Schematic representation of the hypothesis of this study. Left: cross sections of two merging sunspots in (a) the monolithic model and (c) the cluster model. The black solid arrows indicate magnetic field lines. The yellow region is a magnetic field-free region. The vertical dashed line indicates the convergent interface. The red circular arrows indicate the general convection cells. The opaque red circular arrows indicate the magneto-convection cells. Right: distributions of the oscillation centers on the plane of the sky (panels b and d). The oscillation centers are indicated with red concentric circles.