Probing astrophysical environment with eccentric extreme mass-ratio inspirals

The discovery of gravitational waves and black holes has started a new era of gravitational wave astronomy that allows us to probe the underpinning features of gravity and astrophysics in extreme environments of the universe. In this article, we investigate one such study with an extreme mass -ratio inspiral system where the primary object is a spherically symmetric static black hole immersed in a dark matter halo governed by the Hernquist density distribution. We consider the eccentric equatorial orbital motion of the steller-mass object orbiting around the primary and compute measurable effects. We examine the behaviour of dark matter mass and halo radius in generated gravitational wave fluxes and the evolution of eccentric orbital parameters- eccentricity and semi-latus rectum. We further provide an estimate of gravitational wave dephasing and find the seminal role of low -frequency detectors in the observational prospects of such an astrophysical environment.