Lazy Model Expansion: Interleaving Grounding with Search

Finding satisfying assignments for the variables involved in a set of constraints can be cast as a (bounded) model generation problem: search for (bounded) models of a theory in some logic. The state-of-the-art approach for bounded model generation for rich knowledge representation languages, like ASP, FO(.) and Zinc, is ground-and-solve: reduce the theory to a ground or propositional one and apply a search algorithm to the resulting theory. An important bottleneck is the blowup of the size of the theory caused by the reduction phase. Lazily grounding the theory during search is a way to overcome this bottleneck. We present a theoretical framework and an implementation in the context of the FO(.) knowledge representation language. Instead of grounding all parts of a theory, justifications are derived for some parts of it. Given a partial assignment for the grounded part of the theory and valid justifications for the formulas of the non-grounded part, the justifications provide a recipe to construct a complete assignment that satisfies the non-grounded part. When a justification for a particular formula becomes invalid during search, a new one is derived; if that fails, the formula is split in a part to be grounded and a part that can be justified. The theoretical framework captures existing approaches for tackling the grounding bottleneck such as lazy clause generation and grounding-on-the-fly, and presents a generalization of the 2-watched literal scheme. We present an algorithm for lazy model expansion and integrate it in a model generator for FO(ID), a language extending first-order logic with inductive definitions. The algorithm is implemented as part of the state-of-the-art FO(ID) Knowledge-Base System IDP. Experimental results illustrate the power and generality of the approach

LAMOST observations in the Kepler field. Analysis of the stellar parameters measured with the LASP based on the low-resolution spectra

All of the 14 subfields of the Kepler field have been observed at least once with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, Xinglong Observatory, China) during the 2012-2014 observation seasons. There are 88,628 reduced spectra with SNR$_g$ (signal-to-noise ratio in g band) $\geq$ 6 after the first round (2012-2014) of observations for the LAMOST-Kepler project (LK-project). By adopting the upgraded version of the LAMOST Stellar Parameter pipeline (LASP), we have determined the atmospheric parameters ($T_{\rm eff}$ , $\log g$, and $\rm [Fe/H]$) and heliocentric radial velocity $v_{\rm rad}$ for 51,406 stars with 61,226 spectra. Compared with atmospheric parameters derived from both high-resolution spectroscopy and asteroseismology method for common stars in Huber et al. (2014), an external calibration of LASP atmospheric parameters was made, leading to the determination of external errors for the giants and dwarfs, respectively. Multiple spectroscopic observations for the same objects of the LK-project were used to estimate the internal uncertainties of the atmospheric parameters as a function of SNR$_g$ with the unbiased estimation method. The LASP atmospheric parameters were calibrated based on both the external and internal uncertainties for the giants and dwarfs, respectively. A general statistical analysis of the stellar parameters leads to discovery of 106 candidate metal-poor stars, 9 candidate very metal-poor stars, and 18 candidate high-velocity stars. Fitting formulae were obtained segmentally for both the calibrated atmospheric parameters of the LK-project and the KIC parameters with the common stars. The calibrated atmospheric parameters and radial velocities of the LK-project will be useful for studying stars in the Kepler field.Comment: 53 pages, 21 figures, 5 tables, Accepted for publication by ApJ

The LAMOST spectroscopic survey of stars in the Kepler field of view: Activity indicators and stellar parameters

We summarize the results of the completed first round of the LAMOST-Kepler project, and describe the status of its on-going second round. As a result of the first round of this project, the atmospheric parameters (T eff , log g , and [Fe/H]), the spectral classification (spectral type and luminosity class), and the radial velocities (RV ) have been measured for 51,385 stars. For 4031 stars, we were able to measure the projected rotational velocity, while the minimum detectable v sin i was 120 km s−1 . For 8821 stars with more than one observation, we computed the χ -square probability that the detected RV variations have a random occurrence. Finally, we classified 442 stars as chromospherically active on the basis of the analysis of their Hα and Ca II-IRT fluxes. All our results have been obtained from the low-resolution (R ∼ 1800) spectroscopic observations acquired with the LAMOST instrument

Asteroseismology of massive stars with the TESS mission: the runaway Beta Cep pulsator PHL 346 = HN Aqr

We report an analysis of the first known Beta Cep pulsator observed by the TESS mission, the runaway star PHL 346 = HN Aqr. The star, previously known as a singly-periodic pulsator, has at least 34 oscillation modes excited, 12 of those in the g-mode domain and 22 p modes. Analysis of archival data implies that the amplitude and frequency of the dominant mode and the stellar radial velocity were variable over time. A binary nature would be inconsistent with the inferred ejection velocity from the Galactic disc of 420 km/s, which is too large to be survivable by a runaway binary system. A kinematic analysis of the star results in an age constraint (23 +- 1 Myr) that can be imposed on asteroseismic modelling and that can be used to remove degeneracies in the modelling process. Our attempts to match the excitation of the observed frequency spectrum resulted in pulsation models that were too young. Hence, asteroseismic studies of runaway pulsators can become vital not only in tracing the evolutionary history of such objects, but to understand the interior structure of massive stars in general. TESS is now opening up these stars for detailed asteroseismic investigation.Comment: accepted for ApJ

Multi-technique investigation of the binary fraction among A-F type candidate hybrid variable stars discovered by Kepler

Hundreds of candidate hybrid pulsators of intermediate type A-F were revealed by the recent space missions. Hybrid pulsators allow to study the full stellar interiors, where p- and g-modes are simultaneously excited. The true hybrid stars must be identified since other processes, due to stellar multiplicity or rotation, might explain the presence of (some) low frequencies observed in their periodograms. We measured the radial velocities of 50 candidate Delta Sct - Gamma Dor hybrid stars from the Kepler mission with the Hermes/Ace spectrographs over a span of months to years. We aim to derive the fraction of binary and multiple systems and to provide an independent and homogeneous determination of the atmospheric properties and vsini for all targets. The objective is to identify the physical cause of the low frequencies. We computed 1-D cross-correlation functions (CCFs) in order to find the best parameters in terms of the number of components, spectral type and vsini for each target. Radial velocities were measured from spectrum synthesis and by using a 2-D cross-correlation technique in the case of double- and triple-lined systems. Fundamental parameters were determined by fitting (composite) synthetic spectra to the normalised median spectra corrected for the appropriate Doppler shifts. We report on the analysis of 478 high-resolution Hermes and 41 Ace spectra of A/F-type candidate hybrid pulsators from the Kepler field. We determined their radial velocities, projected rotational velocities, atmospheric properties and classified our targets based on the shape of the CCFs and the temporal behaviour of the radial velocities. We derived orbital solutions for seven new systems. Three long-period preliminary orbital solutions are confirmed by a photometric time-delay analysis. Finally, we determined a global multiplicity fraction of 27% in our sample of candidate hybrid stars

Unresolved Rossby and gravity modes in 214 A and F stars showing rotational modulation

Here we report an ensemble study of 214 A- and F-type stars observed by \textit{Kepler}, exhibiting the so-called \textit{hump and spike} periodic signal, explained by Rossby modes (r~modes) -- the \textit{hump} -- and magnetic stellar spots or overstable convective (OsC) modes -- the \textit{spike} -- respectively. We determine the power confined in the non-resolved hump features and find additional gravity~modes (g~modes) humps always occurring at higher frequencies than the spike. Furthermore, we derive projected rotational velocities from FIES, SONG and HERMES spectra for 28 stars and the stellar inclination angle for 89 stars. We find a strong correlation between the spike amplitude and the power in the r and g~modes, which suggests that both types of oscillations are mechanically excited by either stellar spots or OsC modes. Our analysis suggests that stars with a higher power in $m=1$ r~modes humps are more likely to also exhibit humps at higher azimuthal orders ($m$ = 2, 3, or 4). Interestingly, all stars that show g~modes humps are hotter and more luminous than the observed red edge of the $\delta$ Scuti instability strip, suggesting that either magnetic fields or convection in the outer layers could play an important role.Comment: 18 pages, 19 figure

New Beta Cephei Stars from the KELT Project

We present the results of a search for Galactic β Cephei stars, which are massive pulsating stars with both pressure modes and mixed modes. Thus, these stars can serve as benchmarks for seismological studies of the interiors of massive stars. We conducted the search by performing a frequency analysis on the optical light curves of known O- and B-type stars with data from the Kilodegree Extremely Little Telescope exoplanet survey. We identify 113 β Cephei stars, of which 86 are new discoveries, which altogether represent a 70% increase in the number currently known. An additional 97 candidates are identified. Among our targets, we find five new eclipsing binaries and 22 stars with equal frequency spacings suggestive of rotational splitting of nonradial pulsation modes. Candidates for runaway stars among our targets and a number of interesting individual objects are discussed. Most of the known and newly discovered β Cephei stars will be observed by the Transiting Exoplanet Survey Satellite mission, providing by far the most comprehensive observational data set of massive main-sequence pulsating stars of sufficient quality for detailed asteroseismic studies. Future analysis of these light curves has the potential to dramatically increase our understanding of the structure of stellar interiors and the physical processes taking place therein