A spherically symmetric hydrodynamic stellar core collapse under gravity is time-dependent and may become unstable once disturbed. Specifically for a homologously collapse of stellar core characterized by a polytropic exponent Γ=4/3, we examine oscillations and/or instabilities of three dimensional (3D) general polytropic perturbations. For compressible 3D perturbations, the polytropic index γof perturbations can differ from Γ=4/3 of the general polytropic hydrodynamic background flow. Our model formulation here is more general and allows the existence of internal gravity g(-)-modes and/or g(+)-modes. Eigenvalues and eigen-functions of various oscillatory and unstable perturbation modes are computed. As studied in several specialized cases of Goldreich & Weber and of Cao & Lou, we further confirm that acoustic p-modes and surface f-modes remain stable in the current more general situations. In comparison, g(-)-modes and sufficiently high radial order g(+)-modes are unstable, leading to inevitable convective motions within the collapsing stellar interior. Unstable growths of 3D g-mode disturbances are governed dominantly by the angular momentum conservation and modified by the gas pressure restoring force. We note in particular that unstable temporal growths of 3D vortical perturbations exist even when the specific entropy distribution becomes uniform and γ=Γ=4/3. Conceptually, unstable g-modes might bear conceivable physical consequences on supernova explosions, the initial kicks of nascent proto-neutron stars (PNSs) and break-ups of the collapsing core, while unstable growths of vortical perturbations can lead to fast spins of compact objects and other relevant results.
A New Multi-Dimensional General Relativistic Neutrino Hydrodynamics Code for Core-Collapse Supernovae II. Relativistic Explosion Models of Core-Collapse Supernovae
A 3D Hydrodynamics Study of Gravitational Instabilities in a Young Circumbinary Disc
利用三维流体动力学方法研究了一个0.14 M $_{\odot}$环绕原行星盘的引力不稳定性，该原行星盘围绕一颗1 M $_{\odot}$恒星和一颗0.02 M $_{\odot}$褐矮星伴星运行.我们研究的光盘的vacuical状态，并确定GI引起的密度波，非轴对称密度结构，质量流入和流出，和引力矩的强度。结果进行了比较，一个原行星盘没有棕矮星双星同伴的并行模拟。使用CHYMERA，辐射三维流体动力学代码进行模拟。环双星盘中GI的爆发要猛烈得多，这是由于褐矮星激发了一个强的单臂密度波。尽管有这种早期的差异，但详细的分析表明，在模拟开始后的2,500年，两个圆盘都松弛到一个非常相似的准稳定阶段。相似之处包括准稳态相的热力学，最终的表面密度分布，径向质量流入，和非轴对称的功率和扭矩的螺旋臂多重性的两个或更多。在光盘中的二元性的影响是显而易见的重力扭矩分布，温度分布在内部光盘，和径向质量传输。3,800年后，双星的半长轴减少了约1%，偏心率大约增加了一倍。与单臂波相关的外环双星盘的质量输运可能影响行星形成。
3D radiative hydrodynamic simulations of protostellar collapse with H-C-O dynamical chemistry
将协同演化化学、流体动力学和辐射转移结合起来是恒星形成研究的重要一步。它既可以更好地与观测联系起来，又可以对坍缩核心中的磁耗散进行自洽监测。我们的目标是遵循一个减少气体颗粒化学网络的坍塌致密核心的化学动力学演化。本文给出了1 M $_\odot$孤立致密核坍缩的辐射流体动力学（RHD）模拟结果.物理设置包括RHD和化学网络的动力学演化。为了进行这些模拟，我们合并了多维自适应网格细化代码RAMSES和热化学巴黎达勒姆冲击代码。我们模拟了第一个流体静力核心（FHSC）的形成和56个物种的共同进化，主要描述H-C-O化学。进行准确的基准测试，测试减少化学网络对一个完善的复杂网络。我们表明，通过使用一组紧凑的反应，可以密切配合CO丰度与一个更复杂的网络的结果。我们的主要结果是：（a）我们发现，气体-颗粒化学后处理可以导致一个数量级的CO气相丰度比动力学化学低，最强的效果在等温阶段的崩溃。(b)对于我们选择的参数，自由落体时间对化学丰度的影响很小。(c)动态化学演化需要描述的CO气相丰度，以及CO冰的形成大于1 $μ$ m的平均晶粒尺寸。(d)此外，尘埃的平均粒径和粒径分布有很强的影响化学丰度，从而对电离度和磁耗散。我们的结论是，尘埃颗粒的增长崩溃模拟耦合崩溃与化学一样重要。
