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，在马萨诸塞州理工学院（MIT）Kavli天体物理学和空间研究所（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）双星的动力学是特别丰富的动力学，因为广义相对论（GR）的非线性足迹将是最明显的大质量和小分离的制度，可实现这样的大质量紧凑的对象。与经典天体力学不同，这种超相对论双星的运动由于引力波（GW）的能量和角动量损失而变得复杂，这导致轨道天体向内螺旋并最终合并。不幸的是，无论是用数值相对论（计算量太大）还是后牛顿近似（太不准确），都不可能对黑洞双星的螺旋运动进行系统的数值研究。然而，当质量比非常小时，比如恒星质量的黑洞围绕超大质量的星系黑洞运行时，螺旋运动的计算就变得容易处理了。大BH的背景Kerr时空可以看作是静态的，小BH的运动可以很好地近似为该时空中的测试粒子运动，GW发射和守恒量通量可以微扰计算，并确定它们在轨道上的反作用。由此产生的极端质量比inspiral（EMRI）可以计算为通过一系列克尔测地线的绝热过境。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金标准频域代码，可以计算具有任意初始倾角和偏心率的EMRI的极其准确的轨道和波形。可惜的是，该代码仍然需要~1.5 CPU年才能生成一个inspiral，这使得它不适合以目前的形式系统地研究EMRI动力学。Perez-Giz博士将通过利用克尔黑洞周围周期测地线的特殊性质的技术来调整该代码，以实现计算效率的多倍提高。类似于CMBFAST的EMRI，产生的GWFaster将在MIT上批量计算EMRI？的Beowulf集群计算可行。这样一个在大范围参数上批量计算EMRI的工具将允许系统地对EMRI动力学中无数未回答的问题进行数值探索，包括初始条件如何确定合并的路线，在螺旋期间下落物体的不同轨道频率之间是否存在瞬态共振，以及如何将自旋添加到测试粒子将影响动力学。这些结果将填补我们在耗散引力动力学知识中的一个关键空白，在这个领域中，我们可以与解析GR解进行比较。Perez-Giz博士还将开展一个试点项目，帮助少数民族和低收入家庭的学生获得物理科学方面的高等教育。通过与AT基金会，一个旨在解决国家教育不平等的持久危机的慈善组织，以及Prep for Prep和Leadership Enterprise for a Diverse America（LEDA），两个促进少数民族和低收入学生教育的组织，拟议中的教育计划将在“为准备而准备”和“LEDA”中引入高级研究接触和高中分层指导，本科生。这两个群体都已经将他们的低收入和少数族裔参与者安置在波士顿地区的顶级寄宿学校和本科院校，但在他们的项目中没有正式的科学特定研究技能培训，指导或建议。让他们的学生基地有机会发展基本的“刀技能”的物理科学，而他们仍然在高中，并提供指导期间和超出他们的本科生涯将是一个强大的工具，解决这些学生在物理科学代表性不足。

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.