I was wondering.. is there any habitable exoplanet around Tau Ceti?

Yes, Tau Ceti e is a potentially habitable exoplanet orbiting Tau Ceti, at the distance of only 12 light years away from Earth.

The exoplanet was discovered in 2012 with the radial velocity method, but its existance was recently confirmed.

It has an Earth Similarity Index of 74%, an average temperature of 30º C more and an orbital period of 163 days.

Actually, it is the closest Earth like planet and, if we are able to build an antimatter rocket, we could reach Tau Ceti e in less than 20 years.

If you want to know more about the exoplanet, here you can find more information: https://www.youtube.com/watch?v=Lhfu3DXoOCA&feature=youtu.be

TLDR version: probably not, and claims for the habitability of planets in this system are on shaky ground.

Long version follows.

Planets

So as of Feng et al. (2017), there are four planet candidates around Tau Ceti:

• Tau Ceti g, minimum mass $1.75^{+0.25}_{-0.40} M_oplus$, semimajor axis $0.133^{+0.001}_{-0.002} mathrm{AU}$
  


• Tau Ceti h, minimum mass $1.83^{+0.68}_{-0.26} M_oplus$, semimajor axis $0.243^{+0.003}_{-0.003} mathrm{AU}$
  


• Tau Ceti e, minimum mass $3.93^{+0.83}_{-0.64} M_oplus$, semimajor axis $0.538^{+0.006}_{-0.006} mathrm{AU}$
  


• Tau Ceti f, minimum mass $3.93^{+1.05}_{-1.37} M_oplus$, semimajor axis $1.334^{+0.017}_{-0.044} mathrm{AU}$
  

Note that the designations Tau Ceti b, c and d refer to planet candidates that are no longer thought to exist. The error bars refer to the 1% and 99% percentiles. $M_oplus$ is the mass of the Earth.

The Feng et al. (2017) paper also notes that the system is dynamically packed, which does not bode well for the prospects for additional planets between the known planet candidates (note that their figure 17 shows the regions where the planets would interfere with each other, not the regions of stability for an additional planet).

The habitable zone

The conclusion of the paper gives the luminosity of Tau Ceti as 0.52 times solar and the effective temperature as 5344 K. Using these values, the habitable zone limits from Kopparapu et al. (2013) are as follows:

Inner boundaries:

• Recent Venus: 0.551 AU


• Runaway greenhouse: 0.723 AU


• Moist greenhouse: 0.729 AU

Outer boundaries:

• Maximum greenhouse: 1.279 AU


• Early Mars: 1.330 AU

From this we see that Tau Ceti e and Tau Ceti f are located right at the most optimistic habitable zone boundaries (Recent Venus and Early Mars). In particular, planet e is closer to the star than the runaway greenhouse limit so any oceans that may once have existed would likely have boiled off, leaving the planet in a Venus-like state. The recent Venus limit is based on the possibility that Venus may have retained oceans for several Gyr, this is not known for certain. Dry planets would be able to avoid the runaway greenhouse because this requires sufficient quantities of water to occur, whether the resultant planet is habitable is another matter.

Planets g and h are too close to the star. None of the planets fall into the most conservative habitable zone between the moist greenhouse and maximum greenhouse limits.

Planetary masses

A limitation of the radial velocity method is that only the minimum masses can be derived. With Tau Ceti, we have a possible means to estimate the true masses: the star is surrounded by a debris disc (this would likely provide a source of impactors onto the planets, how bad the situation is depends on how much material is being perturbed into the inner system). Using Herschel observations, Lawler et al. (2014) give an inclination of 35±10 degrees. Assuming that the planets lie in the same plane as the disc, the true masses would therefore be approximately 1.74 times greater than the minimum masses.

Under this assumption, the true masses of the planets e and f both come out as about 6.85 Earth masses. Taking the 99% lower limit on the minimum mass error bars and a 45° orbital inclination as a low estimate, these would be 4.65 Earth masses for e and 3.62 Earth masses for f.

The nature of the planets

According to Rogers (2014), the transition between rocky and Neptune-like planets is somewhere in the region of 1.4 to 1.6 Earth radii. Using the mass-radius relationship from Zeng et al. (2016) and their core mass fraction of 0.26 for typical terrestrial planets, these radius limits correspond to terrestrial planets of roughly 3.3 to 5.4 Earth masses.

This suggests that Tau Ceti e and f are fairly likely to be sub-Neptunes rather than rocky planets, although the caveats are that in the optimistic case they can have masses below the rocky/Neptune-like transition, and that there do seem to be a few cases of rocky planets above the transition (most of those are likely to be evaporated cores of Neptune-like planets, which wouldn't apply to Tau Ceti e and f as they have much lower levels of stellar irradiation).

Conclusion

Given the current state of knowledge, Tau Ceti does not look like a good prospect for habitable planets. Tau Ceti e and f fall right at the edge of already-optimistic estimates for the habitable zone boundaries, and their masses are sufficiently high that there is a good chance that they are sub-Neptunes rather than rocky planets. The dynamical packing of the system makes it unlikely that there can be a smaller, temperate planet in the habitable zone between the known planets.