Self-gravity modelling for LISA

Abstract

The Laser Interferometer Space Antenna (LISA) mission, a space-based gravitational wave detector, uses laser metrology to measure distance fluctuations between proof masses aboard three sciencecraft. The total acceleration disturbance to each proof mass is required to be below 3 × 10−15 m s−2 Hz−1/2 at 0.1 mHz. Self-gravity noise due to sciencecraft distortion and motion is expected to be a significant contributor to the acceleration noise budget. To minimize these effects, the gravitational field at each proof mass must be kept as small, flat and constant as possible. It is estimated that the static (non-fluctuating) self-gravity acceleration must be kept below 5 × 10−10 m s−2 with a gradient below 3 × 10−8 s−2 in order to meet the required noise levels. Most likely it will not be possible to directly verify that the LISA sciencecraft meets these requirements by measurements; they must be verified by models. The LISA integrated modelling team developed a new self-gravity tool that calculates the gravitational forces and moments on the proof masses to aid in the design and verification of the LISA sciencecraft. We present here an overview of the tool and the latest self-gravity results calculated using the current baseline design of LISA.

Gravitational mass attraction: properties of a right-angled parallelepiped for the LISA drag-free system

“…Depending on the desired accuracy and location from the mass centre of a cubical attracting body, a point mass approximation for a single point mass may or may not be acceptable along the x-axis. For example, according to figure 2 the force along the x-axis due to the cubical geometry will be on the order of 10 −8 N. Returning to the LISA noise budget, a maximum total static self-gravity acceleration of 5 × 10 −10 m s −2 is necessary for LISA disturbance requirements [9]. If the knowledge of the mass attraction force is desired to have an uncertainty less than 10 −10 N, consistent with the LISA requirements, then from figure 3 it is seen that a point mass approximation may only be used for the ratio of x/2a greater than approximately 2.…”

空间引力波探测惯性传感器及其关键技术

“…直接作用在测试质量上的加速度噪声主要来源 于磁 [54,55] 、热 [56] 、电 [57] 耦合噪声是一个重要而复杂的噪声, 由于其外部 来源不可控制, 耦合效应主要通过耦合刚度来表征, 影响耦合刚度的主要因素有引力梯度和电容传感器 引起电容梯度, 其中引力梯度影响更为剧烈 [52,61,62] , 因而对于惯性传感器设计而言, 从始至终都需要考虑 引力梯度的影响, 而对于电容梯度来说, 其作用主要 表现为电极板和测试质量之间的电位差, 而对于这部 分影响主要是电荷累积以及材料本身由于 patch field 影响, 电荷累积需要加入电荷管理系统来实现, 而这 种影响则需要通过控制相关表面清洁度和化学污染 来降低, 应该控制到 0.1V [59,63] .…”

LISA technology and instrumentation

“…On the ground, a measurement of the self-gravity is not feasible to the precision necessary for LISA, verification of the self-gravity relies on analyses. Such analyses on self-gravity and the design of compensation masses have been successfully performed on LISA Pathfinder [78,79], and the corresponding analysis tools have been developed for LISA [80,81].…”