GWFast(er): Building a Tool to Study Black Hole Orbital Dynamics

Gabriel Perez-Giz博士被授予NSF天文学和天体物理学博士后奖学金，在麻省理工学院(MIT)卡夫利天体物理和空间研究所(MKI)开展研究和教育计划。轨道运动的研究是天文学和天体物理学的核心。黑洞(BH)双星的动力学特别丰富，因为广义相对论(GR)的非线性足迹将在由如此巨大的致密天体实现的大质量和小分离的区域中最为明显。与经典天体力学不同，这种极端相对论双星的运动因引力波(GWS)的能量和角动量损失而变得复杂，引力波导致轨道天体向内螺旋并最终合并。不幸的是，在目前的情况下，无论是使用数值相对论(计算代价太高)还是后牛顿近似(太不准确)，都不可能对鼓舞人心的黑洞双星进行系统的数值研究。但是，当质量比非常小时，例如当恒星质量的BH绕着超大质量星系BH运行时，自旋计算变得容易处理。较大BH的背景克尔时空可以看作是静态的，较小BH的运动可以很好地近似为测试粒子在该时空中的运动，并且可以微扰地计算GW发射和守恒量通量，并确定它们在轨道上的反向反应。由此产生的极端质量比旋涡(EMRI)可以通过一系列克尔测地线的绝热过境来计算。麻省理工学院的斯科特·休斯博士和他的合作者开发了一种黄金标准的频域代码，可以为任意初始倾角和偏心的EMRI计算极其精确的轨道和波形。遗憾的是，该代码仍然需要大约1.5个CPU年才能生成一个激励信号，这使得它目前的形式不适合系统地研究EMRI动力学。Perez-Giz将通过一种利用克尔黑洞周围周期测地线的特殊性质的技术，对该代码进行修改，以实现计算效率的数倍提高。作为对磁共振成像的CMBFAST的模拟，产生的GWFaster将使得在麻省理工学院S Beowulf集群上批量计算磁共振成像在计算上是可行的。这种在大范围参数范围内批量计算核磁共振成像的工具将允许对核磁共振成像动力学中的无数悬而未决的问题进行系统的数值探索，包括初始条件如何确定合并的路线，在激发期间流入物体的不同轨道频率之间是否会有瞬时共振，以及向测试粒子添加自旋将如何影响动力学。这些结果将填补我们对耗散引力动力学知识的一个重要空白，在唯一的区域中，可以与解析GR解进行比较。佩雷斯-吉兹还将开展一项试点计划，帮助少数民族和低收入家庭的学生接受物理学方面的高等教育。通过与AT基金会(一家寻求解决美国长期存在的教育不平等危机的慈善组织)以及促进少数族裔和低收入学生教育的两个组织--Prep for Prep和Leadance Enterprise for a DISTICATED America(LEDA)的合作，拟议中的教育项目将在Prep for Prep和LEDA中引入高级研究经验和针对高中生和本科生的分级指导。这两个群体都已经将他们的低收入和少数族裔参与者安排在波士顿地区的顶级寄宿学校和本科院校，但没有在他们的项目中接受正式的科学研究技能培训、指导或咨询。让他们的学生在他们还在高中的时候就有机会发展物理科学的基本“刀术”，并在他们的本科职业生涯期间和之后提供指导，将是解决这些学生在物理科学中代表性不足的有力工具。

Dr. Gabriel Perez-Giz is awarded an NSF Astronomy and Astrophysics Postdoctoral Fellowship to carry out a program of research and education at the Massachusetts Institute of Technology (MIT) Kavli Institute for Astrophysics and Space Research (MKI). The study of orbital motions is core to astronomy and astrophysics. The dynamics of black hole (BH) binaries is especially dynamically rich since the nonlinear footprint of general relativity (GR) will be most visible in the regime of large masses and small separations achievable by such massive compact objects. Unlike in classical celestial mechanics, the motion in such ultra-relativistic binaries is complicated by the loss of energy and angular momentum to gravitational waves (GWs), which causes the orbiting bodies to spiral inward and eventually merge. Unfortunately, systematic numerical study of inspiraling black hole binaries is not possible in the status quo with either numerical relativity (too computationally expensive) or Post-Newtonian approximations (too inaccurate).However, when the ratio of the masses is extremely small, as when a stellar-mass BH orbits a supermassive galactic BH, the inspiral calculation becomes tractable. The background Kerr spacetime of the larger BH can be regarded as static, the motion of the smaller BH is well approximated as test particle motion in that spacetime, and GW emission and fluxes of conserved quantities can be calculated perturbatively and their back-reaction on the orbit determined. The resulting extreme mass ratio inspiral (EMRI) can be calculated as an adiabatic transit through a sequence of Kerr geodesics. Dr. Scott Hughes at MIT and his collaborators have developed a gold-standard frequency domain code that computes extremely accurate orbits and waveforms for EMRIs of arbitrary initial inclination and eccentricity. Alas, the code still requires ~1.5 CPU-years to generate a single inspiral, making it unsuitable in its present form to study EMRI dynamics systematically.Dr. Perez-Giz will adapt this code to achieve a many-fold improvement in computational efficiency via a technique exploiting special properties of periodic geodesics around Kerr black holes. An analog to CMBFAST for EMRIs, the resulting GWFaster will make batch calculation of EMRIs on MIT?s Beowulf cluster computationally feasible. Such a tool to compute EMRIs in bulk over large ranges of parameters will allow systematic numerical exploration of myriad unanswered questions in the dynamics of EMRIs, including how initial conditions determine the routes to merger, whether there can be transient resonances between the different orbital frequencies of the infalling object during the inspiral, and how adding spin to the test particle would affect the dynamics. The results will fill a crucial gap in our knowledge of dissipative gravitational dynamics in the only regime in which comparisons to analytic GR solutions are possible.Dr. Perez-Giz will also conduct a pilot program to help minority and low-income students to access higher education in the physical sciences. Through partnerships with the AT Foundation, a charitable organization that seeks to address the nation's enduring crisis of inequality in education, and Prep for Prep and the Leadership Enterprise for a Diverse America (LEDA), two organizations that advance the educations of minority and low-income students, the proposed educational program will introduce into Prep for Prep and LEDA both advanced research exposure and tiered mentoring for high school and undergraduate students. Both groups already place their low-income and minority participants in top-tier boarding schools and undergraduate institutions in the Boston area but have no formal science-specific research skills training, mentoring or advising in their programs. Giving their student bases the opportunity to develop basic "knife skills" for the physical sciences while they are still in high school and offering guidance during and beyond their undergraduate careers will be a powerful vehicle for addressing the underrepresentation of these same students in the physical sciences.