where the vector
is aligned with the orbital angular momentum. Its magnitude is
given by
where
, as in Section
4.1
. This predicted rate of precession is small; the three systems
with the highest
values are:
Evidence for long-term profile shape changes is in fact seen
in PSRs B1913+16 and B1534+12. For PSR B1913+16,
profile shape changes were first reported in the 1980s [141], with a clear change in the relative heights of the two profile
peaks over several years (Figure
12). No similar changes were found in the polarization of the
pulsar [31]. Interestingly, although a simple picture of a cone-shaped beam
might lead to an expectation of a change in the
separation
of the peaks with time, no evidence for this was seen until the
late 1990s, at the Effelsberg 100-m telescope [80], by which point the two peaks had begun to move closer together
at a rather fast rate. Kramer [80] used this changing peak separation, along with the predicted
precession rate and a simple conal model of the pulse beam, to
estimate a spin-orbit misalignment angle of about
and to predict that the pulsar will disappear from view in about
2025 (see Figure
13), in good agreement with an earlier prediction by Istomin [64] made before the peak separation began to change. Recent results
from Arecibo [143] confirm the gist of Kramer's results, with a misalignment angle
of about
. Both sets of authors find there are four degenerate solutions
that can fit the profile separation data; two can be discarded as
they predict an unreasonably large misalignment angle of
[13], and a third is eliminated because it predicts the wrong
direction of the position angle swing under the Rotating Vector
Model [111]. The main area of dispute is the actual shape of the emission
region; while Weisberg and Taylor find an hourglass-shaped beam
(see Figure
14), Kramer maintains that a nearly circular cone plus an offset
core is adequate (see Figure
15). In any event, it is clear that the interpretation of the
profile changes requires some kind of model of the beam shape.
Kramer [81
,
82] lets the rate of precession vary as another free parameter in
the pulse-shape fit, and finds a value of
. This is consistent with the GR prediction but still depends on
the beam-shape model and is therefore not a true test of the
precession rate.
PSR B1534+12, despite the disadvantages of a more recent discovery and a much longer precession period, also provides clear evidence of long-term profile shape changes. These were first noticed at 1400 MHz by Arzoumanian [5, 8] and have become more obvious at this frequency and at 430 MHz in the post-upgrade period at Arecibo [124]. The principal effect is a change in the low-level emission near to the main pulse (Figure 16), though related changes in polarization are now also seen. As this pulsar shows polarized emission through most of its pulse period, it should be possible to form a better picture of the overall geometry than for PSR B1913+16; this may make it easier to derive an accurate model of the pulse beam shape.
As for other tests of GR, the pulsar-white-dwarf binary
PSR J1141-6545 promises interesting results. As noted by the
discoverers [72], the region of sky containing this pulsar had been observed at
the same frequency in an earlier survey [70], but the pulsar was not seen, even though it is now very
strong. It is possible that interference corrupted that original
survey pointing, or that a software error prevented its
detection, but it is also plausible that the observed pulsar beam
is evolving so rapidly that the visible beam precessed into view
during the 1990s. Clearly, careful monitoring of this pulsar's
profile is in order.
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Testing General Relativity with Pulsar Timing
Ingrid H. Stairs http://www.livingreviews.org/lrr-2003-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |