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Register a new userGlobal Mapping of an Exo-Earth using Sparse Modeling
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We develop a new retrieval scheme for obtaining two-dimensional surface maps of exoplanets from scattered light curves. In our scheme, the combination of the L1-norm and Total Squared Variation, which is one of the techniques used in sparse modeling, is adopted to find the optimal map. We apply the new method to simulated scattered light curves of the Earth, and find that the new method provides a better spatial resolution of the reconstructed map than those using Tikhonov regularization. We also apply the new method to observed scattered light curves of the Earth obtained during the two-year DSCOVR/EPIC observations presented by Fan et al. (2019). The method with Tikhonov regularization enables us to resolve North America, Africa, Eurasia, and Antarctica. In addition to that, the sparse modeling identifies South America and Australia, although it fails to find the Antarctica maybe due to low observational weights on the poles. Besides, the proposed method is capable of retrieving maps from noise injected light curves of a hypothetical Earth-like exoplanet at 5 pc with noise level expected from coronagraphic images from a 8-m telescope. We find that the sparse modeling resolves Australia, Afro-Eurasia, North America, and South America using 2-year observation with a time interval of one month. Our study shows that the combination of sparse modeling and multi-epoch observation with 1 day or 5 days per month can be used to identify main features of an Earth analog in future direct imaging missions such as the Large UV/Optical/IR Surveyor (LUVOIR).
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Photometric variation of a directly imaged planet contains information on both the geography and spectra of the planetary surface. We propose a novel technique that disentangles the spatial and spectral information from the multi-band reflected light curve. This will enable us to compose a two-dimensional map of the surface composition of a planet with no prior assumption on the individual spectra, except for the number of independent surface components. We solve the unified inverse problem of the spin-orbit tomography and spectral unmixing by generalizing the non-negative matrix factorization (NMF) using a simplex volume minimization method. We evaluated our method on a toy cloudless Earth and observed that the new method could accurately retrieve the geography and unmix spectral components. Furthermore, our method is also applied to the real-color variability of the Earth as observed by Deep Space Climate Observatory (DSCOVR). The retrieved map explicitly depicts the actual geography of the Earth and unmixed spectra capture features of the ocean, continents, and clouds. It should be noted that, the two unmixed spectra consisting of the reproduced continents resemble those of soil and vegetation.
Photometric variability of a directly imaged exo-Earth conveys spatial information on its surface and can be used to retrieve a two-dimensional geography and axial tilt of the planet (spin-orbit tomography). In this study, we relax the assumption of the static geography and present a computationally tractable framework for dynamic spin-orbit tomography applicable to the time-varying geography. First, a Bayesian framework of static spin-orbit tomography is revisited using analytic expressions of the Bayesian inverse problem with a Gaussian prior. We then extend this analytic framework to a time-varying one through a Gaussian process in time domain, and present analytic expressions that enable efficient sampling from a full joint posterior distribution of geography, axial tilt, spin rotation period, and hyperparameters in the Gaussian-process priors. Consequently, it only takes 0.3 s for a laptop computer to sample one posterior dynamic map conditioned on the other parameters with 3,072 pixels and 1,024 time grids, for a total of $sim 3 times 10^6$ parameters. We applied our dynamic mapping method on a toy model and found that the time-varying geography was accurately retrieved along with the axial-tilt and spin rotation period. In addition, we demonstrated the use of dynamic spin-orbit tomography with a real multi-color light curve of the Earth as observed by the Deep Space Climate Observatory. We found that the resultant snapshots from the dominant component of a principle component analysis roughly captured the large-scale, seasonal variations of the clear-sky and cloudy areas on the Earth.
With an emphasis on improving the fidelity even in super-resolution regimes, new imaging techniques have been intensively developed over the last several years, which may provide substantial improvements to the interferometric observation of protoplanetary disks. In this study, sparse modeling (SpM) is applied for the first time to observational data sets taken by the Atacama Large Millimeter/submillimeter Array (ALMA). The two data sets used in this study were taken independently using different array configurations at Band 7 (330 GHz), targeting the protoplanetary disk around HD 142527; one in the shorter-baseline array configuration (~ 430 m), and the other in the longer-baseline array configuration (~ 1570 m). The image resolutions reconstructed from the two data sets are different by a factor of ~ 3. We confirm that the previously known disk structures appear on the images produced by both SpM and CLEAN at the standard beam size. The image reconstructed from the shorter-baseline data using the SpM matches that obtained with the longer-baseline data using CLEAN, achieving a super-resolution image from which a structure finer than the beam size can be reproduced. Our results demonstrate that on-going intensive development in the SpM imaging technique is beneficial to imaging with ALMA.
In this article, theory-based analytical methodologies of astrophysics employed in the modern era are suitably operated alongside a test research-grade telescope to image and determine the orbit of a near-earth asteroid from original observations, measurements, and calculations. Subsequently, its intrinsic orbital path has been calculated including the chance it would likely impact Earth in the time ahead. More so specifically, this case-study incorporates the most effective, feasible, and novel Gausss Method in order to maneuver the orbital plane components of a planetesimal, further elaborating and extending our probes on a selected near-earth asteroid (namely the 12538-1998 OH) through the observational data acquired over a six week period. Utilizing the CCD (Charge Coupled Device) snapshots captured, we simulate and calculate the orbit of our asteroid as outlined in quite detailed explanations. The uncertainties and deviations from the expected values are derived to reach a judgement whether our empirical findings are truly reliable and representative measurements by partaking a statistical analysis based systematic approach. Concluding the study by narrating what could have caused such discrepancy of findings in the first place, if any, measures are put forward that could be undertaken to improve the test-case for future investigations. Following the calculation of orbital elements and their uncertainties using Monte Carlo analysis, simulations were executed with various sample celestial bodies to derive a plausible prediction regarding the fate of Asteroid 1998 OH. Finally, the astrometric and photometric data, after their precise verification, were officially submitted to the Minor Planet Center: an organization hosted by the Center for Astrophysics, Harvard and Smithsonian and funded by NASA, for keeping track of the asteroids potential trajectories.
Understanding the total flux and polarization signals of Earth-like planets and their spectral and temporal variability is essential for the future characterization of such exoplanets. We provide computed total (F) and linearly (Q and U) and circularly (V) polarized fluxes, and the degree of polarization P of sunlight that is reflected by a model Earth, to be used for instrument designs, optimizing observational strategies, and/or developing retrieval algorithms. We modeled a realistic Earth-like planet using one year of daily Earth-observation data: cloud parameters (distribution, optical thickness, top pressure, and particle effective radius), and surface parameters (distribution, surface type, and albedo). The Stokes vector of the disk-averaged reflected sunlight was computed for phase angles alpha from 0 to 180 degrees, and for wavelengths lambda from 350 to 865 nm. The total flux F is one order of magnitude higher than the polarized flux Q, and Q is two and four orders of magnitude higher than U and V, respectively. Without clouds, the peak-to-peak daily variations due to the planetary rotation increase with increasing lambda for F, Q, and P, while they decrease for U and V. Clouds modify but do not completely suppress the variations that are due to rotating surface features. With clouds, the variation in F increases with increasing lambda, while in Q, it decreases with increasing lambda, except at the largest phase angles. In earlier work, it was shown that with oceans, Q changes color from blue through white to red. The alpha where the color changes increases with increasing cloud coverage. Here, we show that this unique color change in Q also occurs when the oceans are partly replaced by continents, with or without clouds. The degree of polarization P shows a similar color change. Our computed fluxes and degree of polarization will be made publicly available.
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