Coherent Search for Binary Pulsars across all Five Keplerian Parameters in Radio Observations using the template-bank algorithm

Relativistic binary pulsars orbiting white dwarfs and neutron stars have already provided excellent tests of gravity. However, despite observational efforts, a pulsar orbiting a black hole has remained elusive. One possible explanation is the extreme Doppler smearing caused by the pulsar's orbital motion which changes its apparent spin frequency during an observation. The classical solution to this problem has been to assume a constant acceleration or jerk for the entire observation. However, this assumption breaks down when the observation samples a large fraction of the orbit. This limits the length of search observations, and hence their sensitivity. This provides a strong motivation to develop techniques that can find compact binaries in longer observations. Here we present a GPU-based radio pulsar search pipeline that can perform a coherent search for binary pulsars by directly searching over three or five Keplerian parameters using the template-bank algorithm. We compare the sensitivity obtained from our pipeline with acceleration and jerk search pipelines for simulated pulsar-stellar-mass black hole binaries and observations of PSR J0737-3039A. We also discuss the computational feasibility of our pipeline for untargeted pulsar surveys and targeted searches. Our benchmarks indicate that circular orbit searches for P-BH binaries with spin-period P$_{\rm spin} \geq 20 \rm ms$ covering the 3-10 T$\mathrm{_{obs}}$ regime are feasible for the High Time Resolution Universe pulsar survey. Additionally, an elliptical orbit search in Globular clusters for P$_{\rm spin} \geq 20 \rm ms$ pulsars orbiting intermediate-mass black holes in the 5-10 T$\mathrm{_{obs}}$ regime is feasible for observations shorter than 2 hours with an eccentricity limit of 0.1.