Measuring Pulsar Distances from Chirping Orbital Periods

Abstract

The observed orbital period time derivative (or orbital "chirp") of a millisecond binary pulsar (MSP) encodes information about both the intrinsic properties of the binary system and its environment. Orbital chirp has contributions from intrinsic energy loss due to gravitational wave emission, kinematic effects due to motion in the plane of the sky, and dynamical effects due to galactic acceleration, with the latter two contributions depending on the MSP distance. We use orbital chirp data to infer distances to 21 MSPs; and for four of which we obtain smaller uncertainties than those reported in previous distance measurements. We incorporate multiple realistic galactic acceleration models to assess the sensitivity of the inferred distances to the choice of galactic gravitational potential, finding a significant dependence for four MSPs.

Figures (6)

• Figure 1: Top: Galactic acceleration profile determined from the C20 galactic gravitational potential model. Left: Radial acceleration in the x-y plane (galactic plane). Middle–Top: Radial acceleration in the x-z plane. Middle–Bottom: Vertical acceleration in the x-z plane. Right: Line-of-sight differential acceleration. Spatial variations in acceleration are on the order of $10^{-9}\,{\rm m/s^2}$. The location of the Sun is marked with a star ($\star$), and the gray squares outline the region highlighted in the zoomed-in profiles below. The middle panels demonstrate that radial acceleration is dominant over vertical acceleration ($a_R>a_z$) in the solar neighborhood. Bottom: Zoomed-in view of the galactic acceleration profile in the solar neighborhood. Local variations in acceleration are at the level of $10^{-10}\,{\rm m/s^2}$. We note that the radial acceleration is dominant over the vertical acceleration ($a_R>a_z$) in this region of the galaxy. The color scale in the right plot is selected to approximately reflect the sensitivity of pulsar orbital period measurements to acceleration effects. Open circles mark the positions of the millisecond binary pulsars (MSPs) analyzed in this work.
• Figure 2: Fractional differences in predicted gravitational accelerations between galactic potential models. The maps show the relative differences of the M17 and B15 models compared to C20 as the reference model. Generically, the fractional difference is $\lesssim 10\%$. Open circles indicate the positions of millisecond binary pulsars (MSPs) in our dataset. Red crosses indicate MSPs B1534+12, J0437–4715, J1600–3053, and J1909–3744, for which we find that the inferred distances are significantly sensitive to the choice of galactic gravitational potential model.
• Figure 3: Comparison of the three terms ($a^{\rm GW}$, $a^{\rm Shk}$, and $a^{\rm Gal}$) contributing to the observed apparent acceleration $a^{\rm obs}$ for millisecond binary pulsars (MSPs) analyzed in this work. Top: Relative contribution of each term to the total observed acceleration, shown as the ratios $|a^{\rm GW}/a^{\rm obs}|$, $|a^{\rm Shk}/a^{\rm obs}|$, and $|a^{\rm Gal}/a^{\rm obs}|$. Bottom: Amplitude of each term relative to the measurement uncertainty in the observed acceleration $|a^{\rm GW}/\sigma_{a^{\rm obs}}|$, $|a^{\rm Shk}/\sigma_{a^{\rm obs}}|$, and $|a^{\rm Gal}/\sigma_{a^{\rm obs}}|$. The dashed line marks the level at which any term's contribution equals the measurement uncertainty; below this line (shaded in gray) approximately indicates contributions that are not statistically significant for our analysis. Left: MSPs for which we obtain convergent distance measurements. For all of these, the Shklovskii term contributes significantly and lies above the significance threshold in the bottom panel. While the galactic acceleration term is subdominant for many MSPs, it still exceeds the uncertainty level in several cases and thus is significant in the analysis (Sec. \ref{['sec:results']}). Right: MSPs for which distance measurements do not converge. These are dominantly binary systems for which the approximation $a^{\rm obs} \approx a^{\rm GW}$ holds well. As a result, our analysis lacks sensitivity to distance for these sources. There are, however, two notable exceptions: PSR J1829 and PSR J2339, where distance-dependent terms are significant; however, the large uncertainty in the intrinsic gravitational wave contribution (indicated by the green cross near the dashed line) limits our ability to constrain the distance.
• Figure 4: Inferred distances for the millisecond binary pulsars (MSPs) analyzed in this work. The top panel for each MSP shows distance measurement results derived using the C20, M17, and B15 galactic potential models. Violin plots represent the distribution of distances obtained by minimizing the orbital chirp residual. In the gray shaded area we show distance measurements reported in the literature (see Table \ref{['tab:nominal']} for references). The bottom panel shows the residual of the orbital chirp in Eq. \ref{['eq:residual']} for each MSP distance. Our minimization procedure yields improved agreement between the model predictions and the observed orbital chirps.
• Figure 5: Normalized probability distribution functions of millisecond binary pulsar (MSP) distances that minimize the residual in Eq. \ref{['eq:residual']}. B1534+12 and J0437, with the highest $a^{\rm Gal}/\sigma_{a^{\rm obs}}\sim 10$ (Fig. \ref{['fig:a_contributions']}), are sensitive to the galactic gravitational potential. Among MSPs with $a^{\rm Gal}/\sigma_{a^{\rm obs}}\sim1$, only J1600 and J1909 show significant sensitivity. The remaining MSPs with $a^{\rm Gal}/\sigma_a^{\rm obs}<1$ have minimal sensitivity to the galactic gravitational potential.