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 multiband 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 nonnegative matrix factorization 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. 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.
Abstract
We present a comprehensive catalog of cool (period
P
≳ 2 yr) transiting planet candidates in the 4 yr light curves from the prime
Kepler
mission. Most of the candidates show only one or two ...transits and have largely been missed in the original
Kepler
Object of Interest catalog. Our catalog is based on all known such candidates in the literature, as well as new candidates from the search in this paper, and provides a resource to explore the planet population near the snow line of Sun-like stars. We homogeneously performed pixel-level vetting, stellar characterization with
Gaia
parallax and archival/Subaru spectroscopy, and light-curve modeling to derive planet parameters and to eliminate stellar binaries. The resulting clean sample consists of 67 planet candidates whose radii are typically constrained to 5%, in which 23 are newly reported. The number of Jupiter-sized candidates (29 with radius
) in the sample is consistent with the Doppler occurrence. The smaller candidates are more prevalent (23 with
, 15 with
) and suggest that long-period Neptune-sized planets are at least as common as the Jupiter-sized ones, although our sample is yet to be corrected for detection completeness. If the sample is assumed to be complete, these numbers imply the occurrence rate of 0.39 ± 0.07 planets with
and
per FGK dwarf. The stars hosting candidates with
have systematically higher Fe/H than do the
Kepler
field stars, providing evidence that giant planet–metallicity correlation extends to
.
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 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 the 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 3072 pixels and 1024 time grids, for a total of ∼3 × 106 parameters. We applied our dynamic mapping method to 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 multicolor 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 principal component analysis roughly captured the large-scale, seasonal variations of the clear-sky and cloudy areas on the Earth.
We report high-resolution spectroscopic detection of TiO molecular signature in the day-side spectra of WASP-33b, the second hottest known hot Jupiter. We used the High Dispersion Spectrograph (HDS; ...R ∼ 165,000) on the Subaru telescope in the wavelength range of 0.62-0.88 m to obtain the day-side spectra of WASP-33b. We suppress and correct the systematic effects of the instrument and the telluric and stellar lines using the SYSREM algorithm after the selection of good orders based on Barnard's star and other M-type stars. We detect a 4.8 signal at an orbital velocity of km s−1 and systemic velocity of km s−1, which agree with the derived values from a previous analysis of the primary transit. Our detection with the temperature inversion model implies the existence of a stratosphere in its atmosphere; however, we were unable to constrain the volume mixing ratio of the detected TiO. We also measure the stellar radial velocity and use it to obtain a more stringent constraint on the orbital velocity, km s−1. Our results demonstrate that high-dispersion spectroscopy is a powerful tool to characterize the atmosphere of an exoplanet, even in the optical wavelength range, and shows a promising potential in using and developing similar techniques with high-dispersion spectrograph on current 10 m class and future extremely large telescopes.
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 Deep Space Climate Observatory/Earth Polychromatic Imaging Camera observations presented by Fan et al. 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 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 Earthlike exoplanet at 5 pc with a noise level expected from coronagraphic images from a 8 m space telescope. We find that the sparse modeling resolves Australia, Afro-Eurasia, North America, and South America using 2 yr observation with a time interval of one month. Our study shows that the combination of sparse modeling and multiepoch 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.
Previous analyses of Doppler and Kepler data have found that Sun-like stars hosting "cold Jupiters" (giant planets with a 1 au) almost always host "inner super-Earths" (1-4 R⊕, a 1 au). Here we ...attempt to determine the degree of alignment between the orbital planes of the cold Jupiters and the inner super-Earths. The key observational input is the fraction of Kepler stars with transiting super-Earths that also have transiting cold Jupiters. This fraction depends on both the probability for cold Jupiters to occur in such systems and the mutual orbital inclinations. Since the probability of occurrence has already been measured in Doppler surveys, we can use the data to constrain the mutual inclination distribution. We find = 11 8−5 5+12 7 (68% confidence) and > 3 5 (95% confidence), where is the scale parameter of the Rayleigh distribution. This suggests that planetary orbits in systems with cold Jupiters tend to be coplanar-although not quite as coplanar as those in the solar system, which have a mean inclination from the invariable plane of 1 8. We also find evidence that cold Jupiters have lower mutual inclinations relative to inner systems with higher transit multiplicity. This suggests a link between the dynamical excitation in the inner and outer systems. For example, perturbations from misaligned cold Jupiters may dynamically heat or destabilize systems of inner super-Earths.
ABSTRACT We consider the time-frequency analysis of a scattered light curve of a directly imaged exoplanet. We show that the geometric effect due to planetary obliquity and orbital inclination induce ...the frequency modulation of the apparent diurnal periodicity. We construct a model of the frequency modulation and compare it with the instantaneous frequency extracted from the pseudo-Wigner distribution of simulated light curves of a cloudless Earth. The model provides good agreement with the simulated modulation factor, even for the light curve with Gaussian noise comparable to the signal. Notably, the shape of the instantaneous frequency is sensitive to the difference between the prograde, retrograde, and pole-on spin rotations. While our technique requires the albedo map to be static, it does not need to solve the albedo map of the planet. The time-frequency analysis is complementary to other methods which utilize the amplitude modulation. This paper demonstrates the importance of the frequency domain of the photometric variability for the characterization of directly imaged exoplanets in future research.
Recent core-collapse supernova (CCSN) simulations have predicted several distinct features in gravitational-wave (GW) spectrograms, including a ramp-up signature due to the g-mode oscillation of the ...protoneutron star (PNS) and an excess in the low-frequency domain (100 to ∼300 Hz) potentially induced by the standing accretion shock instability (SASI). These predictions motivated us to perform a sophisticated time-frequency analysis (TFA) of the GW signals, aimed at preparation for future observations. By reanalyzing a gravitational waveform obtained in a three-dimensional general-relativistic CCSN simulation, we show that both the spectrogram with an adequate window and the quadratic TFA separate the multimodal GW signatures much more clearly compared with a previous analysis. We find that the observed low-frequency excess during the SASI active phase is divided into two components, a stronger one at 130 Hz and an overtone at 260 Hz, both of which evolve quasistatically during the simulation time. We also identify a new mode with frequency varying from 700 to 600 Hz. Furthermore, we develop the quadratic TFA for the Stokes I, Q, U, and V parameters as a new tool to investigate the circular polarization of GWs. We demonstrate that the polarization states that randomly change with time after bounce are associated with the PNS g-mode oscillation, whereas a slowly changing polarization state in the low-frequency domain is connected to the PNS core oscillation. This study demonstrates the capability of sophisticated TFA to diagnose polarized CCSN GWs in order to explore their complex nature.
Abstract
The time series of light reflected from exoplanets by future direct imaging can provide spatial information with respect to the planetary surface. We apply sparse modeling to the retrieval ...method that disentangles the spatial and spectral information from multiband reflected light curves termed as spin–orbit unmixing. We use the
ℓ
1
-norm and the total squared variation norm as regularization terms for the surface distribution. Applying our technique to a toy model of cloudless Earth, we show that our method can infer sparse and continuous surface distributions and also unmixed spectra without prior knowledge of the planet surface. We also apply the technique to the real Earth data as observed by DSCOVR/EPIC. We determined the representative components that can be interpreted as cloud and ocean. Additionally, we found two components that resembled the distribution of land. One of the components captures the Sahara Desert, and the other roughly corresponds to vegetation, although their spectra are still contaminated by clouds. Sparse modeling significantly improves the geographic retrieval, in particular, of clouds and leads to higher resolutions for other components when compared with spin–orbit unmixing using Tikhonov regularization.
ABSTRACT We visually inspected the light curves of 7557 Kepler Objects of Interest (KOIs) to search for single transit events (STEs) that were possibly due to long-period giant planets. We identified ...28 STEs in 24 KOIs, among which 14 events are newly reported in this paper. We estimate the radius and orbital period of the objects causing STEs by fitting the STE light curves simultaneously with the transits of the other planets in the system or with prior information on the host star density. As a result, we found that STEs in seven of those systems are consistent with Neptune- to Jupiter-sized objects of orbital periods ranging from a few to ∼ 20 years . We also estimate that 20 % of the compact multi-transiting systems host cool giant planets with periods 3 years on the basis of their occurrence in the KOIs with multiple candidates, assuming the small mutual inclination between inner and outer planetary orbits.
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