A new exoplanet has been just discovered around the star Teegarden, at only 12 light years away.
TLDR version: at this point there are too many unknowns to determine whether this planet candidate is habitable.
The discovery paper for this system, Zechmeister et al. (2019) "The CARMENES search for exoplanets around M dwarfs. Two temperate Earth-mass planet candidates around Teegarden's Star" is available on the arXiv. Table 1 lists the properties of the star and table 2 lists the properties of the planets.
The planetary quantities we have reliable estimates for are the minimum masses, the orbital periods and the distances. The eccentricities are consistent with zero so I'm going to assume for the moment that the orbits are circular. The reason that minimum mass is relevant is that this is an example of a radial velocity detection, which results in a degeneracy between the inclination of the planet's orbit to the line-of-sight and the mass of the planet.
According to figure 13 in the discovery paper, Teegarden b is too close to the star to be in the conservative estimate of the habitable zone, though it is in the optimistic habitable zone. The Earth Similarity Index (ESI) appears to be a fairly misleading metric (I am of the opinion that ESI is a bad metric that should be abandoned), from the discovery paper:
In addition, planet b receives nearly the same stellar flux as the Earth and therefore has a nearly identical equilibrium temperature, but is outside the conservative HZ. As discussed by Kopparapu et al. (2014), this is caused by a runaway greenhouse effect that is due to water vapour starting at lower insolation for low-mass stars. This effect is neglected in the ESI calculation and leads to the curious fact that planet b has a higher ESI value than planets inside the conservative HZ.
The position of Teegarden b therefore suggests it may have undergone a runaway greenhouse effect, though this might be avoided if it can build up enough reflective cloud cover on the daylight hemisphere, or if it is a desert planet without enough water to destabilise the climate.
Even if a planet is located in the habitable zone, it is not necessarily habitable. An obvious counterexample would be the Moon.
Terrestrial or not?
The next question: are these planets terrestrial? Unfortunately we don't know: Teegarden b does not transit the star, and there has so far been insufficient coverage of Teegarden c to say whether it transits. As a result, we do not know the radii of the planets so we cannot tell whether or not the planets have densities compatible with being terrestrial. The minimum masses are low enough that these planets do likely fall below the transition region between rocky and non-rocky planets suggested by Kepler data, see for example Rogers (2015) "Most 1.6 Earth-Radius Planets are not Rocky" - using the mass-radius relationships of Zeng et al. (2016) "Mass-Radius Relation for Rocky Planets based on PREM" the transition is somewhere around 3–5 Earth masses.
Another point of comparison here is the other known system of low-mass planets around an ultracool dwarf star: TRAPPIST-1. In this case, despite the small size of the planets, the inferred masses indicate the presence of substantial amounts of volatiles, e.g. Dorn et al. (2018) "Interior characterization in multiplanetary systems: TRAPPIST-1" where the volatile contents of the planets are estimated to correspond to a few percent by mass, compared with 0.02% by mass for the Earth. A planet like this would be very different to the Earth, in an optimistic scenario it might result in an ocean planet. The habitable zone for ocean planets would be different to that for Earthlike planets, since the negative feedback of continental weathering would not occur.
Red dwarf stars
Red dwarf stars have a variety of problems when it comes to habitability. One issue is that they have an extended high-luminosity pre-main sequence phase which might result in runaway greenhouse effects and/or severe water-loss on close-in planets, see Ramirez & Kaltenegger (2014) "The Habitable Zones of Pre-Main-Sequence Stars".
An additional problem is that red dwarf stars have severe stellar activity that would erode an Earth-like atmosphere in a very short amount of time, as an example Garcia-Sage et al. (2017) "On the Magnetic Protection of the Atmosphere of Proxima Centauri b" estimate an Earthlike atmosphere at Proxima Centauri would be lost in less than 400 million years. Teegarden's Star is fairly quiet for its spectral type, but it is an old star and was likely far more active in its youth.
These issues are not necessarily fatal, outgassing from volcanism might be able to replenish the atmosphere to some extent after the stellar activity dies down, or if the planet was born with a large amount of volatiles it might be able to emerge as a habitable planet. Unfortunately we don't have sufficient data on habitable zone planets around red dwarf stars to know for sure.
A further issue is that the atmospheric chemistry on planets around stars like Teegarden's Star would likely result in substantial quantities of carbon monoxide accumulating in the atmosphere, see Schwieterman et al. (2019) "A Limited Habitable Zone for Complex Life". This would be lethally unpleasant for any human visitors (or other organisms that use haemoglobin as their oxygen carrier) caught outside without an air supply. Note that haemoglobin is not the only possible oxygen carrier: some groups of life on Earth use alternatives (haemerythrin, haemocyanin) that are less vulnerable to carbon monoxide poisoning, as noted by Howell (2019) "Comment on "A Limited Habitable Zone for Complex Life" (Schwartzman et al. 2019 ApJ 878, 19)":
In short, there is a notable diversity of extant invertebrates on this planet that would be quite comfortable outside of the range of CO concentrations proposed by Schwieterman et al. to constrain the habitable zone. There is no a priori reason to rule out the possibility that these lineages could have given rise to intelligent life during the history of life on this planet. A significantly higher atmospheric CO concentration would have prevented the evolution of hemoglobin, but not necessarily prevented astronomically observable biosignatures from Earth.
It is too early to be able to say whether the planets around Teegarden's Star are habitable. There are plenty of reasons to be sceptical but worlds like Teegarden b are still promising enough to be worth investigating in more detail. It is unfortunate that it is not a transiting planet, but similar systems like TRAPPIST-1 should be helpful in constraining what the possibilities are.
It is potentially habitable.
Teegarden b has a minimum mass almost identical to Earth and it orbits within the star's habitable zone.
The exoplanet has a 60% chance of having a temperate surface environment where temperature should be closer to 28°C assuming a similar terrestrial atmosphere.
Moreover, it is the exoplanet with the highest Earth Similarity Index discovered so far: 95%. This means that it has the closest mass and insolation to terrestrial values.