Gravitational lensing effects on parameter estimation in gravitational wave detection with advanced detectors

The gravitational lensing effect is important to the detection of electromagnetic signals in astrophysics. The gravitational wave lensing effect has also been found significant to gravitational wave detection in the past decade. Recent analysis shows that the lensing events for advanced detectors could be quite plausible. The black holes in our Milky Way Galaxy may play the role of lens objects. These facts motivate us to study the lensing effects on gravitational wave signals for advanced detectors. Taking advanced LIGO and Einstein Telescope for examples, we investigate the lensing effects on the parameter extraction of gravitational wave signals. Using the Markov chain Monte Carlo simulation together with matched filtering methods, we find that the lensing effect for a lens object with small mass is negligible. But when the mass of the lens object increases to larger than 1000M(circle dot) the lensing effect becomes important. Using the template without lensing corrections would result in loss of signal detections. In contrast if we consider templates with lensing effects, the lensed signal may provide much information about the lens black hole. These facts may give us a new way to determine the parameters of the lensing object. For example, this kind of signal may also help us estimate the mass and the distance of the supermassive black hole hosted at the center of our Galaxy.