On Constraining the Proposed Hierarchical Triple Scenario for an Eccentric Milli-Second Pulsar Binary PSR J1618-3921

Abstract

A very recent and meticulous timing effort suggests that an eccentric millisecond pulsar (eMSP) binary, namely PSR J1618-3921, is likely to be a part of a hierarchical triple (HT) system with a $0.6M_{\odot}$ companion in a $\sim 300$yr orbit. We investigate observational implications of the proposed HT scenario for PSR J1618-3921 and our ability to constrain the scenario. We model the MSP-Helium White Dwarf binary to be a part of bound point-mass HT, while incorporating the effects due to the quadrupolar interactions between the inner and outer binaries, along with dominant order general relativistic contributions to the periastron precession of the inner binary. If the proposed HT system is indeed undergoing Kozai oscillations at the present epoch, the orbital eccentricity ($e$) would be expected to decrease, while the rate of periastron advance ($\dot{\omega}$) would correspondingly increase, for plausible ranges of the HT parameters. Furthermore, the fractional variations in $e$ are anticipated to be at the level of a few parts in $10^{5}$-a magnitude that is substantially larger than the current measurement precision of $e$. We find that, for this eccentric MSP binary, the HT configurations that minimize the temporal evolution of orbital eccentricity and argument of periastron are mutually incompatible. This indicates that the continued high-precision timing of PSR J1618-3921-when analyzed within the framework introduced here-should place stringent limits on the presence and properties of a potential third body in the system.