Revisiting wideband pulsar timing measurements

TL;DR

The paper addresses the challenge of robustly extracting wideband TOA and DM measurements from frequency-resolved pulsar portraits while accurately accounting for measurement noise. It develops a Bayesian, noise-marginalized framework that analytically integrates over channel amplitudes $a_\alpha$ and noise terms $\sigma_\alpha$, yielding a marginalized likelihood $\ln \Lambda$ and a posterior $\mathfrak{p}[\varphi_0,D|P,T]$ for the wideband parameters. A fiducial frequency $\bar{\nu}_{\text{ref}}$ is introduced to decouple $\varphi_0$ and $D$, ensuring independent measurements and stable uncertainties. The method is validated on simulated portraits and applied to InPTA GMRT data for PSR J2124--3358, showing more realistic uncertainty estimates than the standard method and improving reliability for pulsar timing array analyses targeting nanohertz gravitational waves. The work provides a practical, noise-aware path toward scaling wideband timing in growing PTA datasets.

Abstract

In the wideband paradigm of pulsar timing, the time of arrival of a pulsar pulse is measured simultaneously with the corresponding dispersion measure from a frequency-resolved integrated pulse profile. We present a new method for performing wideband measurements that rigorously accounts for measurement noise. We demonstrate this method using observations of PSR J2124$-$3358 made as part of the Indian Pulsar Timing Array experiment using the upgraded Giant Metre-wave Radio Telescope, and show that our method produces more realistic measurement uncertainty estimates compared to the existing wideband measurement method.

Figures (7)

• Figure 1: The top plot shows the simulated pulse portrait based on the analytic two-peaked template given in equation \ref{['eq:templ-sim']}, also containing white noise in each frequency channel. Ten randomly selected channels have noise injections with a significantly higher amplitude, simulating RFI, and these are visible in the plot as horizontal stripes. The bottom plot shows the post-fit residuals of the portrait, which are determined by subtracting the best-fitting model from the simulated data. The residuals show only noise, indicating a successful fit.
• Figure 2: The posterior distribution obtained from the simulated portrait described in Section \ref{['sec:sim-ex']}. This analysis was done using a fiducial frequency value such that the measurement covariance between the two parameters vanishes (i.e., $\bar{\nu}_\text{ref}$), as described in Appendix \ref{['sec:nurefbar']}. The blue lines represent the injected values shifted according to the $\bar{\nu}_\text{ref}$. This corresponds to $\varphi_{0\text{;inj}}-\kappa DF\left(\nu_{\text{ref;inj}}^{2}-\bar{\nu}_{\text{ref}}^{2}\right)$ for the $\varphi_0$ measurement whereas the $D$ measurement is expected to be consistent with $D_\text{inj}$, where the label 'inj' represents the injected value. The simulated portrait and the post-fit residuals are plotted in Figure \ref{['fig:dataprof']}. The estimated parameters are consistent with the injected values up to a shift described above. The contours represent 68% and 95% credible intervals.
• Figure 3: The top plot shows the measurement correlation $\rho$ between $\varphi_0$ and $D$ as a function of $\nu_\text{ref}$. The $\bar{\nu}_\text{ref}$ value computed based on Appendix \ref{['sec:nurefbar']} is indicated using a vertical dotted line, and the corresponding correlation estimated from posterior samples is indicated using a horizontal red line. The correlation at $\bar{\nu}_\text{ref}$ is very close to zero. The bottom plot shows the determinant of the covariance matrix between $\varphi_0$ and $D$ as a function of ${\nu}_\text{ref}$. This determinant is a measure of the total measurement uncertainty, and does not show any significant variation as a function of ${\nu}_\text{ref}$ except for random scatter. The scatter seen in the two plots is due to the numerical error from using a finite number of posterior samples.
• Figure 4: DM time series for PSR J2124--3358 obtained using the standard and MLAN measurement methods. The measurements are consistent but not identical, except for a few epochs where there is a significant difference between the two methods.
• Figure 5: Comparison of TOA and DM measurement uncertainties obtained using the standard and MLAN methods. The S/N at each epoch is represented as the color of each point. The MLAN uncertainties are consistently higher than their standard method counterparts. This is most prominent in high-S/N epochs.