Measuring scattering variations in pulsar timing observations: A test of the fidelity of current methods

TL;DR

This study assesses the fidelity of current IISM noise models used in pulsar timing arrays by combining large-scale simulations of refractive scattering with an analysis of the MeerKAT PTA 4.5-year data. It demonstrates that anisotropy can cause substantial frequency decorrelation of scattering delays and that DM–scattering fitting artefacts can generate spurious anticorrelations and inflated chromatic indices. Through injection tests with Gaussian-process-based and non-Gaussian centroid signals, the work shows that misspecification can bias measurements of scattering delays, underscoring the need for decorrelation-enabled and non-Gaussian scattering models for robust IISM inferences. The findings have direct implications for high-precision PTA experiments and future facilities (e.g., SKA), where accurate IISM modelling will be critical for gravitational-wave detection and IISM physics.

Abstract

The turbulent nature of the ionised interstellar medium (IISM) causes dispersion measure (DM) and scattering variations in pulsar timing measurements. To improve precision of gravitational wave measurements, pulsar timing array (PTA) collaborations have begun the use of sophisticated and intricate noise modelling techniques such as modelling stochastic variations induced by the turbulent IISM and quasi-deterministic processes attributed to discrete structures. However, the reliability of these techniques has not been studied in detail, and it is unclear whether the recovered processes are physical or if they are impacted by misspecification. In this work, we present an analysis to test the efficacy of IISM noise models based on the data from the MeerKAT Pulsar Timing Array (MPTA) 4.5-year data release. We first performed multi-frequency, long-length (500 refractive length scale) simulations of multipath propagation in the IISM to study the properties of scattering variations under a variety of scattering conditions. The results of our simulations show the possibility of significant radio-frequency decorrelation in the scattering variations, particularly for the anisotropic scattering medium. Our analysis of the observed DM and scattering variations using the MPTA 4.5-year data set shows that there can be apparent anticorrelations between DM and scattering variations, which we attribute to the model fitting methods. We also report a possibility that plasma underdensities might exist along the sight lines of PSR J1431$-$5740 and PSR J1802$-$2124. Finally, using simulations, we show that the IISM noise models can result in the apparent measurement of strong frequency dependence of scattering variations observed in the MPTA data set. Our analysis shows that improvements in the IISM noise modelling techniques are necessary to accurately measure the IISM properties.

Figures (9)

• Figure 1: Dynamic spectra for an isotropic scattering screen. The top panel shows the dynamic spectrum for the entire simulation spanning a length of $500\,S_{\rm ref}$ in the $x$ direction. The bottom panel shows the zoom in of the top panel, spanning a length of $1\,S_{\rm ref}$. The tilting of the structure seen in the bottom panel is the result of the presence of refractive phase gradients in the screen. The right panel shows the flux density in arbitrary units as defined in equation \ref{['eq:flux']}.
• Figure 2: Simulations of isotropic scattering. The strength of scattering in these simulations is $m_b^2 = 20$. Panel a: The bottom plot shows the DM variation from one instance of the isotropic phase screen. Equation \ref{['eqn:DM_from_phases']} was used to obtain DM values from a slice through the simulated phase screen at $L_{y}/2$ along the $x$ direction. The middle plot shows the measured centroid variation (scattering noise) and the top plot shows the associated flux density variation. Panel b: The main plot shows the average power spectrum of the DM variation and centroid variation signal obtained from ten instances of the phase screens. The best-fitting power law to the averaged power spectrum is given in the bottom left of the figure. The shaded region around each plot represents the scatter due to the stochastic nature of the phase variations. The dashed line in light brown shows a power law fit to DM variations with a spectral steepness of $\gamma=8/3$ as expected from a Kolmogorov medium. The inset shows the relationship between the centroid variation and the square of the gradient of the DM variation. Panel C: The plot shows the correlation between the centroid variations across the radio frequencies with respect to the center frequency of 1400 MHz. Different colors show the measurements obtained from ten instances of the phase screens Panel D: The plots show the DM, centroid and flux density variations when a Gaussian dip was added at the middle of the phase screen in order to simulate a region of under-density in the ISM. The shaded blue region represents one standard deviation of the Gaussian dip.
• Figure 3: Averaged power spectra of chromatic processes for different levels and types of anisotropy. The best-fitting power law to the averaged power spectra in each case is given in the bottom left of each subplot. The shaded regions represent the scatter due to the stochastic nature of the phases. The strength of scattering is these simulations is $m_b^2 = 20$. The inner panel of each figure shows the scatter plot of the centroid variation with the square of the gradient of the DM variation.
• Figure 4: Correlation coefficient between the centroid variations measured at different frequency channels with respect to the center frequency ($1400$ MHz). The strength of scattering in these simulations is $m_b^2 = 20$. A significant decorrelation can be seen for orientation angles greater than $\psi = 45^\circ$.
• Figure 5: Time series of noise processes and flux densities for a sample of MPTA pulsars. The top panels of all plots show the band-averaged flux density variations. The corresponding time series of different noise processes are shown in the bottom panels. These are obtained from the noise analysis of MPTA data set and are referenced to $\rm 1400\,MHz$. The yellow shaded region around the DM-epoch time series represents the error region based on the DM uncertainties reported by tempo2. The blue shaded region in the plots for PSR J1431$-$5740 and PSR J1802$-$2124 represents the underdensity in the IISM.