论文标题
激动人心的模式由于引力波的畸变：极端质量比率的测量性
Exciting modes due to the aberration of gravitational waves: Measurability for extreme-mass-ratio inspirals
论文作者
论文摘要
来自源与我们移动的电源的重力波可能会遭受特殊的相关作用，例如像差。这些意义的所需速度按$ 1000 \，\ textrm {km s}^{ - 1} $的顺序。该值对应于在星系簇中发现的速度分散体。因此，我们预计大量的引力波源在信号中会产生这种影响。特别是，来自移动源的信号将激发其更高的模式，即$（3,3）$及以后。我们得出了描述这种效果的表达式，并研究了其对圆形，非旋转极端比率灵感的特定情况的可测量性。我们发现，对于$ 1000 \，\ textrm {km \，s}^{ - 1} $的奇特速度激发了较高的模式。使用Fisher矩阵分析，我们表明，对于100的信噪比，可以将源的速度测量到仅几％的精度。如果可以忽略源的运动估计值，例如，可以通过多普勒移位来偏置组件的估计质量。相反，通过将这种效果包括在波形模型中，我们可以测量在光线无法访问的距离处的星系簇的速度分散。
Gravitational waves from a source moving relative to us can suffer from special-relativistic effects such as aberration. The required velocities for these to be significant are on the order of $1000\,\textrm{km s}^{-1}$. This value corresponds to the velocity dispersion that one finds in clusters of galaxies. Hence, we expect a large number of gravitational-wave sources to have such effects imprinted in their signals. In particular, the signal from a moving source will have its higher modes excited, i.e., $(3,3)$ and beyond. We derive expressions describing this effect, and study its measurability for the specific case of a circular, non-spinning extreme-mass-ratio inspiral. We find that the excitation of higher modes by a peculiar velocity of $1000\,\textrm{km\,s}^{-1}$ is detectable for such inspirals with signal-to-noise ratios of $\gtrsim20$. Using a Fisher matrix analysis, we show that the velocity of the source can be measured to a precision of just a few percent for a signal-to-noise ratio of 100. If the motion of the source is ignored parameter estimates could be biased, e.g., the estimated masses of the components through a Doppler shift. Conversely, by including this effect in waveform models, we could measure the velocity dispersion of clusters of galaxies at distances inaccessible to light.
