GPU-Accelerated Periodic Source Identification in Large-Scale Surveys: Measuring $P$ and $\dot{P}$

Many inspiraling and merging stellar remnants emit both gravitational and electromagnetic radiation as they orbit or collide. These gravitational wave events together with their associated electromagnetic counterparts provide insight about the nature of the merger, allowing us to further constrain parameters about the properties of the binary. With the future launch of the Laser Interferometer Space Antenna (LISA), follow up observations and models are needed of ultracompact binary (UCB) systems. Current and upcoming long baseline time domain surveys will observe many of these UCBs. We present a new fast periodic object search tool based on the Conditional Entropy algorithm. This new implementation of Conditional Entropy allows for a grid search over both the period ($P$) and the time derivative of the period ($\dot{P}$). To demonstrate the performance and usage of this tool, we use a galactic population of UCBs generated from the population synthesis code COSMIC, as well as a Curated catalog for varying periods at fixed intrinsic parameters. We simulate light curves as likely to be observed by future time domain surveys by using an existing eclipsing binary light curve model accounting for the change in orbital period due to gravitational radiation. We find that a search with $\dot{P}$ values is necessary for detecting binaries at orbital periods less than $\sim$10 min. We also show it is useful in finding and characterizing binaries with longer periods, but at a higher computational cost. Our code is called gce (GPU-Accelerated Conditional Entropy). It is available at https://github.com/mikekatz04/gce.