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

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). In this work, we incorporate for the first time low-frequency observations from LOFAR $(100-200\,\mathrm{MHz})$ and NenuFAR $(30-90\,\mathrm{MHz})$ 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 DR2new+, which includes only data from the new backends). This new combined dataset, labeled DR2low, consists of 12 pulsars observed over a time span of $\sim$11 years, with radio frequencies spanning the range $30-2500\,\mathrm{MHz}$. The expanded frequency coverage of DR2low enables us to update and refine the noise models of DR2new+, and this is crucial to increase the PTA sensitivity in 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, that is posed to achieve the 5$\sigma$ detection of the GWB. We use the pulsar timing software packages Libstempo and Enterprise to perform a noise analysis of DR2low. At first, we apply a standard noise model including red noise (RN) and time-variable dispersion measure (DMv) as powerlaws, with Fourier components up to 30 and 100 frequencies respectively. Secondly, we perform a fully-Bayesian model selection to identify the favored noise model for each pulsar and compute Bayes factors across all combinations of RN, DMv, and a noise term with a chromatic index of 4 (CN$_4$). Lastly, we carry out a detailed analysis on the choice of the chromatic index for CN$_4$ and the contribution of the solar wind. The comparison between DR2low and DR2new+ using the standard noise model highlights the benefits of including low-frequency data. In particular, the additional frequency coverage improves the constraints on the DM variations and helps to disentangle the DM and RN noise components in most pulsars. Through a Bayesian model selection, we find that the RN is required in the final model for ten out of twelve pulsars, compared to only five in the DR2new+ dataset. The improved sensitivity to plasma effects provided by DR2low also favors the identification of significant CN$_4$ in eight pulsars, while none showed such evidence in DR2new+. The chromatic index of this process is consistent with 4 in 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.