Water On -and In- Terrestrial Planets

Earth has a unique surface character among Solar System worlds. Not only does it harbor liquid water, but also large continents. An exoplanet with a similar appearance would remind us of home, but it is not obvious whether such a planet is more likely to bear life than an entirely ocean-covered waterworld---after all, surface liquid water defines the canonical habitable zone. In this proceeding, I argue that 1) Earth's bimodal surface character is critical to its long-term climate stability and hence is a signpost of habitability, and 2) we will be able to constrain the surface character of terrestrial exoplanets with next-generation space missions.Comment: 4 pages, 1 figure; to appear in the proceedings of the Comparative Climates of Terrestrial Planets II conferenc

A Model for Thermal Phase Variations of Circular and Eccentric Exoplanets

We present a semi-analytic model atmosphere for close-in exoplanets that captures the essential physics of phase curves: orbital and viewing geometry, advection, and re-radiation. We calibrate the model with the well-characterized transiting planet, HD 189733b, then compute light curves for seven of the most eccentric transiting planets. We present phase variations for a variety of different radiative times and wind speeds. In the limit of instant re-radiation, the light curve morphology is entirely dictated by the planet's eccentricity and argument of pericenter: the light curve maximum leads or trails the eclipse depending on whether the planet is receding from or approaching the star at superior conjunction, respectively. For a planet with non-zero radiative timescales, the phase peak occurs early for super- rotating winds, and late for sub-rotating winds. We find that for a circular orbit, the timing of the phase variation maximum with respect to superior conjunction indicates the direction of the dominant winds, but cannot break the degeneracy between wind speed and radiative time. For circular planets the phase minimum occurs half an orbit away from the phase maximum -despite the fact that the coolest longitudes are always near the dawn terminator- and therefore does not convey any additional information. In general, increasing the advective frequency or the radiative time has the effect of reducing the peak-to-trough amplitude of phase variations, but there are interesting exceptions to these trends. Lastly, eccentric planets with orbital periods significantly longer than their radiative time exhibit "ringing" whereby the hot spot generated at periastron rotates in and out of view. The existence of ringing makes it possible to directly measure the wind speed (the frequency of the ringing) and the radiative time constant (the damping of the ringing).Comment: 13 pages, 13 figures, accepted for publication in Ap

Revisiting the Energy Budget of WASP-43b: Enhanced day-night heat transport

The large day--night temperature contrast of WASP-43b has so far eluded explanation. We revisit the energy budget of this planet by considering the impact of reflected light on dayside measurements, and the physicality of implied nightside temperatures. Previous analyses of the infrared eclipses of WASP-43b have assumed reflected light from the planet is negligible and can be ignored. We develop a phenomenological eclipse model including reflected light, thermal emission, and water absorption, and use it to fit published Hubble and Spitzer eclipse data. We infer a near-infrared geometric albedo of 27$\pm1\%$ and a cooler dayside temperature of $1527 \pm 10~$K. Additionally, we perform lightcurve inversion on the three published orbital phase curves of WASP-43b and find that each requires unphysical, negative flux on the nightside. By requiring non-negative brightnesses at all longitudes, we correct the unphysical parts of the maps and obtain a much hotter nightside effective temperature of $1076 \pm 11~$K. The cooler dayside and hotter nightside suggests a heat recirculation efficiency of $47\%$ for WASP-43b, essentially the same as for HD 209458b, another hot Jupiter with nearly the same temperature. Our analysis therefore reaffirms the trend that planets with lower irradiation temperatures have more efficient day-night heat transport. Moreover, we note that 1) reflected light may be significant for many near-IR eclipse measurements of hot Jupiters, and 2) phase curves should be fit with physically possible longitudinal brightness profiles --- it is insufficient to only require that the disk-integrated lightcurve be non-negative.Comment: Accepted for publication in ApJL. 7 pages, 4 figure

Knot a Bad Idea: Testing BLISS Mapping for Spitzer Space Telescope Photometry

Much of transiting exoplanet science relies on high-precision photometry. The current generation of instruments can exhibit sensitivity variations greater than the astrophysical signals. For the InfraRed Array Camera (IRAC) on the Spitzer Space Telescope, a popular way to handle this is BiLinearly-Interpolated Subpixel Sensitivity (BLISS) mapping. As part of a Markov Chain Monte Carlo (MCMC), BLISS mapping estimates the sensitivity at many locations (knots) on the pixel, then interpolates to the target star's centroids. We show that such embedded optimization schemes can misfit or bias parameters. Thus, we construct a model of $\textit{Spitzer}$ eclipse light curves to test the accuracy and precision of BLISS mapping. We compare standard BLISS mapping to a variant where the knots are fit during the MCMC, as well as to a polynomial model. Both types of BLISS mapping give similar eclipse depths, and we find that standard knots behave like real parameters. Standard BLISS mapping is therefore a reasonable shortcut to fitting for knots in an MCMC. BLISS maps become inaccurate when the photon noise is low, but typically approximate the real sensitivity well. We also find there is no perfect method for choosing the ideal number of BLISS knots to use on given data. BLISS mapping gives fits that are usually more accurate than precise (i.e. they are overly conservative), and the routine is more precise than polynomial models for significant eclipses or pixels with more varied sensitivities. BLISS mapping has better predictive power for most of these particular synthetic data, depending on how one treats time-correlated residuals. Overall, we conclude that BLISS mapping can be a reasonable sensitivity model for IRAC photometry.Comment: 32 pages, 13 figures; Accepted by PASP 9/26/16. Major updates: higher amplitude for main detector signals, estimating good number of BLISS knots for given data, more/better synthetic light curves, trying projected sensitivity along pixel axes, uncertainties in Figures 10-13. Most edits in Abstract, Sections 4-6. New findings but main conclusion same (i.e. BLISS Mapping can be acceptable

Wavelength Does Not Equal Pressure: Vertical Contribution Functions and their Implications for Mapping Hot Jupiters

Multi-band phase variations in principle allow us to infer the longitudinal temperature distributions of planets as a function of height in their atmospheres. For example, 3.6 micron emission originates from deeper layers of the atmosphere than 4.5 micron due to greater water vapor absorption at the longer wavelength. Since heat transport efficiency increases with pressure, we expect thermal phase curves at 3.6 micron to exhibit smaller amplitudes and greater phase offsets than at 4.5 micron; this trend is not observed. Of the seven hot Jupiters with full-orbit phase curves at 3.6 and 4.5 micron, all have greater phase amplitude at 3.6 micron than at 4.5 micron, while four of seven exhibit a greater phase offset at 3.6 micron. We use a 3D radiative-hydrodynamic model to calculate theoretical phase curves of HD 189733b, assuming thermo-chemical equilibrium. The model exhibits temperature, pressure, and wavelength dependent opacity, primarily driven by carbon chemistry: CO is energetically favored on the dayside, while CH4 is favored on the cooler nightside. Infrared opacity therefore changes by orders of magnitude between day and night, producing dramatic vertical shifts in the wavelength-specific photospheres, which would complicate eclipse or phase mapping with spectral data. The model predicts greater relative phase amplitude and greater phase offset at 3.6 micron than at 4.5 micron, in agreement with the data. Our model qualitatively explains the observed phase curves, but is in tension with current thermo-chemical kinetics models that predict zonally uniform atmospheric composition due to transport of CO from the hot regions of the atmosphere.Comment: 9 pages, 5 figures, accepted for publications in ApJ Letter

The Feeding Zones of Terrestrial Planets and Insights into Moon Formation

[Abridged] We present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of the stochastic late stages of planet formation. We quantify the feeding zone width, Delta a, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planet's feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planet's mass and its volatile inventory. Instead, we find that the feeding zone of any planet more massive than 0.1M_Earth is roughly proportional to the radial extent of the initial disk from which it formed: Delta a~0.25(a_max-a_min), where a_min and a_max are the inner and outer edge of the initial planetesimal disk. These wide stochastic feeding zones have significant consequences for the origin of the Moon, since the canonical scenario predicts the Moon should be primarily composed of material from Earth's last major impactor (Theia), yet its isotopic composition is indistinguishable from Earth. In particular, we find that the feeding zones of Theia analogs are significantly more stochastic than the planetary analogs. Depending on our assumed initial distribution of oxygen isotopes within the planetesimal disk, we find a ~5% or less probability that the Earth and Theia will form with an isotopic difference equal to or smaller than the Earth and Moon's. In fact we predict that every planetary mass body should be expected to have a unique isotopic signature. In addition, we find paucities of massive Theia analogs and high velocity moon-forming collisions, two recently proposed explanations for the Moon's isotopic composition. Our work suggests that there is still no scenario for the Moon's origin that explains its isotopic composition with a high probability event.Comment: 16 pages, 22 figures, accepted for publication in Icarus; fixed typo

Water Cycling Between Ocean and Mantle: Super-Earths Need Not be Waterworlds

Large terrestrial planets are expected to have muted topography and deep oceans, implying that most super-Earths should be entirely covered in water, so-called waterworlds. This is important because waterworlds lack a silicate weathering thermostat so their climate is predicted to be less stable than that of planets with exposed continents. In other words, the continuously habitable zone for waterworlds is much narrower than for Earth-like planets. A planet's water is partitioned, however, between a surface reservoir, the ocean, and an interior reservoir, the mantle. Plate tectonics transports water between these reservoirs on geological timescales. Degassing of melt at mid-ocean ridges and serpentinization of oceanic crust depend negatively and positively on seafloor pressure, respectively, providing a stabilizing feedback on long-term ocean volume. Motivated by Earth's approximately steady-state deep water cycle, we develop a two-box model of the hydrosphere and derive steady-state solutions to the water partitioning on terrestrial planets. Critically, hydrostatic seafloor pressure is proportional to surface gravity, so super-Earths with a deep water cycle will tend to store more water in the mantle. We conclude that a tectonically active terrestrial planet of any mass can maintain exposed continents if its water mass fraction is less than ~0.2%, dramatically increasing the odds that super-Earths are habitable. The greatest source of uncertainty in our study is Earth's current mantle water inventory: the greater its value, the more robust planets are to inundation. Lastly, we discuss how future missions can test our hypothesis by mapping the oceans and continents of massive terrestrial planets.Comment: 8 pages, 2 figures, ApJ in pres

Eccentricity is Not Responsible for Odd Harmonics in HAT-P-7 and Kepler-13A

The exquisite photometry of Kepler has revealed reflected light from exoplanets, tidal distortion of host stars and Doppler beaming of a star's light due to its motion (Borucki 2016; Demory et al. 2012; Welsh et al. 2010; Bloemen et al. 2012). Esteves et al. (2013, 2015) and Shporer et al. (2014) reported additional odd harmonics in the light curves of two hot Jupiters: HAT-P-7b and Kepler-13Ab. They measured non-zero power at three times the orbital frequency that persisted while the planet was eclipsed and hence must originate in the star (Esteves et al. 2015). Penoyre & Sandford (2018) showed that orbital eccentricity could result in time-dependent tidal deformation of the star that manifests itself at three times the orbital frequency and suggested this could be the origin of the measured odd modes. In this Research Note, we show that the small orbital eccentricities of HAT-P-7b and Kepler-13Ab cannot generate the odd harmonics observed in these systems. Esteves et al. (2015) hypothesized that the odd modes could be due to tidal distortion of the star if its spin is misaligned with the system's orbital motion, as is the case in both of these systems (Benomar et al. 2014; Herman et al. 2018), but this mechanism has yet to be verified theoretically or numerically.Comment: 2 pages, 1 figure, RNAAS in pres

Increased Heat Transport in Ultra-Hot Jupiter Atmospheres Through H2_2 Dissociation/Recombination

A new class of exoplanets is beginning to emerge: planets whose dayside atmospheres more closely resemble stellar atmospheres as most of their molecular constituents dissociate. The effects of the dissociation of these species will be varied and must be carefully accounted for. Here we take the first steps towards understanding the consequences of dissociation and recombination of molecular hydrogen (H$_2$) on atmospheric heat recirculation. Using a simple energy balance model with eastward winds, we demonstrate that H$_2$ dissociation/recombination can significantly increase the day$-$night heat transport on ultra-hot Jupiters (UHJs): gas giant exoplanets where significant H$_2$ dissociation occurs. The atomic hydrogen from the highly irradiated daysides of UHJs will transport some of the energy deposited on the dayside towards the nightside of the planet where the H atoms recombine into H$_2$; this mechanism bears similarities to latent heat. Given a fixed wind speed, this will act to increase the heat recirculation efficiency; alternatively, a measured heat recirculation efficiency will require slower wind speeds after accounting for H$_2$ dissociation/recombination.Comment: 8 pages, 5 figures, accepted for publication in ApJ

Brief Follow-up on Recent Studies of Theia's Accretion

Kaib & Cowan (2015) recently used terrestrial planet formation simulations to conclude that the moon-forming impactor (Theia) had only a ~5% or less chance of having the same oxygen isotope composition as Earth, while Mastrobuono-Battisti et al. (2015) used seemingly similar simulations and methods to arrive at a higher value of ~20% or more. Here we derive the results of both papers from a single set of simulations. Compared to Kaib & Cowan (2015), the analysis of Mastrobuono-Battisti et al. (2015) systematically yields more massive Theia analogs and imposes flatter isotopic gradients across the original protoplanetary disk. Both of these effects diminish isotopic differences between Earth and Theia analogs. While it is notoriously difficult to produce systems resembling our actual terrestrial planets, the analysis of Kaib & Cowan (2015) more often selects and analyzes Earth and Mars analogs at orbital locations near the real planets. Given this, we conclude that the greater isotopic differences between Earth and Theia found in Kaib & Cowan (2015) better reflect the predictions of terrestrial planet formation models. Finally, although simulation uncertainties and a terrestrial contribution to Moon formation enhance the fraction of Theia analogs consistent with the canonical giant impact hypothesis, this fraction still remains in the 5-8% range.Comment: 5 pages, 4 figures, accepted to Icaru