What are Alpha Centauri, Proxima Centauri and Proxima b?
Alpha Centauri (or Alpha Cen) is a triple star system. It is the closest stellar system from the Sun (4.24 light years). This ensemble of 3 stars includes two Sun-like stars - Alpha Centauri A and B - and a red dwarf called either Alpha Centauri C or Proxima Centauri. The name Proxima comes from the fact that it is currently the closest of the 3 Alpha Centauri stars.
Alpha Centauri A and B are separated by only 20 Astronomical Units (1 Astronomical Unit, or AU, is the Earth-Sun distance), while Proxima is on a 15,000 AU-wide orbit around the pair.
Proxima b (short for Proxima Centauri b) is the name given to the planet discovered around Proxima Centauri.
What do we know about the star Proxima?
Being the nearest star to the Sun we know this star quite well. It's a small reddish star that belongs to the largest population of stars in the galaxy: the red dwarfs. Its distance from the Sun is accurately determined by parallax: 4.24 light years. We also know its temperature - 3100 K, the Sun is 5800 K - and its luminosity: Proxima is 700 times less bright than the Sun. Its radius - 14.5% of Sun's radius - was measured directly by interferometry thanks to its proximity. The mass of Proxima is fairly well constrained by models at 12% the mass of the Sun.The age of Proxima is deduced from that of its solar-type companions Alpha Cen A and B - much easier to determine - and assuming they are siblings. Proxima, as the whole Alpha Centauri system, is about as old as the Sun: 4.5 to 5 billion years.
Proxima is also a very active star. Its luminosity varies, producing frequent flares. Also it is overall much fainter than the Sun but it emits nearly as much X-rays and extreme UV as the Sun.
While the luminosity of our Sun increases with time, the luminosity of Proxima decreases significantly during the first hundred million years of its life and then stopped evolving.
What do we know about the planet Proxima b?
We know very accurately its orbital period: 11.2 days. Because we know fairly well the mass of its star we can use Kepler's 3rd law to convert this orbital period into an orbital distance of 0.05 UA: 5% of the Sun-Earth distance. We also know the luminosity of the star so we know how much energy Proxima b receives from Proxima: about 65% of what the Earth receives from the Sun.
To induce the measured velocity modulations on its star, the mass of Proxima b must be higher than 1.3 Earth masses. A better constraint on its mass would require to know well the inclination of its orbit from the line of sight, which will require observations that we cannot achieve today. But the actual mass of the planet is likely to be close to its minimum mass. It has a 87% chance to be less than twice the mass of the Earth and a 96% chance to be less than 5 times the mass of the Earth. It is almost certainly a rocky planet. Almost.
Is there water and an atmosphere on the planet Proxima b?
We don't know. We will need new types of observations to find out. Hopefully such observations will be possible during this decade.
About 0.1% of the mass of the Earth is water. Most of it is not in the ocean but mixed with the mantle. The diversity of exoplanet densities as well as planet formation theories tell us that planets can be born dryer but also with more than 20% of water.
For a period of 100 to 200 million years scientists believe that Proxima b received so much incident starlight that it was too hot for liquid water. During this hot phase and because of the harsh radiation from its active star (X-rays, extreme UV, particles) the planet must have lost to space quite a lot of gas and one ocean's worth of water. However depending on the initial inventory, there could still be a lot of it.
So as far as we know, Proxima b could resemble Mercury, with no water and no atmosphere, or it could be covered by deep oceans beneath a thick atmosphere.
Could Proxima b be another Earth?
It depends on what this means but the short answer must be NO. Proxima b and the Earth differ by too many aspects. Putting aside the fact that only the minimum mass of Proxima b is known, the two planets must have formed differently. The spectrum of these two stars is very different, which has strong implications on the climate. Because of its close distance to its star and contrary to the Earth, Proxima b is subjected to strong tidal forces that affected its internal structure and its rotation. The tides only allow two types of rotation for Proxima b. If the orbit is circular then the rotation period must equal the orbital period: rotation and orbits are synchronized and the planet always presents the same hemisphere to its star (like the Moon to the Earth). If the orbit is slightly eccentric (which is not known but possible) then the planet rotates 3 times every 2 orbits, like Mercury. Proxima experienced an early hot period when its star was brighter and was subjected to strong energetic radiations eroding its atmosphere.
Therefore, even if Proxima b could be habitable and, why not, inhabited, it is not another Earth.