Expected insights into Type Ia supernovae from LISA's gravitational wave observations

The nature of progenitors of Type Ia supernovae has long been debated, primarily due to the elusiveness of the progenitor systems to traditional electromagnetic observation methods. We argue that gravitational wave observations with the upcoming Laser Interferometer Space Antenna (LISA) offer the most promising way to test one of the leading progenitor scenarios - the double-degenerate scenario, which involves a binary system of two white dwarf stars. In this study we review published results, supplementing them with additional calculations for the context of Type Ia supernovae. We discuss the fact that LISA will be able to provide a complete sample of double white dwarf Type Ia supernova progenitors with orbital periods shorter than 16-11 minutes (gravitational wave frequencies above 2-3 millihertz). Such a sample will enable a statistical validation of the double-degenerate scenario by simply counting whether LISA detects enough double white dwarf binaries to account for the measured Type Ia merger rate in Milky Way-like galaxies. Additionally, we illustrate how LISA's capability to measure the chirp mass will set lower bounds on the primary mass, revealing whether detected double white dwarf binaries will eventually end up as a Type Ia supernova. We estimate that the expected LISA constraints on the Type Ia merger rate for the Milky Way will be 4-9%. We also discuss the potential gravitational wave signal from a Type Ia supernova assuming a double-detonation mechanism and explore how multi-messenger observations could significantly advance our understanding of these transient phenomena.