The discovery of pulsars three decades ago sparked the beginning of investigations and breakthroughs in an extraordinarily wide field of physics and astronomy. Measurements of the time of arrival of the pulses and pulse characteristics themselves have allowed a deeper understanding of topics ranging from condensed matter with densities of about 1014 g-cm-3 and the extreme physical conditions in the environment of neutron stars, to the evolution of binary systems and mass transfer within them, supernova remnants, and the properties and characteristics of the interstellar medium. Observations of pulsars proved for the first time the existence of planets outside the solar system (Wolszczan and Frail 1992) and have demonstrated the existence of gravitational waves (Hulse and Taylor, 1975). Pulsars can be used, through a combination of accurate pulse timing and VLBI, to tie the earth-orbit oriented solar system reference frame to the quasi-inertial earth-spin oriented extragalactic reference frame (Bartel et al. 1996) and to allow, in the future, more accurate navigation of interplanetary spacecraft. As cosmological clocks they can rival in their long-term stability cesium clocks on earth. Finally pulsars are used in tests of general relativity and in searches for the cosmological background of gravity waves predicted as a remnant from the early universe. Nobel prizes have twice been awarded to pulsar researchers, to A. Hewish in 1974, and to J. Taylor and R. Hulse in 1993. Pulsar research will certainly remain one of the most exciting and productive scientific areas for years to come. The SKA has the sensitivity to revolutionize the field by discovering many thousands of pulsars and making some of the most precise measurements possible in physics to constrain fundamental theories of gravitation, cosmology and nuclear matter.
From the density distributions of pulsars in luminosity, L, distance
from the galactic plane, and radial distance from the galactic center,
it is estimated that the total number of active pulsars is (
)
for L > 0.3 mJy-kpc2 of which the radio beams of
about 20% sweep past the earth. That gives a total of about 70,000
observable pulsars in the Galaxy with L > 0.3 mJy-kpc2 which
represents the luminosity limit of the most sensitive surveys with the
(sky-limited) Arecibo telescope. The total number of pulsars detected so
far, with L > 0.3 mJy-kpc2 is about 1000. Of these only about 30 are
millisecond pulsars with periods from 1.6 to 20 milliseconds and a
median value of a few milliseconds. Note
that, due to sensitivity limitations, only about 4% of the detected
pulsars have luminosities between 0.3 and 3 mJy-kpc2, although they
represent the vast majority, 80% to 90%, of the galactic distribution.
Most pulsars have been discovered in large scale surveys performed by single dishes such as the Arecibo 305m, Parkes 64m and Jodrell Bank 76m telescopes. There are two exciting ways that SKA could be used to discover pulsars in large numbers. The first is in targeted searches of locations known to be rich in pulsars, such as globular clusters, the Magellanic Clouds and the Andromeda Galaxy. In radio images of these regions with good spectral and spatial resolution, pulsars will manifest themselves as steep-spectrum unresolved point sources. By using the SKA in tied array mode where up to one hundred pencil beams can be formed within the primary beam searches of the best pulsar candidates could be made at the full sensitivity of the instrument. We conservatively estimate that the SKA could find of order 1000 pulsars in the SMC/LMC system in a survey lasting just one month. Globular clusters would be another rich source of pulsars, with their dense cores proven breeding grounds for the formation of relativistic binaries. The most interesting pulsars in these dense regions could be timed using the multiple beams available with the SKA. The potential to uncover black hole neutron star and other relativistic binaries is enormous due to the sheer numbers of new pulsars that would be found.
The other less exotic mode for pulsar searching with the SKA would be to
form an incoherent addition of the signals from each antenna element
and use traditional search techniques. Although the effective area of
the instrument only scales as the square root of the number of
elements, the instrument would still be a very effective search
instrument. This is because the area surveyed in each pointing is
that of the primary beam of a single element, and the loss of
sensitivity over a single dish is exactly made up by this increased
search area, making the instrument as good (per square metre) for
searching as a single dish with a square km of collecting area! In
this mode SKA could survey 80% of the entire sky at 70cm in 6 months
with a sensitivity 20 times that of the Parkes 70cm survey of the
Southern sky which detected 298 pulsars, 19 of them with millisecond
periods. Given that pulsars are disk population, we might expect a
survey with SKA to detect 
6000 pulsars in the Southern sky
alone. In practice, interstellar dispersion and scattering would
probably prevent us from following the expected Log-N, Log-S
relationship, but it is obvious that SKA would find pulsars by the
thousands, and several hundred millisecond pulsars. The potential for
the discovery of the first black hole and dual-line binary pulsars
would be great. Such systems would be ideal gravitational
laboratories. The number of relativistic neutron-star binaries would
probably increase by at least an order of magnitude and better
constrain the poorly-known coalescence rate of neutron star binaries.
The best-studied planetary system outside the solar system is that
orbiting the millisecond pulsar PSR B1257+12 (Wolzsczan 1994), and it
is possible that several more instances of pulsar planetary systems
would be found.
The tied array would have a much higher sensitivity than the incoherent search mode, and would be able to time any pulsars found in the all-sky survey in a small fraction of the time it took to discover them. Although the final configuration of the SKA is yet to be determined, with 625 45m dishes, the tied array could achieve the survey sensitivity in 1/625th of the time. It would be thus be possible to time thousands of pulsars in a day.
The tremendous increase in the sensitivity of the tied array means that sub-microsecond timing residuals could be obtained on several hundred millisecond pulsars. This would make possible the formation of the ultimate pulsar timing array (Foster and Backer 1990). It has already been demonstrated that millisecond pulsars rival the best atomic clocks for stability on timescales of a year or so. Several hundred pulsars would establish a highly precise pulsar time standard. The Earth's ephemeris is constantly being revised because of uncertainties in the position of the solar system barycenter. The pulsar timing array would be extremely sensitive to the masses and motion of the planets. Long-period gravitational waves are detectable in pulse timing experiments (Rajagopal and Romani 1995). The millisecond pulsar timing array would place the strongest limit yet on the background of gravitational waves and make a sensitive detector for sources of long-period gravitational waves, such as ultra-massive black hole binaries.
This new population of pulsars would contain at least twenty double neutron star systems suitable for exhaustive tests of general relativity. In particular a dual-line binary pulsar would allow the strictest tests yet of strong-field gravity. All of the known double neutron-star binaries have only one visible pulsar. By detecting a dual-line pulsar, both the mass ratio and the sum of the masses could be determined to extraordinarily high accuracy, probably greater than one part in 106. This would, in conjunction with the three Keplerian parameters, completely specify the orientation and masses of the binary system. Therefore measurements of all of the remaining post-Keplerian parameters would allow tests of relativistic theories of gravity. A black hole neutron star system would also be of special interest. The relativistic effects would be much larger than in a double neutron star binary. Millisecond pulsars with edge-on orbits could have their Shapiro delays measured, and this in turn would provide information on neutron star masses. The increase in computer power by the time of the survey would allow the data to be searched at a frequency resolution much greater than is currently possible, making sub-millisecond pulsars detectable. The discovery of such a pulsar would strongly constrain the equation of state of condensed nuclear matter (Phinney and Kulkarni 1994).
Radio pulsars are highly-magnetized neutron stars which are formed during the core-collapse of massive stars in an event known as a supernova explosion. They represent the densest form of matter possible. Although weighing around 500,000 Earth masses, they are only 20-30 km in diameter making them ideal ``point-masses'' in physical experiments. They are formed approximately once every 250 years in our Galaxy, and the fastest known object rotates once every 1.55 milliseconds. Radio astronomers routinely make observations of these systems that enable them to determine the arrival time of the pulse to an accuracy of a microsecond or better. By making observations at several epochs astronomers have been able to establish that millisecond pulsars have rotational stability that rivals the Earth's best atomic clocks (Kaspi, Taylor and Ryba 1994).
In some special cases, pulsars orbit unseen companions, allowing tests of relativistic gravity. Using the powerful pulse timing method, astronomers have shown that the orbit of the binary pulsar PSR 1913+16 is shrinking at a rate of 3.1 mm per orbit, precisely the amount predicted by general relativity. At this rate the system will coalesce in 300 Million years in a spectacular death-spiral that will emit an enormous burst of gravitational radiation which may be detected by gravitational wave observatories.
The stability of the pulsar rotation has been used to place important limits on the density of gravitational waves in the Universe and rule out some cosmological models (Kaspi, Taylor and Ryba 1994). Remarkably, an ensemble of millisecond pulsars with sub-microsecond timing accuracy could be used as a gravity wave telescope to detect ultra-massive black hole binaries anywhere in the Hubble volume (Rajagopal and Romani 1995). Above we argue that SKA will be capable of discovering thousands of pulsars and performing pulse timing observations with a precision far in excess of that currently possible. This will enable rigorous tests of relativistic theories of gravity, the establishment of a gravity-wave telescope suitable for detecting long-period gravitational radiation, and the determination of a large number of accurate neutron star masses. Other applications will include reference frame ties, studies of the interstellar medium, improvements in the solar system ephemeris, and advances in the theory of stellar evolution and pulsar emission mechanisms.
The SKA would be capable of discovering many thousands of radio pulsars. Many of these pulsars would be members of binary systems, permitting exhaustive tests of general relativity. The millisecond pulsars found by the instrument would form a pulsar timing array capable of detecting long-period gravitational waves such as those emitted in the early formation of the Universe and by ultra-massive black-hole binaries. The timing array would form a new standard of time and furnish information about the solar system ephemeris. The mass of neutron stars in binaries and the minimum spin of millisecond pulsars are both paths to a mini holy grail - the equation of state of nuclear matter in the center of neutron stars which exceeds that in atomic nuclei even when collided at high energy. Surveys with SKA would provide the best opportunity to discover a sub-millisecond pulsar.