标题： m=1模在星系盘中的弯曲不稳定性：暗物质晕与垂直压力之间的相互作用 显示英文标题

标题： Bending instabilities of m=1 mode in disc galaxies: interplay between dark matter halo and vertical pressure

摘要： 一个在垂直流体静力平衡下自引力且不同旋转的星系盘，通过垂直压力梯度力来抵抗引力坍缩。 这样的盘已知可以支持各种弯曲模式，例如翘曲、波纹或波浪状（通常为高阶弯曲模式），其中m=1的弯曲模式（翘曲）在星系盘中最为常见。 在这里，我们对处于垂直平衡状态并位于冷刚性暗物质晕中的真实盘星系模型中的弯曲不稳定性进行了详细的理论分析。 建立了一个描述弯曲模式的二次特征值方程，并通过改变盘的物理特性（如盘尺度高度和暗物质晕质量）来求解一组盘星系模型的完整特征谱。 结果表明，垂直压力梯度力可以在这种盘中激发不稳定的弯曲模式以及大尺度离散模式。 此外，结果还表明，在较薄的盘中不稳定的特征模式增长速度比在较厚的盘中更快。 发现由大质量暗物质晕主导的盘中弯曲不稳定性受到抑制。 我们估计了类似银河系的星系中m=1不稳定弯曲模式的增长时间尺度及其对应的波长，并讨论了其意义。 显示英文摘要

摘要： A self-gravitating, differentially rotating galactic disc under vertical hydrostatic equilibrium is supported by the vertical pressure gradient force against the gravitational collapse. Such discs are known to support various bending modes e.g., warps, corrugation, or scalloping (typically, higher order bending modes) of which m=1 bending modes (warps) are the most prevalent ones in galactic discs. Here, we present a detailed theoretical analysis of the bending instability in realistic models of disc galaxies in which an exponential stellar disc is under vertical equilibrium and residing in a cold rigid dark matter halo. A quadratic eigenvalue equation describing the bending modes is formulated and solved for the complete eigen spectrum for a set of model disc galaxies by varying their physical properties such as disc scale-height, and dark matter halo mass. It is shown that the vertical pressure gradient force can excite unstable bending modes in such a disc as well as large scale discrete modes. Further, it is shown that the unstable eigen-modes in a thinner disc grow faster than those in a thicker disc. The bending instabilities are found to be suppressed in discs dominated by massive dark matter halo. We estimate the growth timescales and corresponding wavelength of the m=1 unstable bending modes in Milky Way like galaxies and discuss its implication.