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

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 can be calculated from Kopparapu et al. (2013), which assumes that habitable conditions are maintained by the carbonate-silicate cycle with carbon dioxide as the main (non-condensible) greenhouse gas.

Inner boundaries

• Recent Venus: 0.551 AU


• Runaway greenhouse: 0.723 AU


• Moist greenhouse: 0.729 AU

The moist greenhouse limit is the most conservative inner boundary, it occurs where sufficient water vapour enters the upper atmosphere that water loss begins to occur from the planet. In our solar system, Earth is located close to this limit in the inner part of the most conservative habitable zone.

The runaway greenhouse limit occurs where the positive feedback from water vapour overwhelms the stabilising negative feedback from the silicate-carbonate cycle, driving further evaporation of the oceans and higher temperatures. This is thought to have occurred on Venus, leaving the planet in the state it is in today.

The recent Venus limit is based on the possibility that Venus may have retained oceans for several billion years. This is not known for certain as our knowledge of Venus's evolution is rather incomplete and the conditions on the planet's surface are not favourable for driving rovers around investigating the geology.

From this we see that Tau Ceti e is located close to the recent Venus limit and is closer to the star than the runaway greenhouse limit. This suggests that any oceans that may once have existed would likely have boiled off, leaving the planet in a Venus-like state.

Planets g and h are too close to the star.

Outer boundaries

• Maximum greenhouse: 1.279 AU


• Early Mars: 1.330 AU

The maximum greenhouse limit is the furthest distance from the star that a cloud-free carbon dioxide atmosphere can support conditions compatible with liquid water. Beyond this, the increased scattering leads to increased reflectivity of the planet and the CO₂ would begin to condense, removing it from the atmosphere and leading to runaway cooling. This is the most conservative outer habitable zone boundary. Note that by this point, the planet would require several bars of CO₂ which would make it toxic for humans.

The early Mars limit is based on the observation that Mars managed to maintain surface water (e.g. various rivers, and a possible northern ocean) in the early solar system when the Sun was significantly fainter than it is today. Tau Ceti f is located right at this limit.

Extensions to the habitable zone

None of the planets fall into the most conservative habitable zone, and Tau Ceti e and f are at the boundaries of the most optimistic estimates for the habitable zone boundaries. There are nevertheless options for extending the habitable zone.

At the inner boundary, a runaway greenhouse effect could be avoided on dry planets, where there simply isn't enough water to evaporate to drive the positive feedback, see Zsom et al. (2013). It isn't clear to me that such a planet can be described as habitable, since such planets may lack the hydrothermal systems that could act as the sites for abiogenesis. Their geological evolution would likely be substantially different to Earth's without water to lubricate plate tectonics.

Another possibility is on slowly-rotating planets, where substantial cloud layers can build up on the day side of the planet and increase the reflectivity, as noted by Yang et al. (2014). On the other hand, Scholz et al. (2018) have noted that there appears to be a universal mass-spin relationship that extends from planets to brown dwarfs. This predicts that super-Earths would likely spin too fast for this mechanism to work unless they have been spun down by stellar tides or a large moon.

On the outer boundary, adding additional greenhouse gases such as methane may work to extend the outer habitable zone, see for example Ramirez & Kaltenegger (2018). This has been suggested as the mechanism for allowing surface water on Mars, which would suggest that the "Early Mars" limit is an observed data point within the methane habitable zone. Another possibility is that a dense hydrogen atmosphere could maintain liquid water, e.g. Pierrehumbert & Gaidos (2011) though the pressure of such an atmosphere may well have implications for the geology of the planet and hence the potential for abiogenesis.

Planets whose climates are stabilised by something other than the carbonate-silicate cycle, or have substantially different atmospheric compositions would have different habitable zone boundaries (if subsurface oceans on icy worlds are habitable, there may be interesting prospects for dwarf planets in the outer debris belt), but this is already getting speculative enough, besides there is another possible objection to the habitability of these planets...

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 are rather marginal in terms of their location within the habitable zone, 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.