  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.
