arXiv:2409.00145v1 Announce Type: new
Abstract: This paper studies gravitational lensing degeneracies in the wave-optics regime, focusing on lensed gravitational waves (GWs). Considering lensing degeneracies as re-scaling (or transformations) of arrival time delay surface, we can divide them into local and global types. Local degeneracies only affect the time delay surface in localized regions, whereas global degeneracies re-scale the whole time delay surface by a constant while keeping the various observed image properties unchanged. We show that local degeneracies can be broken in the wave-optics regime since lensing effects become sensitive to the overall arrival time delay surface and not only to the time delay values at the image positions. On the other hand, global degeneracies (such as similarity transformation and mass-sheet degeneracy) multiply the amplification factor by a constant factor (let us say, $lambda$). However, in GW lensing, as the GW signal amplitude depends on the source distance, it turns out that $lambda$ is completely degenerate with the Hubble constant, similar to what we see in geometric optics. Hence, with the lensing of GWs, global degeneracies are as hard to break in wave optics as they are in geometric optics.
Gravitational Lensing Degeneracies in the Wave-Optics Regime: Challenges and Opportunities
In this paper, we examine the phenomenon of gravitational lensing degeneracies in the wave-optics regime, with a focus on lensed gravitational waves (GWs). By understanding these degeneracies as transformations of the arrival time delay surface, we find that they can be classified into two types: local and global.
Local Degeneracies
Local degeneracies only affect the time delay surface in specific, localized regions. This implies that they can be broken and overcome in the wave-optics regime. Unlike in geometric optics, where lensing effects are primarily dependent on the time delay values at the image positions, wave optics considers the overall arrival time delay surface. Therefore, the sensitivity to the overall surface allows us to overcome local degeneracies in GW lensing.
Global Degeneracies
In contrast to local degeneracies, global degeneracies involve re-scaling the entire arrival time delay surface by a constant factor. There are two common types of global degeneracies: similarity transformation and mass-sheet degeneracy.
The similarity transformation multiplies the amplification factor by a constant factor, denoted as lambda (λ). However, it is important to note that λ is completely degenerate with the Hubble constant in GW lensing. This similarity to geometric optics presents a significant challenge in breaking global degeneracies in the wave-optics regime.
Roadmap for the Future
While local degeneracies can be overcome in the wave-optics regime due to the sensitivity to the overall arrival time delay surface, global degeneracies, such as the similarity transformation and mass-sheet degeneracy, remain difficult to break. This presents both challenges and opportunities for future research and exploration in the field of GW lensing.
Challenges
- Understanding the impact of global degeneracies on the accuracy of GW lensing measurements.
- Developing techniques to differentiate between the effects of global degeneracies and genuine astrophysical phenomena.
- Exploring alternative approaches to break global degeneracies in GW lensing, such as combining multiple observational data sets.
Opportunities
- Investigating the potential effects of global degeneracies on cosmological model fitting and parameter estimation.
- Pursuing advancements in computational methods and algorithms to address global degeneracies.
- Expanding the study of GW lensing to incorporate other factors, such as the presence of dark matter or gravitational wave sources with different characteristics.
By tackling these challenges and exploring these opportunities, we can make significant progress in understanding and overcoming global degeneracies in GW lensing within the wave-optics regime.
“The sensitivity to the overall arrival time delay surface allows us to overcome local degeneracies in GW lensing.”