to such stars.

For a moment, imagine a Sun-like hypervelocity star with an entire system of planets orbiting it, where one of the planets is an Earth-like world that is not too different from ours. The Sun-like star and its system of planets are traveling in excess of 1000 kilometers per second, on a trajectory that has already taken them far from the home galaxy. How will the night sky from the surface of such an Earth-like world appear as it wanders the dark and immense distances of intergalactic space?

In the vast and starless voids of intergalactic space, the night sky from the surface of this Earth-like planet will be totally devoid of any stars. Assuming that the Earth-like planet and its parent star left their home galaxy a hundred million years ago, an alien observer on the surface of the Earth-like planet will be able to see the entire galaxy as a disk of wispy arms spiraling out from a glowing central bulge. The galaxy will span across a huge swath of the starless night sky and none of the hundreds of billions of stars that make up the galaxy will be individually distinguishable with unaided eyes. Every several years or so, a star in the galaxy will end its life in a supernova explosion and it will appear as a brilliant point of light which will suddenly appear and gradually fade.

It may take a huge leap of imagination and ingenuity for an extraterrestrial civilization living on this planet to realize that each of the hundreds of billions of miniscule points of light that comprise the galaxy are actually stars not too different from their yellow Sun. Imagine the idea of interstellar space travel in such a scenario where instead of a mere 4.37 light years away, the nearest stars are many thousands of light years away! Additionally, this extraterrestrial civilization might even contemplate about the possibilities of other extraterrestrial civilizations living on worlds within the galaxy and how these civilizations might possibly figure out the shape of the galaxy in which they live in!

Discovering Tyche

Is there an undiscovered massive object orbiting the Sun in the Oort Cloud, elusively hidden in the perpetual frigid darkness? The Oort Cloud occupies an immense region of space surrounding the Sun; from a couple of thousand AU to as far as 50000 AU from the Sun! The term AU is the acronym for Astronomical Unit, where one AU is the mean distance of the Earth from the Sun and it has a value of 149.6 million kilometers.

The Oort Cloud is estimated to contain several trillion objects larger than 1 kilometer in diameter, with each object spaced tens of millions of kilometers away from its closest neighbor! To put the size of the Oort Cloud into perspective, even the distance of Pluto from the Sun is less than 0.1 percent the distance to the edge of the Oort Cloud!

A paper by John J. Matese and Daniel P. Whitmire (2010) entitled “Persistent Evidence of a Jovian Mass Solar Companion in the Oort Cloud” describes the possibilities of a Jupiter-mass object orbiting the Sun at a distance large enough to place it within the Oort Cloud. Tyche is the name that has been suggested for this hypothetical object. The name Tyche, which means “luck” in Greek, is also the good sister of Nemesis in Greek mythology.

In this paper, the possible existence of Tyche was inferred from dynamical and statistical analysis of the orbits of comets entering the Solar System from the Oort Cloud. The gravitational perturbations from a distant Jupiter-mass object like Tyche could also explain the peculiar orbits of extended scattered disc objects such as Sedna. These objects orbit the Sun on highly elliptical orbits that take them out to hundreds of AU from the Sun. Sedna for example, has a very elongated orbit which takes it from a minimum of 76 AU from the Sun out to an incredible 976 AU from the Sun and it takes over 12 thousand years to orbit the Sun once.

Being located at such a huge distance from the Sun, the amount of insolation that Tyche gets from the Sun will be negligible. Tyche will be a gas giant world like Jupiter and it is expected to glow feebly at a temperature of about 200 Kelvin from heat emanating from its warm interior. Therefore, Tyche can only be detected in the infrared band since such a cool object is expected to emit almost no visible light. Interestingly, NASA’s recently launched Wide-field Infrared Survey Explorer (WISE) will be able to easily detect the presence of such an object in the Oort Cloud! Visit http://wise.ssl.berkeley.edu/ to find out more about WISE.

Although a positive detection of Tyche might not be much of a surprise, the discovery of such a world will be extremely fascinating. Jupiter is currently by far the most massive known object in orbit around the Sun and the discovery of something more massive than Jupiter will have interesting implication regarding our perspectives of things in orbit around the Sun. What kind of moons will orbit this object and might some of these moons be similar to the ones in orbit around Jupiter? What kind of exploratory robotic spacecraft might possibly be sent there? Additionally, since the formation mechanisms for such an object are probably be very different compared to the formation mechanisms for the planets in our Solar System, should Tyche be classified as a planet or a brown dwarf?

Quaoar-Weywot

Quaoar is the name of a Kuiper Belt object which orbits the Sun at a mean distance of 43.6 times the Earth-Sun distance. At that orbital distance, Quaoar takes 288 Earth years to go around the Sun once. Travelling at a speed of 20 kilometres per second, it will take roughly a decade to travel from the Earth to Quaoar. Additionally, Quaoar also has a moon named Weywot which orbits it with period of close to twelve and a half days. Weywot orbits Quaoar at a mean orbital distance of approximately 14500 kilometres from Quaoar.

A paper by W. C. Fraser and M. E. Brown (2010) entitled “Quaoar: a Rock in the Kuiper Belt” describes the unique properties of the Quaoar-Weywot system and some new observations of this fascinating far-flung system. Quaoar is about 900 kilometres in diameter and in comparison; Pluto has a diameter of 2300 kilometres. The orbit of Weywot around Quaoar reveals that Quaoar has a mass that is approximately 12 percent of Pluto’s. This gives Quaoar an estimated mean density of 4.2 grams per cubic centimetre which makes Quaoar one of the densest known objects in the Kuiper Belt. Additionally, Quaoar’s moon Weywot is estimated to have a diameter of 74 kilometres. A human being with a weight of 70 kilograms on the Earth’s surface will weigh less than 4 kilograms on the surface of Quaoar!

Quaoar’s unusually high density implies that it contains proportionally less icy materials than other Kuiper Belt objects and its high density is also reminiscent of objects in the main asteroid belt which are located much closer to the Sun than Quaoar. Therefore, a substantial bulk of Quaoar is probably made up of much denser rocky material instead of the less dense icy materials.

One theory which explains Quaoar’s unusually high density states that Quaoar collided with another object which stripped away most of Quaoar’s less dense icy mantle and left behind the denser rocky core. This collision event increased the mean density of Quaoar to the current observed value as a larger proportion of Quaoar’s mass is now comprised of denser rocky material.

Another theory which might explain Quaoar unusually high density states that Quaoar formed much closer to the Sun in the main asteroid belt where objects formed there typically have densities similar to the current density observed for Quaoar. Subsequently, gravitational interaction with the planets scattered Quaoar further from the Sun and into the frigid realm of the distant Kuiper Belt objects where Quaoar has been residing ever since.

Regarding the exploration of objects in the Kuiper Belt, NASA’s New Horizons spacecraft is currently on its way to Pluto and it is scheduled to make closest approach to Pluto on 14 July 2015. This will be the first ever flyby of a Kuiper Belt object. In fact on 17 October 2010, New Horizons would have travelled half the flight time to reach Pluto since its launch on 19 January 2006. After making its flyby of Pluto and its moons, Charon, Nix and Hydra, New Horizons is also scheduled to flyby one or more Kuiper Belt objects. Visit http://pluto.jhuapl.edu/ to obtain all the latest news about this mission.

True Heavyweight

In the previous two posts, I wrote about some fascinating stuff involving the application of micro black holes and I also explored an interesting alternative to conventional black holes. In this post, I am going to write about the most massive black hole currently known in the universe, even though there are probably a lot more yet-to-be-discovered black holes which can be more massive than this current record holder.

OJ 287 is a pair of supermassive black holes residing in the heart of a distant galaxy located 3.5 billion light years away, where one light year is the distance light travels in one year. The primary black hole of OJ 287 contains an incredible 18 billion times the mass of the Sun while the secondary black hole contains 150 million times the mass of the Sun. This makes the primary black hole of OJ 287 one of the most massive known black holes in the universe. To put things into perspective, the supermassive black hole in the core of our Milky Way Galaxy is a mere 4 million times the mass of our Sun and the Sun alone is already 333 thousand times more massive than the Earth.

With 18 billion times the mass of the Sun, the event horizon of the monstrous primary black hole of OJ 287 will span an astonishing 110 billion kilometres in diameter. This means that about 80 thousand Suns or 9 million Earths placed end-to-end are required to span the diameter of the black hole’s event horizon. Note that the event horizon of a black hole is a region surrounding it where gravity becomes so strong that it does not let even light to escape.

The much less massive secondary black hole of OJ 287 orbits the primary black hole with a period of 11 to 12 years. Two outbursts are observed from OJ 287 every 11 to 12 years as the secondary black hole intersects the accretion disk of the much more massive primary black hole with a frequency of twice per orbit. The orbit of the secondary black hole around the primary black hole is gradually decaying via the emission of gravitational radiation and the secondary black hole is expected to merge with the primary black hole within 10 thousand years.

Eternally Collapsing Object

Last week, I wrote about some fascinating applications of micro black holes and in my first sentence, I defined a black hole as an object that is so dense and compact that within a certain distance from it, its gravitational pull becomes so strong that it does not let even light to escape. This boundary is known as the black hole’s event horizon and anything that happens to enter it will never escape. By this definition, a black hole does not have a true physical surface and its event horizon is basically a region of space within which nothing, including light, can escape.

In this article, I investigate a kind of black hole that is very different from what was defined in the above paragraph and I will be using the phase “progenitor star” to define an object that is currently in the process of collapsing under its own immense gravity towards forming a black hole. As the progenitor star collapses, it never reaches a true black hole state, but instead becomes a General Relativistic Radiation Pressure Supported Star (GRRPSS). What a mouthful! Although this scenario is purely theoretical, its exciting properties are surely worth considering.

The name “General Relativistic Radiation Pressure Supported Star” somewhat speaks for itself. So, how does radiation pressure works? Take for example our Sun - a ferocious hot ball of hydrogen and helium with 333 thousand times the mass of the Earth, sitting in the middle of our Solar System. The enormous amount of radiation produced via nuclear fusion within the Sun’s core produces an incredible amount of radiation pressure which tries to blow the Sun apart, while gravity tries to crush the Sun inwards. It is this perfect balance between radiation pressure and gravity which gives our Sun the size that we constantly observe it to be.

As the progenitor star collapses, the gravitational field in the vicinity of the star becomes increasingly stronger as the star becomes ever more dense and compact. As the physical diameter of the progenitor star collapses and approaches the diameter of the event horizon for a black hole of its mass, radiation emitted from the surface of the progenitor star will become increasingly red-shifted. This means that the radiation emitted from the progenitor star’s surface gets stretch into ever longer wavelengths.

When the progenitor star collapses below one and a half times the diameter of the event horizon for a black hole of its mass, light emitted at or near the tangent to the star’s surface will not be able to escape into space and will eventually fall back to the surface. As the progenitor star collapses until its physical size approaches the diameter of the event horizon for a black hole of its mass, only light that is being emitted vertically upwards from the star’s surface will escape into space instead of falling back somewhere else on the star’s surface. Therefore, as the progenitor star collapses, only light that is emitted at an ever decreasing angle from the local vertical will escape into space and the self-gravitational trapping of radiation by the progenitor star becomes more and more effective.

The radiation pressure created from the self-gravitational trapping of radiation by the progenitor star prevents it from collapsing to a true black hole state. Instead, the progenitor star will continue collapsing as an incredibly hot ball of quark gluon plasma which asymptotically tends towards a true black hole state but never reaches it. In fact, such an object will appear totally dark since almost no radiation will be able to escape the super strong gravity of the star and it will appear very much like a true black hole.

It might also be true that as the collapsing General Relativistic Radiation Pressure Supported Star tends to become a true black hole, its lifetime in this phase becomes infinite. Such as object can be called an Eternally Collapsing Object (ECO) and this class of objects represents an alternative to conventional black holes.

Sources:

1. Abhas Mitra and Norman K. Glendenning (2010), “Likely Formation of General Relativistic Radiation Pressure Supported Stars or Eternally Collapsing Objects”, arXiv:1003.3518v2

2. Abhas Mitra (2006), “Radiation Pressure Supported Stars in Einstein Gravity - Eternally Collapsing Objects”, arXiv:gr-qc/0603055v3

3. Abhas Mitra (2006), “Sources of Stellar Energy, Einstein- Eddington Timescale of Gravitational Contraction and Eternally Collapsing Objects”, arXiv:astro-ph/0608178v3

Micro Black Holes

A black hole is an object that is so dense and compact that within a certain distance from it, its gravitational pull becomes so strong that it does not let even light to escape. This distance is where the event horizon of the black hole is located and anything which crosses the event horizon, including light, can never escape. If the entire Earth is crushed to form a black hole, its event horizon will have a diameter of only 1.8 centimetres. In comparison, the black hole version of the Sun will have an event horizon that is 5910 meters in diameter.

In this article, I will explore the theoretical possibilities of using micro black holes as energy generators, antimatter factories, propulsion for interstellar space travel and gravity wells for artificial planets. These ideas are just theoretical possibilities that could be possible in the distant future. The micro black holes that I’m referring to are those with masses at or below the planetary mass regime. Unless a micro black hole can be found naturally, forming such a black hole will first require compressing a large amount of mass into an incredibly tiny volume of space. After the creation of an initial black hole, additional matter can be thrown into the black hole to increase its mass.

Hawking radiation is a form of radiation that is predicted to be emitted by black holes due to quantum effects and it is named after the physicist Stephen Hawking who theorized its existence in the 1970s. Since the emission of Hawking radiation allows black holes to lose mass, black holes that lose more mass than they accrete will eventually disappear. An isolated black hole will eventually vanish by emitting all of its mass in the form of Hawking radiation and the lifespan of a black hole is directly proportional to its mass. The amount of Hawking radiation and the mean energy of the radiation particles being emitted by the black hole are both inversely proportional to the mass of the black hole. For this reason, smaller black holes are expected to emit much more Hawking radiation than their more massive counterparts.

The first area to be investigated is the use of micro black holes as antimatter factories. Compared to ordinary matter particles, antimatter particles have the same mass but opposite charge. For example, the antimatter counterpart of an electron is a positron and it has a positive charge instead of a negative charge. On its own, antimatter is stable. However, when an antimatter particle meets an ordinary matter particle, they will annihilate with total conversion of matter to energy. The amount of energy produced when one gram of matter annihilates with one gram of antimatter is about 3 times the amount of energy produced from the detonation of the Hiroshima atomic bomb.

A micro black hole can be used as an antimatter factory since matter and antimatter are expected to be produced in equal quantities as the black hole evaporates via the emission of Hawking radiation. Since the mean energy of the radiation particles being emitted increases as the mass of the black hole decreases, the production of more massive particles will require a smaller black hole. For example, a black hole with a mass of 65 billion tons is optimal for the production of electrons and positrons. For heavier particles such as protons and antiprotons, a black hole with a much smaller mass of 35 million tons will be required.

Black holes of planetary mass can be used to create artificial planets by providing the source of mass necessary to generate the required amount of gravity. An artificial planet can be created by constructing a large spherical shell with the black hole in the center. For example, a spherical shell that is 12760 kilometres in diameter can be constructed around an Earth-mass black hole to form an artificial planet with Earth-like gravity on the external surface of the shell. In another example, a spherical shell that is 227000 kilometres in diameter can be constructed around a Jupiter-mass black hole to form an artificial planet that has over 300 times the surface area of the Earth, with Earth-like gravity on its external surface.

Such artificial planets with Earth-like environments can range from hundreds of kilometres to hundreds of thousands of kilometres in diameter. This concept can be especially useful in planetary systems with insufficient silicate and metallic elements to build solid planets. Hence, hydrogen and helium from the gas giant planets or from the local star can be used as a source of mass to form the black hole. In addition, energy can be generated by dropping mass into the black hole located at the center of such an artificial world as the accretion of even a small amount of mass into the black hole is expected to generate a tremendous quantity of energy.

Now, I shall describe the evaporation of a micro black hole with an initial mass of a billion metric tons and the amount of energy emitted by the black hole as it evaporates via the emission of Hawking radiation. The event horizon of this billion metric ton black hole is about the same size as the atomic nucleus of a hydrogen atom and it will have a luminosity of 356 million watts due to the emission of Hawking radiation, which is approximately twice the power output of a Nimitz-class aircraft carrier. This black hole will have a lifespan of over 2 and a half trillion years, which is much longer than the current age of the Universe.

As the black hole evaporates by emitting Hawking radiation over 2 and a half trillion years or so, it will eventually reach a mass of 10 million metric tons. At this mass, the size of the black hole’s event horizon is about 100 times smaller than the atomic nucleus of a hydrogen atom and it will have a luminosity of 3.56 trillion watts from the emission of Hawking radiation, which is roughly the average total power consumption of the entire United States in 2008. At this mass, the black hole still has a life span of another 2 and a half million years.

Now, I’ll fast forward until the black hole has just one year remaining. At this time, the black hole will have a mass of 72 thousand metric tons, an event horizon that is 15000 times smaller than the atomic nucleus of a hydrogen atom and it will shine with a luminosity of 68.5 thousand trillion watts, which is approximately 4000 times the average total power consumption of the human world in 2008. A black hole around this order of magnitude of mass can be use as a propulsive device to accelerate a spaceship to relativistic velocities, tens of thousands to hundreds of thousands of kilometres per second. This can be done by directing the high energy radiation particles emitted from the black hole to produce thrust. Ordinary matter can also be fed into the black hole to sustain it.

As the black hole gets smaller and smaller, it will lose more and more of its mass in the form of Hawking radiation at an increasing rate. When the black hole reaches a remaining lifespan of 10 seconds, it will have a mass of 492 metric tons, a diameter of 1.46E-021 meters and a luminosity of 1.47E+021 watts. At this stage, the black hole is just over a million times smaller than the atomic nucleus of a hydrogen atom and in one second, it emits more energy than the detonation of 23 million Hiroshima atomic bombs.

Finally, when the black hole reaches the final second of its existence, it will have a mass of 22.8 metric tons, a diameter of 6.78E-022 meters and a luminosity of 6.84E+021 watts. At this stage, the black hole is over two million times smaller than the atomic nucleus of a hydrogen atom and in its final second, it will emit more energy than the detonation of 300 million Hiroshima atomic bombs. To further put it into perspective, the amount of energy emitted in the final second of the black hole’s existence is over 40 times the total worldwide energy consumption in 2008. You will certainly want to be very far away during the final moments of the black hole’s existence as it disappears in an incredible burst of energy.

All the values which I have used in this article to describe black holes were calculated using a program which I have developed a few years ago. It is interesting to note that there is a possible natural source for micro black holes. A primordial black hole is a hypothetical type of black hole that is theorized to form out from the extreme densities present during the beginning of the Universe and these black holes are expected to be very low in mass. On way to detect such black holes is via their Hawking radiation, but none have been detected so far. A primordial black hole with a mass of 173 million metric tons will have a lifespan that is equal to the current age of the Universe and if such primordial black holes exist in sufficient numbers, their demise might be detectable as they emit an extraordinary burst of Hawking radiation in their final seconds. NASA’s Fermi Gamma-ray Space Telescope which was launched in 2008 might have the sensitivity necessary to detect the energetic demise of primordial black holes if they exist.

Cannonball Super-Earths

A super-Earth is an extrasolar planet with a mass between 1 to 10 times the mass of the Earth and our Solar System does not have any planets that are within this mass regime. A number of super-Earths have already been discovered around other stars. The four distinct types of materials that could make up a super-Earth with different proportions are iron alloys, silicates, volatiles/ices and hydrogen-helium gas. For a given mass, a less dense super-Earth will have a larger diameter while a denser super-Earth will have a smaller diameter. Thus, a pure hydrogen-helium gas planet will have the largest possible diameter while a pure iron planet with have the smallest possible diameter. However, the upper and lower limiting diameters for a super-Earth of a given mass are highly unlikely with regard to the physical processes involved in planet formation.

A paper by Robert A. Marcus, et al. (2010) entitled “Minimum Radii of Super-Earths: Constraints from Giant Impacts” examines the smallest possible diameter a super-Earth of a given mass can have. Therefore, volatiles/ices and hydrogen-helium gas are not considered and only rocky planets with an iron core and a silicate mantle are considered here. The only way to significantly increase the density of a planet requires the removal of the silicate mantle while preserving the iron core. An effective way to do that is by the stripping of the planet’s silicate mantle by giant impacts.

An example of mantle stripping via collision in our own Solar System is the planet Mercury. By mass, Mercury is 70 percent iron and 30 percent silicate, while the Earth is one-third iron and two-thirds silicates and other materials. Proportional to its mass, Mercury has a higher iron content than any other planet in the Solar System. It is currently theorized that Mercury was initially over twice its current mass with an iron core and a substantial silicate mantle. A large object, roughly one-third Mercury’s current mass, struck the planet and stripped away much of the planet’s original crust and silicate mantle, leaving behind the iron core together with a thin layer of the original crust and silicate mantle.

The conclusions derived from this paper show that the collision stripping of mantle material is an effective mechanism in producing a super-Earth with a higher mean density by increasing the iron mass fraction. It is easier for the collision stripping of mantle material for a lower mass super-Earth to produce a large iron mass fraction as compared to a higher mass super-Earth.

However, even with the most extreme impact conditions, the collision stripping of mantle material from a super-Earth is still unable to produce anything close to a pure iron planet. The maximum mass of a super-Earth with over 70 percent iron by mass is most probably 5 Earth masses since its formation via the stripping of its silicate mantle by a giant impact requires an initial object of 10 Earth masses. The maximum mass of a super-Earth is expected to be around 10 times the mass of the Earth since a more massive planet will probably undergo runaway growth via accretion of hydrogen-helium gas and become an even more massive gas giant planet.

NASA’s Kepler space telescope is expected to find a few hundred planets in the super-Earth mass regime and a sample of them will probably have masses too large for their observed diameters based on standard planet formation. The formation of such dense “cannonball” super-Earths can then be explained by the collision stripping of mantle material to produce a larger iron mass fraction.

Alien Earths

Earth-size and probably even Earth-like planets are expected to be common throughout the galaxy; orbiting stars not too different from our Sun. How will such Earth-like worlds differ from our own? A paper by Courtney D. Dressing, et al. (2010) entitled “Habitable Climates: The Influence of Eccentricity” examines how factors such as obliquity, spin rate, orbital eccentricity, orbital distance from host star and the fraction of surface covered by ocean might affect the habitability of Earth-like extrasolar planets. In this paper, regions of a planet that are at temperatures between 273 to 373 degrees Kelvin are considered habitable while regions outside that temperature range are considered uninhabitable.

Obliquity refers to the tilt of a planet’s axis, spin rate refers to the time required for a planet to complete one rotation about its axis, orbital eccentricity refers to how much a planet’s orbit around its star deviates from a perfect circle and orbital semimajor axis refers to the mean distance of a planet from its host star. An orbital eccentricity of zero denotes a perfect circle and an orbital eccentricity of one denotes a parabola. The Earth for example, has an obliquity of 23.4 degrees, a spin rate of 24 hours, an orbital eccentricity of 0.0167 and an orbital semimajor axis of 149.6 million kilometres. In addition, the surface of the Earth is 70 percent ocean and 30 percent land.

Of all the extrasolar planets with measured orbital eccentricities, a large fraction of them have significant orbital eccentricities and this suggests that Earth-like planets in near circular orbits, like ours, probably represent only a small subset of potentially habitable worlds. This paper basically studies the numerous possible types of Earth-like planets and many of the models of Earth-like planets presented are particularly interesting.

Take for example, a desert planet with an obliquity of 90 degrees, an orbital semimajor axis of 1.225 AU and an orbital eccentricity of 0.2. Winter at the southern hemisphere of this planet occurs when the planet is furthest from its star and during this long winter, the southern pole freezes and reaches an incredibly cold temperature of minus 120 degrees Centigrade. For this planet, the southern pole becomes transiently habitable only during northern winter when the planet is closest to its star. The southern pole of this planet experiences the most extreme temperature variations. During southern winter, the planet is furthest from its star and the southern pole experiences perpetual darkness. During southern summer, the planet is closest to its star and the southern pole experiences perpetual daylight.

This paper can be obtained at http://arxiv1.library.cornell.edu/abs/1002.4875 and it investigates the many types of possible Earth-like worlds that can exist. Notable examples described in this paper include:

- An Earth-like planet whose spin axis is tilted 90 degrees, such that the entire northern hemisphere can be in constant daylight while the entire southern hemisphere can be in constant darkness and vice versa, during specific points of the planet’s orbits around its host star.

- A planet where one day has a length of 8 hours or another where one day has a length of 72 hours.

- An Earth-like planet whose highly eccentric orbits around its host star brings it from a distance where most of its surface is scorching hot out to a distance where most of the planet’s surface plunges into a deep freeze. 

Dissipating Planet

A paper by Shu-lin Li, et al. (2010) entitled “WASP-12b as a Prolate, Inflated and Disrupting Planet from Tidal Dissipation” describes some peculiar properties of an extrasolar planet. WASP-12b is an extrasolar gas giant planet that has 1.4 times the mass of Jupiter and it is located so remarkably close to its parent star that it takes only a little over an Earth day to orbit the star. In fact, WASP-12b orbits its parent star at a distance of just 2 stellar radii from the star’s surface and the planet is distorted by the star’s gravity into a prolate shape, similar to that of a rugby ball.

The nonzero orbital eccentricity of WASP-12b makes it very susceptible to the strong tidal effects from its parent star which heats the planet’s interior and causes the planet to expand. WASP-12b has an orbital eccentricity of about 0.05 and this is odd because orbital circularization should have already circularized its orbit into a zero eccentricity orbit. Another planet with a mass of a few Earths is probably responsible for perturbing WASP-12b to maintain its nonzero orbital eccentricity. WASP-12b is extremely “bloated” and it has a diameter that is 80 percent larger than Jupiter’s. The atmospheric temperature of WASP-12b is estimated to be a scorching 2500 degrees Kelvin.

WASP-12b has ballooned so much that its own gravity is unable to retain its mass from the gravitational pull of its parent star. Gas from WASP-12b is flowing towards the parent star through a nozzle that is located at the L1 Lagrangian point, a region that is situated between the planet and the star. WASP-12b is losing mass to its host star at a rate of a few billion metric tons each second. The material that is pulled off from WASP-12b forms an accretion disk around the parent star and gradually spiral inwards into the star.