Yan-Ning Fu

Symmetry of planar four-body convex central configurations

We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

The empirical mass-luminosity relation for low mass stars

Abstract This work is devoted to improving empirical mass-luminosity relations (MLR) and mass-metallicity-luminosity relation (MMLR) for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the MLR. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28M⊙ to 0.50M⊙. Three-piecewise continuous improved MLRs in K, J, H and V bands, respectively, are obtained. The visual MMLR is also improved based on our K band MLR and the available observational metallicity data.

HIPPARCOS PHOTOCENTRIC ORBITS OF 72 SINGLE-LINED SPECTROSCOPIC BINARIES

By fitting the Hipparcos Intermediate Astrometric Data (HIAD), photocentric orbits can be obtained for the single-lined spectroscopic binaries (SB1s). In previous work, a simplifying approximation used in the fitting process was that the photocenter coincides with the primary, but simple arguments based on a mass-luminosity relation show that this approximation will introduce non-negligible deviation into photocentric orbits of a few SB1s. By fitting the revised HIAD without the approximation, the present paper tries to provide reliable photocentric orbits for those SB1s in the 9th Catalogue of Orbits of Spectroscopic Binaries having a reliable spectroscopic orbit of period between 50 days and 3.2 years. After a stringent assessment and screening process, we finally accept the photocentric orbits of 72 systems. Among these results, 37 orbits are obtained here for the first time. So far, only three of these systems are resolved with a known relative orbit. For each of them, the paired photocentric and relative orbits are in reasonably good agreement. For the 25 systems with a main-sequence primary, the masses of component stars and the semimajor axes of relative orbits are estimated for the purpose of planning ground-based observations.

Relative equilibria of four identical satellites

We consider the Newtonian 5-body problem in the plane, where four bodies have the same mass m, which is small compared with the mass M of the remaining body. We consider the (normalized) relative equilibria in this system and follow them to the limit when m/M→0. In some cases, two small bodies will coalesce at the limit. We call the other equilibria the relative equilibria of four separate identical satellites. We prove rigorously that there are only three such equilibria, all already known after the numerical researches by H. Salo and C. F. Yoder. Our main contribution is to prove that any equilibrium configuration possesses a symmetry, a statement indicated by J. Llibre as the missing key to proving that there is no other equilibrium.

Formation of bulges in very late-type galaxies from super star clusters

The dynamical evolution of super star clusters (SSCs) moving in the background of a dark matter halo has been investigated as a possible event responsible for the formation of bulges in late-type spirals. The underlying physical processes include sinking of SSCs due to the dynamical friction and stripping of SSCs on their way to the centre. Our model calculations show that only sinking of circumnuclear SSCs contributes to the formation of galactic bulges at the early stage. Based on the assumption of a universal density profile for the dark matter halo, and an isothermal model for the SSCs, our simulations have yielded bulges that are similar in many aspects to the observational ones. In particular, the derived surface density profiles can be well fitted by an exponential structure with nuclear cusps, which is consistent with Hubble Space Telescope observations.

Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to rb, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.

Orbit Determination of Double-lined Spectroscopic Binaries by Fitting the Revised Hipparcos Intermediate Astrometric Data

Untill now, the Hipparcos intermediate astrometric data (HIAD) have contributed little to the full orbit determination of double-lined spectroscopic binaries (SB2s). This is because the photocenter of such a binary system is usually not far from the system mass center, and its orbital wobble is generally weak with respect to the accuracy of the HIAD. However, the HIAD have been recently revised and the accuracy is increased by a factor of 2.2 in the total weight. Therefore, it is interesting to see if the revised HIAD can be used in the orbit determination at least for some SB2s. In this paper, we first search the 9th Catalogue of Orbits of Spectroscopic Binaries (S B 9 ) for SB2s with reliable spectroscopic orbital solutions and with periods between 50 days and 3.2 years. This leaves us with 56 systems. The full orbital solutions of these systems are then determined from the HIAD by a highly efficient grid search method developed in this paper. The high efficiency is achieved by reducing the number of nonlinear model parameters to one, and by allowing all parameters to be adjustable within a region centered at each grid point. After a variety of tests, we finally accept orbital solutions of 13 systems. Among these systems, six (HIP 677, 20894, 87895, 95995, 101382, and 111170) are well resolved with reliable interferometric data. Orbital solutions from these data are consistent with our results. The full orbital solutions of the other seven systems (HIP 9121, 17732, 32040, 57029, 76006, 102431, and 116360) are determined for the first time.

MAPPING MODELS FOR NEAR-CONSERVATIVE SYSTEMS WITH APPLICATIONS *

A systematic method is presented to construct a mapping model for a near-conservative system, based on that of Hadjidemetriou for a Hamiltonian system [1]. The mapping we constructed preserves the basic features of the actual system. We apply this method to the forced oscillating system and to the 3 : 1 resonant grain motion in the presence of Poynting-Robertson drag.

Mass segregation of embedded clusters in the Milky Way

Embedded clusters are ideal laboratories for understanding the early phase of the dynamical evolution of clusters as well as massive star formation. An interesting observational phenomenon is that some of the embedded clusters show mass segregation, i.e., the most massive stars are preferentially found near the cluster center. We develop a new approach to describe mass segregation. Using this approach and the Two Micron All Sky Survey Point Source Catalog (2MASS PSC), we analyze 18 embedded clusters in the Galaxy. We find that 11 of them are mass-segregated and that the others are not mass-segregated. No inversely mass-segregated cluster is found.

Adapting Marchal's test of escape to real triple stars

Context. For a general N-body system, Marchal constructed an analytical test of escape, which uses only a one-dimensional projected motion state of the system at any given instant. This test is well adapted to identifying real, disintegrating small stellar systems, of which the full motion states are generally unavailable. However, to our knowledge, there has been no practical application of this test until the present-day.