The pulsations of ZZ Ceti stars - IV. The instability strip

DA models become unstable to the observable g-mode oscillations when the hydrogen ionization zone is sufficient to excite modes with periods ≥ 100 s. As the effective temperature decreases, modes of longer period are excited up to a maximum period of about 1000 s. Further cooling does not lead to the excitation of the high-order modes of still longer period (to a detectable amplitude) and the brightness changes associated with the excited modes decrease below the detection threshold. The position of the theoretical instability strip in the $$T_\text e-\text {log}\enspace g$$ plane is thus determined. The width of this instability strip (at fixed g) is less than 1000 K. It is argued that this value is consistent with the statistics of ZZ Ceti stars and that the much wider spread in temperature which has been found in several investigations may be due to observational errors. Calibration for the mixing length theory of convection on the basis of the mean temperature of the ZZ Ceti stars is in broad agreement with the solar calibration.