Planets Orbiting White Dwarfs

An extrasolar planet is basically a planet which orbits a star other than our Sun and a transiting extrasolar planet is one which periodically blocks a small fraction of the light from its parent star as its orbit brings it in front of the star’s luminous disk. Current missions such as NASA’s Kepler space telescope are sensitive enough to detect transiting extrasolar planets that are as small as the Earth around Sun-like stars.

Transits only occur when a planet’s orbit around its parent star happens to be orientated nearly edge-on with respect to our line of sight. Stars have randomly orientated planetary orbits and the probability that a planet is observed to transit its parent star is inversely proportional to the distance of the planet from its star. Therefore, a planet orbiting at a smaller distance from its star will have a higher probability of being observed to transit its star as compared to a planet orbiting at a larger distance.

For stars like the Sun, the fraction of light that a transiting planet blocks is small because the size of the star is much larger than the size of the planet. For example, if the Earth were to be observe transiting the Sun, it will cause the brightness of the Sun to dip by approximately 0.01 percent while if Jupiter were to be observe transiting the Sun, it will cause the brightness of the Sun to dip by approximately 1 percent.

White dwarfs are basically the end result of the evolution of main sequence stars such as the Sun and stars with less than 8 times the mass of the Sun eventually end up as white dwarfs. The Sun is 333 thousand times more massive than the Earth and a typical white dwarf can contain as much mass as the Sun gravitationally compactified into a dense sphere that is approximately the size of the Earth. In comparison, the Sun has a diameter that is 109 times larger than the Earth’s and a volume that can fit 1.3 million Earths.

As a result, when it comes to the relative fraction of starlight that can be blocked by a transiting planet, white dwarfs do offer a huge advantage over main sequence stars like the Sun. This is because the size of a white dwarf is much smaller than the size of a main sequence star and this allows a much greater fraction of a white dwarf’s light to be blocked by a transiting planet to generate a proportionally stronger transit signal. In fact, a Jupiter-size transiting planet can completely block out the light from a white dwarf since such a planet will be larger in size than the white dwarf.

The transit of an Earth-size planet across the luminous disk of a white dwarf will block out a significant fraction of the white dwarf’s light. In certain cases, it is even possible for the Earth-size planet to completely block out the white dwarf. Even the transit of an object as small as the Earth’s Moon in front of a white dwarf will occult a few percent of the white dwarf’s light. In comparison, the transit of an object as small as the Moon in front of a star like our Sun will only block out a minuscule 6 parts-per-million of the star’s light and such a weak signal will probably be hardly distinguishable from background noise. Therefore, white dwarfs offer an enormous advantage over main sequence stars as a means to detect small planetary objects.

Nonetheless, the detection of small transiting planetary objects around white dwarfs will require a higher observational cadence as compared to the detection of planets around main sequence stars like our Sun. This is because the small size of a white dwarf means that any transiting planet takes on the order of only a few minutes to transit across the entire luminous disk of the white dwarf. In comparison, the transit of a planet across the luminous disk of a main sequence star like our Sun takes on the order of a few hours which permits a much lower observational cadence.

White dwarfs are the final result of the evolution of main sequence stars like our Sun and there are ways in which planets can exist around white dwarfs. Before a star becomes a white dwarf, it will undergo a red giant phase where it will swell to many times its original size and engulf or vaporize planets that might be orbiting it in close vicinity. However, planets that orbit further out and planets that are sufficiently massive can survive the star’s evolution to a white dwarf and continue to orbit the white dwarf.

As a star evolves to a white dwarf, it can lose a significant fraction of its mass and this can destabilize any system of planets that is in orbit around the star. In such a scenario, planets can gravitationally interact with each other and can either be scattered into a tighter orbit around the white dwarf or get boosted into a more distant orbit around the white dwarf. It is also possible for planets to get completely ejected from the system. Planets that are scattered into a tighter orbit around the white dwarf will improve their probability of being observed to transit the white dwarf because the transit probability of a planet is inversely proportional to the distance of the planet from its star.

Interestingly, there is also an alternate mechanism that can allow planets to exist around white dwarfs. When a closely spaced pair of white dwarfs eventually merges due to the loss of orbital energy via the emission of gravitational radiation, a second generation of planets can form out from the disk of debris from the tidal disruption of the lower mass white dwarf. Therefore, the existence of an entire second generation system of planets, moons and asteroids in close orbit around a white dwarf is quite plausible.

The detection of transiting planetary objects around white dwarfs will help constrain the effectiveness of the mechanisms in which planets can exist around white dwarfs. To detect such transits, a large number of white dwarfs have to be continuously sampled at a high observational cadence. Currently, NASA’s Kepler space telescope is most suited for the detection of transiting planetary objects around white dwarfs. This is because Kepler has an extremely high observational cadence since its CCDs are read out every six seconds and Kepler is theoretically sensitive enough to detect objects as small as asteroids as they transit in front of white dwarfs.

Rogue Worlds

The formation of planets in protoplanetary disks around stars is a messy process and a significant number of protoplanets with masses similar to planets such as the Earth or Mars may get ejected from their solar systems by gravitational interactions with massive gas giant planets. It is even possible that more protoplanets are ejected than retained in protoplanetary disks around stars and a considerable number of such ejected worlds might be wandering in the immense and dark expanses of interstellar space. Interstellar space is basically the vast and enormous spaces between stars.

An ejected planet with the mass of the Earth can retain an atmosphere of hydrogen in the frigid temperatures of interstellar space since the atmosphere of hydrogen will be cold enough to be bounded by the gravity of the planet. In comparison, at the distance where the Earth is from the Sun, a planet has to be over 10 times more massive than the Earth for its own gravity to be sufficiently strong enough to keep an atmosphere of hydrogen from escaping into space. In this article, I shall denote such ejected worlds as interstellar planets. From a distance, an interstellar planet will appear as a dark silhouette against a field of distant background stars.

The effective temperature of an interstellar planet is expected to be just several degrees Kelvin above absolute zero and any form of water at this temperature will be frozen solid. However, if an interstellar planet has a sufficiently thick atmosphere of hydrogen where the pressure at the bottom of such an atmosphere ranges from a hundred to a few thousand bars, the pressure-induced infrared opacity of molecular hydrogen will greatly insulate the planet from dissipating its internal radiogenic heat into space. At high pressures, molecular hydrogen is very effective at trapping heat and this significantly reduces the amount of heat lost into space.

With such an overlying atmosphere of hydrogen, the surface temperature of an interstellar planet can potentially exceed the meting point of water! In an environment like this, it will be possible for oceans of liquid water to exist on the planet’s surface and the ocean can be kept warm by the persistent flux of heat generated by the decay of radioactive isotopes in the planet’s interior.

On the surface of an interstellar planet, the sky will appear totally back and it is highly unlikely that stars will be visible from the planet’s surface due to the thick hydrogen atmosphere. However, areas of the planet’s surface can still be illuminated by occasional flashes of lightning. In the lower and warmer reaches of the atmosphere, it is possible for clouds of water droplets to form and drive a hydrological cycle. The atmospheric temperature decreases higher up in the atmosphere, possibly enabling other gases such as ammonia and nitrogen that have lower condensation temperatures to condense into clouds at these higher altitudes. Therefore, an interstellar planet can have several cloud layers of different condensates in its atmosphere.

To consider the Earth as the only populated world in infinite space is as absurd as to assert that in an entire field sown with millet, only one grain will grow.

- Metrodorus of Chios, 4th century BC

An interstellar planet can provide a stable environment for life for billions of year until the surface temperature declines below the meting point of water as the heat generating radioisotopes in the interior of the planet slowly gets depleted. Interstellar planets will be extremely difficult to detect as the amount of radiation they emit is exceedingly miniscule compared to the large amount of solar radiation the Earth reflects back into space as the Earth basks in the warm vicinity of the Sun. Finally, if interstellar planets do exist in significant numbers in the vast and uncharted expanses between the stars, these dark worlds might serve as common sites for life-supporting environments in the universe.