The effect of redshift degeneracy and the damping effect of viscous medium on the information extracted from gravitational wave signals

Abstract

Considering the cosmological redshift $z_c$ , the mass of GW source extracted from GW signal is $1+z_c$ times larger than its intrinsic value, and distance between detector and GW source should be regarded as luminosity distance. However, besides cosmological redshift, there are other kinds of redshifts should be considered, which is actually ignored, in the analysis of GW data, such as Doppler redshift and gravitational redshift, so the parameters extracted from GW may deviate from their intrinsic values. Another factor that may affect GW is the viscous medium in propagation path of GW, which may damp the GW with a damping rate of $16{\pi}G{\eta}$. Some studies indicate dark matter may interact with each other, thus dark matter may be the origin of viscosity of cosmic medium. Then the GW may be rapidly damped by the viscous medium that is made of dark matter, such as dark matter "mini-spike" around intermediate mass black hole. In this article, we mainly discuss how Doppler and gravitational redshift, together with the damping effect of viscous medium, affect the informations, such as the mass and redshift of GW source, extracted from GW signals.