arXiv subjects

Aomawa L. Shields

Publications and source records attributed to Aomawa L. Shields.

18 recordsLinked to original sources

arXiv2025

A One-Dimensional Energy Balance Model Parameterization for the Formation of CO2 Ice on the Surfaces of Eccentric Extrasolar Planets

Eccentric planets may spend a significant portion of their orbits at large distances from their host stars, where low temperatures can cause atmospheric CO2 to condense out onto the surface, similar to the polar ice caps on Mars. The radiative effects on the climates of these planets throughout their orbits would depend on the wavelength-dependent albedo of surface CO2 ice that may accumulate at or near apoastron and vary according to the spectral energy distribution of the host star. To explore these possible effects, we incorporated a CO2 ice-albedo parameterization into a one-dimensional energy balance climate model. With the inclusion of this parameterization, our simulations demonstrated that F-dwarf planets require 29% more orbit-averaged flux to thaw out of global water ice cover compared with simulations that solely use a traditional pure water ice-albedo parameterization. When no eccentricity is assumed, and host stars are varied, F-dwarf planets with higher bond albedos relative to their M-dwarf planet counterparts require 30% more orbit-averaged flux to exit a water snowball state. Additionally, the intense heat experienced at periastron aids eccentric planets in exiting a snowball state with a smaller increase in instellation compared with planets on circular orbits; this enables eccentric planets to exhibit warmer conditions along a broad range of instellation. This study emphasizes the significance of incorporating an albedo parameterization for the formation of CO2 ice into climate models to accurately assess the habitability of eccentric planets, as we show that, even at moderate eccentricities, planets with Earth-like atmospheres can reach surface temperatures cold enough for the condensation of CO2 onto their surfaces, as can planets receiving low amounts of instellation on circular orbits.

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arXiv2025

Rising Stargirls: Benefits of a Creative Arts-Based Approach to Astronomy Education for Middle-School Girls from Underrepresented Groups

Women from historically marginalized groups in the sciences continue to be severely underrepresented in the fields of physics and astronomy. Young girls identifying with these groups often lose interest in science, technology, engineering, and math (STEM) fields well before college. Middle school (grades 6-8) emerges as a pivotal phase for nurturing science identities among girls. The educational program Rising Stargirls offers creative arts-based astronomy workshops for middle-school girls, with the aim of cultivating their science identities. We retrospectively analyze participants' responses to four key assessment items through which their engagement in science and their science identities before and after the workshops are assessed. Our findings overwhelmingly indicate that girls exhibit heightened engagement in science and enhanced science identities after engaging in the Rising Stargirls program. These outcomes underscore the merits of fostering creativity and integrating the arts into science education.

physics.ed-ph↗

arXiv2024

Increased Surface Temperatures of Habitable White Dwarf Worlds Relative to Main-Sequence Exoplanets

Discoveries of giant planet candidates orbiting white dwarf stars and the demonstrated capabilities of the James Webb Space Telescope bring the possibility of detecting rocky planets in the habitable zones of white dwarfs into pertinent focus. We present simulations of an aqua planet with an Earth-like atmospheric composition and incident stellar insolation orbiting in the habitable zone of two different types of stars - a 5000 K white dwarf and main-sequence K-dwarf star Kepler-62 with a similar effective temperature - and identify the mechanisms responsible for the two differing planetary climates. The synchronously-rotating white dwarf planet's global mean surface temperature is 25 K higher than that of the synchronously-rotating planet orbiting Kepler-62, due to its much faster (10-hr) rotation and orbital period. This ultra-fast rotation generates strong zonal winds and meridional flux of zonal momentum, stretching out and homogenizing the scale of atmospheric circulation, and preventing an equivalent build-up of thick, liquid water clouds on the dayside of the planet compared to the synchronous planet orbiting Kepler-62, while also transporting heat equatorward from higher latitudes. White dwarfs may therefore present amenable environments for life on planets formed within or migrated to their habitable zones, generating warmer surface environments than those of planets with main-sequence hosts to compensate for an ever shrinking incident stellar flux.

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arXiv2024

Climate Regimes Across the Habitable Zone: a Comparison of Synchronous Rocky M- and K-dwarf Planets

M- and K-dwarf stars make up 86% of the stellar population and host many promising astronomical targets for detecting habitable climates in the near future. Of the two, M dwarfs currently offer greater observational advantages and are home to many of the most exciting observational discoveries in the last decade. But K dwarfs could offer even better prospects for detecting habitability by combining the advantage of a relatively dim stellar flux with a more stable stellar environment. Here we explore the climate regimes that are possible on Earth-like synchronous planets in M- and K-dwarf systems, and how they vary across the habitable zone. We focus on surface temperature patterns, water availability, and implications for habitability. We find that the risk of nightside cold-trapping decreases with increased orbital radius and is overall lower for K-dwarf planets. With reduced atmospheric shortwave absorption, K-dwarf planets have higher dayside precipitation rates and less day-to-night moisture transport, resulting in lower nightside snow rates. These results imply a higher likelihood of detecting a planet with a moist dayside climate in a habitable "eyeball" climate regime orbiting a K-dwarf star. We also show that "terminator habitability" can occur for both M- and K-dwarf land planets, but would likely be more prevalent in M-dwarf systems. Planets in a terminator habitability regime tend to have slightly lower fractional habitability, but offer alternative advantages including instellation rates more comparable to Earth in regions that have temperatures amenable to life.

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arXiv2022

Terminator Habitability: the Case for Limited Water Availability on M-dwarf Planets

Rocky planets orbiting M-dwarf stars are among the most promising and abundant astronomical targets for detecting habitable climates. Planets in the M-dwarf habitable zone are likely synchronously rotating, such that we expect significant day-night temperature differences, and potentially limited fractional habitability. Previous studies have focused on scenarios where fractional habitability is confined to the substellar or "eye" region, but in this paper we explore the possibility of planets with terminator habitability, defined by the existence of a habitable band at the transition between a scorching dayside and a glacial nightside. Using a global climate model, we show that for water-limited planets it is possible to have scorching temperatures in the "eye" and freezing temperatures on the nightside, while maintaining a temperate climate in the terminator region, due to a reduced atmospheric energy transport. Whereas on water-rich planets, increasing stellar flux leads to increased atmospheric energy transport and a reduction in day-night temperature differences, such that the terminator does not remain habitable once the dayside temperatures approach runaway or moist greenhouse limits. We also show that, while water-abundant simulations may result in larger fractional habitability, they are vulnerable to water loss through cold-trapping on the nightside surface or atmospheric water vapor escape, suggesting that even if planets were formed with abundant water, their climates could become water-limited and subject to terminator habitability.

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arXiv2022

The Sparse Atmospheric MOdel Sampling Analysis (SAMOSA) intercomparison: Motivations and protocol version 1.0. A CUISINES model intercomparison project

Planets in synchronous rotation around low-mass stars are the most salient targets for current ground- and space-based missions to observe and characterize. Such model calculations can help to prioritize targets for observation with current and future missions; however, intrinsic differences in the complexity and physical parameterizations of various models can lead to different predictions of a planet's climate state. Understanding such model differences is necessary if such models are to guide target selection and aid in the analysis of observations. This paper presents a protocol to intercompare models of a hypothetical planet with a 15 day synchronous rotation period around a 3000 K blackbody star across a parameter space of surface pressure and incident instellation. We conduct a sparse sample of 16 cases from a previously published exploration of this parameter space with the ExoPlaSim model. By selecting particular cases across this broad parameter space, the SAMOSA intercomparison will identify areas where simpler models are sufficient as well as areas where more complex GCMs are required. Our preliminary comparison using ExoCAM shows general consistency between the climate state predicted by ExoCAM and ExoPlaSim except in regions of the parameter space most likely to be in a steam atmosphere or incipient runaway greenhouse state. We use this preliminary analysis to define several options for participation in the intercomparison by models of all levels of complexity. The participation of other GCMs is crucial to understand how the atmospheric states across this parameter space differ with model capabilities.

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arXiv2020

The Effect of Land Albedo on the Climate of Land-Dominated Planets in the TRAPPIST-1 System

Variations in the reflective properties of the bulk material that comprises the surface of land-dominated planets will affect the planetary energy balance by interacting differently with incident radiation from the host star. Furthermore, low-mass cool stars, such as nearby M8V dwarf TRAPPIST-1, emit a significant fraction of their flux in longer wavelengths relative to the Sun in regions where terrestrial materials may exhibit additional variability in albedo. Using the Community Earth System Model (CESM) we investigate the effect of the composition of the land surface and its albedo on planetary climate in the context of spatially homogeneous, entirely land-covered planets with dry atmospheres at the orbital separation of TRAPPIST-1d, TRAPPIST-1e, and TRAPPIST-1f. We use empirically derived spectra of four terrestrial compositional endmembers (granite, calcite, aridisol, and dune sand) and a composite spectrum of TRAPPIST-1 for these simulations and compare these model output to an aquaplanet and several Sol-spectrum control cases. We report a difference of approximately 50 K in global mean surface temperature, variations in atmospheric rotational features, and a reduction in cross-equatorial heat transport between scenarios in which materials with higher albedo in the infrared (calcite and dune sand) were used and those with more absorptive crustal material, such as granite or dry soils. An aquaplanet TRAPPIST-1d scenario results in an unstable runaway greenhouse regime. Therefore, we demonstrate that determining the composition and albedo of continental landmasses is crucial for making accurate determinations of the climate of terrestrial exoplanets.

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arXiv2019

The Effect of Land Fraction and Host Star Spectral Energy Distribution on the Planetary Albedo of Terrestrial Worlds

The energy balance and climate of planets can be affected by the reflective properties of their land, ocean, and frozen surfaces. Here we investigate the effect of host star spectral energy distribution (SED) on the albedo of these surfaces using a one-dimensional (1-D) energy balance model (EBM). Incorporating spectra of M-, K-, G- and F-dwarf stars, we determined the effect of varying fractional and latitudinal distribution of land and ocean surfaces as a function of host star SED on the overall planetary albedo, climate, and ice-albedo feedback response. While noting that the spatial distribution of land masses on a given planet will have an effect on the overall planetary energy balance, we find that terrestrial planets with higher average land/ocean fractions are relatively cooler and have higher albedo regardless of star type. For Earth-like planets orbiting M-dwarf stars the increased absorption of water ice in the near-infrared (NIR), where M-dwarf stars emit much of their energy, resulted in warmer global mean surface temperatures, ice lines at higher latitudes, and increased climate stability as the ice-albedo feedback became negative at high land fractions. Conversely, planets covered largely by ocean, and especially those orbiting bright stars, had a considerably different energy balance due to the contrast between the reflective land and the absorptive ocean surface, which in turn resulted in warmer average surface temperatures than land-covered planets and a stronger potential ice-albedo feedback. While dependent on the properties of individual planetary systems, our results place so constraints on a range of climate states of terrestrial exoplanets based on albedo and incident flux.

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arXiv2019

Energy Budgets for Terrestrial Extrasolar Planets

The pathways through which incoming energy is distributed between the surface and atmosphere has 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 and water vapor, and 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 a F-dwarf planet receiving 108% of the modern solar constant, resulting in climates similar to 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.

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arXiv2019

The Climates of Other Worlds: A Review of the Emerging Field of Exoplanet Climatology

The discovery of planets orbiting stars other than the Sun has accelerated over the past decade, and this trend will continue as new space- and ground-based observatories employ next-generation instrumentation to search the skies for habitable worlds. However, many factors and processes can affect planetary habitability and must be understood to accurately determine a planet's habitability potential. While climate models have long been used to understand and predict climate and weather patterns on the Earth, a growing community of researchers has begun to apply these models to extrasolar planets. This work has provided a better understanding of how orbital, surface, and atmospheric properties affect planetary climate and habitability; how these climatic effects might change for different stellar and planetary environments; and how the habitability and observational signatures of newly discovered planets might be influenced by these climatic factors. This review summarizes the origins and evolution of the burgeoning field of exoplanet climatology, discusses recent work using a hierarchy of computer models to identify those planets most capable of supporting life, and offers a glimpse into future directions of this quickly evolving subfield of exoplanet science.

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arXiv2019

The Importance of 3D General Circulation Models for Characterizing the Climate and Habitability of Terrestrial Extrasolar Planets

While recently discovered exotic new planet-types have both challenged our imaginations and broadened our knowledge of planetary system workings, perhaps the most compelling objective of exoplanet science is to detect and characterize habitable and possibly inhabited worlds orbiting in other star systems. For the foreseeable future, characterizations of extrasolar planets will be made via remote sensing of planetary spectroscopic and temporal signals, along with careful fitting of this data to advanced models of planets and their atmospheres. Terrestrial planets are small and significantly more challenging to observe compared to their larger gaseous brethren; however observatories coming on-line in the coming decade will begin to allow their characterization. Still, it is not enough to invest only in observational endeavors. Comprehensive modeling of planetary atmospheres is required in order to fully understand what it is that our grand telescopes see in the night-sky. In our quest to characterize habitable, and possibly inhabited worlds, 3D general circulation models (GCMs) should be used to evaluate potential climate states and their associated temporal and spatial dependent observable signals. 3D models allow for coupled, self-consistent, multi-dimensional simulations, which can realistically simulate the climates of terrestrial extrasolar planets. A complete theoretical understanding of terrestrial exoplanetary atmospheres, gained through comprehensive 3D modeling, is critical for interpreting spectra of exoplanets taken from current and planned instruments, and is critical for designing future missions that aim to measure spectra of potentially habitable exoplanets as one of their key science goals. We recommend continued institutional support for 3D GCM modeling teams that focus on planetary and exoplanetary applications.

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arXiv2018

Hydrohalite Salt-albedo Feedback Could Cool M-dwarf Planets

A possible surface type that may form in the environments of M-dwarf planets is sodium chloride dihydrate, or "hydrohalite" (NaCl $\cdot$ 2H$_2$O), which can precipitate in bare sea ice at low temperatures. Unlike salt-free water ice, hydrohalite is highly reflective in the near-infrared, where M-dwarf stars emit strongly, making the effect of the interaction between hydrohalite and the M-dwarf SED necessary to quantify. We carried out the first exploration of the climatic effect of hydrohalite-induced salt-albedo feedback on extrasolar planets, using a three-dimensional global climate model. Under fixed CO$_2$ conditions, rapidly-rotating habitable-zone M-dwarf planets receiving 65% or less of the modern solar constant from their host stars exhibit cooler temperatures when an albedo parameterization for hydrohalite is included in climate simulations, compared to simulations without such a parameterization. Differences in global mean surface temperature with and without this parameterization increase as the instellation is lowered, which may increase CO$_2$ build-up requirements for habitable conditions on planets with active carbon cycles. Synchronously-rotating habitable-zone M-dwarf planets appear susceptible to salt-albedo feedback at higher levels of instellation (90% or less of the modern solar constant) than planets with Earth-like rotation periods, due to their cooler minimum day-side temperatures. These instellation levels where hydrohalite seems most relevant correspond to several recently-discovered potentially habitable M-dwarf planets, including Proxima Centauri b, TRAPPIST-1e, and LHS 1140b, making an albedo parameterization for hydrohalite of immediate importance in future climate simulations.

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arXiv2017

Constraints on Climate and Habitability for Earth-like Exoplanets Determined from a General Circulation Model

Conventional definitions of habitability require abundant liquid surface water to exist continuously over geologic timescales. Water in each of its thermodynamic phases interacts with solar and thermal radiation and is the cause for strong climatic feedbacks. Thus, assessments of the habitable zone require models to include a complete treatment of the hydrological cycle over geologic time. Here, we use the Community Atmosphere Model from the National Center for Atmospheric Research to study the evolution of climate for an Earth-like planet at constant CO2, under a wide range of stellar fluxes from F-, G-, and K-dwarf main sequence stars. Around each star we find four stable climate states defined by mutually exclusive global mean surface temperatures (Ts); snowball (Ts < 235 K), waterbelt (235 K < Ts < 250 K), temperate (275 K < Ts < 315 K), and moist greenhouse (Ts > 330 K). Each is separated by abrupt climatic transitions. Waterbelt, temperate, and cooler moist greenhouse climates can maintain open-ocean against both sea-ice albedo and hydrogen escape processes respectively, and thus constitute habitable worlds. We consider the warmest possible habitable planet as having Ts ~ 355 K, at which point diffusion limited water-loss could remove an Earth ocean in ~1 Gyr. Without long timescale regulation of non-condensable greenhouse species at Earth-like temperatures and pressures, such as CO2, habitability can be maintained for an upper limit of ~2.2, ~2.4 and ~4.7 Gyr around F-, G- and K-dwarf stars respectively due to main sequence brightening.

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arXiv2016

The Habitability of Planets Orbiting M-dwarf Stars

The prospects for the habitability of M-dwarf planets have long been debated, due to key differences between the unique stellar and planetary environments around these low-mass stars, as compared to hotter, more luminous Sun-like stars. Over the past decade, significant progress has been made by both space- and ground-based observatories to measure the likelihood of small planets to orbit in the habitable zones of M-dwarf stars. We now know that most M dwarfs are hosts to closely-packed planetary systems characterized by a paucity of Jupiter-mass planets and the presence of multiple rocky planets, with roughly a third of these rocky M-dwarf planets orbiting within the habitable zone, where they have the potential to support liquid water on their surfaces. Theoretical studies have also quantified the effect on climate and habitability of the interaction between the spectral energy distribution of M-dwarf stars and the atmospheres and surfaces of their planets. These and other recent results fill in knowledge gaps that existed at the time of the previous overview papers published nearly a decade ago by Tarter et al. (2007) and Scalo et al. (2007). In this review we provide a comprehensive picture of the current knowledge of M-dwarf planet occurrence and habitability based on work done in this area over the past decade, and summarize future directions planned in this quickly evolving field.

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arXiv2016

The Effect of Orbital Configuration on the Possible Climates and Habitability of Kepler-62f

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 $0.00 \leqslant e \leqslant 0.32$, 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 CO$_2$ 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$^\circ$ and 90$^\circ$). A climate similar to modern-day Earth is possible for the entire range of stable eccentricities if atmospheric CO$_2$ is increased to 5-bar levels. In a low-CO$_2$ 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, CO$_2$ 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.

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arXiv2014

Spectrum-driven Planetary Deglaciation Due to Increases in Stellar Luminosity

Distant planets in globally ice-covered, "snowball", states may depend on increases in their host stars' luminosity to become hospitable for surface life. Using a General Circulation Model (GCM), we simulated the equilibrium climate response of a planet to a range of instellations from an F-, G-, or M- dwarf star. The range of instellation that permits both complete ice cover and at least partially ice-free climate states is a measure of the climate hysteresis that a planet can exhibit. An ice-covered planet with high climate hysteresis would show a higher resistance to the initial loss of surface ice coverage with increases in instellation, and abrupt, extreme ice loss once deglaciation begins. Our simulations indicate that the climate hysteresis depends sensitively on the host star spectral energy distribution. Under fixed CO2 conditions, a planet orbiting an M-dwarf star exhibits a smaller climate hysteresis, requiring a smaller instellation to initiate deglaciation than planets orbiting hotter, brighter stars. This is due to the higher absorption of near-IR radiation by ice on the surfaces and greenhouse gases and clouds in the atmosphere of an M-dwarf planet. Increases in atmospheric CO2 further lower the climate hysteresis, as M-dwarf snowball planets exhibit a larger radiative response than G-dwarf snowball planets for the same increase in CO2. For a smaller hysteresis, planets near the outer edge of the habitable zone will thaw earlier in their evolutionary history, and will experience a less abrupt transition out of global ice cover.

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arXiv2013

The Effect of Host Star Spectral Energy Distribution and Ice-Albedo Feedback on the Climate of Extrasolar Planets

Planetary climate can be affected by the interaction of the host star spectral energy distribution with the wavelength-dependent reflectivity of ice and snow. Here we explore this effect using 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 general circulation model is 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 simulate 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 exhibit a stronger ice-albedo feedback. We find that ice-covered conditions occur 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). A similar planet orbiting the Sun at an equivalent flux distance requires an 8% reduction in instellation, while a planet orbiting an M-dwarf star requires an additional 19% reduction in instellation to become ice-covered, equivalent to 73% of the modern solar constant. The surface ice-albedo feedback effect becomes less important at the outer edge of the habitable zone, where atmospheric CO2 can be expected to be high in order to maintain clement conditions for surface liquid water. We show that 3-10 bars of CO2 will entirely mask the climatic effect of ice and snow, leaving the outer limits of the habitable zone unaffected by the spectral dependence of water ice and snow albedo. However, less CO2 is needed to maintain open water for a planet orbiting an M-dwarf star, than would be the case for hotter main-sequence stars.

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arXiv2011

Rotational Variability of Earth's Polar Regions: Implications for Detecting Snowball Planets

We have obtained the first time-resolved, disc-integrated observations of Earth's poles with the Deep Impact spacecraft as part of the EPOXI Mission of Opportunity. These data mimic what we will see when we point next-generation space telescopes at nearby exoplanets. We use principal component analysis (PCA) and rotational lightcurve inversion to characterize color inhomogeneities and map their spatial distribution from these unusual vantage points, as a complement to the equatorial views presented in Cowan et al. (2009). We also perform the same PCA on a suite of simulated rotational multi-band lightcurves from NASA's Virtual Planetary Laboratory 3D spectral Earth model. This numerical experiment allows us to understand what sorts of surface features PCA can robustly identify. We find that the EPOXI polar observations have similar broadband colors as the equatorial Earth, but with 20-30% greater apparent albedo. This is because the polar observations are most sensitive to mid-latitudes, which tend to be more cloudy than the equatorial latitudes emphasized by the original EPOXI Earth observations. The cloudiness of the mid-latitudes also manifests itself in the form of increased variability at short wavelengths in the polar observations, and as a dominant gray eigencolor in the south polar observation. We construct a simple reflectance model for a snowball Earth. By construction, our model has a higher Bond albedo than the modern Earth; its surface albedo is so high that Rayleigh scattering does not noticeably affect its spectrum. The rotational color variations occur at short wavelengths due to the large contrast between glacier ice and bare land in those wavebands. Thus we find that both the broadband colors and diurnal color variations of such a planet would be easily distinguishable from the modern-day Earth, regardless of viewing angle.

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