About Pulsars

A pulsar (short for pulsating radio star) is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation which can only be observed when the beam of emission is pointing toward the Earth. A good analogy is a lighthouse whose light can only be seen when the lens is pointed in the direction of an observer, and gives a pulsed appearance to the steady light of the emitting light source.

The First Pulsar

The first pulsar was observed on November 28, 1967, by Jocelyn Bell who observed pulses separated by 1.33 seconds that originated from the same location on the sky, and kept to sidereal time.

The signal was nicknamed LGM-1, for "little green men" (a playful name for intelligent beings of extraterrestrial origin). It was not until a second pulsating source was discovered in a different part of the sky that the "LGM hypothesis" was entirely abandoned. The pulsar was later dubbed CP 1919, and is now known by a number of designators including PSR 1919+21, PSR B1919+21 and PSR J1921+2153.

Neutron Stars

Neutron stars are very dense, and have short, regular rotational periods. This produces a very precise interval between pulses. Pulse periods range from roughly milliseconds to seconds and are unique to each individual pulsar.

A neutron star is the product of the explosive transformation of a massive star. Any star's life is a careful balancing act: the gravity of its own material pulls inward, while pressure from the heat and light produced by the burning of hydrogen into helium in the star's core pushes outward. For a massive star, this delicate dance goes on for millions of years, until the hydrogen supply in the core runs low. Gravity begins to take over and the core contracts and heats up. This increase in temperature allows the star to fuse helium into even heavier elements, temporarily staving off gravitational collapse.

The cycle continues over millennia, with the star's core becoming increasingly hot and dense. In the innermost regions of the core, a mass of iron ashes begins to build up. This is the end of the line: iron cannot be fused into heavier elements without an input of energy. When enough iron accumulates within the core, it collapses rapidly. Electrons and protons are "squeezed" together to form neutrons. These neutrons temporarily but violently halt the collapse. In the process the outer layers of the star are blown off in a supernova, nature's most spectacular explosion. The remnant core, roughly twenty kilometers wide and densely packed with neutrons, is called a neutron star.

Neutron stars are a study in extremes. They weigh roughly twice as much as the sun but have a radius only 1/30,000 as great (which translates to a density roughly equivalent to that of an atomic nucleus).

Any remnant rotational momentum of the original star results in a rapid spin-up of the collapsed neutron star, in much the same manner as an ice skater is able to spin-up by pulling their outstretched arms close to their chest.

Apparent spin frequencies range from over 700 revolutions per second (42,000 RPM !!!) to just 1 revolution in 12 secs (5 RPM). The Vela Pulsar rotates at a moderate 672 RPM.

Spin Frequency Stability

For some millisecond pulsars, the regularity of pulsation is more precise than an atomic clock. This stability allows millisecond pulsars to be used in establishing ephemeris time or building pulsar clocks. It also allows a unique way of separating the pulsar signal out from other sources.

Timing noise is the name for rotational irregularities observed in all pulsars. This timing noise is observable as random wandering in the pulse frequency or phase.

Spin Down

Most pulsars exhibit a slow decay in spin frequency caused by energy loss through various mechanisms - especially rotational powered pulsars (pulsars can be powered by other mechanisms, e.g., mass accretion). This is an addition marker as other signals (e.g., earth-based RFI) are unlikely to exhibit the same change in frequency over time as a pulsar.

However, it is important to note that 'glitches' are observed in the rotation velocity of many neutron stars. The rotational velocity is decreasing slowly but steadily, except by sudden variations. One model put forward to explain these glitches is that they are the result of "starquakes" that adjust the crust of the neutron star. Models where the glitch is due to a decoupling of the possibly superconducting interior of the star have also been advanced. In both cases, the star's moment of inertia changes, but its angular momentum does not, resulting in a change in rotation rate.

The Vela Pulsar is a particularly 'glitch-prone' pulsar - with a sudden spin-up of the order of several ppm occurring, on average, every couple of years. This means that, when using historical ephemeris data, that some adjustment should be made to account for the deviation from the simple spin-down model for the Vela Pulsar caused by those glitches.

Dispersion

The radio signals from a pulsar suffer dispersion as they travel through the ionized interstellar medium (ISM), resulting in a frequency dependent arrival time of the pulses. The effect is quantified by the pulsar’s dispersion measure (DM).

Pulse arrival times are increasingly delayed when received at lower frequencies. In other words, pulses emitted at higher frequencies arrive earlier than those emitted at lower frequencies. As the receiving bandwidth is increased the difference between the arrival times for the lower frequencies and the higher frequencies in the passband increase. If that delay is not accounted for, the summed pulse will be blurred and smeared. If the delay is too big, the pulses may become undetectable.

Scattering

Electron distribution along the line of sight to the pulsar is not homogeneous throughout the interstellar medium, but it shows a certain "clumpiness". These clumps are large enough to scatter the radio waves into different paths.

Due to this scattering, some rays can now make their way to the telescope which would otherwise have missed it. These rays, however, have a longer path length and will therefore be slightly delayed compared to those signals which travel straight. The pulses become smeared again, showing an exponentially decaying tail and are therefore again more difficult to detect than without scattering. Scattering is heavily reduced at higher frequencies, e.g. it is a factor of 250 less severe at 1400 MHz than it is at 400 MHz.

Scattering is strongest in those regions where we expect the largest densities of electrons, i.e. the Galactic plane and in particular the regions towards the Galactic Centre.

Scintillation

Scintillation can be observed visually as the twinkling of stars. They seem to change slightly in position and brightness moment to moment due to the effects of the atmosphere. The magnitude of this effect is proportional to the level of instability in the atmosphere. Likewise, radio sources can experience the same effect - but instead it is largely the ISM which is the source of the effect. It is caused, basically, by the constructive/destructive interference of signals scattered by the ISM.

Diffractive Scintillation

The observed effect on radio signals from pulsars is a variation in the strength of the pulses on timescales from minutes to hours. Depending on the pulsar this can mean that a signal might be, at one instance, be much stronger than its long term average, or conversely, much weaker. It may mean that during an observation covering a few hours, the excision of periods where the pulsar has faded in strength from the data record, whilst keeping the enhanced portions, can mean an improvement in S/N. Also the range of frequencies (decorrelation bandwidth) over which this interference occurs varies from pulsar to pulsar.

The rate of change of the diffractive scintillation modulation for the Vela Pulsar is relatively fast (timescale of the order of a few seconds) and the decorrelation bandwidth is narrow (a few tens of Hz). This is thought to be due to the closest of the bulk of scattering medium to the pulsar. The Vela Pulsar is unusual in this respect.

Refractive Scintillation

A longer term effect called refractive scintillation causes variations of the order of days to months. It is thought that this is due to wholesale focussing/defocussing of signals by the ISM. The exact type of material which causes this effect is not known.

This effect is fairly mild for Vela, but can result in a variation of up to a couple of dB day-to-day and nearly 3 dB over time scales of a couple of months and years. This means where attempts are being made to incoherently sum daily Vela data there can be expected to be runs of days where the S/N is substantially better than other periods.

It is noted, however, that the Crab Pulsar has been observed to vary in strength by almost 10 dB over a year of elapsed time, with 4 dB variation day-to-day. This is in addition to the short-term variations due to diffractive scintillation which are of the order, in time, of a single observation run of a few hours.

Polarisation

In general most radio signals emanating from outside the solar system are randomly polarised - meaning that they can be received at equal strength with any orientation of a linearly-polarised antenna. In contrast, signals from pulsars are relatively strongly linearly polarised - meaning that at any instance there will be an orientation of a linearly polarised antenna which will return maximum signal. At that same instance an antenna orthogonal to that orientation will receive no signal.

For the receiving system it becomes a problem of making sure the alignment of a linearly polarised antenna is orientated for best pickup. If the polarisation of the incoming pulsar signal was known then this could be achieved by rotating the antenna polarisation to match. However, in practice this is not feasible as the orientation is not only affected by the ISM, but also by an additional variable Faraday rotation in the ionosphere. But the over-riding factor that makes it impractical is that the orientation of the polarisation from the pulsar itself swings significantly even during the on-phase of the pulse. For the Vela Pulsar there is more than a 90° shift in polarisation over the W10 time (4.5 ms) of the on-pulse !!!

To circumvent the effects of the polarisation swing, one can use a circularly polarised antenna. This carries a 3 dB penalty compared to a linearly polarised antenna orientated for maximum pickup, but as it is impractical to implement a dynamic linear polarisation tracking system, that deficit must be accepted.