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 similar to 22 500 K and log g similar to 5.6 dex. Combining Gaia parallax, 3D extinction, and evolution tracks, we estimate a radius of similar to 0.12 R-circle dot and a mass of similar to 0.22 M-circle dot. 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-circle dot and is similar to 0.79 M-circle dot for an inclination of 60.0 degrees, indicating most probably a CO core white dwarf. The system is expected to merge in about 1 Gyr. With present period and distance (similar to 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.