Astron. Astrophys. 342, L57-L61 (1999)
2. Analysis and results
Presently we have data for three pulsars, where a clear change from
linear to circular polarization towards high frequencies is observed
(see Fig. 5 in von Hoensbroech et al. 1998b). It is obvious from
Fig. 1 that the three objects have very different rotational periods
P and period time derivatives
. Hence they do not form an isolated
group with respect to their rotational parameters. Since the change
from linear to circular polarization is superposed by general
depolarization effects, which affect both types of polarization
likewise, the degrees of polarization cannot be compared directly with
the theory. Therefore we choose the ratio
![[EQUATION]](img17.gif)
between the degrees of linear ( )
and the circular ( ) polarization as
an depolarization independent parameter. R and its statistical
error can easily be calculated from
the data.
![[FIGURE]](img15.gif) |
Fig. 1. Position of the three pulsars in the -diagram for which the change from linear to circular polarization has been observed. They do not form a coherent group within the pulsar sample. One of them is very young, one is rather average and the third one is a relatively old object.
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The polarization data we used for this analysis were accessed
through the online EPN-database
(http://www.mpifr-bonn.mpg.de/pulsar/data/
). The calibrated data were extracted in the EPN-format (Lorimer et
al. 1998). The degrees of polarization were calculated using the same
routine for all profiles. All relevant parameters and references are
listed in Table 1.
![[TABLE]](img23.gif)
Table 1. Polarization data and references for all three pulsars. Note: Reference-code: [1] Gould & Lyne (1997), [2] von Hoensbroech et al. (1998a), [3] Qiao et al. (1995), [4] unpublished Effelsberg data.
The theoretical functional dependence of R can be derived
from Eq. (25) in (von Hoensbroech et al. 1998b). Applying a
Taylor-expansion in inverse frequency
to the first order yields
![[EQUATION]](img25.gif)
Here is the local electron gyro
frequency at the PLR, the angle
between the propagating wave and the direction of the local magnetic
field at the PLR and the streaming
velocity of the plasma. Higher order terms can be neglected as long as
the wave frequency is different from
.
Obviously, a -frequency dependence
of R is required by the theory. A comparison of the observed
frequency dependence of R with the predicted one is therefore a
strong test for the theory. Figs. 2-4 show a comparison of the data
points and the theoretical curve (dashed line) for R.
![[FIGURE]](img51.gif) |
Fig. 2. PSR B0144+59, versus frequency. The theoretical change of R (dashed line) is compared to measured data. The horizontal dotted line corresponds to , i.e. linear and circular polarization are of equal strength (here at GHz). Parameters for theoretical line: of .
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![[FIGURE]](img66.gif) |
Fig. 3. PSR B1737-30, see caption of Fig. 2 and text for details (here at GHz). See text about the two "outriders'. Parameters for theoretical line: of .
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![[FIGURE]](img79.gif) |
Fig. 4. PSR B1913+10, see caption of Fig. 2 and text for details (here at GHz). Parameters for theoretical line:
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There are a couple of parameters which indirectly enter Eq. (2) as
scaling factors. is proportional to
the local magnetic field strength .
This value again depends on basic pulsar parameters such as the
period, its time derivative and, if known, on the inclination angle
between the rotation- and the magnetic dipole axis. Furthermore the
angle between the propagating wave
and the local magnetic field depends on the chosen field line and the
assumed emission height. For the background plasma Lorentz factor we
made the assumption . Finally we
chose the PLR at 20% of . As the
values of the PLR and the emission height (2% of
are given as fractions of
, their absolute values depend on the
period. The combination of and PLR
was chosen without restriction of generality as various other
combinations yield the same result (see Fig. 5).
![[FIGURE]](img85.gif) |
Fig. 5. Possible combinations of PLR and which yield consistent results for the prefactor in Eq. (2) which fit to the observed data of each pulsar. A variation of this factor results into a parallel displacement of the theoretical curves in Figs. 2-4. The solid line below corresponds to the assumed emission height at 2% of the as the minimum PLR.
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However, apart from the known intrinsic pulsar parameters P
and , the same set of
parameters was used for all three pulsars. Please note that these
parameters only enter Eq. (2) as scaling factors, yielding a parallel
displacement of the function. Hence they determine the frequency range
where the transition from linear to circular polarization takes place,
but not the functional dependence
.
2.1. PSR B0144+59
This pulsar is the first one in which we found the effect of
increasing circular polarization to high frequencies. Its rotational
parameters are ms and
, yielding to a weak surface magnetic
field of `only' T, an average value
for W and the characteristic age
yrs. Reasonable data in full
polarization was available between 610 MHz and 4.85 GHz.
Fig. 2 shows the measured values and the theoretical curve for the
change of R with frequency.
2.2. PSR B1737-30
PSR B1737-30 has a spin period of ms
and a period derivative of . The
resulting spin down energy loss
places it amongst the top 10% of the pulsar sample. The very low
characteristic age yrs and the very
high surface magnetic field T make
this one an extreme object. Note that in terms of the surface magnetic
field, this object is at the opposite end of the "normal" pulsar
sample compared to PSR B0144+59.
The change of R with frequency is shown in Fig. 3. Although
the two low frequency points do not fit the theoretical function, the
frequency change of R smoothly follows this function at higher
frequencies. Note that the two outrider profiles are significantly
affected by interstellar scattering which could also alter the
polarization state when emission from different pulse phases with
different polarization states are superposed (see also Sect. 2.4).
2.3. PSR B1913+10
With a spin period ms and its
temporal derivative this is an
average pulsar. This is also reflected by its parameters
W,
T and yrs.
Fig. 4 shows the measured values for R and the theoretical
function. As for PSR B1737-30 the lower frequency points are too
small, but at higher frequencies the theoretical curve is matched
perfectly. As for the previous pulsar, the two outrider profiles are
significantly scattered.
2.4. Outriders
The systematic deviation of the low frequency points is certainly a
draw back of these observations. However they can be understood
through the following argument: von Hoensbroech et al. (1998a) have
shown that the polarization properties in general are much less
systematic at low radio frequencies compared to higher ones. This
indicates that the polarization of pulsars undergo some sort of
randomization at low radio frequencies. This can be caused either
through intrinsic variations - e.g. non constant PLR at low
frequencies - or through additional propagation effects in the highly
magnetized medium close to the pulsar, which mainly affect low radio
frequencies.
© European Southern Observatory (ESO) 1999
Online publication: February 23, 1999
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