Pulsation of High Luminosity Helium Stars

A study has been made of the radial pulsation of high luminosity helium stars in the region of the HR diagram occupied by the R Coronae Borealis and other hydrogen-deficient carbon stars. As well as instability of the fundamental mode when log $${T}_\text{eff}\lt3\cdot 88$$, overtone instability is found in the region $$3\cdot 93\lt\text{log}\,{T}_\text{eff}\lt4\cdot 12$$, and possibly when log $${T}_\text{eff}\gt4\cdot2$$ if the luminosity to mass ratio is high enough. Non-adiabatic effects are very large and there is no one-to-one correspondence between linear adiabatic and nonadiabatic modes. This can cause the periods of two overtones in the same star to be identical at certain effective temperatures. Non-linear calculations show the fundamental pulsation to be very violent but the full amplitude overtone pulsation is well behaved.