Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

Using bright ellipticals as dark energy cosmic clocks

The age of the Universe has been increasingly constrained by different techniques, such as the observations of type Ia supernovae (SNIa) at high redshift or dating the stellar populations of globular clusters. In this paper, we present a complementary approach using the colours of the brightest elliptical galaxies in clusters over a wide redshift range  ( z ≲ 1)  . We put new and independent bounds on the dark energy equation of state parametrized by a constant pressure-to-density ratio   w _Q  and by a parameter (ξ) which determines the scaling between the matter and dark energy densities. We find that accurate estimates of the metallicities of the stellar populations in moderate and high-redshift cluster galaxies can pose stringent constraints on the parameters that describe dark energy. Our results are in good agreement with the analysis of dark energy models using SNIa data as a constraint. Accurate estimates of the metallicities of stellar populations in cluster galaxies at   z ≲ 2  will make this approach a powerful complement to studies of cosmological parameters using high-redshift SNIa.     

用PCI中断实现射电望远镜跟踪的方法

讨论运用PCI 9054(美国PLX公司生产的接口芯片)作为接口芯片的PCI(Peripheral Component Interconnect)板卡的软硬件设计,以实现天线跟踪的两个时间同步中断。利用标准秒信号中断作为系统时钟同步信号,并同步产生时间间隔为20ms(或40、50ms,可选)的中断信号,来处理天线跟踪指令输出。中断信号通过PCI中断口INTA#接入计算机,在驱动中识别不同的中断信号,并在应用程序响应中断处理后,命令ACU(Antenna Control Unit)机,实现射电天文望远镜的同步跟踪。其控制过程分3部分阐述:硬件设计、驱动程序设计、安装及应用;着重讨论了前两者的设计方法及思路。     

The planets capture model of V838 Monocerotis: conclusions for the penetration depth of the planet(s)

V838 Mon is the prototype of a new class of objects. Understanding the nature of its multistage outburst and similar systems is challenging. So far, several scenarios have been invoked to explain this group of stars. In this work, the planets-swallowing model for V838 Mon is further investigated, taking into account the findings that the progenitor is most likely a massive B-type star. We find that the super-Eddington luminosity during the eruption can explain the fast rising times of the three peaks in the optical light curve. We used two different methods to estimate the location where the planets were consumed. There is a nice agreement between the values obtained from the luminosities of the peaks and from their rising time-scale. We estimate that the planets were stopped at a typical distance of one solar radius from the centre of the host giant star. The planets-devouring model seems to give a satisfying explanation to the differences in the luminosities and rising times of the three peaks in the optical light curve of V838 Mon. The peaks may be explained by the consumption of three planets or alternatively by three steps in the terminal falling process of a single planet. We argue that only the binary merger and the planets-swallowing models are consistent with the observations of the new type of stars defined by V838 Mon.