Extracting astrophysical information of highly eccentric binaries in the millihertz gravitational wave band

Wide, highly eccentric ($e>0.9$) compact binaries can naturally arise as progenitors of gravitational wave (GW) mergers. These systems are expected to have a significant population in the mHz band (e.g., $\ensuremath{\sim}3--45$ detectable stellar-mass binary black holes with $e>0.9$ in the Milky Way), with their GW signals characterized by ``repeated bursts'' emitted upon each pericenter passage. In this study, we show that the detection of mHz GW signals from highly eccentric stellar mass binaries in the local universe can strongly constrain their orbital parameters. Specifically, it can achieve a relative measurement error of $\ensuremath{\sim}{10}^{\ensuremath{-}6}$ for orbital frequency and $\ensuremath{\sim}1%$ for eccentricity (as $1\ensuremath{-}e$) in most of the detectable cases. On the other hand, the binary's mass ratio, distance, and intrinsic orbital orientation may be less precisely determined due to degeneracies in the GW waveform. We also perform mock LISA data analysis to evaluate the realistic detectability of highly eccentric compact binaries. Our results show that highly eccentric systems could be efficiently identified when multiple GW sources and stationary Gaussian instrumental noise are present in the detector output. This work highlights the potential of extracting the signal of ``bursting'' LISA sources to provide valuable insights into their orbital evolution, surrounding environment, and formation channels.