Detecting Gravitational Wave Bursts From Stellar-Mass Binaries in the Milli-hertz Band

The dynamical formation channels of gravitational wave (GW) sources typically involve a stage when the compact object binary source interacts with the environment, which may excite its eccentricity, yielding efficient GW emission. For the wide eccentric compact object binaries, the GW emission happens mostly near the pericenter passage, creating a unique, burst-like signature in the waveform. This work examines the possibility of stellar-mass bursting sources in the millihertz band for future LISA detections. Because of their long lifetime ($\sim 10^{7}\rm\, yr$) and promising detectability, the number of millihertz bursting sources can be large in the local universe. For example, based on our estimates, there will be $\sim 3 - 45$ bursting binary black holes in the Milky Way, with $\sim 10^{2} - 10^{4}$ bursts detected during the LISA mission. Moreover, we find that the number of bursting sources strongly depends on their formation history. If certain regions undergo active formation of compact object binaries in the recent few million years, there will be a significantly higher bursting source fraction. Thus, the detection of millihertz GW bursts not only serves as a clue for distinguishing different formation channels, but also helps us understand the star formation history in different regions of the Milky Way.