4. Comparison with the standard method
The standard method for the measurement of consists in the determination of the direction for the plane of polarization at a certain pulse longitude at two or a few different frequencies, and consequently obtain RM. From other measurements the Dispersion Measure DM is obtained, and from the ratio of RM and DM the value of is computed (e.g. Hamilton & Lyne 1987). The errors in measured with the standard method are not smaller than 5% in the vast majority of cases (e.g. Hamilton & Lyne 1987) with some of the exceptions being the Crab pulsar, 1.2%, and the Vela pulsar, 0.16%. In the standard method, the measurement of the polarization angle at two or three frequencies lends itself to ambiguous values of RM due to possible additional rotations by between the observing frequencies. In principle the ambiguities could be resolved by observing at three carefully chosen frequencies, however, errors in the measurements require least-square fittings and computations to choose the right RM, which sometimes even with this approach will remain indeterminate (e.g. Rand & Lyne 1994). There are no ambiguities in the absolute value of (and resulting RM) we measure, since we observe the rotation of the electric vector continuously throughout the bandwidth. Although the sign of is not determined in our method, the ionospheric correction may provide it.
Contrary to our method, in the classical one a careful selection of the pulse longitude range over which the electric vector angle is measured has to be done, otherwise the swing of the polarization angle with pulse longitude may introduce large errors.
When observing in the classical method the rotation of the electric vector in the frequency domain, a sine appears whose frequency is variable and function of the receiver frequency, as can be seen from Eq. (2). Fitting to the frequency-modulated sine to obtain implies fitting for the DM as well, a disadvantage when compared to our method.
As we see from Table 2 the accuracy in the determination of RM with our method is substantially better than that of previous measurements, in most cases by more than an order of magnitude. We have chosen to compare RM values because they are the primary (directly measured) values for the classical measurement methods, however, they are secondary (resulting from two independent measurements) values for our method and include the error in the DM measurement, which we obtain from tables. Even so, our method has substantially smaller RM errors.
The increase in accuracy in measuring the physically important with our method is due to two reasons: first to the least squares fitting procedure to a simple sine, where the direction of the plane of polarization is determined at many frequencies simultaneously vs. the standard measurements where it is determined at two or three frequencies only. The second reason is that the primary parameter determined here is , and has the smallest errors (being measured directly), and not RM, which is determined with the help of other DM measurements and includes the errors of both DM and . This is a consequence of the new method, where the contributions of DM cancel in the measurement of . By contrast, in the standard method the primary measured parameter is RM, and is obtained with the help of DM values measured separately, and includes the errors of both RM and DM.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998