Ying Wang

With the advancement of observational techniques, over one million stars have been observed to search for exoplanets. The vast amounts of light curve data generated necessitate an automated, rapid, and efficient method for screening exoplanet candidates. In recent years, deep learning methods, particularly convolutional neural networks (CNNs), have been employed to automate the screening of light curves for exoplanet candidates. However, CNNs have several drawbacks, such as slow training times due to their large network structures and a lack of ability to explain the physical meaning behind their classifications. In this paper, we propose a convolutional neural network classification model that incorporates a channel attention mechanism, which captures significant features in transit signals and enhances the model's classification capability and interpretability. Furthermore, we have improved the fully connected neural network by incorporating the residual network structure, significantly increasing the model's training speed. \textcolor{blue}{Our model is highly adaptable to various datasets, achieving 96.2\% accuracy and 95.7\% F1 Score on the Kepler dataset, and 99.9\% accuracy with 99.5\% F1 Score on the TESS dataset, with training times ranging from 0.3 to 0.6 hours per dataset. We also analyze the feature heat maps of the channel attention mechanism to better explain the model's classifications. Our study demonstrates that deep learning can assist in managing the current era of astronomical big data and suggests that the channel attention mechanism and residual network structure could be applied to other astronomical classification tasks.

A possible polar-ring debris disk, the dynamics of which can be described by the outer hierarchical restricted three-body problem, has been detected in 99 Herculis. An empirical formula for the minimum radius beyond which test particles in polar orbits can keep stable within 10⁷ binary periods is provided through numerical fitting, applying to the binary eccentricity e 1 ∈ 0 , 0.8 and the mass ratio of the binary λ ∈ 0.1 , 1 , where λ = m ₀/m ₁ (m ₀ and m ₁ represent the masses of the two binary stars). The polar planetary disk has the lowest statistical accretion efficiency and a moderate impact frequency of collisions among planetesimals (with radii of 1–10 km) compared to those in a circumbinary coplanar disk and a standard disk around the single host star. The collision timescale in the circumbinary disk (both polar and coplanar configurations) is longer than 10⁷ yr, exceeding the dissipation timescale of the gas disk. Stochastic simulations show that successive collisions cannot make planetesimals grow, which may explain the formation of the debris disk observed in 99 Herculis.

Many Hamiltonian problems in the solar system are separable into two analytically solvable parts, and thus serve as a great chance to develop and apply explicit symplectic integrators based on operator splitting and composing. However, such constructions are not in general available for curved spacetimes in general relativity and modified theories of gravity because these curved spacetimes correspond to nonseparable Hamiltonians without the two-part splits. Recently, several black hole spacetimes such as the Schwarzschild black hole were found to allow for the construction of explicit symplectic integrators, since their corresponding Hamiltonians are separable into more than two explicitly integrable pieces. Although some other curved spacetimes including the Kerr black hole do not have such multipart splits, their corresponding appropriate time-transformation Hamiltonians do. In fact, the key problem in obtaining symplectic analytically integrable decomposition algorithms is how to split these Hamiltonians or time-transformation Hamiltonians. Considering this idea, we develop explicit symplectic schemes in curved spacetimes. We introduce a class of spacetimes whose Hamiltonians are directly split into several explicitly integrable terms. For example, the Hamiltonian of a rotating black ring has a 13-part split. We also present two sets of spacetimes whose appropriate time-transformation Hamiltonians have the desirable splits. For instance, an eight-part split exists in a time-transformed Hamiltonian of a Kerr–Newman solution with a disformal parameter. In this way, the proposed symplectic splitting methods can be used widely for long-term integrations of orbits in most curved spacetimes we know of.

In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all splitting parts have analytical solutions as explicit functions of proper time. To cope with this difficulty, we introduce a time transformation function to the Hamiltonian of Kerr geometry so as to obtain a time-transformed Hamiltonian consisting of five splitting parts, whose analytical solutions are explicit functions of the new coordinate time. The chosen time transformation function can cause time steps to be adaptive, but it is mainly used to implement the desired splitting of the time-transformed Hamiltonian. In this manner, new explicit symplectic algorithms are easily available. Unlike Runge–Kutta integrators, the newly proposed algorithms exhibit good long-term behavior in the conservation of Hamiltonian quantities when appropriate fixed coordinate time steps are considered. They are better than same-order implicit and explicit mixed symplectic algorithms and extended phase-space explicit symplectic-like methods in computational efficiency. The proposed idea on the construction of explicit symplectic integrators is suitable for not only the Kerr metric but also many other relativistic problems, such as a Kerr black hole immersed in a magnetic field, a Kerr–Newman black hole with an external magnetic field, axially symmetric core–shell systems, and five-dimensional black ring metrics.

Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the construction of explicit symplectic integrators is frequently difficult in general relativity because all variables are inseparable. Moreover, even if two analytically integrable splitting parts exist in a relativistic Hamiltonian, all analytical solutions are not explicit functions of proper time. Naturally, implicit symplectic integrators, such as the midpoint rule, are applicable to this case. In general, these integrators are numerically more expensive to solve than same-order explicit symplectic algorithms. To address this issue, we split the Hamiltonian of Schwarzschild spacetime geometry into four integrable parts with analytical solutions as explicit functions of proper time. In this manner, second- and fourth-order explicit symplectic integrators can be easily made available. The new algorithms are also useful for modeling the chaotic motion of charged particles around a black hole with an external magnetic field. They demonstrate excellent long-term performance in maintaining bounded Hamiltonian errors and saving computational cost when appropriate proper time steps are adopted.

A type of compactly spaced and comparably sized multi-exoplanet system similar to TRAPPIST-1 has been discovered recently. The stability of these systems is an important issue, requiring further study. We examined how the initial inclinations influence the stability of multi-planet systems and derived an empirical formula describing the dependence of the instability time-scale on planetary mass, space separation and initial inclination. We find the following. (i) If space separations between planets are greater than 12RH (mutual Hill radius), coplanar multi-planet systems with 10−6 ≤ μ ≤ 10−3 (reduced planetary mass μ = m/M*) will remain stable within 1010Tin (the innermost orbital period). (ii) If initial inclinations of planets are smaller than 10° and space separations are greater than 10RH, multi-planet systems consisting of ≥5 planets with μ ≥ 10−5 will remain stable within 1010Tin. (iii) Initial inclinations in [0°, 10°] have inconsequential effects on the instability time-scales of massive multi-planet systems (μ ≥ 10−5), because eccentricities (excited during evolution) dominate the stability of these systems. (iv) If the initial inclinations are large enough (≥10°), sharp increases of instability time-scales in groups with 10−3 ≥ μ ≥ 10−5 will be moderated. This article presents a comprehensive study of the influence of inclination on the stability of multi-planet systems and discusses critical space separations for a multi-planet system becoming unstable.