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

TL;DR

This paper tests the hypothesis that PSR J1618--3921 is in a hierarchical triple, with a distant $m_2\sim 0.6\,M_\odot$ companion in a $\sim 300$ yr orbit, by modeling the inner MSP–HeWD binary under secular quadrupole interactions and leading-order $1$PN periastron corrections. The authors derive evolution equations for the inner eccentricity $e_1$ and argument of periastron $g_1$ in terms of parameters like $\alpha=(a_1/a_2)$, $\theta=\cos\iota$, and use stability bounds to connect the outer orbit to observable inner-binary quantities; they explore whether the system could currently experience Kozai-Lidov oscillations. Their analysis shows that HT configurations that minimize changes in $e_1$ and $\dot g_1$ are mutually incompatible, implying that ongoing, high-precision timing can tightly constrain or rule out the presence of a third body. If Kozai oscillations were active, the expected changes in $e_1$ and $\dot\omega$ would be detectable within years, providing a critical test of the HT scenario for this eMSP. Overall, the work provides a framework to leverage precise timing to probe triple-star dynamics in eccentric millisecond pulsar binaries and informs the viability of the HT hypothesis for 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 ($\dotω$) 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.

Figures (3)

• Figure 1: Plots showing the temporal evolution of fractional changes in our eMSP binary's orbital eccentricity, namely $\Delta e = ( e_1(t) - e_1)/e_1$, if PSR J1618--3921 is part of a HT that experiences the Kozai resonance at the present epoch. The four panels are for HT configurations when the third body perturbations are characterized by $\alpha = (a_1/a_2) =$ 1/200, 1/320, 1/420, and 1/510, and we vary the inclination $\iota$ between the inner and outer orbits in the allowed region: [$39^\circ$ and $141^\circ$]. It should be obvious that $\Delta e(t) \sim 10^{-5}$ and such variations are substantially larger than the observational precision of $10^{-8}$ for $e$ as reported in Grunthal_2024 and marked by the red dashed line. These plots indicate that the ongoing timing campaign of PSR J1618--3921 should be able to rule out the presence of Kozai resonance in this eMSP binary.
• Figure 2: We plot fractional changes in the rate of periastron advance of our eMSP binary, namely $\Delta \dot{\omega}(t) = \frac{\dot{g}_1(t) - \dot{\omega}}{\dot{\omega}}$ where $\dot{\omega} \sim 0.00142^\circ\, \mathrm{yr}^{-1}$, as a function of time for scenarios depicted in Fig. \ref{['fig:frac_change_e1']}. The above plots and those in Fig. \ref{['fig:frac_change_e1']} indicate that a few additional months of MeerKat timing should allow one to rule out the presence of Kozai resonance in PSR J1618--3921.
• Figure 3: Plots that probe observational implications of PSR J1618--3921 being part of a HT configuration. We choose $\iota$ so as to minimize the perturbations induced by the third body on the timed eMSP binary, which demands that $(\theta^2 = 1 - e_1^2) \rightarrow \iota \approx 1.1^\circ$. The predicted $\dot e_1$ for such an almost coplanar HT configuration is $\sim 10^{-10}$/yr and this is $\sim 10^5$ times larger than what is expected from General Relativity ($\dot e_{\rm GR} \sim 10^{-15}$/yr). The right panel plots are for $\dot g_1$ - $\dot \omega$ where $\dot{\omega} \sim 0.00142^\circ\, \mathrm{yr}^{-1}$ as reported in Grunthal_2024, and it clearly shows that even if PSR J1618--3921 is part of an almost coplanar HT configuration, the resulting periastron advance rate should be different from the currently measured $\dot \omega$ value. These plots are for $P_2\sim$ 300yr, and similar plots for $P_2\sim$ 600yr are rather indistinguishable from the ones displayed above, indicating that these estimates are largely insensitive to outer orbit parameters.