Understanding the formation history of brightest cluster galaxies is an important topic in galaxy formation. Utilizing the Planck Sunyaev-Zel'dovich cluster catalog, and applying the Ansatz that the most massive halos at one redshift remain among the most massive ones at a slightly later cosmic epoch, we have constructed cluster samples at redshift z ∼ 0.4 and z ∼ 0.2 that can be statistically regarded as progenitordescendant pairs. This allows us to study the stellar mass assembly history of BCGs in these massive clusters at late times, finding the degree of growth between the two epochs is likely at only few percent level, which is far lower compared to the prediction from a state-of-the-art semi-analytic galaxy formation model.

A systematic study of gravitational waves from galaxy mergers, through N -body simulations, was performed. In particular, we investigated the relative importance of galaxy components (disk, bulge and halo) and effects of initial relative velocity, relative angular momentum and mass ratio of the galaxies. We found that the features of light curve of gravitational waves, such as peak width and luminosity, are reliably simulated with particle numbers larger than ∼ 10 4 . Dominant contribution to gravitational wave emission came from the halo component, while peak luminosity amounted to 10 31 erg/sec for the collision of two halos with mass 3.8 × 10 12 h −1 M⊙. We also found that the initial relative velocity in the direction of the initial separation did not significantly affect gravitational wave emission, while the initial relative angular momentum broadened the peak width and suppressed the luminosity. Mass dependence of the peak luminosity was also investigated, and we obtained evidence that the luminosity is proportional to the cubic mass when the scaling relation is satisfied. This behavior was considered by a simple analysis.PACS numbers:

The stochastic gravitational wave background (GWB) from halo mergers is investigated by a quasianalytic method. The method we employ consists of two steps. The first step is to construct a merger tree by using the extended Press-Schechter formalism or the Sheth & Tormen formalism, with Monte Carlo realizations. This merger tree provides evolution of halo masses. From N-body simulation of two-halo mergers, we can estimate the amount of gravitational wave emission induced by the individual merger process. Therefore, the second step is to combine this gravitational wave emission with the merger tree and obtain the amplitude of the GWB. We find GW $ 10 À19 for f $ 10 À17 -10 À16 Hz, where GW is the energy density of the GWB. It turns out that most of the contribution on the GWB comes from halos with masses below 10 15 M and mergers at low redshift, i.e., 0 < z < 0:8.