Figure 1: Artist’s impression of what could be an isolated Neptune-like planet.
The orbits of some Kuiper Belt Objects suggest the presence of a planet with ~10 times the mass of Earth on a very distant ~700 AU semimajor axis orbit around the Sun. Assuming the hypothesized planet is Neptune-like (i.e. the planet is modelled as a simple two-layer model that consists of a rocky/icy core and a hydrogen/helium envelope), Ginzburg et al. (2016) show that the planet can potentially be detected via the internal flux it gives off as it cools over time. Because the planet is so far from the Sun, its own internal flux is much greater than the incident irradiation it gets from the Sun. As a result, the thermal evolution of the planet progresses as if the planet were an isolated object. Measuring the temperature of the planet can allow the mass of its hydrogen-helium envelope to be constrained. This is because a thick hydrogen-helium envelope acts as an insulator, slowing down the planet’s rate of cooling. If the planet’s effective temperature is ~50 K, its wavelength at peak emission will be ~60 μm.
Figure 2: Effective temperature as a function of age for a planet with ~10 times the mass of Earth and whose hydrogen-helium envelope accounts for 14 percent of its total mass. Ginzburg et al. (2016)
Figure 3: Effective temperature of 4.5 billion year old Neptune-like planets as a function of their atmospheric mass. The curves are for three values of the planet’s radius in units of Neptune’s radius: 3/4 (bottom black line), 1.0 (middle blue line), and 4/3 (top red line). These radii correspond to planet masses of about 5.4, 17, and 54 times the mass of Earth, respectively, assuming Neptune’s composition and accounting for the gravitational compression of the planet’s core. Ginzburg et al. (2016)
Figure 4: Contours of the effective planetary temperature (solid blue lines) and of the temperature at the atmosphere-core boundary (dashed black lines), at an age of 4.5 billion years, as a function of the planet’s radius and atmospheric mass. A solid crust forms below the bottom dashed black line and cooling is no longer dominated by the insulating effect of the atmosphere as the atmosphere is too thin. An atmospheric mass fraction of 0.5 is also indicated (dotted red line), assuming Neptune’s composition and accounting for the gravitational compression of the planet’s core. Ginzburg et al. (2016)
Ginzburg et al. (2016), “Blackbody Radiation from Isolated Neptunes”, arXiv:1603.02876 [astro-ph.EP]