What day/night cycles, climate and seasons would experience Alpha Centauri Bb inhabitants?

Question

Alpha Centauri Bb is an exoplanet orbiting Alpha Centauri B. It is asserted that given the close distance to the star the planet should be tidally locked.

The orbiting period of the planet is about 3.2 days.

If the planet has no atmosphere (which is very possible due to proximity to the star), its dark side should experience low temperatures like permanently-shadowed areas of Mercury do.

At the same time the planet is about 11 AU from the other star, Alpha Centauri A.

This possibly means that the planet should experience quasi-day/night cycle each 3.2 days.

My questions are:

1. To what temperatures the dark surface of such planet could be heated? Is there possibility of liquid water?

2. Will the radiation of the second star be enough to provide normal day-like illumination and heating?

3. Will the calendar on such a planet differ sufficiently from a calendar of a planet that experiences day/night cycles from the nearest star?

4. Will such planet experience seasons and how they would be arranged?

Answer 1

The Wikipedia article on the system says $\alpha$ Cen A has a luminosity of $L = 1.5~\mathrm{L}_\odot$, and that the A-B system has a period of $80$ years. At a distance of $d = 11~\mathrm{AU}$ (which is not mentioned in the wiki, so I'm trusting the OP has a good source for this), the power per unit area received at the location of B from A is $$ x = \frac{L}{L_\odot} \left(\frac{d}{1~\mathrm{AU}}\right)^{-2} = 0.012 $$ times that which the Earth receives from the Sun, which is certainly not much.

Now, let's assume the dark side of the planet is indeed cold. The $80$-year period means the thermal equilibration timescale is much shorter than the timescale of variation in power received.¹ If we just consider the case when A is in opposition, the ratio of light-intercepting cross-sectional area to heat-emitting blackbody area will be $1$, not $1/4$ as it is for a spinning planet. Throw in a little Stefan-Boltzmann Law, and you find the planet's temperature to be $$ (4x)^{1/4} T_\text{Earth} = 120~\mathrm{K}, $$ where $T_\text{Earth} = 254~\mathrm{K}$ is the non-greenhouse average temperature of the Earth.

This is a rough calculation of course, but it shows that there is no significant heating, even under the best circumstances, from $\alpha$ Cen A. This makes sense, since the distance from A to the planet is further than from the Sun to Saturn.

Thus:

1. No, there will not be liquid water due to this effect. A quick check of the phase diagram of water assures us it is not liquid at any pressure at $-150^\circ\mathrm{C}$.

2. Just as there is very little heat, there is very little lighting. However, the amount is not vanishingly small. As this blog points out, you can read a book on Pluto just using the Sun's light, so this planet would not be completely dark to our eyes with their remarkable dynamic range.

3. I will interpret "calendar" to mean "progression of seasons," in which case...

4. I suppose there might be some changes as certain gasses sublimate, similar to how Pluto or comets start outgassing when they approach the Sun. The more interesting "seasonal" variation will be spatial, not temporal. There could be a very thin strip of nice temperatures near the terminator,² though I wouldn't be surprised if this moved around too much for there to be a permanent region conducive to liquid water.

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¹ If you think the planet might have more thermal inertia than this, consider how quickly the Earth cools off as the seasons change.

² This seems like it would make for a good science fiction setting.