A Novel Technique for Long-term Timing of Redback Millisecond Pulsars

TL;DR

The paper introduces a novel Ransom-O'Neill Isolation (ROI) technique to time redback millisecond pulsars (RBs) with dramatic orbital variations by removing orbital timing delays and fitting local, piecewise binary solutions to recover the MSP spin behavior over nearly two decades. It combines measurements of time of periastron passage $T_{0,x}$, piecewise-continuous binary modeling, TEMPO/PINT refinement, and Gaussian Process Regression to predict missing $T_{0,x}$ values, enabling phase connection without reliance on high-order orbital frequency derivatives. Applying ROI to five RBs in three globular clusters yields long-term, phase-connected timing that agrees with conventional methods while revealing significant orbital wander and Applegate-like quasi-periodic variations in Ter5P. The work also uncovers a striking correlation between the fractional phase-variation amplitude $\sigma_{\Delta T_0}/P_b$ and the spin frequency, highlighting a potential link between spin state and orbital perturbations, and discusses future improvements including multi-frequency DM modeling and broader systematics mitigation. Overall, ROI provides a robust alternative for studying RBs with strong orbital variations, particularly when densely sampled monitoring is not available, and it opens pathways for using RBs in clusters as precision clocks and dynamical probes.

Abstract

We present timing solutions spanning nearly two decades for five redback (RB) systems found in globular clusters (GC), created using a novel technique that effectively "isolates" the pulsar. By accurately measuring the time of passage through periastron ($T_0$) at points over the timing baseline, we use a piecewise-continuous, binary model to get local solutions of the orbital variations that we pair with long-term orbital information to remove the orbital timing delays. The isolated pulse times of arrival can then be fit to describe the spin behavior of the millisecond pulsar (MSP). The results of our timing analyses via this method are consistent with those of conventional timing methods for binaries in GCs as demonstrated by analyses of NGC 6440D. We also investigate the observed orbital phase variations for these systems. Quasi-periodic oscillations in Terzan 5P's orbit may be the result of changes to the gravitational-quadruple moment of the companion as prescribed by the Applegate model. We find a striking correlation between the standard deviation of the phase variations as a fraction of a system's orbit ($σ_{ΔT_0}$) and the MSP's spin frequency, as well as a potential correlation between $σ_{ΔT_0}$ and the binary's projected semi-major axis. While long-term RB timing is fraught with large systematics, our work provides a needed alternative for studying systems with significant orbital variations, especially when high-cadence monitoring observations are unavailable.

Figures (7)

• Figure 1: Summed pulse profiles from coherently dedispered 2 GHz observations for each of the five RBs analyzed in this work.
• Figure 2: Each panel shows different measurements of time of periastron passage ($T_0$) deviations over time for M28H as black points. In panel (a), we show the $\Delta T_{0}$ values derived from the SPIDER_TWISTER values described in §\ref{['subsec:detections']}, and we overlay in orange the predicted values from the phase-connected, BTX model described in §\ref{['subsec:btx-gp']}. In panel (b), we show the $\Delta T_{0}$ values accounting for BTX predictions, as well as a Gaussian process regression (GPR) to interpolate between the BTX-informed, $T_0$ values and the remaining SPIDER_TWISTER measurements. In panel (c), we show the remaining values set to those GPR predictions, as well as a new regression to describe the updated measurements. This process still benefits from manual improvement to ensure $\Delta T_{0}$ is relatively smooth with time, and we show the resultant values and their errors in panel (d).
• Figure 3: Left: As in Figure \ref{['fig:T0_progression']}, phase variations ($\Delta T_0$) for each system over time using their final $T_{0, x}$ values. Note that NGC 6440D and Ter5P are shown with their respective $\dot{P_{\rm b}}$'s removed. Right: Over-sampled Power Spectral Densities (PSD; grey points) of the $\Delta T_0$s for each system from a Lomb-Scargle periodogram with an arbitrary normalization. In dark red we show the best fit power-law to the frequencies between the dashed and dash-dotted lines for two systems. The $\gamma$ values and their error for these fits are given in the bottom left of each plot. In red, we show a multi-variate gaussian sampling representing the error region of our fit.
• Figure 4: Timing residuals for the five RBs described in this work after applying the ROI technique. We note that the errors shown here are our measured uncertainties from §\ref{['subsec:roi']}, not the inflated errors used to measure the spin properties in §\ref{['subsec:fitting']}. Each inset plot shows the same data, but with axes noting $\pm0.5$ pulse phase to highlight how close to zero the residuals are.
• Figure 5: Phase variation ($\Delta T_0$) trends over time for Ter5P (left) and NGC 6440D (right) assuming a constant orbital period (upper panels) and after the removal of the best-fit $\dot{P_{\rm b}}$ (lower panels). Also shown in the bottom panels are Gaussian process regressions to the measured $T_{0, x}$ values (note these values match those in Figure \ref{['fig:deltaT0']}). The quasi-periodic oscillations described in §\ref{['subsec:Ter5P']} for Ter5P are evident.