Microlensing of long-duration gravitational wave signals originating from Galactic sources

TL;DR

The paper studies microlensing of long-duration Galactic CW signals in the wave-optics regime using a point-mass lens. It derives the amplification mechanism for CWs and demonstrates that microlensing induces a time-dependent signal amplitude, making CWs transient-like in detectability. Through simulations analyzed with the Time-Domain F-statistic, the authors show that the observed SNR evolution per time segment tracks the predicted amplification, enabling recovery of lensing signatures. These results inform detection strategies for second-generation GW detectors and motivate future work on more complex lens models and parallax effects to probe Galactic lens populations and CW sources.

Abstract

Detection of quasi-monochromatic, long-duration (continuous) gravitational wave radiation emitted by, e.g., asymmetric rotating neutron stars in our Galaxy requires a long observation time to distinguish it from the detector's noise. If this signal is additionally microlensed by a lensing object located in the Galaxy, its magnitude would be temporarily magnified, which may lead to its discovery and allow probing of the physical nature of the lensing object and the source. We study the observational effect of microlensing of continuous gravitational wave signals for Galactic sources and lenses in the point mass lens approximation. In particular, we examine the regions of the parameter space that are promising for lensed CW searches, and perform example simulations to demonstrate how the lensing effect affects the continuous-wave signal. We show that an analytical lensing pattern can be identified from the lensed continuous wave signal using the Time-Domain F-statistic search, as the estimated signal-to-noise ratio in each time-domain segment scales directly with the amplification factor.

Figures (11)

• Figure 1: Strong lensing illustration. A lensing system consists of an observer, lens (of mass $M_L$), and source. The angle at which the observer sees the signal arriving at the lens plane is denoted as $\theta$, while the angle representing the position of the unlensed source as seen by the observer is referred to as $\beta$. $D_\text{S}$ represents the distance between the source and the observer, $D_\text{LS}$ is the distance between the lens and the source. $D_\text{L}$ is the distance between the lens and the observer.
• Figure 2: The amplification factor ($|\mathcal{A}|$) is a function of $W$ and varying $y$. At each value of $W$, a degeneracy exists with multiple $M_\text{L}$ and $f$ combinations. The dashed line in the graph represents one of the possible combinations of $M_\text{L}$ and $f$ at that particular $W$ value. When $W < 1$, regardless of the value of $y$, the $|\mathcal{A}|$ remains small, indicating insignificant oscillatory behavior (Diffraction). For $W > 1$, there is an increase in the $|\mathcal{A}|$ at a lower $y$ values, while a decrease is observed at higher $y$ values, indicating high oscillatory behavior (Interference).
• Figure 3: The amplification factor $|\mathcal{A}|$ varies with the parameter $y$, ranging up to [-3, 3] for two specific scenarios (i) $M_\text{L} =1000 \; M_\odot$, $f=500$ Hz, (ii) $M_\text{L} =10 \; M_\odot$, $f=1000$ Hz. The first case have greater $W=61.9$, leading to a higher $|\mathcal{A}|$ at lower $y$ and a more oscillatory nature compared to the second case $W=1.2$. As $y$ increases, the value of $|\mathcal{A}|$ decreases in both cases. The dashed black line indicates the position where $|\mathcal{A}|=1$.
• Figure 4: The correlation between the frequency ($f$) and the mass of lensing object ($M_\text{L}$) is explored for various values of $W$. Since $W \propto M_\text{L}$ and $f$, $W$ exhibits degeneracy values for different combinations of $f$ and $M_\text{L}$. For example, the white dashed line in the graph represents the degeneracy value of $W$ at specific points, namely $W$ = 1, 10, and 100.
• Figure 5: Schematic scenario for a stationary lens and a source moving transversely $x(t)$ from right to left in the line of sight, crossing the Einstein radius $R_\text{E}$. The closest distance between the lensing object and the source at time $t_0$ is denoted by $y_0$.