The double neutron star PSR J1946+2052 I. Masses and tests of general relativity

TL;DR

PSR J1946+2052 provides a stringent GR test in a double neutron star with a very short orbital period. By combining seven years of timing from Arecibo, GBT, and FAST and modeling DM variations and relativistic spin precession, the authors extract five PK parameters using both theory-independent and GR-based timing models, yielding precise masses ($M\approx2.53186\,M_{\odot}$, $m_p\approx1.284\,M_{\odot}$, $m_c\approx1.248\,M_{\odot}$) and three GR tests. The intrinsic orbital decay matches GR to within $1.00005(91)$ of the prediction, and Shapiro-delay measurements further confirm GR with orthometric parameters $h_3$ and $\varsigma$ consistent with GR; higher-order effects (2PN and LT) significantly affect the total mass, underscoring the need to model them for accurate inferences. The results strengthen GR in the strong-field regime and highlight the potential to measure the pulsar’s moment of inertia with future distance determinations, advancing neutron-star equation-of-state constraints and tests of gravity.

Abstract

We conducted high-precision timing of PSR J1946+2052 to determine the masses of the two neutron stars in the system, test general relativity (GR) and assessed the system's potential for future measurement of the moment of inertia of the pulsar. We analysed seven years of timing data from the Arecibo 305-m radio telescope, the Green Bank Telescope (GBT), and the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The data processing accounted for dispersion measure variations and relativistic spin precession-induced profile evolution. We employed both DDFWHE and DDGR binary models to measure the spin parameters, kinematic parameters and orbital parameters. The timing campaign has resulted in the precise measurement of five post-Keplerian parameters, which yield very precise masses for the system and three tests of general relativity. One of these is the second most precise test of the radiative properties of gravity to date: the intrinsic orbital decay, $\dot{P}_{\rm b,int}=-1.8288(16)\times10^{-12}\rm\,s\,s^{-1}$, represents $1.00005(91)$ of the GR prediction, indicating that the theory has passed this stringent test. The other two tests, of the Shapiro delay parameters, have precisions of 6\% and 5\% respectively; this is caused by the moderate orbital inclination of the system, $\sim 74^{\circ}$; the measurements of the Shapiro delay parameters also agree with the GR predictions. Additionally, we analysed the higher-order contributions of $\dotω$, including the Lense-Thirring contribution. Both the second post-Newtonian and the Lense-Thirring contributions are larger than the current uncertainty of $\dotω$ ($δ\dotω=4\times10^{-4}\,\rm deg\,yr^{-1}$), leading to the higher-order correction for the total mass.

Figures (12)

• Figure 1: The frequency-averaged template we used to fit ToAs and some examples of the observed pulse profile (Stokes I) are displayed in red and black solid lines, respectively. We generated the template with the pulse profile of 2019-03-29 and aligned each profile with the centre of the two Gaussian functions that we used to fit the pulse, indicated by the blue dashed lines. The less severe profile evolution in the main pulse can be seen in this figure compared to that in the interpulse, which makes it reasonable to fit ToAs only with the main pulse. One can also notice that the separation between the main pulse and the interpulse is increasing over time.
• Figure 2: ToA offsets derived from the standard template of the first observation and the integrated pulse profile are displayed in blue points. The pulse width (the unit is the same as ToA offset) of each integrated pulse profile is plotted in red points. The correlation between the ToA offsets and pulse widths indicates the strong influence introduced by the profile evolution on measuring the ToAs. The blue solid line is the linear fit between MJD and ToA offsets, which is used to correct ToAs.
• Figure 3: DM variations, derived from the DMX model with a time bin of 1 day, are displayed in this figure. Panels (a) and (b) represent the DM variation before and after the DM correction, respectively. DM measurements from Arecibo and GBT are represented by black points, and those from FAST are represented by red points. The red dashed line indicates the final measurement of the DM, which is 93.9281$\,\rm pc\, cm^{-3}$. We display the 10-order DM derivative fit in panel (b) with the blue dashed line.
• Figure 4: The $\chi^2$ and reduced $\chi^2$ with different numbers of DM derivatives are shown in black solid circles and red solid stars, respectively. The 10-order DM derivative fit generates the lowest $\chi^2$ and reduced $\chi^2$. Using a higher order DM derivative will overfit, indicated by the larger $\chi^2$ and reduced $\chi^2$ after 10 DM derivatives.
• Figure 5: Residuals obtained using the DDFWHE timing solution in Table \ref{['tab:timsol']}. The residuals in blue, orange, green and red are derived from L-band/PUPPI data, P-band/PUPPI data, single GBT observation and FAST data. Top: residuals as a function of time. Bottom: residuals as a function of orbital phase. The post-fit residuals' root-mean-square (RMS) is consistent with the ToA uncertainties, and the RMS of the residuals from Arecibo L-band, Arecibo P-band, GBT and FAST are 66.088$\,\upmu \rm s$, 87.709$\,\upmu \rm s$, 138.936$\,\upmu \rm s$ and 13.581$\,\upmu \rm s$, respectively. No unmodeled trends are seen in the ToA residuals, indicating that, within measurement uncertainty, the DDFWHE timing solution provides an adequate description of the timing of the system.