Unconstrained Astrometric Orbits for Hipparcos Stars with Stochastic Solutions

A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax and linear proper motion, were observed by the Hipparcos satellite. Some of them remain non-discovered, and their observational data have not been properly processed with the more adequate astrometric model that includes nonlinear orbital motion. We develop an automated algorithm based on "genetic optimization", to solve the orbital fitting problem with no prior information about the orbital elements is available (from, e.g., spectroscopic data or radial velocity monitoring). We test this method on Hipparcos stars with known orbital solutions in the catalog, and further apply it to stars with stochastic solutions, which may be unresolved binaries. At a confidence level of 99%, orbital fits are obtained for 65 stars, most of which have not been known as binary. A few of the new probable binaries with A-type primaries with periods 444-2015 d are chemically peculiar stars, including Ap and \lambda Boo type. The anomalous spectra of these stars are explained as admixture of the light from the unresolved, sufficiently bright and massive companions. We estimate the apparent orbits of four stars which have been identified as members of the 300 Myr-old UMa kinematic group. Another four new nearby binaries may include low-mass M-type or brown dwarf companions. Similar astrometric models and algorithms can be used for binary stars and planet hosts observed by SIM PlanetQuest and Gaia

Secular Orbital Dynamics of the Possibly Habitable Planet K2-18 b with and without the Proposed Inner Companion

The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two possible configurations: a single planet orbiting the host star, and a two-planet system including the proposed inner planet close to the 4:1 mean motion rationalization. The emphasis is made on the secular changes of eccentricity and orbital inclination, which are important for the climate stability of the planet. It is demonstrated that the secular orbital dynamics of planet K2-18 b with an internal companion are accurately represented by the periodic eccentricity and inclination exchange on the time scales of a few Kyr. A single planet is not expected to experience fast orbital changes, with the much weaker tidal and rotation-driven perturbations mostly reflecting in a slow periastron and nodal precession. The tidal decay of the orbit is too insignificant on the time scale of the stellar age. However, the conditions for the habitability of a single K2-18 b planet are much improved if, like the Earth, it rotates faster than the mean motion and its rotation angle is tilted by a hypothetical moon. Milankovi{\'c}'s cycles of the habitable planet's climate are discussed for both configurations.Comment: Published in Universe 2023, 9, 46

Thermal destruction of vessels with liquid upon heating

A new engineering technique of calculating the heating and thermal destruction of vessels containing liquid under extreme thermal loading conditions is offered. The heating of the shell and the internal vessel volume is described on the basis of the thermodynamic approach. The pressure growth in a vessel is a result of gas heating and liquid evaporation. Stresses within the shell and its destruction conditions are determined, which allows predicting the critical time of destruction upon heating. The calculation and experimental data for pressure growth inside the vessel are in good agreement

Manifolds associated with (Z2)n(Z_2)^n-colored regular graphs

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\mathbb Z_2)^{n+1}$-manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2)^n$-action for which its moment graph is a given colored grap

Gyr-timescale destruction of high-eccentricity asteroids by spin and why 2006 HY51 has been spared

Asteroids and other small celestial bodies have markedly prolate shapes, and the perturbative triaxial torques which are applied during pericenter passages in highly eccentric orbits trigger and sustain a state of chaotic rotation. Because the prograde spin rate around the principal axis of inertia is not bounded from above, it can accidentally reach the threshold value corresponding to rotational break-up. Previous investigations of this process were limited to integrations of $\sim 10^3$ orbits because of the stiff equation of motion. We present here a fast 1D simulation method to compute the evolution of this spin rate over $\sim 10^9$ orbits. We apply the method to the most eccentric solar system asteroid known, 2006 HY51 (with $e = 0.9684$), and find that for any reasonably expected shape parameters, it can never be accelerated to break-up speed. However, primordial solar system asteroids on more eccentric orbits may have already broken up from this type of rotational fission. The method also represents a promising opportunity to investigate the long-term evolution of extremely eccentric triaxial exo-asteroids ($e > 0.99$), which are thought to be common in white dwarf planetary systemsComment: Accepted in ApJ. The computer-heavier version of chaotic rotation simulation with reparameterization is available as a Julia code at https://github.com/agoldin/2006HY5

Chaos over Order: Mapping 3D Rotation of Triaxial Asteroids and Minor Planets

Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term orderly and predictable within the commensurate spin-orbit resonances, while at eccentricity approaching unity, chaos completely takes over. Here, we present the full 3D rotational equations of motion around all three principle axes for triaxial minor planets and two independent methods of numerical solution based on Euler rotations and quaternion algebra. The domains of chaotic rotation are numerically investigated over the entire range of eccentricity with a combination of trial integrations of Euler's equations of motion and the GALI($k$) method. We quantify the dependence of the order--chaos boundaries on shape by changing a prolateness parameter, and find that the main 1:1 spin-orbit resonance disappears for specific moderately prolate shapes already at eccentricities as low as 0.3. The island of short-term stability around the main 1:1 resonance shrinks with increasing eccentricity at a fixed low degree of prolateness and completely vanishes at approximately 0.8. This island is also encroached by chaos on longer time scales indicating longer Lyapunov exponents. Trajectories in the close vicinity of the 3:2 spin-orbit resonance become chaotic at smaller eccentricities, but separated enclaves of orderly rotation emerge at eccentricities as high as 0.8. Initial perturbations of rotational velocity in latitude away from the exact equilibrium result in a spectrum of free libration, nutation, and polar wander, which is not well matched by the linearized analysis omitting the inertial terms.Comment: Accepted in MNRA

Slope stability monitoring from microseismic field using polarization methodology

International audienceNumerical simulation of seismoacoustic emission (SAE) associated with fracturing in zones of shear stress concentration shows that SAE signals are polarized along the stress direction. The proposed polarization methodology for monitoring of slope stability makes use of three-component recording of the microseismic field on a slope in order to pick the signals of slope processes by filtering and polarization analysis. Slope activity is indicated by rather strong roughly horizontal polarization of the respective portion of the field in the direction of slope dip. The methodology was tested in microseismic observations on a landslide slope in the Northern Tien-Shan (Kyrgyzstan)