Gravitational Wave Radiation of Double Degenerates with Extremely low-mass WD companions

Double Degenerate systems (DDs) are supposed to be significant gravitational wave (GW) sources for future space-based gravitational-wave detectors, e.g., Laser Interferometer Space Antenna (LISA). Recently, one type of DDs with Extremely low-mass WD (ELM WD; $\leq 0.30\; M_\odot$) companions has been largely found in the ELM Survey. They have very short orbital periods and are therefore important sources for LISA detection. Besides, due to the thick envelope of ELM WDs compared with massive WDs (e.g. CO WDs), they are much easier to be found by the combination of electromagnetic (EM) and GW observations. In this paper, we first obtain the population of ELM WDs in DDs with considering the detailed evolutionary tracks of ELM WDs, and then analyse the GW radiation of these systems. We found that about $6\times10^3$ sources could be solely detected by LISA, including $\sim2\times10^3$ chirping sources, and $\sim13$ ($\sim107$) more sources are expected to be detected by both LISA and ELM Survey (Gaia).