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*Astron. Astrophys. 321, 305-310 (1997)*
## 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
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