分类： 天文学 >> 天文学 提交时间： 2024-06-08
摘要： The Standards of Fundamental Astronomy (SOFA) is a service provided by the International Astronomical Union (IAU) that offers algorithms and software for astronomical calculations, which was released in two versions by FORTRAN 77 and ANSI C, respectively. In this work, we implement the python package PyMsOfa for SOFA service by three ways: (1) a python wrapper package based on a foreign function library for Python (ctypes), (2) a python wrapper package with the foreign function interface for Python calling C code (cffi), and (3) a python package directly written in pure python codes from SOFA subroutines. The package PyMsOfa has fully implemented 247 functions of the original SOFA routines. In addition, PyMsOfa is also extensively examined, which is exactly consistent with those test examples given by the original SOFA. This python package can be suitable to not only the astrometric detection of habitable planets of the Closeby Habitable Exoplanet Survey (CHES) mission (Ji et al. 2022), but also for the frontiers themes of black holes and dark matter related to astrometric calculations and other fields. The source codes are available via https://github.com/CHES2023/PyMsOfa.
分类： 天文学 >> 天文学 提交时间： 2024-06-03
摘要： The planetary obliquity plays a significant role in determining physical properties of planetary surfaces and climate. As direct detection is constrained due to the present observation accuracy, kinetic theories are helpful to predict the evolution of the planetary obliquity. Here the coupling effect between the eccentric Kozai-Lidov (EKL) effect and the equilibrium tide is extensively investigated, the planetary obliquity performs to follow two kinds of secular evolution paths, based on the conservation of total angular momentum. The equilibrium timescale of the planetary obliquity $t_{ mathrm{eq}}$ varies along with $r_{t}$, which is defined as the initial timescale ratio of the tidal dissipation and secular perturbation. We numerically derive the linear relationship between $t_{ mathrm{eq}}$ and $r_{t}$ with the maximum likelihood method. The spin-axis orientation of S-type terrestrials orbiting M-dwarfs reverses over $90^ circ$ when $r_{t} > 100$, then enter the quasi-equilibrium state between $40^ circ$ and $60^ circ$, while the maximum obliquity can reach $130^ circ$ when $r_{t} > 10^4 $. Numerical simulations show that the maximum obliquity increases with the semi-major axis ratio $a_1$/$a_2$, but is not so sensitive to the eccentricity $e_2$. The likelihood of obliquity flip for S-type terrestrials in general systems with $a_2 < 45$ AU is closely related to $m_1$. The observed potential oblique S-type planets HD 42936 b, GJ 86 Ab and $ tau$ Boot Ab are explored to have a great possibility to be head-down over the secular evolution of spin.
分类： 地球科学 >> 空间物理学 分类： 其他 分类： 其他 分类： 其他 提交时间： 2024-06-03
摘要： The Closeby Habitable Exoplanet Survey (CHES) is dedicated to the astrometric exploration for habitable-zone Earth-like planets orbiting solar-type stars in close proximity, achieving unprecedented micro-arcsecond precision. Given the elevated precision, thorough consideration of photocenter jitters induced by stellar activity becomes imperative. This study endeavors to model the stellar activity of solar-type stars, compute astrometric noise, and delineate the detection limits of habitable planets within the astrometric domain. Simulations were conducted for identified primary targets of CHES, involving the generation of simulated observed data for astrometry and photometry, accounting for the impact of stellar activity. Estimation of activity levels in our samples was achieved through chromospheric activity indices, revealing that over 90% of stars exhibited photocenter jitters below 1 $ mu mathrm{as}$. Notably, certain proximate stars, such as $ alpha$ Cen A and B, displayed more discernible noise arising from stellar activity. Subsequent tests were performed to evaluate detection performance, unveiling that stellar activity tends to have a less pronounced impact on planetary detectability for the majority of stars. Approximately 95% of targets demonstrated a detection efficiency exceeding 80%. However, for several cold stars, e.g., HD 32450 and HD 21531, with the habitable zones close to the stars, a reduction in detection efficiency was observed. These findings offer invaluable insights into the intricate interplay between stellar activity and astrometric precision, significantly advancing our understanding in the search for habitable planets.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Nonrestricted hierarchical three-body configurations are common in various scales of astrophysical systems. Dynamical structures of the quadrupole-order resonance (the von Zeipel-Lidov-Kozai resonance) and the octupole-order resonance (the apsidal resonance) under the nonrestricted hierarchical planetary systems are investigated in this work by taking advantage of perturbative treatments. Under the quadrupole-order Hamiltonian model, the distribution of libration and circulation regions as well as the distribution of flipping region are analytically explored in the parameter space spanned by the conserved quantities. The fundamental frequencies of system are produced and then the nominal location of octupole-order resonance is identified. From the viewpoint of perturbative theory, the quadrupole-order Hamiltonian determines the unperturbed dynamical model and the octupole-order Hamiltonian plays an role of perturbation to the quadrupole-order dynamics. The resonant Hamiltonian for octupole-order resonances is formulated by means of averaging theory, giving rise to a new constant of motion. Phase portraits are produced to analyse dynamical structures of octupole-order resonance, including resonant centres, saddle points, dynamical separatrices and islands of libration. By analysing phase portraits, it is found that there are four branches of libration centre and eight libration zones in the considered space. Applications to orbit flips show that there are five flipping regions.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： $\gamma$ Cep Ab is a typical S-type planet, which occupies a nearly perpendicular planetary orbit relative to the binary. Here we use the Markov Chain Monte Carlo (MCMC) sampler to conduct full N-body fitting and derive self-consistent orbital solutions for this hierarchical system. Then we employ the Eccentric Kozai-Lidov (EKL) mechanism to explain the extremely inclined orbit of S-type planet $\gamma$ Cep Ab. The EKL mechanism plays an essential role in exploring significant oscillations of the mutual inclination $i_{\mathrm{mut}}$ between the planet and the secondary star. We perform qualitative analysis and extensive numerical integrations to investigate the flip conditions and timescales of $\gamma$ Cep Ab's orbit. When the planetary mass is 15 $M_{\mathrm{Jup}}$, the planet can reach $i_{\mathrm{mut}} \sim$ 113$^{\circ}$ with the critical initial conditions of $i_{\mathrm{mut}} < 60^{\circ}$ and $e_1<0.7$. The timescale for the first orbital flip decreases with the increase of the perturbation Hamiltonian. Flipping orbits of $\gamma$ Cep Ab are confirmed to have a large possibility to retain stable based on surfaces of section and the secular stability criterion. Furthermore, we extend the application of EKL to general S-type planetary systems with $a_1/a_2\leq0.1$, where the most intense excitation of $i_{\mathrm{mut}}$ occurs when $a_1/a_2=0.1$ and $e_2 \sim 0.8$, and the variation of planetary mass mainly affect the flip possibility where $e_1\leq 0.3$.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Secular dynamics inside MMRs plays an essential role in governing the dynamical structure of the trans-Neptunian region and sculpting the orbital distribution of trans-Neptunian objects (TNOs). In this study, semi-analytical developments are made to explore the von Zeipel-Lidov-Kozai (ZLK) resonance inside mean motion resonances (MMRs). To this end, a semi-secular model is formulated by averaging theory and then a single-degree-of-freedom integrable model is achieved based on the adiabatic invariance approximation. In particular, we introduce a modified adiabatic invariant, which is continuous around the separatrices of MMRs. During the long-term evolution, both the resonant Hamiltonian and the adiabatic invariant remain unchanged, thus phase portraits can be produced by plotting level curves of the adiabatic invariant with given Hamiltonian. The phase portraits provide global pictures to predict long-term behaviors of the eccentricity, inclination and argument of pericenter. Applications to some representative TNOs inside MMRs (2018 VO137, 2005 SD278, 2015 PD312, Pluto, 2004 HA79, 1996 TR66 and 2014 SR373) show good agreements between the numerically propagated trajectories under the full N-body model and the level curves arising in phase portraits. Interestingly, 2018 VO137 and 2005 SD278 exhibit switching behaviors during the long-term evolution and currently they are inside 2:5 MMR with Neptune.
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