TABLE OF CONTENTS
Title Page i
Certification ii
Dedication iii
Acknowledgements iv
Table of Contents v
List of Tables vii
List of Figures viii
Abstract xi
CHAPTER ONE: INTRODUCTION
- What are6 Pulsars? 1
- History of Discovery of Radio Pulsars 2
- Classification of Pulsars 4
1.4 Neutron Star – A Member of the Compact Stars 6
1.5 The Internal Structure of a Typical Neutron Star 7
1.6 Neutron Star Magnetosphere 9
1.7 The Emitting Regions of Pulsars 10
1.8 Radio Pulse Characteristics 11
1.8.1 Integrated Pulse Profile 11
1.8.2 Pulse Shapes 11
1.8.3 Profile Evolution with Frequency 13
1.8.4 Flux Density Spectra 13
1.8.5 Polarization of Pulsar Radiation 14
1.9 Pulsars as Astrophysical Tools 15
1.9.1 Pulsars as High-Precision Timing and Time Keeping Devices 15
1.9.2 Laboratory for Testing the Predictions of General Relativity 17
1.9.2.1 The Use of Double Neutron Star (DNS) Binaries 17
1.9.3 The Study of the Galaxy and the Interstellar Medium 19
1.9.4 The Study of Super-Dense Matter 20
1.9.5 The Discovery of Extra-Solar Planets 22
1.9.6 The Study of Plasma Physics under Extreme Conditions 22
1.10 Purpose of Study 23
CHAPTER TWO: LITERATURE REVIEW
2.1 Pulsar Spin-Down Evolution 24
2.2 The Interstellar Medium (ISM) 26
2.3 Propagation Effects in the Interstellar Medium 28
2.3.1 Homogeneity of the ISM 28
2.3.2 Pulse Dispersion 29
2.3.3 Scintillation 30
2.3.4 Scattering 32
2.3.5 Faraday Rotation 34
2.4 Dispersion Measures 36
2.5 Rotation Measures 40
CHAPTER THREE: MATERIALS AND METHODS
3.1 Source of Data 42
3.2 Data Analysis and Results 43
3.2.1 Simple Descriptive Analysis 43
3.2.2 Simple Regression Analysis 49
3.3 Analysis of Time Rate of Change of DM ( ) of a Sample of Radio Pulsars 58
3.3.1 Features of some Peculiar Pulsars 62
3.4 Further Analysis of DM and RM Dependence on Radio Pulsar Spin-Down Parameters 62
CHAPTER FOUR: DISCUSSION AND CONCLUSION
4.1 Discussion 68
4.2 Conclusion 71
References 73
LIST OF TABLES
Table 2.1: A breakdown of the properties of the components of the ISM of the Milky Way 27
Table 3.1: A summary of correlation coefficient, r results 51
Table 3.2: Properties of the peculiar pulsars 62
LIST OF FIGURES
Figure 1.1: A typical structure of a neutron star interior based on soft equation of state 7
Figure 1.2: Toy model for the rotating neutron star and its magnetosphere 9
Figure 1.3: Emission region of a pulsar 11
Figure 1.4: Integrated pulse profile for a sample of nine pulsars 12
Figure 1.5: Multi-frequency pulse profiles for two pulsars 13
Figure 1.6: Comparing the stability of PSRs B1855+09 and B1937+21 with various atomic clock differences 16
Figure 1.7: The shift in the periastron passage of the binary pulsar B1913+16 plotted as a Function of time 18
Figure 2.1: The PSRs thin screen 32
Figure 2.2: Pulsar scatter-broadening times as a function of dispersion measure 33
Figure 2.3: The geometry of scattering 34
Figure 3.1: Histogram of the distribution of the dispersion measure (a) and rotation measure (b) of the 668 radio pulsars on logarithmic scales 46
Figure 3.2: Histogram of Z – height of 665 radio pulsars from the galactic plane 47
Figure 3.4: Histogram of 668 radio pulsars’ characteristic age on logarithmic scale 48
Figure 3.5: Histogram of 668 radio pulsars’ surface magnetic field on logarithmic scale 48
Figure 3.6: Histogram of 668 radio pulsars’ rotation period on logarithmic Scale 49
Figure 3.7: Scatter plot of the absolute values of the rotation measure (RM) against the dispersion measure (DM) on logarithmic scales for the 668 radio pulsars 52
Figure 3.8: Scatter plot on Logarithmic scale of the dispersion measure (DM) against pulsars’ distance from the galactic plane (Z) for the 665 radio pulsars 53
Figure 3.9: Scatter plot on Logarithmic scale of absolute values of rotation measure against pulsars’ distance from the galactic plane (Z) for the 665 radio pulsars 53
Figure 3.10: Scatter plot of the dispersion measure (DM) against period derivative ( ) on Logarithmic scales for the 668 radio pulsars 54
Figure 3.11: A scatter plot of logarithm of absolute values of rotation measure against logarithm of period derivative for the 668 radio pulsars 54
Figure 3.12: Scatter plot of the dispersion measure (DM) against characteristic age ( ) on logarithmic scales for the 668 radio pulsars 55
Figure 3.13: A scatter plot of logarithm of absolute values of rotation measure against logarithm of characteristic age for the 668 radio pulsars 55
Figure 3.14: Scatter plot of dispersion measure (DM) against surface magnetic field (Bsurf) on logarithmic scales for the 668 radio pulsars 56
Figure 3:15: Scatter plot of absolute values of rotation measure against surface magnetic field on logarithmic scales for the 668 radio pulsars 56
Figure 3.16: Scatter plot of logarithmic dispersion measure against logarithm of rotation period for the 668 radio pulsars 57
Figure 3.17: Scatter plot of logarithm of absolute values of rotation measure against logarithm of rotation period for the 668 radio pulsars 57
Figure 3.18: Scatter plot of absolute values of dispersion measure derivative against dispersion measure on logarithmic scales for the 349 pulsars 59
Figure 3.19: Scatter plot of absolute values of dispersion measure derivative against absolute values of rotation measure on logarithmic scales for the 266 pulsars 59
Figure 3.20: Scatter plot of absolute values of dispersion measure derivative against period derivative on logarithmic scales for the 349 pulsars 60
Figure 3.21: Scatter plot of absolute values of dispersion measure derivative against characteristic age on logarithmic scales for the 349 pulsars 60
Figure 3.22: Scatter plot of absolute values of dispersion measure derivative against surface magnetic field on logarithmic scales for the 349 pulsars 61
Figure 3.23: Scatter plot of absolute values of dispersion measure derivative against rotation period on logarithmic scales for the 349 pulsars 61
Figure 3.24: Plot of the mean values of logarithmic dispersion measure against mean values of logarithmic characteristic age 65
Figure 3.25: Plot of the mean values of logarithmic absolute values of rotation measure against mean values of logarithmic characteristic age65
Figure 3.26: Plot of the mean values of logarithmic dispersion measure against mean values of logarithmic period derivative 66
Figure 3.27: Plot of the mean values of logarithmic absolute values of rotation measure against mean values of logarithmic period derivative 66
Figure 3.28: Plot of the mean values of logarithmic dispersion measure against mean values of logarithmic surface magnetic field 67
Figure 3.29: Plot of the mean values of logarithmic absolute values of rotation measure against mean values of logarithmic surface magnetic field 67
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.
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.
