The proximity of this system means that the orbital motion of the Earth changes the apparent inclination angle i of the pulsar orbit on the sky, an effect known as the annual-orbital parallax [76]. This results in a periodic change of the projected semi-major axis x of the pulsar's orbit, written as
where
is the time-dependent vector from the centre of the Earth to the
SSB, and
is a vector on the plane of the sky perpendicular to the line of
nodes. A second contribution to the observed
i
and hence
x
comes from the pulsar system's transverse motion in the plane of
the sky [77]:
where
is the proper motion vector. By including both these effects in
the model of the pulse arrival times, both the inclination angle
i
and the longitude of the ascending node
can be determined [139
]. As
is equivalent to the shape of the Shapiro delay in GR (PK
parameter
s), the effect of the Shapiro delay on the timing residuals can
then easily be computed for a range of possible companion masses
(equivalent to the PK parameter
r
in GR). The variations in the timing residuals are well
explained by a companion mass of
(Figure
11). The measured value of
, together with
i, also provide an estimate of the companion mass,
, which is consistent with the Shapiro-delay value.
While this result does not include a true self-consistency check in the manner of the double-neutron-star tests, it is nevertheless important, as it represents the only case in which an independent, purely geometric determination of the inclination angle of a binary orbit predicts the shape of the Shapiro delay. It can thus be considered to provide an independent test of the predictions of GR.
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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 |