Planets orbiting binary stars

Let us now take a closer look at thermal properties of the Janus type planets. To recap - for these, in the center of the system are two closely orbiting binary stars which are in turn orbited by a planet sufficiently far away so that its orbit is stable from perturbations. What temperature variations can be expected on the planet suface?

First, from an outer orbit, the two stars will always be reasonably close together in the sky (similar to how Mercury is never far from the Sun). Thus, there will be a regular day and night pattern driven by the length of the rotation period of the planet, a situation that both hemispheres are illuminated can not arise.

Second, if the stars are different in luminosity, as they orbit each other within one orbital period there will be the brighter star close to the planet, and a bit more than half an orbit later the fainter. To the degree of luminosity difference and distance between the stars, this will cause a temperature variation on the planet.

Third, if the planet's axis is tilted, there will be a northern / southern hemisphere difference in irradiation dependent on whether the axis is tilted towards the binary or away.

Finally, if the orbit of the planet is eccentric (or the orbit of the binary stars is), this will also lead to temperature differences (but this is not special for a binary).

Thus, in addition to daily and regular seasonal patterns, there can be a binary-specific seasonal pattern with a different frequency - which means there can be muted seasons when planetary 'summer' aligns with binary 'winter' and super-seasons when they co-incide.

Observing 'binary' seasons

Let's start with the following configuration file (note that Janus has been moved out to 4 au distance from the barycenter):

orbital_sim_timestep 10.0

mass 0.96
T_surf 5600.0
name Janus-A

mass 2.0
T_surf 8000.0
name Janus-B

name Janus
mass 1.28
radius 1.0
semimajor_au 4.0
eccentricity 0.01
semimajor_binary_au 0.3
eccentricity_binary 0.01
axis_tilt 35
dec_offset 0.0
rot_period_h 12.0
mean_albedo 0.3
mean_heat_capacity 2.0
mean_depth 0.05
elements_lat 16
elements_lon 24

evolve_d 35
timestep 100.0
file janus_T.dat
var_z temperature


This runs for a bit more than one orbital period of the central stars. The configuration is initialized with the heavier and hotter Janus-B close to the planet. Running to day 52.5 get the system half an orbit further, i.e. to a situation where the cooler Janus-A is closest to the planet and Janus-B is as far away as possible.

Running the file gets this, i.e. the difference amounts to a bit more than 10 K maximal temperature.

Temperatures for Janus-B closest and farthest to the planet.

At both positions, the stars are aligned with the barycenter of the system. A quarter of an orbital period away, they apparently move forward (resp. backward) in the sky. This slightly shifts and distorts the location of the daylight peak in longitude:

Temperatures for the Janus-B forward and backward of the barycenter.

Investigating seasons

In order to see the temperature evolution for a summer or winter axis alignment, we might opt to run the full simulation for a quarter or three quarter orbital periods. With the chosen high resolution of the orbital and thermal timesteps, this may take a while though. There are a couple of steps that can be used to get a result faster.

First, inserting a block

evolve_d 500

runs the orbital simulation without thermal simulation (which is much faster) before the thermal simulation is started. To study the response of the system close to the end of the orbital period of 1698 days, say at day 1500, we may e.g. run the orbital simulation for 1400 days and then switch to full evolution for 100 days to get the thermal solution converging.

For a (near)-circular orbit, another possibility is (since the main thing that varies over the course of an orbit is the alignment of the axis tilt) to set dec_offset to a non-zero value, for instance 90 degrees starts in northern summer.

If the orbit is eccentric, the keyphrase apoapsis_init true can be used to change from the default start at periapsis to apoapsis. This effectively means half an orbit of evolution is skipped.

The combination of these techniques usually allows to get reasonably fast result anywhere during the orbit.

Continue with Eclipses.

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