Combining the second data release of the European Pulsar Timing Array with low-frequency pulsar data

TL;DR

The paper tackles improving pulsar timing array sensitivity to the stochastic gravitational-wave background by combining very low-frequency data from LOFAR and NenuFAR with the DR2new+ dataset to form DR2low, extending frequency coverage to 30-2500 MHz over ~11 years for 12 pulsars. A Bayesian noise analysis using Libstempo and Enterprise models red noise, dispersion-measure variations, and CN4, plus a solar-wind component, and uses Bayes factors to select the favored combination of noise components per pulsar. DR2low tightens DM variation constraints and reveals CN4 in eight pulsars while red noise is required in ten, with several chromatic indices consistent with a thin-screen expectation of about 4, though solar-wind effects bias a few cases. This work demonstrates the value of very low-frequency data for disentangling DM variations from red noise, informing the IPTA DR3 plan, and has implications for GWB detection and solar wind modelling in PTA analyses.

Abstract

Low-frequency radio data improve the sensitivity of pulsar timing arrays (PTAs) to propagation effects such as dispersion measure (DM) variations, enabling better noise characterization essential for detecting the stochastic gravitational wave background (GWB). We combined LOFAR (100-200 MHz) and NenuFAR (30-90 MHz) observations with the recent European and Indian PTA release (DR2new+) into a new dataset, DR2low, spanning ~11 years for 12 pulsars. DR2low allows updated noise models, increasing PTA sensitivity to the GWB. Using Libstempo and Enterprise, we applied standard noise models including red noise (RN) and time-variable DM (DMv) as power laws, and performed Bayesian model selection over RN, DMv, and an additional chromatic noise term (CN4). Compared to DR2new+, DR2low improves DM constraints and separates DM and RN contributions. We found that the RN is required in the final model for 10 out of 12 pulsars, compared to only 5 in the DR2new+ dataset. The improved sensitivity to plasma effects provided by DR2low also favors the identification of significant CN4 in eight pulsars, while none showed such evidence in DR2new+. The analysis also reveals unmodelled solar wind effects, particularly near solar conjunction, with residual delays absorbed into the DM component, highlighting the importance of accurately modelling the solar wind in PTA datasets.

Figures (9)

• Figure 1: Mollweide sky projection of the 25 DR2new+ pulsars (blue stars) in equatorial coordinates. The red circles and green squares display sources observed by respectively LOFAR and NenuFAR. The names of the pulsars studied in this work are written next to the position. The orange line (and area) are representing the Sun's position (± 20 degrees angle) along the year, denoting the influence zone of the solar wind.
• Figure 2: Spectral index vs. amplitude posterior distributions of the power-law PSD for DMv (left) and RN (right) obtained for 12 pulsars from DR2low (blue) and DR2new+ (orange) using the standard noise models. The green vertical lines show the predicted spectral index from a Kolmogorov turbulence in the IISM for DMv (left), and from circular and GW-driven SMBHBs (right). The black crosses display the $99.7\%$ credible intervals of posterior distributions obtained with NANOGrav-15yr and PPTA DR3, displaying the principal directions.
• Figure 3: Posterior distributions of spectral indices ($\gamma$) and amplitudes ($A$) of DMv and RN for PSRs J1024$-$0719 (top) and J1738+0333 (bottom) obtained with DR2low (blue) and DR2new+ (red), using the standard noise models.
• Figure 4: Posterior distribution of the chromatic index (blue violins) and their $99.7\%$ credible intervals (errorbars) obtained for the pulsars that favor the presence of CN$_4$ in their noise model. Here we use the favored noise model and replace the CN$_4$ noise component by a Gaussian process power-law PSD signal with the same number of frequency bins, but a free chromatic index, with a prior defined as $\mathcal{U}(0,10)$. The black horizontal line displays the fixed value for the case of CN$_4$.
• Figure 5: Free spectra for DMv (referred to 1.4GHz) and RN for PSR J0030+0451 (top) and PSR J1022+1001 (bottom). Each violin represents the posterior distribution of the RMS amplitude in a given Fourier bin. The blue violins correspond to the full DR2low dataset; the green and orange violins show the results obtained after applying solar angle cuts of 45° and 75°, respectively. The vertical dashed lines indicate the harmonics of the $1\mathrm{yr^{-1}}$ frequency, which is representative of the SW effect. The number of Fourier bins displayed matches that of the preferred noise model listed in Table \ref{['tab:favmod']}.