Exploring the effect of periastron advance in small-eccentricity binary pulsars

Short-orbital period small-eccentricity binary pulsars can, in principle, experience substantial advance of periastron. We explore the possibility of measuring this effect by implementing a timing model, ELL1k, in the popular TEMPO2 pulsar timing package. True secular variations in the Laplace-Lagrange parameters, present in our ELL1k model, can lead to measurable timing residuals while pursuing decade-long timing campaigns using the existing ELL1 timing model of Lange et al. (2001), especially for binaries exhibiting significant periastron advance. We also list the main differences between our approach and various implementations of the ELL1 model present in both TEMPO and TEMPO2 packages. Detailed TEMPO2 simulations suggest the possibility of constraining the apsidal motion constant of pulsar companions in certain observed binary pulsars with minuscule eccentricities such as PSR J1719-1438. Fortunately, the ELL1k timing model does not pose any challenges to the on-going Pulsar Timing Array campaigns that routinely employ the ELL1 timing model. Detailed TEMPO2 simulations suggest the possibility of constraining the apsidal motion constant of pulsar companions in certain observed binary pulsars with minuscule eccentricities such as PSR J1719-1438. Fortunately, the ELL1k timing model does not pose any challenges to the on-going Pulsar Timing Array campaigns that routinely employ the ELL1 timing model.