The search for habitable Earth-size planets has primarily been focused on stars similar to our Sun. In recent years, the search has also gone on to focus on low mass red dwarf stars as these stars are by far the most common and an Earth-size planet around such a star will be much easier to detect due to the lower mass and luminosity of a red dwarf star. In this article, I will be exploring the possibility of detecting Earth-size planets located in the habitable zone of cool white dwarf stars. White dwarf stars are the final evolutionary state of all stars that are not massive enough to explode as supernovae and this includes stars such as our Sun. Typically, a white dwarf star has a mass that is comparable to our Sun and all its mass is contained within a tiny volume that is comparable to the size of the Earth. Hence, a white dwarf star is a very dense object as each cubic centimetre of its material can weight over a metric ton.
White dwarf stars are as common as Sun-like stars and as they slowly cool, they can provide energy to planets in orbit around them for billions of years. A paper entitled “Transit Surveys for Earths in the Habitable Zones of White Dwarfs” describes the prospect of detecting habitable Earth-size planets around white dwarf stars by searching for transits of such planets in front of white dwarf stars. Compared to a typical Sun-like star, the habitable zone around a white dwarf star will be located much closer in due to the much lower luminosity of a white dwarf star. The most common surface temperature for white dwarf stars is around 5000 degrees Kelvin and white dwarf stars with surface temperatures of over 10000 degrees Kelvin are rare because white dwarf stars spend little time at high temperatures as they cool very rapidly at such high temperatures. Furthermore, the high ultraviolet flux from a hot white dwarf star that has a surface temperature of over 10000 degrees Kelvin will affect the retention of an atmosphere around an Earth-size planet. Therefore, only cool white dwarf stars will surface temperatures that are considerably less than 10000 degrees Kelvin are considered for the detection of habitable Earth-size planets.
A white dwarf star does not have an internal source of energy like a typical star and this means that it will gradually radiate away its energy and cool down over a period of billions to trillions of years. Hence, the term “continuously habitable zone” is defined as the range of orbital distances from a white dwarf star where an Earth-size planet can stay habitable for a specified minimum duration. For an Earth-size planet to remain habitable for at least 3 billion years, the continuously habitable zone will extend from a distance of 0.005 AU to 0.02 AU for white dwarf stars with masses ranging from 0.4 to 0.9 times the mass of our Sun, whereby 1.0 AU is basically the mean distance of the Earth from our Sun.
The orbital period of any planet in the continuously habitable zone of white dwarf stars will range from around 4 to 32 hours and the planets are expected to be tidally-locked whereby the star-facing hemisphere of the planet will experience permanent day, while the other hemisphere will experience permanent night. The night side of such a planet can be warmed by the global circulation of heat from the day side of the planet which can prevent the formation of a cold-trap on the night side. Since the orbital period and spin period of a tidally-locked planet are both the same, an Earth-size planet in the continuously habitable zone of a white dwarf star will experience Coriolis and thermal forces that are similar to those on the Earth.
Earth-size planets in or near the continuously habitable zone of white dwarf stars can be detected via the transit method where the individual photometric output of a large number of white dwarf stars can be continuously monitored to look for any dimming that can be associated with the transit of an Earth-size planet in front of a white dwarf star. Due to the small size of a white dwarf star, the transit of an Earth-size planet will block out a significant fraction of the white dwarf star’s total photometric output or even completely block out the entire star if the star is sufficiently small. The small size of a white dwarf star also favours the detection of transiting objects that are smaller than the size of the Earth. The transit durations of Earth-size planets in the continuously habitable zone of white dwarf stars are estimated to last for a couple of minutes or so, thereby requiring high cadence observations to record the proper light curves that are indicative of such transit events.
Measurements of the distance and spectrum of a white dwarf star will allow its mass, luminosity, atmospheric composition and radius to be determined. Therefore, with the size of the white dwarf star known, the measured transit depth of a transiting planet enables the size of the transiting planet to be directly determined. On the contrary, the mass of the transiting planet cannot be determined from Doppler measurements as the spectra of cool white dwarf stars are generally featureless. However, if the white dwarf star has multiple transiting planets, gravitational interactions among the planets can cause measurable transit timing variations which can be use to estimate the mass for each of the planets.