Orbital parameters for an ELM white dwarf with a white dwarf companion: LAMOST J033847.06+413424.2

Double white dwarf systems are of great astrophysical importance in the field of gravitational wave and Type Ia supernova. While the binary fraction of CO core white dwarf is about a few per cents, the extremely low mass white dwarfs are all thought to be within binary systems. In this work, we report the orbital solution of a double degenerate system: J033847.06+413424.24, an extremely low mass He core white dwarf orbiting a CO core white dwarf. With LAMOST and P200, time domain spectroscopic observations have been made and spectral atmosphere parameters are estimated to be T_eff ~ 22 500 K and log g ~ 5.6 dex. Combining Gaia parallax, 3D extinction, and evolution tracks, we estimate a radius of ~0.12 R_⊙ and a mass of ~0.22 M_⊙. With the 37 single exposure spectra, the radial velocities are measured and the orbital parameters are estimated to be P = 0.1253132(1) d, K1 = 289 ± 4 km s^-1 and V_sys = -41 ± 3 km s^-1. The radial velocity based system ephemeris is also provided. The light curves from several photometric surveys show no orbital modulation. The orbital solution suggests that the invisible companion has a minimum mass of about 0.60 M_⊙ and is ~0.79 M_⊙ for an inclination of 60.0°, indicating most probably a CO core white dwarf. The system is expected to merge in about 1 Gyr. With present period and distance (~596 pc) it cannot irradiate strong enough gravitational wave for LISA. More double degenerate systems are expected to be discovered and parametrized as the LAMOST survey goes on.