标题： 拟微扰分析银河盘中的准径向密度波 显示英文标题

标题： A perturbative analysis of Quasi-Radial density waves in galactic disks

摘要： 密度波在星系盘中的理论理解始于对紧密螺旋扰动的经典的WKB摄动分析，关键假设是由于密度波产生的势大约是径向的。 上述内容在帮助理解模拟和观测到的星系方面一直是一个有价值的指导，尽管存在一些需要注意的地方。 在真实星系中观测到的螺旋或棒状结构通常仅勉强符合紧密螺旋假设，实际上常常是完全不一致的。 在这里，我们通过在简化假设下处理准径向密度波，在线性范围内推导出该问题的一个互补公式。 我们假设由于密度波产生的势大约是切向的，并推导出相应的问题色散关系。 我们得到了准径向密度波开始的不稳定性准则，这有助于清楚地理解高阶模态的增加稳定性，这些模态出现在逐渐增大的半径上，如在真实星系中经常看到的那样。 该理论自然地给出了这些旋臂的一系列图案速度，这些速度受到条件$\Omega_{p}<\Omega_{0} \pm \kappa /m$的限制。 对于星系中心区域，可能适用刚体旋转曲线，我们发现振荡区域内有弱棒结构，具有各种图案速度，包括反向旋转的，还预测了$\Omega_{p}$随着向中心靠近而增加，这在某些数值模拟中的内部快速旋转棒中可以看到。 我们通过详细数值模拟星系盘和对出现的扰动进行仔细的傅里叶分析来补充这项研究，这些结果支持了所提出的理论。 显示英文摘要

摘要： The theoretical understanding of density waves in disk galaxies starts from the classical WKB perturbative analysis of tight-winding perturbations, the key assumption being that the potential due to the density wave is approximately radial. The above has served as a valuable guide in aiding the understanding of both simulated and observed galaxies, in spite of a number of caveats being present. The observed spiral or bar patterns in real galaxies are frequently only marginally consistent with the tight-winding assumption, often in fact, outright inconsistent. Here we derive a complementary formulation to the problem, by treating quasi-radial density waves under simplified assumptions in the linear regime. We assume that the potential due to the density wave is approximately tangential, and derive the corresponding dispersion relation of the problem. We obtain an instability criterion for the onset of quasi-radial density waves, which allows a clear understanding of the increased stability of the higher order modes, which appear at progressively larger radii, as often seen in real galaxies. The theory naturally yields a range of pattern speeds for these arms which appears constrained by the condition $\Omega_{p}<\Omega_{0} \pm \kappa /m$. For the central regions of galaxies where solid body rotation curves might apply, we find weak bars in the oscillatory regime with various pattern speeds, including counter rotating ones, and a prediction for $\Omega_{p}$ to increase towards the centre, as seen in the rapidly rotating bars within bars of some numerical simulations. We complement this study with detailed numerical simulations of galactic disks and careful Fourier analysis of the emergent perturbations, which support the theory presented.