The NANOGrav 15-Year Data Set: Improved Timing Precision With VLBI Astrometric Priors

TL;DR

The paper tackles biases in pulsar timing caused by red noise absorption into astrometric fits and proposes using VLBI-derived astrometry as priors. By calibrating a frame tie between the ICRS (RFC) and the timing frame defined by DE440 and by integrating VLBI priors into a maximum-posterior timing framework, the authors demonstrate improved agreement between VLBI and timing astrometry. The maximum-posterior solutions diverge from NG15 values for some MSPs by up to about $2\sigma$, and residual analyses show $1\,\mathrm{yr}^{-1}$ and $1/(2\mathrm{yr})$ periodic power that can be absorbed when astrometric fits drift away from the maximum-posterior solution; crucially, there is no significant low-frequency absorption of red noise into the GW background band for the analyzed cases. The approach reduces parameter covariances, mitigates biases in astrometry and GW searches, and provides a path toward earlier, more robust astrometric constraints for newly discovered or noisy pulsars, with publicly available data products to enable reproducibility and broader adoption.

Abstract

Accurate pulsar astrometric estimates play an essential role in almost all high-precision pulsar timing experiments. Traditional pulsar timing techniques refine these estimates by including them as free parameters when fitting a model to observed pulse time-of-arrival measurements. However, reliable sub-milliarcsecond astrometric estimations require years of observations and, even then, power from red noise can be inadvertently absorbed into astrometric parameter fits, biasing the resulting estimations and reducing our sensitivity to red noise processes, including gravitational waves (GWs). In this work, we seek to mitigate these shortcomings by using pulsar astrometric estimates derived from Very Long Baseline Interferometry (VLBI) as priors for the timing fit. First, we calibrated a frame tie to account for the offsets between the reference frames used in VLBI and timing. Then, we used the VLBI-informed priors and timing-based likelihoods of several astrometric solutions consistent with both techniques to obtain a maximum-posterior astrometric solution. We found offsets between our results and the timing-based astrometric solutions, which, if real, would lead to absorption of spectral power at frequencies of interest for single-source GW searches. However, we do not find significant power absorption due to astrometric fitting at the low-frequency domain of the GW background.

Figures (6)

• Figure 1: Celestial sphere diagram showing the sequence of Euler rotations, $\boldsymbol{R}_z(\phi) \boldsymbol{R}_x (\theta) \boldsymbol{R}_z(\psi)$, that transform the ICRS (IC) into the timing reference system (DE). The magnitude of the Euler angles $\phi,\theta,\psi$ is exaggerated for visualization purposes; in practice, they are smaller than $10^8$ rad.
• Figure 2: PDFs of the astrometric parameters derived using VLBI (green) or timing (blue) for a selected subsample of our pulsars when referred to the same reference frame. The VLBI-derived PDFs are based on the measurements from Table \ref{['table:input_data_table']}, now converted to the dynamical Solar System reference frame by means of the frame tie in Eq. \ref{['eq:my_frame_tie']}.
• Figure 3: Parameter sampling for PSR J2145$-$0750. Panel \ref{['subfig:parallax_sampling']} shows the PDFs derived from the VLBI- (green) and timing- (blue) based parallax estimations. The vertical dashed lines correspond to a $3\sigma$ deviation from the mean value of each distribution. The sampled $\varpi_i$ values are selected from the overlap of these ranges. In panel \ref{['subfig:proper_motion_sampling']}, the side plots show the marginal distributions in $\mu_\alpha$ and $\mu_\delta$ derifved from timing, and the central color plot is the 2D joint distribution of both parameters. The solid green line represents the total proper motion derived from VLBI, and the dashed green lines on each side are its $3\sigma$ deviations; the sampled $({\mu_{\alpha}}_i , {\mu_{\delta}}_i)$ pairs are selected from this range.
• Figure 4: 2-dimensional example of prior calculation for a trial timing solution of J2145$-$0750 with $(\alpha,\varpi)=(21^\mathrm{h}45^\mathrm{m}50\fs4586,1.625~\mathrm{mas})$. The side plots show the VLBI-derived PDF of the parameter on the corresponding axis. When evaluated on the trial parameter value (dotted lines), this PDF gives the corresponding parameter prior. The total prior is given by the joint probability of these values (black cross on color map).
• Figure 5: Corner plots of posterior probability. In each subplot, the colormap displays the normalized posterior distribution (yellow: higher posterior, purple: lower posterior) as a function of one pair of astrometric parameters, after marginalizing the posteriors over the three other astrometric parameters. Grey areas correspond to regions of the parameter space that were not sampled in this work. Each bin is a trial astrometric solution. The red error bars show the NG15's timing astrometric solution.