The efficiency of the spiral-in of a black hole to the Galactic Centre

We study the efficiency at which a black hole or dense star cluster spirals in to the Galactic Centre. This process takes place on a dynamical friction time-scale, which depends on the value of the Coulomb logarithm (ln Λ). We determine the accurate value of this parameter using the direct N -body method, a tree algorithm and a particle-mesh technique with up to two million plus one particles. The three different techniques are in excellent agreement. Our measurement for the Coulomb logarithm appears to be independent of the number of particles. We conclude that  ln Λ= 6.6 ± 0.6  for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, such as a dense star cluster, ln Λ is smaller, with a value of the logarithm argument Λ inversely proportional to the object size.     

Radio spectra of the low-luminosity active galactic nucleus NGC 266 at centimetre-to-submillimetre wavelengths

We report multi-frequency and multi-epoch radio continuum observations with multi-spatial resolution for the low-luminosity active galactic nucleus (LLAGN) NGC 266. In the centimetre regime, we find diffuse components with Very Large Array (VLA) observations, and a variable compact core with a rising spectrum with Very Long Baseline Array (VLBA) observations. Although the spectral index of the rising spectrum is consistent with the prediction of the simple advection-dominated accretion flow (ADAF) model, the observed radio power is slightly high compared with that of the model prediction. A spectral break at centimetre-to-millimetre wavelengths is inferred from the upper limits of flux densities from Nobeyama Millimetre Array (NMA) and James Clerk Maxwell Telescope (JCMT) data at millimetre and submillimetre wavelengths, respectively. More complicated considerations are required for the theoretical model to interpret such observed radio properties.     

γ射线暴的研究进展（Ⅳ：特强γ射线暴和软γ重复暴

最近CGRO上的仪器观测到了两个迄今为止发现的最强的λ暴GB930131和GB940217,其光子最高能量均达GeV量级;GB930131的峰值计数率达2×10~6个光子s~(-1);而GB940217的持续时间竟长达90min。另外沉寂了多年的软重复暴源SGR1900 14和SGR1806-20的再次爆发也由BATSE发现。一系列的观测还发现这些软重复暴均与X射线源对应且与超新星遗迹成协。文中对特强暴和软重暴(SGR)的性质及研究进展作了较为详细的评述。     

The time-scale for core collapse in spherical star clusters

The collapse time for a cluster of equal-mass stars is usually stated to be either 330 central relaxation times (t_rc) or 12-19 half-mass relaxation times (t_rh). But the first of these times applies only to the late stage of core collapse, and the second only to low-concentration clusters. To clarify how the time depends on the density profile, the Fokker-Planck equation is solved for the evolution of a variety of isotropic cluster models, including King models, models with power-law density cusps of ρ ∼ r^−γ, and models with nuclei. The collapse times for King models vary considerably with the cluster concentration when expressed in units of t_rc or t_rh, but vary much less when expressed in units of t_rc divided by a dimensionless measure of the temperature gradient in the core. Models with cusps have larger temperature gradients and evolve faster than King models, but not all of them collapse: those with 0 < γ < 2 expand because they start with a temperature inversion. Models with nuclei collapse or expand as the nuclei would in isolation if their central relaxation times are short; otherwise their evolution is more complicated. Suggestions are made for how the results can be applied to globular clusters, galaxies, and clusters of dark objects in the centers of galaxies.Scott D. Tremaine     

有限元法与伪谱法混合求解弹性波动方程

在地震波场数值模拟中,有限差分法、有限元法和伪谱法都是常用的基本方法,但它们各有不同的适应性和优缺点,如有限差分法、有限元法都存在减弱网格频散和提高计算效率的矛盾,而伪谱法的网格频散小且计算效率高.有限差分法和伪谱法在处理地表结构复杂或地表剧烈起伏以及地下结构复杂的情况时存在较大的难度,而有限元法可较为理想地拟合起伏地表和任意弯曲界面,且可方便地处理自由边界条件和界面边界条件.尝试将有限元法和伪谱法相结合,形成地震波场数值模拟的一种混合方法,利用二者的优点,克服二者的缺点,达到既减弱网格频散又提高计算精度和效率的目的.并采用所谓的‘过度区域‘技术解决两种不同算法的衔接问题.模拟实例表明,给出的混合模拟方法不失为弹性波场数值模拟的一种有效方法.     

HD 82943行星系统的2:1共振与稳定性

用直接数值积分方法通过模拟不同的行星构型探讨了HD82943行星系统(由两颗共振的巨行星组成)的长期动力演化,同时,还研究了在相空间的轨道运动.在对系统长达107年数值积分中,发现所有的稳定轨道均与2:1共振相关联.典型地,在相同的时标内,两个共振幅角θ1和θ2同时(或其中之一)存在秤动.由于共振幅角在一定范围内的秤动,因而使两颗行星轨道半长径被约束而表现为规则运动模式.另外,利用分析模型(包含了外行星偏心率e2的因素),还讨论了对于不同取值的e2和相对近星点经度θ时,内行星在相空间的运动,并发现2:1轨道共振对于相对较小的e2以及当θ=0°时易于保持.此外,适中的e2将导致系统的两颗行星进入深度共振状态.再者,分析模型和数值计算的结果吻合得很好,两者都揭示了行星系统的2:1共振结构.