Dispersive delays due to the Solar wind introduce excess noise in high-precision pulsar timing experiments, and must be removed in order to achieve the accuracy needed to detect, e.g., low-frequency gravitational waves. In current pulsar timing experiments, this delay is usually removed by approximating the electron density distribution in the Solar wind either as spherically symmetric, or with a two-phase model that describes the contributions from both high- and low-speed phases of the Solar wind. However, no dataset has previously been available to test the performance and limitations of these models over extended timescales and with sufficient sensitivity. Here we present the results of such a test with an optimal dataset of observations of pulsar J0034-0534, taken with the German stations of LOFAR. We conclude that the spherical approximation performs systematically better than the two-phase model at almost all angular distances, with a residual root-mean-square (rms) given by the two-phase model being up to 28% larger than the result obtained with the spherical approximation. Nevertheless, the spherical approximation remains insufficiently accurate in modelling the Solar-wind delay (especially within 20 degrees of angular distance from the Sun), as it leaves timing residuals with rms values that reach the equivalent of 0.3 microseconds at 1400 MHz. This is because a spherical model ignores the large daily variations in electron density observed in the Solar wind. In the short term, broadband observations or simultaneous observations at low frequencies are the most promising way forward to correct for Solar-wind induced delay variations.
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