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Mergers of luminous early-type galaxies in the local universe and gravitational wave background

Supermassive black hole (SMBH) coalescence in galaxy mergers is believed to be one of the primary sources of very low frequency gravitational waves (GWs). Significant contribution of the GWs comes from mergers of massive galaxies with redshifts z<2. Very few previous studies gave the merger rate of massive galaxies. % We selected a large sample (1209) of close pairs of galaxies with projected separations 7<r_p<50 kpc from 87,889 luminous early-type galaxies (M_r<-21.5) from the Sloan Digital Sky Survey Data Release 6. These pairs constitute a complete volume-limited sample in the local universe (z<0.12). Using our newly developed technique, 249 mergers have been identified by searching for interaction features. From them, we found that the merger fraction of luminous early-type galaxies is 0.8%, and the merger rate in the local universe is % R_g=(1.0+/-0.4)*10^{-5} Mpc^{-3} Gyr^{-1}} % with an uncertainty mainly depending on the merging timescale. % We estimated the masses of SMBHs in the centers of merging galaxies based on their luminosities. We found that the chirp mass distribution of the SMBH binaries follows a power law with an index of -3.0+/-0.5 in the range 5*10^8--5*10^{9} M_{\odot}. % Using the SMBH population in the mergers and assuming that the SMBHs can be efficiently driven into the GW regime, we investigated the stochastic GW background in the frequency range 10^{-9}--10^{-7} Hz. We obtained the spectrum of the GW background of h_c(f)=10^{-15}(f/yr^{-1})^{-2/3}, which is one magnitude higher than that obtained by Jaffe & Backer in 2003, but consistent with those calculated from galaxy-formation models.