5 Refraction correction

Our model provides valid estimates of large-scale ionospheric gradients, i.e. gradients with scale sizes of 1000 km or more. By ray-tracing through the model ionosphere that is determined every few minutes, we can estimate the refraction that the model ionosphere would cause and predict the resulting phase shifts on the various VLA interferometer baselines. Two examples of 327 MHz phases in the A configuration are shown in Figs. 4 and 5.

Figure 4: An example of the large-scale phase corrections generated by our ionospheric modeling. The small dots are the raw phases; the solid line is the phase predicted by ray tracing through ionospheric models produced at 5 min intervals; the large dots are the phases after correction by the model predictions. These data were taken on a long N-S baseline between telescope 26 located at VLA Station N72 and telescope 14 located at N16

Figure 5: Same as Fig. 4 except that these data were taken on a long SW baseline between telescope 21 located at VLA Station W72 and telescope 14 located at N16

The predictions follow the general trends of the measured phases quite well. Therefore, we are able to correct for the effects of large-scale ionospheric structures. This may be important over longer, VLBI baselines, where the effects of large-scale structures strongly dominate those of smaller-scale structures. However, over VLA baselines, the measured phases display many short period variations, caused by unmodeled small-scale structures, that are of similar magnitude to the slower variations caused by large-scale structures. When the measured phases are corrected by the model predictions, the phase fluctuations are appreciably decreased, but the correction is far from being perfect. The standard deviations of the corrected phases are 20 to 50% lower than those of the original phases. This rather modest reduction in phase fluctuations corresponds to a reduction in phase noise power by a factor of 1.5 to 4.

Correction of the small-scale phase fluctuations was attempted by measuring the phase gradients along each arm of the VLA and applying the appropriate corrections. Previous studies (Jacobson & Erickson 1992) have shown that the 327 MHz phase gradients along each arm of the array are very nearly linear, so it should be possible to estimate the phase at each VLA telescope by interpolation between phase-TEC measurements at the ends of the arms. We recognized that the principal problem in making any correction would be caused by the angular separation between the source under observation and any of the GPS satellites. To alleviate this problem and to determine the angular separation over which the correction would remain useful, we choose an observation in which the source was nearly aligned with a GPS satellite (see Fig. 6).

Figure 6: A horizon plot showing the tracks of the various satellites in the sky along with the track of the radio source for which the corrections in Figs. 7 and 8 were made. North is at the top and the circles are at 0$^\circ$, 30$^\circ$, and 60$^\circ$ elevation. The satellite PRN's are given at the ends of each track

Figure 7: The measured and predicted phases for a long SE-arm baseline are shown in the top panel. The dots are the measured phases; the solid line is the prediction. The vertical line represents the point of closest approach between 3C 461 and PRN 27. The middle panel shows the angular separations in degrees (dots) and the linear separations between the satellite and radio source ionospheric puncture points in units of 10 km (dashed line). The bottom panel gives the position angles of the satellite-to-source lines

When making a correction by means of a simple interpolation of the phase gradients, we find, as illustrated in the middle panels of Figs. 7 and 8, that the correction is good when the source and satellite lie within the same isoplanatic patch, i.e. within about 4$^\circ$ of each other. For larger separations the correction, as illustrated in the upper panels of Figs. 7 and 8, quickly becomes useless.

Figure 8: The same as Fig. 7 but for a long NS-arm

The lines-of-sight to the satellite being used for correction from the four receivers puncture the ionosphere at four points in the vicinity of the source line-of-sight. The data at these four points can be fit with a model that has not only a linear component but a parabolic component as well, and it was hoped that this model would be valid over larger separations between the source and satellite. We attempted to fit the data with such a model and to use this model to predict the observed phases. However, we found that only four data points are not sufficient to accurately define the parabolic component and that results obtained from these more sophisticated models were no better than those obtained by simple, linear interpolation. A network of GPS receivers spread over a large area would be required to provide many more puncture points and adequately characterize the relevant ionospheric structures in the general direction of the source. We could then hope to extend the corrections over a larger fraction of the sky.