We can haz finded Equestria! :O · 9:46pm
Well... maybe if Equestria suddenly had 3 suns... uhm...
But at any rate, close-by red dwarf Earth-size planet! Yay! We can actually SEE this thing in a few years with planned space-based telescopes!
Now, there are some significant factors to consider which tend to make the possibility of it being habitable drop considerably:
1. Tidally-locked. The habitable zone around a red dwarf star is MUCH closer to the star than for a yellow or orange main-sequence star. This means the star's gravity can apply the breaks to a planet's rotation rather quickly. This planet is 10 times closer to its star than Mercury, and Mercury's tidally locked.
2. Solar wind and radiation. The sun-facing side is being BLASTED by solar wind, flares, and X-ray radiation from its close proximity to the star. This tends to be bad for squishy organic life.
3. No magnetic field. To put it simply, a planet needs a liquid iron core or some form of conducting fluid (salty water works for icy bodies like Europa and Ganymede) along with a dynamo effect from rotation in order to generate a global magnetic field. Tidally-locked or nearly tidally-locked planets (Mercury and Venus) will only posses small residual regions of magnetism (like Mars has, since Mars' global field collapsed when it cooled and the core solidified) and thus the solar wind and radiation can merrily pummel the atmosphere and ionize the crap out of it, as well as gradually strip it away. Water is VERY vulnerable to this, since the hydrogen generated by photolysis is very light and readily escapes from the upper atmosphere. CO2, with its powerful CO bonds, is much less vulnerable and stays behind... hence, Venus.
4. It's a bit larger than Earth. This means it can hold a denser atmosphere for a longer period even without a magnetic field. But that atmosphere will be composed almost entirely of carbon dioxide and possibly such gasses as cyanide ion, nitriles, and nitrogen oxides if nitrogen was present at high levels during its formation or from cometary bombardment afterward.... a very possible situation given it's likely Proxima Centauri is a captured star by Alpha Centauri A and B, an event which would have generated massive gravitational perturbations through the dwarf star's equivalent Oort Cloud as well as A and B's (assuming all possessed a field of distant icy bodies), flinging them all over the place!
5. Total solar flux vs fractional effects of the spectrum. Proxima Centauri b receives about 65% of the solar flux Earth receives. However, looking only at the total flux a planet received from its star doesn't give the full story. Different wavelengths heat materials differently (just think of microwaves, for instance). Red dwarf stars emit far more infrared light than our Sun. Infrared heats dark materials and water MUCH more effectively than visible light. Think of a heat lamp. That's infrared. The habitable zones of red dwarfs, I believe, should be moved outward significantly to compensate for this fact. Given that Proxima Centauri b is close to the inner edge of the speculated habitable zone... I believe they will find it quite a bit more toasty than they currently believe, at least for the sunlit side (the atmospheric density will determine how much heat transfer occurs between the light and dark sides).
So, Proxima Centauri b will likely be a very hot Earth, with an atmosphere in-between densities and composition between Venus and Earth, but at a temperate probably several hundred degrees lower than Venus on the daylight side (atmospheric composition and density are two huge variables which affect temperature tremendously) of between 50-to-350 C. If the atmosphere is thin enough from solar wind stripping, there may be a sizeable temperate zone far into the night side as the hot wind from the day side cools as it rushes to the dark side, which might not be always in total darkness all the time due to the light from the much larger A and B stars which would come into view periodically as Planet b orbits Proxima... but since they are quite distant (15,000 AUs from Proxima), they'd be only very bright stars and the total light would likely be akin to what Pluto receives at its furthest distance from the Sun... a very pale twilight. BUUUUUT, that assumes the sky is cloudless on the dark side, which is UNLIKELY if there is significant vapors of water and/or sulfuric acid and/or nitrogen oxide hazes forming thick clouds which would be more or less permanent.
Another note, IF water is present in large quantities, expect VIOLENT and permanent rings of massive thunderstorms some ways into the dark side. The heat transfer would be quite extensive, resulting in a rapidly convecting atmosphere of high winds at the upper levels rushing hot, moist air to the dark side, with cooled air having sunk at the dark side, rushing then toward the day side... a perpetual world-spanning heat dynamo.
Possible attenuating factors:
a) the planet may have spiraled inward over the course of the capture of Proxima by the A-B pair. This would mean it may have had much more water and volatiles if it formed further out, AND might not have been tidally locked initially, thus a much stronger residual magnetic field could still exist, protecting it to a degree from the solar wind. However, this would also mean a denser atmosphere would remain intact, and if it was as denser or denser than Earth's, the runaway greenhouse from the infrared radiation would soon take effect and the water would turn to super-heated steam, turning the planet into a giant autoclave.
b) It could have been smacked really hard in the side by a Pluto-sized body during the perturbment from the Proxima-A-B capture event, which might temporarily spin up its rotation if the blow was glancing and generate a transient magnetic field. It could also spin up more as all the fragments from the collision coalesced back onto the main body, due to the conservation of momentum rule (the commonly cited example is ice skaters pulling their arms inward to spin faster).
But, barring those two events, the planet will likely be hot, dry, and heavily irradiated or some sort of in-between steam bath.
Alas, if it had only been in a positive equivalent to Mars. It's larger size and denser atmosphere would have been much more conducive to life at that relative position, given the infrared heating. Though in that case, the life would have issues with any form of photosynthesis due to the visible light being so much less. I suppose it's possible life could utilize a different molecule to capture energy from infrared (we don't know how likely it is for random biochemistry to form such compounds and incorporate them into a phytochemical system of electron exchange, but there's nothing to suggest it can't occur), but as it has a lower total energy per photon, even with it, any presumptive photosynthetic life on PCb would end up growing at a much slower rate than Earth plants and photosynthetic microorganisms are capable of. They'd also likely appear black, since they'd have to evolve many phytopigments to capture as much light energy as possible and there'd be very strong evolutionary pressure to do so if plant-eating creatures also arose.
EDIT: Oh, and there's also the uncertainty of orbital eccentricity to think about... which could change rotational dynamics significantly and result in a non-permanent dark side, or even retrograde rotation... which could give it a slow rotation equivalent to Mercury's if the eccentricity is above about 0.15 and thus generate a magnetic field a fraction of Earth's, and perhaps enough to shield the atmosphere significantly. BUT, that is only likely if the planet was perturbed or was impacted, otherwise it's orbit will be almost perfectly circular as has been observed in many red dwarf planetary systems identified by the transit method. High eccentricity would ALSO result in tremendous gravitational tidal forces upon the core, increasing its temperature and fluidity... creating perhaps a high level of volcanism. SO MANY VARIABLES!!!