The Pulsar Radial Acceleration Relation

Technical Summary: The Pulsar Radial Acceleration Relation

Problem and Motivation
The Radial Acceleration Relation (RAR) is a tight empirical correlation between observed centripetal acceleration ($g_{\text{obs}}$) and baryonic gravitational acceleration ($g_{\text{bar}}$), primarily established in the rotation curves of late-type disc galaxies. While its near-zero intrinsic scatter and simple functional form have been interpreted as evidence for non-Newtonian dynamics or specific baryon–halo assembly scenarios in $\Lambda$CDM, it remains an open question whether this phenomenology extends beyond the radial dynamics of galactic discs. Current tests are largely confined to rotation curves. This paper investigates whether pulsar timing, which measures line-of-sight (LOS) differential accelerations, can serve as a novel probe of the RAR in directions outside the Galactic disc, specifically testing a vector generalization of the relation: $g_{\text{obs}} = \nu(|g_{\text{bar}}|)g_{\text{bar}}$.

Methodology
The authors utilize the v3 catalogue from T. Donlon et al. (2025), comprising 26 independent LOS accelerations inferred from the orbital-period derivatives of binary pulsars, corrected for Shklovskii and relativistic effects. While a sample of spin-only millisecond pulsars was available, it was excluded due to larger uncertainties.

To model the baryonic field, the authors employ an analytic approximation of the Milky Way census by J. Bland-Hawthorn & O. Gerhard (2016). This model represents the thin disc, thick disc, cold gas, and bulge/inner-disc components using three Miyamoto–Nagai discs and a Hernquist bulge, with parameters calibrated to reproduce local surface densities. Pulsar positions are transformed into Galactocentric coordinates using standard solar parameters ($R_0 = 8.20$ kpc, $z_{\odot} = 20.8$ pc), with distance uncertainties propagated by re-evaluating the field at $d \pm \sigma_d$.

The core of the analysis involves converting the measured differential LOS acceleration ($a^{\text{diff}}_{\text{LOS}}$) into the pulsar's Galactocentric acceleration projected onto the Sun–pulsar sightline ($a^{\text{obs}}_{\text{LOS}}$) by adding the Solar acceleration component ($g_{\odot} \cdot \hat{\ell}$). The authors compare these observed values against predictions from a vector RAR model using the "Simple" interpolating function (constrained by galaxy dynamics in H. Desmond 2023b) and a Newtonian baryon-only model ($\nu=1$). The goodness of fit is evaluated using a reduced $\chi^2$ statistic ($\chi^2_{\text{LOS}}/N$), accounting for timing, Solar-correction, and distance-propagated uncertainties. A critical control test involves a "Solar-only" null hypothesis where the measured differential acceleration is set to zero, isolating the contribution of the Solar acceleration term.

Key Results

• Fit Quality: For the binary sample ($N=26$), the projected vector RAR yields a reduced $\chi^2$ of 3.58, a substantial improvement over the Newtonian baryonic gravity prediction of 10.86.
• Dominance of Solar Acceleration: The "Solar-only" test (setting $a^{\text{diff}}_{\text{LOS}} = 0$) produces a reduced $\chi^2$ of 3.75. This value is nearly identical to the result obtained using the full binary sample, indicating that the current statistical power of the test is dominated by the Solar acceleration contribution rather than the pulsar-specific differential accelerations.
• Data Limitations: The scatter in the data is large, and the sampled range of $|g_{\text{bar}}|$ is limited to approximately 0.8 dex around the critical acceleration scale $a_0$. Consequently, the data cannot currently distinguish between non-radial RAR extensions or specific Galactic acceleration field theories.
• Systematic Insensitivity: Replacing the analytic baryonic potential with the full Milky Way potential from P. J. McMillan (2017) results in qualitatively similar $\chi^2$ values (3.94 for RAR vs. 10.74 for Newtonian), demonstrating that the results are robust against this specific systematic uncertainty.

Significance and Claims
The paper concludes that while pulsar timing offers a direct and unique probe of acceleration-based scaling relations outside the Galactic plane, the current binary pulsar sample is not yet sufficiently informative to test the vector RAR beyond the contribution of the Solar acceleration alone. The authors modestly assert that the current data is "dominated by the Solar acceleration," preventing a definitive test of the pulsar-specific dynamics.

The significance of this work lies in establishing the framework for using pulsar timing as a non-rotation-curve probe of the RAR. The authors identify that future progress requires more precise binary acceleration measurements, larger samples, improved distance estimates, and, crucially, sightlines where the Solar centripetal acceleration projects weakly onto the Sun–pulsar line of sight (e.g., binary pulsars at lower $|g_{\text{bar}}|$, larger $|z|$, or specific Galactic longitudes). Until such data is available, the test remains a validation of the Solar acceleration component rather than a confirmation of the RAR in the general Galactic field.