where SNR
is the threshold signal-to-noise ratio,
and
are the receiver and sky noise temperatures,
G
is the gain of the antenna,
is the observing bandwidth,
is the integration time,
W
is the detected pulse width and
P
is the pulse period.
The smearing across the individual frequency channels,
however, still remains and becomes significant at high
dispersions when searching for short-period pulsars. Multi-path
scattering results in a one-sided broadening due to the delay in
arrival times which scales roughly as
, which can not be removed by instrumental means. A simple
scattering model is shown in Fig.
13
in which the scattering electrons are assumed to lie in a thin
screen between the pulsar and the observer [210].
Dispersion and scattering are most severe for distant pulsars
in the inner Galaxy where the number of free electrons along the
line of sight becomes large. The strong frequency dependence of
both effects means that they are considerably less of a problem
for surveys at observing frequencies
[56,
109
] compared to the usual 400 MHz search frequency. An added
bonus for such observations is the reduction in
, since the spectral index of the non-thermal Galactic emission
is about -2.8 [126]. Pulsars themselves have steep radio spectra. Typical spectral
indices are -1.6 [136], so that flux densities are roughly an order of magnitude lower
at 1400 MHz compared to 400 MHz. Fortunately, this can
usually be compensated for by the use of larger receiver
bandwidths at higher radio frequencies. For example, the 1370-MHz
system at Parkes has a bandwidth of 288 MHz [147
] compared to the 430-MHz system, where 32 MHz is
available [160
].
As an example of this effect, as seen in the time domain,
Fig.
14
shows a 22.5-min search mode observation of Hulse & Taylor's
famous binary pulsar B1913+16 [102,
239
,
240
]. Although this observation covers only about 5% of the orbit
(7.75 hr), the effects of the Doppler smearing on the pulse
signal are very apparent. While the standard search code (seeking
constant periodicity) nominally detects the pulsar with a
signal-to-noise ratio of 9.5 for this observation, it is clear
that the Doppler shifting of the pulse period seen in the
individual sub-integrations results in a significant reduction in
signal-to-noise.
It is clearly desirable to employ a technique to recover the
loss in sensitivity due to Doppler smearing. One such technique,
the so-called ``acceleration search'' [168], assumes the pulsar has a constant acceleration during the
integration. Each time series can then be re-sampled to refer it
to the frame of an inertial observer using the Doppler formula to
relate a time interval
in the pulsar frame to that in the observed frame at time
t, as
. Searching over a range of accelerations is desirable to find
the time series for which the trial acceleration most closely
matches the true value. In the ideal case, a time series is
produced with a signal of constant period for which full
sensitivity is recovered (see right panel of Fig.
14). Anderson et al. [5
] used this technique to find PSR B2127+11C, a double neutron
star binary in M15 which has parameters similar to B1913+16.
Camilo et al. [47
] have recently applied the same technique to 47 Tucanae to
discover 9 binary pulsars, including one in a 96-min orbit around
a low-mass (
) companion. This is currently the shortest binary period for any
known radio pulsar.
For the shortest orbital periods, the assumption of a constant
acceleration during the observation clearly breaks down. Ransom
et al. [199] have developed a particularly efficient algorithm for finding
binaries whose orbits are so short that many orbits can take
place during an integration. This phase modulation technique
exploits the fact that the pulses are modulated by the orbit to
create a family of periodic sidebands around the nominal spin
period of the pulsar. This technique has already been used to
discover a 1.7-hr binary pulsar in NGC 6544 [199
]. The existence of these short-period radio pulsar binaries, as
well as the 11-min X-ray binary X1820-303 in NGC 6624 [226], implies that there must be many more short-period binaries
containing radio or X-ray pulsars in globular clusters that are
waiting to be discovered by more sensitive searches.
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Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer http://www.livingreviews.org/lrr-2001-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |