Because of their large numbers, low-mass stars may be the most abundant planet hosts in our Galaxy. Furthermore, terrestrial planets in the habitable zones (HZs) around M-dwarfs can potentially be characterized in the near future and hence may be the first such planets to be studied. Recently, Dressing & Charbonneau used Kepler data and calculated the frequency of terrestrial planets in the HZ of cool stars to be $0.15^{+0.13}_{-0.06}$ per star for Earth-size planets (0.5-1.4 R ⊕). However, this estimate was derived using the Kasting et al. HZ limits, which were not valid for stars with effective temperatures lower than 3700 K. Here we update their result using new HZ limits from Kopparapu et al. for stars with effective temperatures between 2600 K and 7200 K, which includes the cool M stars in the Kepler target list.
Identifying terrestrial planets in the habitable zones (HZs) of other stars is one of the primary goals of ongoing radial velocity (RV) and transit exoplanet surveys and proposed future space missions. Most current estimates of the boundaries of the HZ are based on one-dimensional (1D), cloud-free, climate model calculations by Kasting et al. However, this model used band models that were based on older HITRAN and HITEMP line-by-line databases. The inner edge of the HZ in the Kasting et al. model was determined by loss of water, and the outer edge was determined by the maximum greenhouse provided by a CO2 atmosphere. A conservative estimate for the width of the HZ from this model in our solar system is 0.95-1.67 AU. Here an updated 1D radiative-convective, cloud-free climate model is used to obtain new estimates for HZ widths around F, G, K, and M stars. New H2O and CO2 absorption coefficients, derived from the HITRAN 2008 and HITEMP 2010 line-by-line databases, are important improvements to the climate model. According to the new model, the water-loss (inner HZ) and maximum greenhouse (outer HZ) limits for our solar system are at 0.99 and 1.70 AU, respectively, suggesting that the present Earth lies near the inner edge. Additional calculations are performed for stars with effective temperatures between 2600 and 7200 K, and the results are presented in parametric form, making them easy to apply to actual stars. The new model indicates that, near the inner edge of the HZ, there is no clear distinction between runaway greenhouse and water-loss limits for stars with T eff lesssim 5000 K, which has implications for ongoing planet searches around K and M stars. To assess the potential habitability of extrasolar terrestrial planets, we propose using stellar flux incident on a planet rather than equilibrium temperature. This removes the dependence on planetary (Bond) albedo, which varies depending on the host star’s spectral type. We suggest that conservative estimates of the HZ (water-loss and maximum greenhouse limits) should be used for current RV surveys and Kepler mission to obtain a lower limit on η⊕, so that future flagship missions like TPF-C and Darwin are not undersized. Our model does not include the radiative effects of clouds; thus, the actual HZ boundaries may extend further in both directions than the estimates just given.
We study the dynamical stability of planetary systems consisting of one hypothetical terrestrial-mass planet (1 or 10 M ⊕) and one massive planet (10 M ⊕-10 M jup). We consider masses and orbits that cover the range of observed planetary system architectures (including non-zero initial eccentricities), determine the stability limit through N-body simulations, and compare it to the analytic Hill stability boundary. We show that for given masses and orbits of a two-planet system, a single parameter, which can be calculated analytically, describes the Lagrange stability boundary (no ejections or exchanges) but diverges significantly from the Hill stability boundary. However, we do find that the actual boundary is fractal, and therefore we also identify a second parameter which demarcates the transition from stable to unstable evolution. We show the portions of the habitable zones (HZs) of ρ CrB, HD 164922, GJ 674, and HD 7924 that can support a terrestrial planet. These analyses clarify the stability boundaries in exoplanetary systems and demonstrate that, for most exoplanetary systems, numerical simulations of the stability of potentially habitable planets are only necessary over a narrow region of the parameter space. Finally, we also identify and provide a catalog of known systems that can host terrestrial planets in their HZs.
We study the dynamical stability of an additional, potentially habitable planet in the HD 47186 planetary system. Two planets are currently known in this system: a “hot Neptune” with a period of 4.08 days and a Saturn-mass planet with a period of 3.7 years. Here we consider the possibility that one or more undetected planets exist between the two known planets and possibly within the habitable zone (HZ) in this system. Given the relatively low masses of the known planets, additional planets could have masses $ \rlap{<}{\lower1.0ex\hbox{$\sim $}}10 {\,M_\oplus }$, and hence be terrestrial-like and further improving potential habitability. We perform N-body simulations to identify the stable zone between planets b and c and find that much of the inner HZ can harbor a 10 M ⊕ planet. With the current radial velocity threshold of ~1 m s–1, an additional planet should be detectable if it lies at the inner edge of the habitable zone at 0.8 AU. We also show that the stable zone could contain two additional planets of 10 M ⊕ each if their eccentricities are lower than ~0.3.