Radio timing constraints on the orbital orientation and component masses of PSR J1455$-$3330

TL;DR

This study leverages ~30 years of timing data from Lovell, Nançay, Green Bank, and MeerKAT to constrain the 3D orbital geometry and component masses of PSR J1455$-$3330. By detecting a relativistic Shapiro delay and a precise change in the projected semi-major axis, and by combining parallax, proper motion, and kinematic effects within self-consistent GR-based models, the authors derive two viable mass/orientation solutions, both favouring a helium white dwarf companion. The results demonstrate the system’s consistency with standard MSP evolution and provide a valuable data point for neutron star mass distributions, while highlighting future prospects for breaking degeneracies with ongoing/near-future observations (e.g., with SKA) to achieve precise $\\dot{\\omega}$ and a distance-independent mass determination.

Abstract

PSR J1455$-$3330 is a $\sim$7.98 ms pulsar in a $\sim$76.17 day nearly circular orbit with a white dwarf companion. In this work, we combine the available Lovell, Nançay decimetric Radio Telescope, Green Bank, and MeerKAT pulsar timing data spanning $\sim$ 30 years to measure the kinematic and relativistic effects of PSR J1455$-$3330 to constrain its 3D orbital geometry and component masses. We detect a relativistic Shapiro delay signal. We measure a significant orthometric amplitude $h_3 = 0.307^{+0.022}_{-0.026}$ $μ$s and an orthometric ratio $ς= 0.551^{+0.057}_{-0.054}$. We measure the change in projected semi-major axis $\dot{x} = -202.1^{+2.5}_{-2.7} \times10^{-16} \, \rm s\,s^{-1}$ with high significance, parallax, $\varpi$ = 1.11(6) mas, parallax derived distance 0.90(5) kpc, and a precise total proper motion magnitude of 12.432(2) mas yr$^{-1}$. A self-consistent analysis of all kinematic and relativistic effects, assuming general relativity, yields two solutions: (1) a pulsar mass $M_{\rm p} = 1.39^{+0.38}_{-0.18}\, \rm M_{\odot}$, a companion mass $M_{\rm c} = 0.293^{+0.056}_{-0.026}$ $\rm M_{\odot}$, an orbital inclination, $i = 63(2)^{\circ}$, and longitude of the ascending node, $Ω= 212(12)^{\circ}$ or (2) a pulsar mass $M_{\rm p} = 1.53^{+1.10}_{-0.22} \, \rm M_{\odot}$, a companion mass $M_{\rm c} = 0.309^{+0.163}_{-0.026}\, \rm M_{\odot}$, an orbital inclination, $i = 123(4)^{\circ}$, and longitude of the ascending node, $Ω= 334(12)^{\circ}$. All uncertainties represent the 68.27$\%$ credibility region. These results strongly favour a helium-dominated white dwarf companion.

Figures (10)

• Figure 1: Definition of angles and conventions used in this paper. Throughout this paper, we adopt the “observer’s convention” for all geometric quantities. The fundamental reference plane is in green, and the orbital plane is in purple, with the corresponding unit vectors coloured the same way. S denotes the spin angular momentum, which is aligned with the orbital angular momentum. The magnetic axis ($\mu$) is misaligned from S by the misalignment angle $\alpha$. The pulsar emission cone has an opening angle $\rho$, and is cut through by our line of sight at an impact angle $\beta$. $\zeta = \alpha + \beta$ is the latitude of the spin axis, which is the same as the orbital inclination angle ($i$) for spin-aligned systems.
• Figure 2: Polarisation profile of J1455$-$3330 obtained from integrating 32.2 hours of observations with the MeerKAT L-band receiver. The black, red, and blue lines in the top panel indicate the total intensity, linear, and circular polarisation fractions, respectively. The middle panel shows the evolution of the position angle (PA) across the pulsar’s phase. The PA exhibits the characteristic swing as well as some phase jumps. The red solid line corresponds to the Rotating Vector Model (RVM) fit to the PA, and the dashed line shows the RVM solution separated by 90$^{\circ}$ from the main fit to include the jumped PA values (blue dots).
• Figure 3: Corner plot showing the posterior distributions from run 2, fitting the Rotating Vector Model (RVM) to the MeerKAT observed position angle variation.
• Figure 4: Timing residuals across epochs (top, middle) and orbital phase (bottom). Top: We obtain a weighted rms of 3.201 $\mu$s after applying the best-fit values using the T2 timing and noise model described in Sect. \ref{['Section4']}. Middle: Post-fit timing residuals without subtracting the DM noise model, with the time domain realisations of the 100 parameter DM noise model overlaid as orange lines, and black dots showing the median across all the DM model realisations at each ToA. Bottom: MeerKAT residuals as a function of orbital phase, where the orbital phase is measured from the longitude of periastron ($\omega=223.47^\circ$). Superior conjunction = $T_{\rm asc}$ + $90^\circ$, occurs at orbital phase = 0.63. A Shapiro delay signal is discernible at orbital phase 0.63 when setting $M_{\rm c} = 0$ while keeping all other parameters fixed. We overplot the expected theoretical signal based on the best-fit inclination and companion mass values of the full dataset in purple. The line width indicates the 1$\sigma$ deviations in companion mass and inclination angle.
• Figure 5: Output posterior distribution for the relevant orbital and post-Keplerian parameter subset of timing parameters for J1455$-$3330. These were obtained from temponest using the T2 orbital model which includes a DM only noise model. The plot was generated using the chainconsumer package. Full details of the parameters are provided in Table \ref{['Tab:3']}. The obtained pulsar mass ($M_\rm p$) distribution was computed using the mass function and the posterior distributions on $M\rm c$,$i$, $x$, and $P_\rm b$. The 1D marginalised posterior distributions for each parameter are shown on the diagonal subplots and the shaded region indicates the 1-$\sigma$ credibility interval. The 2D contours on the off-diagonal subplots show the correlation between pairs of parameters, where the contours mark the 39%, 86% and 98% credibility regions respectively.