We describe a software package called VPLanet that simulates fundamental aspects of planetary system evolution over Gyr timescales, with a focus on investigating habitable worlds. In this initial release, eleven physics modules are included that model internal, atmospheric, rotational, orbital, stellar, and galactic processes. Many of these modules can be coupled to simultaneously simulate the evolution of terrestrial planets, gaseous planets, and stars. The code is validated by reproducing a selection of observations and past results. VPLanet is written in C and designed so that the user can choose the physics modules to apply to an individual object at runtime without recompiling, i.e., a single executable can simulate the diverse phenomena that are relevant to a wide range of planetary and stellar systems. This feature is enabled by matrices and vectors of function pointers that are dynamically allocated and populated based on user input. The speed and modularity of VPLanet enables large parameter sweeps and the versatility to add/remove physical phenomena to assess their importance. VPLanet is publicly available from a repository that contains extensive documentation, numerous examples, Python scripts for plotting and data management, and infrastructure for community input and future development.
The pathways through which incoming energy is distributed between the surface and atmosphere have been analyzed for the Earth. However, the effect of the spectral energy distribution of a host star on the energy budget of an orbiting planet may be significant given the wavelength-dependent absorption properties of atmospheric CO2, water vapor, surface ice, and snow. We have quantified the flow of energy on aqua planets orbiting M-, G-, and F-dwarf stars, using a 3D Global Climate Model with a static ocean. The atmosphere and surface of an M-dwarf planet receiving an instellation equal to 88% of the modern solar constant at the top of the atmosphere absorb 12% more incoming stellar radiation than those of a G-dwarf planet receiving 100% of the modern solar constant, and 17% more radiation than an F-dwarf planet receiving 108% of the modern solar constant, resulting in climates similar to that of modern-day Earth on all three planets, assuming a 24 hr rotation period and fixed CO2. At 100% instellation, a synchronously rotating M-dwarf planet exhibits smaller flux absorption in the atmosphere and on the surface of the dayside, and a dayside mean surface temperature that is 37 K colder than its rapidly rotating counterpart. Energy budget diagrams are included to illustrate the variations in global energy budgets as a function of host star spectral class, and can contribute to habitability assessments of planets as they are discovered.
As lower-mass stars often host multiple rocky planets, gravitational interactions among planets can have significant effects on climate and habitability over long timescales. Here we explore a specific case, Kepler-62f, a potentially habitable planet in a five-planet system with a K2V host star. N-body integrations reveal the stable range of initial eccentricities for Kepler-62f is 0.00⩽e⩽0.32, absent the effect of additional, undetected planets. We simulate the tidal evolution of Kepler-62f in this range and find that, for certain assumptions, the planet can be locked in a synchronous rotation state. Simulations using LMD Generic GCM indicate that with 3 bars of CO2 in its atmosphere, Kepler-62f would only be warm enough for surface liquid water at the upper limit of this eccentricity range, providing it has a high planetary obliquity (between 60∘ and 90∘). A climate similar to modern-day Earth is possible for the entire range of stable eccentricities if atmospheric CO2 is increased to 5-bar levels. In a low-CO2 case, simulations with CCSM4 and LMD Generic GCM indicate that increases in planetary obliquity and orbital eccentricity coupled with an orbital configuration that places the summer solstice at or near pericenter permit regions of the planet with above-freezing surface temperatures. This may melt ice sheets formed during colder seasons. If Kepler-62f is synchronously rotating and has an ocean, CO2 levels above 3 bars would be required to distribute enough heat to the night side of the planet to avoid atmospheric freeze-out and permit a large enough region of open water at the planet’s substellar point to remain stable. Overall, we find multiple plausible combinations of orbital and atmospheric properties that permit surface liquid water on Kepler-62f.
Planetary climate can be affected by the interaction of the host star spectral energy distribution with the wavelength-dependent reflectivity of ice and snow. In this study, we explored this effect with a one-dimensional (1-D), line-by-line, radiative transfer model to calculate broadband planetary albedos as input to a seasonally varying, 1-D energy balance climate model. A three-dimensional (3-D) general circulation model was also used to explore the atmosphere’s response to changes in incoming stellar radiation, or instellation, and surface albedo. Using this hierarchy of models, we simulated planets covered by ocean, land, and water-ice of varying grain size, with incident radiation from stars of different spectral types. Terrestrial planets orbiting stars with higher near-UV radiation exhibited a stronger ice-albedo feedback. We found that ice extent was much greater on a planet orbiting an F-dwarf star than on a planet orbiting a G-dwarf star at an equivalent flux distance, and that ice-covered conditions occurred on an F-dwarf planet with only a 2% reduction in instellation relative to the present instellation on Earth, assuming fixed CO2 (present atmospheric level on Earth).