ABSTRACT
A statistical analysis of a large sample of 668 radio pulsars was undertaken in other to investigate the possible dependence of interstellar medium (ISM) parameters [dispersion measure (DM) and rotation measure (RM)] on pulsar spin-down parameters [rotation period ( ) and spin-down rate ( )]. The existence of such relationship will have a far reaching implication on the theories of pulsar birth and evolution. A simple descriptive analysis of the data reveals that the sample is quite heterogeneous, consisting of normal and recycled millisecond pulsars. Specifically, the published values of , , DM and RM for objects in the sample were found to vary over a wide range: ~ 0.002 – 9 s, 3 × 10-21 – 2 × 10-11 ss-1, 2 – 1100 cm-3pc and -3000 – 2400 radm-2, respectively, with the corresponding mean values of ~ 0.69 ± 0.02 s, (9.94 ± 0.05) × 10-14 ss-1, 181 ± 7 cm-3pc and 157 ± 10 radm-2. Scatter plots of DM and RM (irrespective of sign) against reveal large amplitude (~ 3 orders of magnitude) scatter in the ISM parameters superimposed on a striking trend in which pulsars with large values of (young pulsars), on average, are characterized by large DM and |RM| values. A simple regression analysis of the DM/|RM| – data yields a moderate correlation (with correlation coefficient r ~ 0.5). A simple interpretation of the moderate DM/|RM| ‒ relationship is that objects with large (corresponding to young pulsars) are, on average, located in a region of ISM with high electron density content (in this case, the galactic plane). On the other hand, smaller values of , DM and |RM| correspond to relatively older pulsars located in regions farther away from the galactic plane (with low electron density content). The DM/|RM| ‒ correlation increased significantly (with correlation coefficient r ~ 0.95), when mean values of the parameters were employed in the analysis. The observed large scatter in the ISM data highlights the complex nature of the electron content distribution in the ISM and the large dispersion in both the magnitude and direction of pulsar space velocities. Similar analysis did show any appreciable dependence of both DM and RM on the pulsar rotation period. Our analysis also reaffirms the existence of a strong correlation (r ~ 0.7) between the DM and RM parameters, which are used to characterize the ISM.
CHAPTER ONE
INTRODUCTION
1.1 What are Pulsars?
A pulsar is a highly magnetized, rapidly rotating neutron star that emits beams of broad band electromagnetic radiation. This radiation can only be observed when the beam of emission sweeps across the earth, much the way a lighthouse can be seen when the light is pointed in the direction of an observer. The events leading to the formation of a pulsar begin when the core of a massive (> 10 ) star is collapsed into a neutron star during a supernova explosion, where is the mass of the sun which is ~ 2 1030 kg. The neutron star retains most of the angular momentum and only a tiny fraction of the size of its progenitor star. The sharp reduction in the stellar moment of inertia results in significant amplification of the rotation speed of neutron stars. Beams of radiation are emitted along the magnetic axis of the pulsar as it spins about the rotation axis of the neutron star. The magnetic axis of the pulsar determines the direction of the electromagnetic beam, with the magnetic axis not necessarily aligned with its rotation axis. This misalignment causes the beam to be modulated by the rotation of the neutron star. The beam originates from the rotational kinetic energy of the neutron star, which generates an electric field from the movement of the very strong magnetic field, resulting in the acceleration of protons and electrons on the star surface and the creation of an electromagnetic beam emanating from the poles of the magnetic field.
The rotation period ( ) of most pulsars are known to increase at constant rates as the pulsars convert their rotational kinetic energy into electromagnetic radiation and particle wind according to the spin-down law (e.g. Manchester and Taylor, 1977):
(1.1)
where is the braking index, is the pulsar spin-down rate and is usually assumed to be a constant. When a pulsar’s spin period slows down sufficiently, the radio pulsar mechanism is believed to turn off (the so-called “death line”). This turn-off seems to take place after about 10 – 100 million years, which means that of all the neutron stars in the 13.6 billion years age of the universe, around 99% no longer pulsate (Young et al., 1999). There are currently over 2000 known radio pulsars and their rotation periods are in the range of about 1.5 ms and 8.5 s (Seiradakis and Wielebinski, 2004; Manchester et al., 2005).
1.2 History of Discovery of Radio Pulsars
The discovery of pulsars by Professor Anthony Hewish and Jocelyn Bell Burnell in 1967 is one of the most important and dramatic advances in the history of radio astronomy (Hewish et al., 1968). The story began in 1965 when Hewish started the construction of an 82 MHz (3.7 m wavelength) array of 2048 dipoles for scintillation studies of compact radio quasars. The dipoles were set horizontally several wavelengths above the ground in regular rows covering an area of 20,000 square metres. Graduate students at Cambridge University helped in the construction of the radio antenna. One of them, Jocelyn Bell from Ireland, was responsible for the network of thousands of cables (transmission lines) between the antenna and receiver. The array was physically fixed but by introducing appropriate phasing with different cable lengths, the beam could be shifted in declination. The earth’s rotation provided scanning in right ascension. Hewish had designed the antenna to investigate the compact quasar radio sources by their scintillation as produced by the irregular structure of the interplanetary medium.
In early measurements by Hey et al. (1946), fluctuations were observed in the radio emission from Cygnus A, which are due to inhomogeneities in the earth’s ionosphere. Hewish (1955) and Vitkevitch (1955) noted that the outer solar corona scattered radio waves, increasing the apparent diameter of radio sources. Both coronal scattering and ionospheric-induced fluctuations are similar scintillation phenomena but only differ in scale. Beginning in 1962, Hewish, Scott and Wills (1964) noted rapid fluctuations (with periods of a few seconds) in the intensity of a number of radio sources, notably 3C48, 3C119, 3C138 and 3C147, as measured at 178 MHz. Two of these sources were already known to possess very small angular diameters. It was concluded that the fluctuations were a scintillation effect produced by the interplanetary medium and is most severe for sources of angular diameter < 1 arcsec and at wavelengths of more than 1 m. The effect was found to become stronger with decreasing angular distance to the sun and the fluctuation rate faster with increasing wavelength. The belief that this scintillation effect could provide a convenient technique for estimating the angular diameter of radio sources in the range < 1 arcsec motivated the new antenna array by Hewish and his co-workers.
The plan was to survey most of the sky north of declination -080 once a week, keeping this region under constant surveillance. By July, 1967 construction of the array was completed and observations were begun with output recorded at short time constant with a pen-on-paper chart. Jocelyn Bell was given the responsibility of analyzing the 100 s of meters of chart paper flowing from the recorder each week in order to note times and declinations of chart deflections having a rapid fluctuation or scintillation. In October, 1967, she noted some unusual deflections lasting a minute or two which she could not readily identify as either a scintillating quasar or as interference from a terrestrial source, e.g. a gasoline engine ignition. Recalling that she had seen something like it several weeks earlier, she searched back through the records and found that it had appeared several times before and at the same declination and right ascension. This suggested that it was of celestial and not terrestrial origin, but curiously, the signals appeared conspicuously near midnight when interplanetary scintillation drops to a very low value.
Systematic investigation of these signals began in November, 1967. High speed recordings showed that they consisted of a series of pulses of about second duration with a repetition period of 1.337 s which was maintained with astonishing precision. The thought that the signal might be the beacon of an extraterrestrial civilization was entertained at one point, but lack of Doppler variation in the pulse rate from planetary motion around a star and the discovery of three more pulsing signals elsewhere in the sky seemed to rule out this possibility. Announcement of the discovering of these pulsating objects or pulsars appeared in the February 24, 1968 issue of “Nature” with a tentative explanation offered that the sources were oscillating white dwarf or neutron stars (Hewish et al., 1968). The discovery of pulsars with periods less than second and a spin-down rate led to the identification of pulsars as rotating neutron stars.
This serendipitous discovery of pulsars was entirely unexpected but so was Karl Guthe Jansky’s discovery of radio emission from our galaxy that marked the beginning of radio astronomy, as well as Arno Penzias and Robert Wilson’s discovering of 3 K sky background. It is remarkable that in all the three cases (pulsars, galactic radio emission and 3 K), the design of the instrument and the circumstances of its use were almost ideally suited for the discovery. Many astronomers around the world joined in further observations and studies of the pulsar and in searching for new ones, generating a vast literature on pulsars.
1.3 Classification of Pulsars
There are three generic classes of pulsars, based on the possible energy source which powers their emissions.
- Rotation-powered pulsars are powered by the rotational kinetic energy of the underlying neutron stars. The Electromagnetic radiation emitted can be across a large portion of the electromagnetic (EM) spectrum, generally from the x-ray region down to the radio region. Typically the radiation is seen in the radio region of the EM spectrum. As such, rotation-powered pulsars are referred to as radio pulsars. There are mainly two groups or types of rotation-powered pulsars which include the normal and the millisecond radio pulsars. The normal radio pulsars are mostly isolated, fast spinning neutron stars. More than 1000 members of this class have been discovered and they all have rotation periods in the range of ~ 0.03 to 8.5 s. The characteristic age of normal radio pulsars is of the order of 108 yr while their surface magnetic field is about 1012 G (Seiradakis and Wielebinski, 2004). More than 90 percent of the known normal radio pulsars have period derivative 10-17 ss-1, however objects with ~ 10-19 ss-1 also exist. Normal radio pulsars are generally expected to spin down steadily with time. However, the normal radio pulsars residing in the globular clusters (Manchester et al., 1985; Wolszczan et al., 2000) are known to be spinning up instead, presumably owing to the gravitational interaction between the pulsars and the other densely packed stars in the cluster. When these interactions result in acceleration in excess of the pulsar spin-down rate, there is a net acceleration which corresponds to spin-up of the pulsar.
Radio pulsars whose spin periods are less than 25 ms (e.g. Kaspi, 1997), and which, according to the standard evolutionary model (e.g. Bhattacharya and van den Heuvel, 1991) acquired these fast spin rates after an episode of “spin-up”, probably through mass and angular momentum accretion from a low mass binary companion are referred to as millisecond pulsars. The fastest millisecond pulsar found to date has a period of 1.56 ms (Backer et al., 1982). The origin of millisecond pulsars is still unknown. The leading theory is that they begin life as longer period pulsars but are spun up or recycled through accretion (Bhattacharya, 1996; Lyne and Smith, 1998). For this reason, millisecond pulsars are sometimes called recycled pulsars. About 40 members of this class have been observed and a significant percentage of them are in binary systems with main sequence stars (Kaspi et al., 1994), or degenerate stars – white dwarfs (Lyne and Smith, 1990) or neutron stars (Taylor and Weisberg, 1982; Nice et al., 1996). The characteristic age of millisecond pulsars is slightly above 109 yr (Seiradakis and Wielebinski, 2004). Millisecond pulsars are characterized by very small spin-down rates, < 10-17 ss-1 and relatively weak surface magnetic field, ~ 108 – 109 G. The low surface magnetic field has been associated with the accretion processes, in which the field is believed to be appreciably buried in the accreted material. However there is, as yet, no physical mechanism which plausibly explains how the magnetic field of a neutron star could significantly decay (Bhattacharya and Srinivasan, 1995).
- X-ray pulsars are powered by energy released during mass accretion from the binary companion and are generally classified into two: High-Mass and Low-Mass X-ray Pulsars. In High-Mass X-ray Binaries (HMXBs), the mass of the companion is greater than 10 solar masses (e.g. Joss and Rappaport, 1984). Examples of HMXBs are LMC X-4, Cen X-3 and SMC X-1. Their rotation periods range from 0.069 to 835 s, while the orbital periods have been found to lie between 0.2 and 187 days. HMXBs are characterized by high surface magnetic fields of ~ 1012 G (Lyne and Smith, 1998). A subclass of X-ray pulsars, in which the mass of the companion is usually less than 1 solar mass, is known as the Low-Mass X-ray Binaries (LMXBs). These objects are more difficult to study owing to the fact that only little light, if any, can be observed directly from the companion star. Orbital periods are generally less than 1 day. X-ray binaries are characterized by rapid decrease in the rotation periods (that is they spun-up with time). This observation suggests that the torque responsible for the spin-up, the accretion torque, could be orders of magnitude greater than the magnetic braking torque (Lyne and Smith, 1998).
- Magnetars are presumably powered by the decay of hyper-strong fields, whose decay timescale is of order ~ 103 – 104 years (Thompson and Duncan, 1996). They are highly magnetized neutron stars in fact much more than conventional neutron stars by a factor of up to 100 or more, with magnetic fields in the order of 1014 Magnetars are capable of emitting bursts of both x-rays and gamma rays through the decay of their very strong magnetic field. The very strong magnetic field of a magnetar is thought to be inherited when the neutron star is first created during a supernova explosion (Duncan, 1998). These magnetars could manifest as soft gamma repeaters (SGR) where x-ray stars sporadically emit bright, short (0.1 s) repeating flashes of low-energy gamma rays and anomalous x-ray pulsars (AXPs) which are slowly rotating pulsars with periods of 6 – 12 seconds (Karttunen et al., 2006). The Fermi space Telescope has uncovered a subclass of rotation-powered pulsars that emits only gamma rays (Atkinson, 2008). There have been only about one hundred gamma-ray pulsars identified out of about over 2000 known pulsars (Atkinson, 2008). Although all the three classes of objects are neutron stars, their observable behaviour and the underlying physics are significantly different.
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