Detection of Gravitational memory effect in LISA using triggers from ground-based detectors

The LIGO-Virgo-Kagra (LVK) collaboration has detected gravitational waves from 90 Compact Binary Coalescences. In addition to fortifying the linearized theory of General Relativity (GR), the statistical ensemble of detections also provides prospects of detecting nonlinear effects predicted by GR, one such prediction being the nonlinear gravitational memory effect. For detected stellar and intermediate mass compact binaries, the induced strain from the memory effect is one or two orders below the detector noise background. Additionally, since most of the energy is radiated at merger the strain induced by the memory effect resembles a step function at the merger time. These facts motivate the idea of coherently stacking up data streams from recorded GW events at these merger times so that the cumulative memory strain is detected with a sufficient SNR. GW detectors essentially record the integrated strain response at time scales of the round trip light travel time, making future space-based long arm interferometers like LISA ideal for detecting the memory effect at low frequencies. In this paper, we propose a method that uses the event catalog of ground-based detectors and searches for corresponding memory strains in the LISA data stream. Given LVK's O3 science run catalog, we use scaling arguments and assumptions on the source population models to estimate the run time required for LISA to accumulate a memory SNR of 5, using triggers from current and future ground-based detectors. Finally, we extend these calculations for using beyond LISA missions like ALIA, AMIGO, and Folkner to detect the gravitational memory effect. The results for LISA indicate a possible detection of the memory effect within the 10 year LISA mission lifetime and the corresponding results for beyond LISA missions are even more promising.