在引力波天文学发展如火如荼的今天，大量双黑洞、双中子星这样的致密天体并合事件被诸如LIGO等大科学装置所观测到。随后引力波以其先天的优势使得我们可以在不依赖任何电磁信息的条件下独立地验证物理理论所给出的预言。同时不断推进的引力波模板研究更是帮助人们从这种时空的涟漪中精确地提取出遥远天体系统内部的物理行为和演化细节。银河系便是一个充斥着复杂纷纭天体物理现象的实验室。在河内的各类恒星系统中，双白矮星系统备受瞩目。原因在于相较于一般主序恒星构成的双星系统由于其轨道更加紧密，对比遥远的双黑洞和双中子星等系统又离我们更近，河内双白矮星系统能释放较强的引力辐射。其引力波信号因所在毫赫兹频段故而预计为空间引力波探测器所捕获。

由于银河系内存在着大量的双白矮星系统并不断辐射引力波，这些双白矮星中又有相当一部分其子星之间存在着相互作用。这些相互作用除了引力相互作用以外，还有物质传递，潮汐相互作用以及磁场的影响等。由于电磁观测的局限性，多数双星之间的相互作用所需要的观测条件十分苛刻。比如对物质传输速率的测量需要相当宽频段的光学信息并需要针对信号中的“亮点”，这为观测增加了一定的难度。于是一个有趣的想法是：利用引力波对河内双白矮星之间的相互作用进行观测，即对双白矮星之间天体行为的物理参数进行测量。而引力波的测量是基于匹配滤波的参数估计，即我们可以先验地同时获得引力波波形模板中所描述的全部参数值及其测量误差。

于是在我们此次的工作中，我们使用后开普勒波形模板和Fisher信息矩阵的方式通过空间引力波探测器对双白矮星之间我们感兴趣的物理参数进行测量：比如物质传输速率和潮汐相互作用的同步时标。对于物质传输速率的测量，我们进行了完整的工作。我们首先讨论了可探测性：对于一个典型的双白矮星系统，我们计算得到了可探测到物质传输效应的距离，以及能精确测定物质传输速率的范围。其次我们将目光放在Gaia第二次发布数据中的光学观测到的存在物质传递的目标源。我们能同时给出这些源在引力波探测下的物质传输速率和轨道周期的不确定度。结果表明引力波测量物质传输速率相对于光学观测其精度能改善至少2个量级。此外此类存在物质传递的双白矮星系统是AM CVn系统构成的候选双星系统之一。通过引力波高精度测量双白矮星系统的物质传输速率和轨道周期使得我们进一步理解AM CVn系统形成机制。

With the development of gravitational wave astronomy, many compact binary mergers have been observed by scientific instruments such as LIGO. The advantage of gravitational waves allows us to independently test the predictions of physical theories without any electromagnetic information. Meanwhile, the ongoing research on gravitational wave templates has helped extract precise physical behavior and evolutionary details from the gravitational waves of remote celestial systems. The Milky Way is an excellent laboratory filled with complex and diverse astrophysical phenomena. Among the various galactic stellar systems, double white dwarfs have accumulated much attention. The reason is that compared to binary star systems composed of general main-sequence stars, double white dwarf systems have a tighter orbit; and are closer to us than binary black hole and neutron star systems, and thus can release stronger gravitational radiation. Their gravitational wave signals are expected to be captured by space-based gravitational wave detectors due to their millihertz frequency.

There are a large amount of double white dwarf systems radiating gravitational waves in the Milky Way. A considerable portion of these systems involve interactions between their components. In addition to gravitational interactions, these interactions also involve material transfer, tidal interactions, and magnetic fields. Due to the limitations of electromagnetic observations, the observational conditions required for most binary interactions are extremely demanding. For example, measuring the rate of mass transfer requires a wide band observation of "hot spots" in signals. Thus, an interesting idea is to use gravitational waves to observe the interactions between double white dwarfs in the Milky Way, that is, to measure the astrophysical parameters of the system. Gravitational wave measurements are based on matched filtering. We could simultaneously obtain all parameter values and their measurement errors described in the gravitational wave template waveform.

In our work, we used post-Keplerian waveform templates and Fisher information matrices to measure the physical parameters of interest between double white dwarfs through space-based gravitational wave detectors, such as the rate of material transfer and the synchronization timescale of tidal interactions. For the measurement of the mass transfer rate, we carried out a complete study. First, we discussed measurability: for a typical double white dwarf system, we calculated the distance at which the source could be detected, as well as the range in which the mass transfer rate could be accurately measured. Second, we focused on the target sources of mass transfer observed optically in the Gaia data release 2. We were able to simultaneously obtain the uncertainty of the material transfer rate and orbital period of these sources with gravitational wave measurement. The results showed that the accuracy of mass transfer rate by gravitational waves could be improved by at least two orders of magnitude compared to optical observations. Such double white dwarf systems with mass transfer are one of the candidate binary systems composed of AM CVn systems. High-accuracy gravitational wave measurements of the mass transfer rate and orbital period in double white dwarfs help us make progress in understanding the formation mechanism of AM CVn.