Rotational Spectral Unmixing of Exoplanets: Degeneracies between Surface Colors and Geography

Unmixing the disk-integrated spectra of exoplanets provides hints about heterogeneous surfaces that we cannot directly resolve in the foreseeable future. It is particularly important for terrestrial planets with diverse surface compositions like Earth. Although previous work on unmixing the spectra of Earth from disk-integrated multi-band light curves appeared successful, we point out a mathematical degeneracy between the surface colors and their spatial distributions. Nevertheless, useful constraints on the spectral shape of individual surface types may be obtained from the premise that albedo is everywhere between 0 and 1. We demonstrate the degeneracy and the possible constraints using both mock data based on a toy model of Earth, as well as real observations of Earth. Despite the severe degeneracy, we are still able to recover an approximate albedo spectrum for an ocean. In general, we find that surfaces are easier to identify when they cover a large fraction of the planet and when their spectra approach zero or unity in certain bands.Comment: 11 pages, 7 figures, published in AJ. Minor text updates from previous versio

Mapping Issues of the Acquisition of L2 Japanese Aspect Markings by Chinese Learners

This paper considers how Chinese learners of Japanese (CLJs) acquire the L2 Japanese aspect marker -teiru in resultative and progressive contexts. It also analyzes the mapping mechanism of the lexical aspect to grammatical markers, with a special focus on achievement and accomplishment verbs. Despite the numerous observations on Chinese aspects (e.g., Dai 2021, Nishizaka 2019, and Sun 2010), only few studies dealt with the issue of acquiring L2 Japanese aspects by L1 Chinese learners. By using the Elicited Acceptability Judgment Test (EAJT) and analyzing the data individually, it was demonstrated that aspect markers corresponding to -teiru are building “one-to-many” rather than “one-to-one” relationships, and CLJs are learning the relationships through mapping while making errors due to other uses

Mapping Earth Analogs from Photometric Variability: Spin-Orbit Tomography for Planets in Inclined Orbits

Aiming at obtaining detailed information of surface environment of Earth analogs, Kawahara & Fujii (2011) proposed an inversion technique of annual scattered light curves named the spin-orbit tomography (SOT), which enables one to sketch a two-dimensional albedo map from annual variation of the disk-integrated scattered light, and demonstrated the method with a planet in a face-on orbit. We extend it to be applicable to general geometric configurations, including low-obliquity planets like the Earth in inclined orbits. We simulate light curves of the Earth in an inclined orbit in three photometric bands (0.4-0.5um, 0.6-0.7um, and 0.8-0.9um) and show that the distribution of clouds, snow, and continents is retrieved with the aid of the SOT. We also demonstrate the SOT by applying it to an upright Earth, a tidally locked Earth, and Earth analogs with ancient continental configurations. The inversion is model independent in the sense that we do not assume specific albedo models when mapping the surface, and hence applicable in principle to any kind of inhomogeneity. This method can potentially serve as a unique tool to investigate the exohabitats/exoclimes of Earth analogs.Comment: 15 pages, 14 figures, 2 tables; published in The Astrophysical Journa

Global Mapping of Earth-like Exoplanets from Scattered Light Curves

Scattered lights from terrestrial exoplanets provide valuable information about the planetary surface. Applying the surface reconstruction method proposed by Fujii et al. (2010) to both diurnal and annual variations of the scattered light, we develop a reconstruction method of land distribution with both longitudinal and latitudinal resolutions. We find that one can recover a global map of an idealized Earth-like planet on the following assumptions: 1) cloudless, 2) a face-on circular orbit, 3) known surface types and their reflectance spectra 4) no atmospheric absorption, 5) known rotation rate 6) static map, and 7) no moon. Using the dependence of light curves on the planetary obliquity, we also show that the obliquity can be measured by adopting the chi-square minimization or the extended information criterion. We demonstrate a feasibility of our methodology by applying it to a multi-band photometry of a cloudless model Earth with future space missions such as the occulting ozone observatory (O3). We conclude that future space missions can estimate both the surface distribution and the obliquity at least for cloudless Earth-like planets within 5 pc.Comment: 20 pages, 19 figures, accepted for publication in Ap