A study of the high-inclination population in the Kuiper belt - II. The Twotinos

As the second part of our study, in this paper we proceed to explore the dynamics of the high-inclination Twotinos in the 1:2 Neptune mean motion resonance (NMMR). Depending on the inclination $i$, we show the existence of two critical eccentricities $e_a(i)$ and $e_c(i)$, which are lower limits of the eccentricity $e$ for the resonant angle $\sigma$ to exhibit libration and asymmetric libration, respectively. Accordingly, we have determined the libration centres $\sigma_0$ for inclined orbits, which are strongly dependent on $i$. With initial $\sigma=\sigma_0$ on a fine grid of $(e, i)$, the stability of orbits in the 1:2 NMMR is probed by 4-Gyr integrations. It is shown that symmetric librators are totally unstable for $i\ge30^{\circ}$; while stable asymmetric librators exist for $i$ up to $90^{\circ}$. We further investigate the 1:2 NMMR capture and retention of planetesimals with initial inclinations $i_0\le90^{\circ}$ in the planet migration model using a time-scale of $2\times10^7$ yr. We find that: (1) the capture efficiency of the 1:2 NMMR decreases drastically with the increase of $i_0$, and it goes to 0 when $i_0\ge60^{\circ}$; (2) the probability of discovering Twotinos with $i>25^{\circ}$, beyond observed values, is roughly estimated to be $\le0.1$ per cent; (3) more particles are captured into the leading rather than the trailing asymmetric resonance for $i_0\le10^{\circ}$, but this number difference appears to be the opposite at $i_0=20^{\circ}$ and is continuously varying for even larger $i_0$; (4) captured Twotinos residing in the trailing resonance or having $i>15^{\circ}$ are practically outside the Kozai mechanism, like currently observed samples.Comment: 13 pages, 10 figures, Accepted by MNRAS. Comments welcome

Formation and transformation of the 3:1 mean-motion resonance in 55 Cancri System

We report in this paper the numerical simulations of the capture into the 3:1 mean-motion resonance between the planet b and c in the 55 Cancri system. The results show that this resonance can be obtained by a differential planetary migration. The moderate initial eccentricities, relatively slower migration and suitable eccentricity damping rate increase significantly the probability of being trapped in this resonance. Otherwise, the system crosses the 3:1 commensurability avoiding resonance capture, to be eventually captured into a 2:1 resonance or some other higher-order resonances. After the resonance capture, the system could jump from one orbital configuration to another one if the migration continues, making a large region of the configuration space accessible for a resonance system. These investigations help us understand the diversity of resonance configurations and put some constrains on the early dynamical evolution of orbits in the extra-solar planetary systems.Comment: 6 pages with 2 figures. Submitted for publication in the proceedings of IAU Symposium No.249. A paper telling much more details than this paper is under preparin

Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems

We investigate the orbit-crossing time (T_c) of protoplanet systems both with and without a gas-disk background. The protoplanets are initially with equal masses and separation (EMS systems) scaled by their mutual Hill's radii. In a gas-free environment, we find log (T_c/yr) = A+B \log (k_0/2.3). Through a simple analytical approach, we demonstrate that the evolution of the velocity dispersion in an EMS system follows a random walk. The stochastic nature of random-walk diffusion leads to (i) an increasing average eccentricity ~ t^1/2, where t is the time; (ii) Rayleigh-distributed eccentricities (P(e,t)=e/\sigma^2 \exp(-e^2/(2\sigma^2)) of the protoplanets; (iii) a power-law dependence of T_c on planetary separation. As evidence for the chaotic diffusion, the observed eccentricities of known extra solar planets can be approximated by a Rayleigh distribution. We evaluate the isolation masses of the embryos, which determine the probability of gas giant formation, as a function of the dust and gas surface densities.Comment: 15 pages, 13 figures (2 color ones), accepted for publication in Ap

Ethyl N-[3-(N,N-dimethyl­carbamo­yl)pyridin-2-ylsulfon­yl]carbamate

In the mol­ecular structure of the title compound, C11H15N3O5S, the amide group is nearly perpendicular to the pyridine ring, making a dihedral angle of 86.30 (13)°. The terminal ethyl group is disordered over two sites of equal occupancy. Inter­molecular N—H⋯O hydrogen bonding is present in the crystal structure

Methyl 4-methyl­sulfonyl-2-nitro­benzoate

The title compound, C9H9NO6S, was prepared by the reaction of methanol and thionyl chloride with 4-methyl­sulfonyl-2-nitro­benzoic acid under mild conditions. The dihedral angle between the nitro group and benzene ring is 21.33 (19)° and that between the carboxyl­ate group and the benzene ring is 72.09 (17)°. The crystal structure is stabilized by weak inter­molecular bifurcated C—H⋯O inter­actions occurring in the (100) plane

Equirectangular image construction method for standard CNNs for Semantic Segmentation

360{\deg} spherical images have advantages of wide view field, and are typically projected on a planar plane for processing, which is known as equirectangular image. The object shape in equirectangular images can be distorted and lack translation invariance. In addition, there are few publicly dataset of equirectangular images with labels, which presents a challenge for standard CNNs models to process equirectangular images effectively. To tackle this problem, we propose a methodology for converting a perspective image into equirectangular image. The inverse transformation of the spherical center projection and the equidistant cylindrical projection are employed. This enables the standard CNNs to learn the distortion features at different positions in the equirectangular image and thereby gain the ability to semantically the equirectangular image. The parameter, {\phi}, which determines the projection position of the perspective image, has been analyzed using various datasets and models, such as UNet, UNet++, SegNet, PSPNet, and DeepLab v3+. The experiments demonstrate that an optimal value of {\phi} for effective semantic segmentation of equirectangular images is 6{\pi}/16 for standard CNNs. Compared with the other three types of methods (supervised learning, unsupervised learning and data augmentation), the method proposed in this paper has the best average IoU value of 43.76%. This value is 23.85%, 10.7% and 17.23% higher than those of other three methods, respectively