SMBH–host galaxy mass relation

Determine the functional scaling relation between supermassive black hole mass (M_SMBH) and host galaxy stellar mass (M_gal), specifying the normalization, scatter, and any systematic dependencies needed to replace the fixed proportionality M_SMBH = 0.01 × M_gal used in wave-optics lensing estimates.

Background

In their lensing forecasts, the authors model supermassive black holes (SMBHs) as point lenses with masses set by a fixed fraction of the host galaxy stellar mass, adopting M_SMBH = 0.01 × M_gal. They then explore how varying this ratio impacts the differential optical depth for detecting wave-optics features in gravitational-wave signals.

Because SMBHs contribute dominantly to the predicted lensing optical depth in several source configurations, the precision of the SMBH–host mass relation directly affects detection rates. The authors note that the exact form of this relation remains uncertain and that improving it would refine lensing probability estimates for LISA sources.