Retrieving the mass of a gravitational-wave (GW) source is a fundamental but difficult problem because it is degenerate with redshift. In astronomy three types of redshift exist, namely cosmological, Doppler, and gravitational redshift, but the latter two are often neglected in the analysis of GW data. We study the effects of Doppler and gravitational redshifts on GWs, motivated by recent proposals that the binary black hole mergers detected by the Laser Interferometer GW Observatory (LIGO) could have happened in the vicinity of supermassive black holes. We find that they together can contribute an effective redshift as large as 1.9 \lt (1 + z) \lt 3.4. Our results imply that black holes of 10 solar masses could masquerade as much bigger ones. Distinguishing them requires simultaneous observation of GWs in both (10 - 100) Hertz and milli-Hertz bands.

BIO：Xian Chen did his Ph.D in Peking University. He had received support from the China Scholarship Council to study in the University of California, Santa Cruz for two years. After graduation, he worded as a postdoc in the Kavli Institute for Astronomy and Astrophysics in China, Max-Planck Institute for Gravitational Physics in Germany, and Pontificia Universidad Catolica de Chile. He is now an assistant professor in the Astronomy Department of the School of Physics.