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

Context. Low radio frequency data are highly valuable for enhancing the sensitivity of pulsar timing arrays (PTAs) to propagation effects, such as dispersion measure (DM) variations. These low-frequency observations are particularly sensitive to DM fluctuations and can therefore significantly improve noise characterization in PTA datasets, which is essential for detecting the stochastic gravitational wave background (GWB). Aims. For this work we incorporated for the first time low-frequency observations from LOFAR (100 − 200 MHz) and NenuFAR (30 − 90 MHz) into a PTA context by combining them with the most recent data release from the European and Indian PTAs (in particular, with the subsample labeled <ns0:monospace>DR2new+</ns0:monospace>, which includes only data from the new backends). This new combined dataset, labeled <ns0:monospace>DR2low</ns0:monospace>, consists of 12 pulsars observed over a time span of ∼11 years, with radio frequencies spanning the range 30 − 2500 MHz. The expanded frequency coverage of <ns0:monospace>DR2low</ns0:monospace> enables us to update and refine the noise models of <ns0:monospace>DR2new+</ns0:monospace>, and this is crucial in order to increase the PTA sensitivity when searching for the stochastic gravitational wave background, which is the primary goal of PTA observations. This work is a milestone in the integration of low-frequency data into the upcoming third data release of the International PTA, which is posed to achieve the 5σ detection of the GWB. Methods. We used the pulsar timing software packages L<ns0:sc>IBSTEMPO</ns0:sc> and E<ns0:sc>NTERPRISE</ns0:sc> to perform a noise analysis of <ns0:monospace>DR2low</ns0:monospace>. At first, we applied a <ns0:monospace>standard noise model</ns0:monospace> including red noise (RN) and time-variable dispersion measure (DMv) as power laws, with Fourier components up to 30 and 100 frequencies, respectively. Next, we performed a fully Bayesian model selection to identify the favored noise model for each pulsar and compute the Bayes factors across all combinations of RN, DMv, and a noise term with a chromatic index of 4 (CN4). Finally, we carried out a detailed analysis on the choice of the chromatic index for CN4 and the contribution of the solar wind. Results. The comparison between <ns0:monospace>DR2low</ns0:monospace> and <ns0:monospace>DR2new+</ns0:monospace> using the <ns0:monospace>standard noise model</ns0:monospace> highlights the benefits of including low-frequency data. In particular, the additional frequency coverage improves the constraints on the DM variations and helps disentangle the DM and RN noise components in most pulsars. Through a Bayesian model selection, we found that the RN is required in the final model for 10 out of 12 pulsars, compared to only 5 in the <ns0:monospace>DR2new+</ns0:monospace> dataset. The improved sensitivity to plasma effects provided by <ns0:monospace>DR2low</ns0:monospace> also favors the identification of significant CN4 in eight pulsars, while none showed such evidence in <ns0:monospace>DR2new+</ns0:monospace>. The chromatic index of this process is consistent with four of the five pulsars, while two (PSRs J0030+0451 and J1022+1001) show significant deviations from such a value. We attribute this discrepancy to unmodeled contributions from the solar wind, especially because of the high DM sensitivity of LOFAR and NenuFAR and the high observing cadence provided by these datasets near solar conjunction. A dedicated analysis confirms that the current solar wind model fails to fully capture the observed delay, and residual power is absorbed into the DM component of the model.