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We study the novel asteroseismology of the chiral magnetic wave (CMW) of thequark number density in relativistic quark matter inside neutron stars andcore-collapse supernovae and the chiral vortical wave (CVW) of the neutrinonumber density in relativistic neutrino matter at the core of supernovae. Wecall the oscillation modes for these chiral waves the chiral magnetic mode(CM-mode) and chiral vortical mode (CV-mode), respectively. We derive thedispersion relations of these new modes in the presence of the chiralityflipping due to the finite quark mass and diffusion. We then estimate thepossible frequencies of these modes and amplitudes of the resultinggravitational waves. In particular, since the CM-mode can exist only in quarkmatter with nearly gapless quarks (such as the two-flavor colorsuperconductivity) for a sufficiently strong magnetic field, correspondinggravitational waves provide a new possible probe for such quark matter and themagnetic field in neutron stars.

Chiral asteroseismology: seismic oscillations caused by chiral transport in neutron stars and supernovae