How Strong Must a Core Be? Using Gravitational Wave Lensing to Determine a Limit on Core Strength and Size in Cored Isothermal Lens Models

Gravitational waves (hereafter GWs) are a key prediction of general relativity, first experimentally verified by the aLIGO array in 2015. Since the first detection, several hundred compact binary GW signals have been detected over four observing runs. Future detectors, such as the space-based LISA, are expected to detect signals coming from supermassive black holes. These are expected to be produced by very distant objects, raising the probability of gravitational lensing; in particular, the probability of strong lensing is of interest. In this regime, multiple images are formed, which can with suitably short time delays interfere with each other. In the geometric optics limit, the amplification factor produced by this interference was derived in Takahashi and Nakamura, 2004. This project concerns the effect of adding a core to the isothermal ellipse and sphere lens models, which is a prediction made by some alternative dark matter models such as fuzzy dark matter. This will add a very faint central image, increasing the number of images by one in both cases; its magnitude depends on the size and strength of the core. I seek to find a limit on the magnitude of this central image such that a 3-image system involving it is distinguishable from a 2-image version, using a distinguishability condition depending on the SNR of the source GW defined in Lindblom, 2008. Then, I will discuss the implications of this test on alternative dark matter models which produce the core including their detectability.