I know it’s a direct follow-up from my last post, but why not? After all, Sirius B’s companion world is a fascinating place in my science-fiction-cum-space-opera setting. I now have hard numbers, which dictate tidal locking, the question of it being a moon, the orbital distance, the seasons, and more; even possibilities for eclipses.
The first and most important question is orbital distance: Cerberus is supposed to be at a more-or-less Earth-like level of illumination, which means, given that white dwarf stars are very dim, it will need to be close. How close? 0.02 AU or so, about 3 million kilometers. For comparison, Mercury never approaches closer than 0.3 AU from the Sun, so Cerberus is less than a tenth as far away from its sun as Mercury is from ours. And that’s just to get Earth-like levels of illumination. The orbit is still dynamically stable, and well outside the Roche limit (within which tidal forces break a planet apart), so it’s all good.
One upshot, however, is it would almost certainly be tidally locked. Ordinarily this means a 1:1 spin-orbit resonance; in other words, the planet rotates once for every orbit it makes around the sun, and always presents the same face to its star, meaning the sun remains motionless in the sky: one hemisphere of eternal day and another of eternal night. But not necessarily.
At higher eccentricities (i.e. more elliptical as opposed to what are called circular orbits), 1:1 tidal locks become unstable, and there could be what are called higher-order spin-orbit resonances. The first that tends to crop up is the 3:2 spin-orbit resonance: the planet rotates three times for every two times it orbits. It’s not just theoretical: Mercury itself exhibits this phenomenon (and has an orbital eccentricity of 0.21 (for reference, 0 is perfectly circular; 0.95 and higher is elliptical to the point of being comet-like). Even higher-order resonances are possible, such as the 2:1 resonance, where the planet spins twice for each orbit. At an eccentricity of, say, 0.3, this becomes likely.
Since I’ve already featured another world in a conventional 1:1 tidal lock (Proxima Centauri’s companion Thalassa) in a previous story, I’ll go with this more exotic spin-orbit resonance. In the case of Mercury these higher-order tidal locks lead to very long solar days (indeed, the solar day as witnessed on Mercury is longer than a year, in Mercury’s case months long), but since Cerberus is orbiting at a very short range the orbital period is correspondingly less. How much less? For Cerberus, orbiting Sirius B at 0.02 AU, a year would go by in 24 hours 32 minutes. A 2:1 tidal lock leads to an apparent solar day (sunrise to sunset) being exactly the same as the local year: in Cerberus’s case, a length almost identical to Earth (and even close to that of the Martian day, or “sol”)! So utterly alien a mechanism, so Earth-like a result. How can I resist?
The high eccentricity of the planet’s orbit also leads to the intriguing property of the sun rising and then stalling, reversing course across the sky somewhat, and then resuming its path; this is seen on Mercury in real life, and is an effect of the planet racing toward the sun in its orbit faster than it rotates (if that makes any sense). With a solar day of just 24 hours (instead of months) and a higher eccentricity of 0.3 this effect will be much more obvious on Cerberus than on Mercury.
The eccentricity leads to a pumping of the daily range of temperatures: at a semi-major axis 0.02 AU, a 0.3 eccentricity means that perihelion is as close as 0.014 AU (2.8 million kilometers), and aphelion swings out to 0.026 AU (5.2 million kilometers). Though since there are mere hours between these extremes the effects on temperature won’t be too pronounced.
More pronounced will be Sirius A’s seasonal effects: Sirius B’s much brighter companion star is only as far away from it as the planets of the outer solar system are to us: 8 AU to 31 AU, varying over the 50-year period of its orbit. At maximum distance Sirius A shines as brightly as 1% of Earth’s sunlight: perhaps enough to make night more like twilight when it’s up, but not a decisive contributor to the climate. At closest approach, however, Sirius A shines 40% as bright as the sun does from Earth! That’s a lot of extra illumination, enough to make it outright daylight when it rises every night, and will lead to really decisive seasonal changes.
Without Sirius A’s influence, the average temperature of Cerberus would be around 5 degrees Fahrenheit; cold, but keep in mind it has a thin atmosphere, a tenth as much as Earth’s, and without the greenhouse effect Earth’s temperature would be around 0 Fahrenheit. A tenth as much greenhouse effect leads to this outcome. Cerberus has very salty oceans, though, so the chances of a global freeze are minimal. In summer, though, the average temperature would rise from 5 degrees Fahrenheit to 45 degrees Fahrenheit, a 40-degree increase. Keep in mind this is a 50-year cycle, not a 1-year cycle.
As for Cerberus being a moon, I’m afraid this option is just about eliminated: the mathematics actually work on it being a moon. Despite it being in such close proximity, a 10-Earth-mass primary (comparable to Neptune) could hold onto a moon of Cerberus’s size if it were orbiting just outside the Roche radius, but the moon’s orbital period (and hence Cerberus’s day) would be a mere 6 hours. Far too short for what I have in mind, which is for a land with an eerily earth-like day and night (in contrast to the other planet humans crossed interstellar distances to colonize, which is tidally locked to Proxima Centauri and doesn’t even really have a day-night cycle).
However, there is another cool option: a planet even closer to Sirius B than Cerberus itself is, so that it may transit in front of the sun as seen from Cerberus. How big could such a planet be as seen from Cerberus? Might it cause a total eclipse of the sun on Cerberus? The answer, perhaps surprisingly, is yes. There is just enough room dynamically for a planet inward of even Cerberus’s 0.02 AU distance. About 0.01 AU would work nicely for this purpose. Cerberus itself swings as close as 0.014 AU, but surprisingly this setup could still be stable, even at such close ranges, considering we’re dealing with planets that are smaller than Earth here.
It would be even more stable if they shared an orbital resonance with each other; at these distances a 3:1 orbital resonance between these two planets would be the likeliest to arise. Orbital resonances often pump eccentricity, especially at such close ranges, and so the chances the inner planet would acquire an orbit that crosses Cerberus’s would be high. However, if the resonance involves what’s called apsidal corotation, the orbits of these two planets would be locked so their perihelia and aphelia are either aligned (i.e. the ellipses stretching out in the same direction from the star), or anti-aligned (i.e. the ellipses stretch out in exact opposite directions from the star). In which case even if their orbits crossed they would never collide, or destabilize. Tentatively, I’ve supposed that the inner planet orbits at 0.01 AU and has an eccentricity of 0.35 (somewhat higher than Cerberus), meaning its aphelion is 0.0135 AU, close to crossing Cerberus’s perihelion, and its perihelion is a mere 0.0065 AU, only a million kilometers from Sirius B. Still well outside the Roche limit.
As for this apsidal corrotation resonance, these resonances also have the helpful property of locking the planets’ orbits so they’re nearly co-planar, meaning that when there’s an alignment of the star, the inner planet, and the outer planet, it will be perfect every time, leading to a transit (or eclipse) as seen from the outer planet. And with a 3:1 orbital resonance, the inner planet would zip around Sirius B in a mere 8 hours, meaning there’s a possibility of multiple eclipses per day on Cerberus. Trippy.
Even the math works out on the inner planet actually being able to eclipse: I haven’t double-checked this, but so far it seems that to always be larger than Sirius B as seen from Cerberus, the inner planet would need to be only 4250 kilometers in radius, about two-thirds that of the Earth. Even at a Mercury-like density, the inner planet would only need to weigh in at 0.3 Earth masses. Somewhat smaller than Cerberus, at a tentative 0.5 Earth masses. It helps that Sirius B only subtends 10 arcminutes in the sky as seen from Cerberus, so it’s much smaller than our sun (it burns hotter than our sun, and outputs more radiation in the ultraviolet, so a planet needs to be correspondingly further away to get an Earth-like level of total energy).
As for the inner planet of the Sirius B system, its nature remains sketchy, but so far the idea is that it might have been similar to Cerberus originally, but the high temperatures (about 500 degrees Fahrenheit at its average distance from Sirius B…) and the close proximity to the sun’s radiation has stripped most of the atmosphere, so only a thin oxygen envelope remains. Perhaps a rarefied 1% of Earth’s pressure, instead of Cerberus’s nigh-breathable 10%. The soil might have been heavily oxygenated, leading to a Mars-like reddish color across the world. Oceans of course have long since evaporated, water and volatiles stripped away, so Martian-style dust storms rage across the desertified surface.
All this comes across like a hot version of Mars, though, so another idea I’ve had has leaned on the thought that at 0.3 Earth masses the planet might have enough geological energy for plate tectonics, like Earth…and Venus. Notice Venus, despite massing almost as much as Earth, doesn’t have obvious plates like Earth but is geologically active: certainly its surface isn’t heavily cratered and billions of years old. The exact reasons remain mysterious, but scientists have speculated that Venus, due to lacking oceans to lubricate its plates, undergoes periods of global mass volcanism rather than steady plate tectonic movements. So a bigger Mars may well have a more Venis-like geology; what if the inner planet, as of when the astronauts visit the system, is in the middle of one of these global resurfacing events? In that case the surface might be Mars-like, but with massive volcanism worldwide. A fascinating planet.
As for the planets that lie beyond the confines of this pair, and in particular around Sirius A…well, that’s for another post. In the meantime, I’m enjoying Cerberus for what it is, and brainstorming the next steps in bringing my vision of the Sirius system to life…