Splitting of the atomic hydrogen 21-cm line induced by gravitational waves from a supermassive black hole binary

Abstract

We investigate the characteristic of the hyperfine splitting of a ground-state hydrogen atom subjected to a field of a gravitational wave. In our consideration, hydrogen atoms are in the source’s local wave zone. The interaction between the atoms and the gravitational wave induces the shifts of some energy levels in the hyperfine structure, computed by the first-order perturbation theory. The splitting of energy levels leads to more than one hyperfine transition. Our analysis suggests that a gravitational wave emitted by supermassive black hole binaries could be strong enough to induce a significant effect on the hyperfine splitting. This radio-wave spectrum provides the gravitational-wave signature and thus offers a way of identifying the merger of supermassive black hole binaries.