Measurable Parameter Combinations of Environmentally-dephased EMRI Gravitational-Wave Signals

The future space-borne Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GW) from Extreme Mass Ratio Inspiral (EMRI) binaries which may live in nontrivial environments such as accretion disks. In this work, we apply the Fisher matrix Principal Component Analysis (PCA) method to assess how well LISA observations can jointly constrain the source parameters and environmental densities around EMRIs. Specifically, we calculate the Fisher matrix from the post-Newtonian parameters of an EMRI binary embedded in a fluid with a constant density profile. We determine that the most dominant measurable parameter combination is dominated by contributions from environmental effects, namely, gravitational drag, accretion, and gravitational pull (in order of contribution). The proposed reparameterization of the PN parameters can be used to improve the power and efficiency of future detection and parameter estimation methods.