Self-consistent response of a galactic disc to vertical perturbations

We study the self-consistent, linear response of a galactic disc to vertical perturbations, as induced, say, by a tidal interaction. We calculate the self-gravitational potential corresponding to a non-axisymmetric, self-consistent density response of the disc using the Green's function method. The response potential is shown to oppose the perturbation potential because the self-gravity of the disc resists the imposed potential, and this resistance is stronger in the inner parts of a galactic disc. For the   m = 1  azimuthal wavenumber, the disc response opposes the imposed perturbation up to a radius that spans a range of 4–6 disc scalelengths, so that the disc shows a net warp only beyond this region. This physically explains the well known but so far unexplained observation that warps typically set in beyond this range of radii. We show that the inclusion of a dark matter halo in the calculation only marginally changes (by ∼10 per cent) the radius for the onset of warps. For perturbations with higher azimuthal wavenumbers, the net signature of the vertical perturbations can only be seen at larger radii – for example, beyond 7 exponential disc scalelengths for   m = 10  . Also, for the high- m cases, the magnitude of the negative disc response due to the disc self-gravity is much smaller. This is shown to result in corrugations of the mid-plane density, which explains the puzzling scalloping with   m = 10  detected in H  i in the outermost regions ∼30 kpc in the Galaxy.     

昆仑山8.1级地震前中国大陆的构造应变背景

利用“网络工程”1998～2001年累积的1181个测站的GPS重复观测资料，采用双三次样条函数模型建立中国大陆水平运动模型速度场，用大地坐标在椭球面上计算各类应变场，详细分析了2001年昆仑山8．1级地震前中国大陆水平构造应变场空间分布特征。各类构造应变场的最高值都出现在喜马拉雅构造带与昆仑山地块内(地震断裂带南侧)，鲜水河—安宁河断裂带次之。分析表明，昆仑山8．1级地震正好发生在张性面膨胀应变率的高值区，第一、第二和最大剪应变率高值区边缘的突变区和最大、最小主应变率的高值区。