How big and how bright is Planet 9 if it really exists? What is its temperature and which telescope could find it? These were the questions that Christoph Mordasini, professor at the University of Bern, and his PhD student Esther Linder wanted to answer when they heard about the possible additional planet in the solar system suggested by Konstantin Batygin and Mike Brown of the California Institute of Technology in Pasadena.
The Swiss scientists are experts in modelling the evolution of planets. They usually study the formation of young exoplanets in disks around other stars light years away and the possible direct imaging of these objects with future instruments such as the James Webb Space Telescope. Therefore, Esther Linder says: “For me candidate Planet 9 is a close object, although it is about 700 times further away as the distance between the Earth and the Sun.” The astrophysicists assume that Planet 9 is a smaller version of Uranus and Neptune – a small ice giant with an envelope of hydrogen and helium. With their planet evolution model they calculated how parameters like the planetary radius or the brightness evolved over time since the solar system has formed 4,6 billion of years ago. The study was financed by the research project of the Swiss National Science Foundation PlanetsInTime and the National Center for Competence in Research (NCCR) PlanetS.
In their paper accepted by the journal “Astronomy & Astrophysics” the scientists conclude that a planet with the projected mass equal to 10 Earth masses has a present-day radius of 3.7 Earth radii. Its temperature is minus 226 degrees Celsius or 47 Kelvin. “This means that the planet’s emission is dominated by the cooling of its core, otherwise the temperature would only be 10 Kelvin,” explains Esther Linder: “Its intrinsic power is about 1000 times bigger than its absorbed power.” Therefore, the reflected sunlight contributes only a minor part to the total radiation that could be detected. This also means that the planet is much brighter in the infrared than in the visual. “With our study candidate Planet 9 is now more than a simple point mass, it takes shape having physical properties,” says Christoph Mordasini.
Simulated structure of planet 9. Christoph Mordasini, Esther Linder
Arxiv - Evolution and magnitudes of candidate Planet Nine (6 pages)
The researchers also checked if their results explain why planet 9 hasn’t been detected by telescopes so far. They calculated the brightness of smaller and bigger planets on various orbits. They conclude that the sky surveys performed in the past had only a small chance to detect an object with a mass of 20 Earth masses or less, especially if it is near the farthest point of its orbit around the Sun. But NASA’s Wide-field Infrared Survey Explorer may have spotted a planet with a mass equal to 50 Earth masses or more. “This puts an interesting upper mass limit for the planet,” Esther Linder explains. According to the scientists, future telescopes like the Large Synoptic Survey Telescope under construction near Cerro Tololo in Chile or dedicated surveys should be able to find or rule out candidate Planet 9. “That is an exciting perspective,” says Christoph Mordasini
he recently renewed interest in a possible additional major body in the outer solar system prompted us to study the thermodynamic evolution of such an object. We assumed that it is a smaller version of Uranus and Neptune. We modeled the temporal evolution of the radius, temperature, intrinsic luminosity, and the blackbody spectrum of distant ice giant planets. The aim is also to provide estimates of the magnitudes in different bands to assess whether the object might be detectable. Simulations of the cooling and contraction were conducted for ice giants with masses of 5, 10, 20, and 50 Mearth that are located at 280, 700, and 1120 AU from the Sun. The core composition, the fraction of H/He, the efficiency of energy transport, and the initial luminosity were varied. The atmospheric opacity was set to 1, 50, and 100 times solar metallicity. We find for a nominal 10 Mearth planet at 700 AU at the current age of the solar system an effective temperature of 47 K, much higher than the equilibrium temperature of about 10 K, a radius of 3.7 Rearth, and an intrinsic luminosity of 0.006 Ljupiter. It has estimated apparent magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.4, 21.0, 20.1, 19.9, and 10.7, and WISE W1-W4 magnitudes of 20.1, 20.1, 18.6, and 10.2. The Q and W4 band and other observations longward of about 13 microns pick up the intrinsic flux. If candidate Planet 9 has a significant H/He layer and an efficient energy transport in the interior, then its luminosity is dominated by the intrinsic contribution, making it a self-luminous planet. At a likely position on its orbit near aphelion, we estimate for a mass of 5, 10, 20, and 50 Mearth a V magnitude from the reflected light of 24.3, 23.7, 23.3, and 22.6 and a Q magnitude from the intrinsic radiation of 14.6, 11.7, 9.2, and 5.8. The latter would probably have been detected by past surveys.