Abstract :
[en] Multi-periodic pulsations have recently been detected in two pre-extremely low mass (pre- ELM) helium-core white dwarfs as reported in Maxted et al. (2013, Nature, 498, 463) and Maxted et al. (2014, MNRAS, 444, 208). As such, they define a new class of pulsating stars in the HR diagram. Both objects are the secondary components in eclipsing close binaries, with solar-type main sequence stars as primaries. They are believed to be the remnants of former red giant stars stripped down of most of their mass through an active phase of binary evolution. The first of those is WASP 0247-25B, characterized by M = 0.186 ± 0.002 Mʘ, log g = 4.576 ± 0.011, and Teff = 11,380 ± 400 K (Maxted et al. 2013). Three pulsation modes have been detected so far, with periods of 381 s, 406 s, and 421 s. The second one, showing two modes with 669 s and 755 s, is WASP 1628+10B, with M = 0.135 ± 0.020 Mʘ, log g = 4.49 ± 0.05, and Teff = 9200 ± 600 K (Maxted et al. 2014). Adiabatic calculations using suitable evolutionary models have been presented in these publications, showing that the pulsation periods correspond to low-degree, mid-order p-mode oscillations (probably including radial modes). The question of the driving mechanism, however, has been left open, and we address that issue here.