Using Optical Spectroscopy to Map the Geometry and Structure of the Irradiated Accretion Discs in Low-mass X-ray Binaries: The Pilot-Study of MAXI J0637$-$430

The recurring transient outbursts in low-mass X-ray binaries (LMXBs) provide us with strong test-beds for constraining the poorly understood accretion process. While impossible to image directly, phase-resolved spectroscopy can provide a powerful diagnostic to study their highly complex, time-dependent accretion discs. We present an 8-month long multi-wavelength (UV, optical, X-ray) monitoring campaign of the new candidate black hole LMXB MAXI J0637$-$430 throughout its 2019/2020 outburst, using the {\em Neil Gehrels Swift Observatory}, as well as three quasi-simultaneous epochs of Gemini/GMOS optical spectroscopy. We find evidence for the existence of a correlation between the X-ray irradiation heating the accretion disc and the evolution of the He {\sc ii} 4686 \AA emission line profiles detected in the optical spectra. Our results demonstrate a connection between the line emitting regions and physical properties of the X-ray irradiation heating the discs during outburst cycles of LMXBs. Further, we are able to show that changes in the physical properties of the irradiation heating the disc in outburst can be imprinted within the H/He emission line profiles themselves in these systems.