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We re-examine the XUV luminosity evolution of TRAPPIST-1 utilizing new observational constraints (XUV and bolometric luminosity) from multi-epoch X-ray/UV photometry. Following the formalism presented in Fleming et al. (2020), we infer that TRAPPIST-1 maintained a saturated XUV luminosity, relative to the bolometric luminosity, of $\log_{10}$(L$_{\rm XUV}$/L$_{\rm bol}$) $= -3.03_{-0.23}^{+0.25}$ at early times for a period of $t_{sat} = 3.14_{-1.46}^{+2.22}$ Gyr. After the saturation phase, we find L$_{\rm XUV}$ decayed over time by an exponential rate of $\beta_{\rm XUV} = -1.17_{-0.28}^{+0.27}$. Compared to our inferred age of the system, ${\rm age} = 7.96_{-1.87}^{+1.78}$ Gyr, our result for $t_{sat}$ suggests that there is only a $\sim4\%$~chance that TRAPPIST-1 still remains in the saturated phase today, which is significantly lower than the previous estimate of 40\%. Despite this reduction in $t_{sat}$, our results remain consistent in the conclusion that the TRAPPIST-1 planets likely received an extreme amount XUV energy -- an estimated integrated XUV energy of $\sim10^{30}-10^{32}$ erg over the star's lifetime., Comment: 4 pages, 1 figure

We simulate the coupled stellar and tidal evolution of short-period binary stars (orbital period $P_{orb} \lsim$8 days) to investigate the orbital oscillations, instellation cycles, and orbital stability of circumbinary planets (CBPs). We consider two tidal models and show that both predict an outward-then-inward evolution of the binary's semi-major axis $a_{bin}$ and eccentricity $e_{bin}$. This orbital evolution drives a similar evolution of the minimum CBP semi-major axis for orbital stability. By expanding on previous models to include the evolution of the mass concentration, we show that the maximum in the CBP orbital stability limit tends to occur 100 Myr after the planets form, a factor of 100 longer than previous investigations. This result provides further support for the hypothesis that the early stellar-tidal evolution of binary stars has removed CBPs from short-period binaries. We then apply the models to Kepler-47 b, a CBP orbiting close to its host stars' stability limit, to show that if the binary's initial $e_{bin} \gsim$0.24, the planet would have been orbiting within the instability zone in the past and probably wouldn't have survived. For stable, hypothetical cases in which the stability limit does not reach a planet's orbit, we find that the amplitudes of $a_{bin}$ and $e_{bin}$ oscillations can damp by up to 10\% and 50\%, respectively. Finally, we consider equal-mass stars with $P_{orb} =$ 7.5 days and compare the HZ to the stability limit. We find that for stellar masses $\lsim0.12M_{\odot}$, the HZ is completely unstable, even if the binary orbit is circular. For $e_{bin} \lsim$0.5, that limit increases to $0.17M_{\odot}$, and the HZ is partially destabilized for stellar masses up to $0.45M_{\odot}$. These results may help guide searches for potentially habitable CBPs, as well as characterize their evolution and likelihood to support life after they are found., Comment: 10 pages, 7 figures

We model the long-term XUV luminosity of TRAPPIST-1 to constrain the evolving high-energy radiation environment experienced by its planetary system. Using Markov Chain Monte Carlo (MCMC), we derive probabilistic constraints for TRAPPIST-1's stellar and XUV evolution that account for observational uncertainties, degeneracies between model parameters, and empirical data of low-mass stars. We constrain TRAPPIST-1's mass to $m_{\star} = 0.089 \pm{0.001}$ M$_{\odot}$ and find that its early XUV luminosity likely saturated at $\log_{10}(L_{XUV}/L_{bol}) = -3.03^{+0.23}_{-0.12}$. From the posterior distribution, we infer that there is a ${\sim}40\%$ chance that TRAPPIST-1 is still in the saturated phase today, suggesting that TRAPPIST-1 has maintained high activity and $L_{XUV}/L_{bol} \approx 10^{-3}$ for several Gyrs. TRAPPIST-1's planetary system therefore likely experienced a persistent and extreme XUV flux environment, potentially driving significant atmospheric erosion and volatile loss. The inner planets likely received XUV fluxes ${\sim}10^3 - 10^4\times$ that of the modern Earth during TRAPPIST-1's ${\sim}1$ Gyr-long pre-main sequence phase. Deriving these constraints via MCMC is computationally non-trivial, so scaling our methods to constrain the XUV evolution of a larger number of M dwarfs that harbor terrestrial exoplanets would incur significant computational expenses. We demonstrate that approxposterior, an open source Python machine learning package for approximate Bayesian inference using Gaussian processes, accurately and efficiently replicates our analysis using $980\times$ less computational time and $1330\times$ fewer simulations than MCMC sampling using emcee. We find that approxposterior derives constraints with mean errors on the best fit values and $1\sigma$ uncertainties of $0.61\%$ and $5.5\%$, respectively, relative to emcee., Comment: Accepted in ApJ, 16 pages, 7 figures

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 simultaneously to 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., Comment: 75 pages, 34 figures, 10 tables, accepted to the Proceedings of the Astronomical Society of the Pacific. Source code, documentation, and examples available at https://github.com/VirtualPlanetaryLaboratory/vplanet

We examine how tides, stellar evolution, and magnetic braking shape the rotation period (P$_{rot}$) evolution of low-mass stellar binaries up to orbital periods (P$_{orb}$) of 100 d across a wide range tidal dissipation parameters using two common equilibrium tidal models. We find that many binaries with P$_{orb} < 20$ d tidally lock, and most with $P_{orb} < 4$ d tidally lock into synchronous rotation on circularized orbits. At short P$_{orb}$, tidal torques produce a population of fast rotators that single-star only models of magnetic braking fail to produce. In many cases, we show that the competition between magnetic braking and tides produces a population of subsynchronous rotators that persists for Gyrs, even in short P$_{orb}$ binaries, qualitatively reproducing the subsynchronous eclipsing binaries (EBs) discovered in the Kepler field by Lurie et al. (2017). Both equilibrium tidal models predict that binaries can tidally-interact out to P$_{orb} \approx 80$ d, while the Constant Phase Lag tidal model predicts that binaries can tidally lock out to P$_{orb} \approx 100$ d. Tidal torques often force the P$_{rot}$ evolution of stellar binaries to depart from the long-term magnetic braking-driven spin down experienced by single stars, revealing that P$_{rot}$ is not be a valid proxy for age in all cases, i.e. gyrochronology can underpredict ages by up to $300\%$ unless one accounts for binarity. We suggest that accurate determinations of orbital eccentricties and P$_{rot}$ can be used to discriminate between which equilibrium tidal models best describes tidal interactions in low-mass binary stars., Comment: Accepted, ApJ

Provided that sufficient resources are deployed, we can look forward to an extraordinary future in which we will characterize potentially habitable planets. Until now, we have had to base interpretations of observations on habitability hypotheses that have remained untested. To test these theories observationally, we propose a statistical comparative planetology approach to questions of planetary habitability. The key objective of this approach will be to make quick and cheap measurements of critical planetary characteristics on a large sample of exoplanets, exploiting statistical marginalization to answer broad habitability questions. This relaxes the requirement of obtaining multiple types of data for a given planet, as it allows us to test a given hypothesis from only one type of measurement using the power of an ensemble. This approach contrasts with a "systems science" approach, where a few planets would be extensively studied with many types of measurements. A systems science approach is associated with a number of difficulties which may limit overall scientific return, including: the limited spectral coverage and noise of instruments, the diversity of exoplanets, and the extensive list of potential false negatives and false positives. A statistical approach could also be complementary to a systems science framework by providing context to interpret extensive measurements on planets of particular interest. We strongly recommend future missions with a focus on exoplanet characterization, and with the capability to study large numbers of planets in a homogenous way, rather than exclusively small, intense studies directed at a small sample of planets., Comment: White paper submitted in response to the solicitation of feedback for the "2020 Decadal Survey" by the National Academy of Sciences

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., Comment: NAS ASTRO 2020, White Paper! 2 figures, and 10 pages

With support from the Self Family Foundation and the South Carolina Education Oversight Committee, the Riley Institute has completed a multi-year study of Montessori education in South Carolina's public schools, the most comprehensive evaluation of public Montessori ever conducted in the United States. Between 2011 and 2016, this mixed-method study examined how Montessori impacts stakeholders in South Carolina and provided information needed to guide future investment in Montessori education. Researchers investigated the following as parts of the study: the extent to which schools implemented Montessori with fidelity; the demographic makeup of public school Montessori students; the effect of Montessori education on academic and behavioral outcomes; the impact of Montessori education on creativity, social skills, work habits, and executive function; and Montessori teachers' perspectives on job satisfaction and the challenges of Montessori in the public sector. The study results demonstrate that students in public school Montessori classrooms across the state are faring well, as compared to similar non-Montessori public school students, when examining academic, behavioral, and affective outcomes.

We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet-planet/planet-moon occultation light curves, as well as thermal (rotational) phase curves. In this paper we also introduce STARRY, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in STARRY is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. STARRY also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body's surface map., Comment: 55 pages, 20 figures. Accepted to the Astronomical Journal. Check out the code at https://github.com/rodluger/starry

Using an energy balance model with ice sheets, we examine the climate response of an Earth-like planet orbiting a G dwarf star and experiencing large orbital and obliquity variations. We find that ice caps couple strongly to the orbital forcing, leading to extreme ice ages. In contrast with previous studies, we find that such exo-Milankovitch cycles tend to impair habitability by inducing snowball states within the habitable zone. The large amplitude changes in obliquity and eccentricity cause the ice edge, the lowest latitude extent of the ice caps, to become unstable and grow to the equator. We apply an analytical theory of the ice edge latitude to show that obliquity is the primary driver of the instability. The thermal inertia of the ice sheets and the spectral energy distribution of the G dwarf star increase the sensitivity of the model to triggering runaway glaciation. Finally, we apply a machine learning algorithm to demonstrate how this technique can be used to extend the power of climate models. This work illustrates the importance of orbital evolution for habitability in dynamically rich planetary systems. We emphasize that as potentially habitable planets are discovered around G dwarfs, we need to consider orbital dynamics., Comment: 37 pages, 26 figures, accepted at the Astronomical Journal

We outline a mechanism that explains the observed lack of circumbinary planets (CBPs) via coupled stellar-tidal evolution of isolated binary stars. Tidal forces between low-mass, short-period binary stars on the pre-main sequence slow the stellar rotations, transferring rotational angular momentum to the orbit as the stars approach the tidally locked state. This transfer increases the binary orbital period, expanding the region of dynamical instability around the binary, and destabilizing CBPs that tend to preferentially orbit just beyond the initial dynamical stability limit. After the stars tidally lock, we find that angular momentum loss due to magnetic braking can significantly shrink the binary orbit, and hence the region of dynamical stability, over time impacting where surviving CBPs are observed relative to the boundary. We perform simulations over a wide range of parameter space and find that the expansion of the instability region occurs for most plausible initial conditions and that in some cases, the stability semi-major axis doubles from its initial value. We examine the dynamical and observable consequences of a CBP falling within the dynamical instability limit by running N-body simulations of circumbinary planetary systems and find that typically, at least one planet is ejected from the system. We apply our theory to the shortest period {\it Kepler} binary that possesses a CBP, Kepler-47, and find that its existence is consistent with our model. Under conservative assumptions, we find that coupled stellar-tidal evolution of pre-main sequence binary stars removes at least one close-in CBP in $87\%$ of multi-planet circumbinary systems., Comment: 26 pages, 16 figures, accepted, ApJ