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Master's Thesis MASTER'S THESIS Pulsars as "Neutromagnets" A Theory About the Magnetic Field of a Neutron Star Anna Ponga 2014 Master of Science in Engineering Technology Space Engineering Luleå University of Technology Institutionen för teknikvetenskap och matematik ABSTRACT Pulsars are believed to be a kind of neutron stars. They rotate very fast; a period of a second is not uncommon. There are also millisecond-pulsars, as well as pulsars with a larger period of about eleven seconds, these are called magnetars. This thesis is about the magnetic field of these pulsars. A normal pulsar has a magnetic field strength in the order of 1012 G (108 T), but there are special cases, the magnetars, that has a magnetic field strength of up to 1016 G (1012 T). The strong magnetic field affects the rotation period of these objects, hence the much longer period. The model in question that is investigated in this thesis claims the neutron star, or pulsar, is a giant nucleus consisting of neutrons with all spins aligned. This is a possible source for the strong magnetic field, and it can also explain the stability of the field as well as why the magnetic field axis is not aligned with the rotational axis, which other models cannot explain in a satisfactory way. With help of the Heisenberg Hamiltonian, which describes ferromagnetism, and the Argonne v14 potential, which is a nucleon-nucleon potential, it will be shown that this model is very possible. i ii SAMMANFATTNING Pulsarer tros vara en sorts neutronstjärnor. De roterar väldigt fort, en period på en sekund är inte alls ovanlig. Det finns även ”millisekunds”-pulsarer, likaväl som det finns pulsarer som har en period på ungefär elva sekunder, dessa kallas magnetarer. Detta examensarbete handlar om magnetfältet hos dessa pulsarer. En normal pulsar har ett magnetfält av storleksordningen av 1012 G (108 T), men det finns särskilda fall, de så kallade magnetarerna, som har en magnetfältstyrka på upp till 1016 G (1012 T). Det starkare magnetfältet påverkar dess rotationsperiod, därav den mycket högre rotationstiden. Modellen som ska undersökas i detta examensarbete säger att neutronstjärnan, eller pulsaren, är en enorm kärna som består av neutroner med sitt spinn riktat åt samma håll. Detta är källan till det starka magnetfältet, och modellen kommer också förklara fältets stabilitet likaväl som varför magnetfältet inte behöver vara riktat åt samma håll som rotationsaxeln. Detta är något som andra modeller inte kan förklara på ett tillfredsställande sätt. Med hjälp av Heisenberg Hamiltonianen, som beskriver ferromagnetismen, och Argonne v14 potentialen, som är en nukleon-nukleon potential, kommer det att visas att denna modell kan stämma. iii iv TABLE OF CONTENT ABSTRACT .............................................................................................................. I SAMMANFATTNING .............................................................................................. III TABLE OF CONTENT .............................................................................................. V 1 INTRODUCTION .............................................................................................. 1 1.1 Task ...................................................................................................... 1 1.2 Method ................................................................................................. 2 2 STELLAR EVOLUTION ..................................................................................... 3 3 NEUTRON STARS ............................................................................................ 5 3.1 Discovery ............................................................................................. 5 3.2 ”Orthodox” model of a neutron star ..................................................... 7 3.2.1 The birth of neutron stars .............................................................. 7 3.2.2 Structure of neutron stars .............................................................. 8 3.2.3 Temperatures ............................................................................... 11 3.2.4 The origin of the magnetic field .................................................. 12 3.3 Pulsar specific properties ................................................................... 13 3.3.1 Pulses .......................................................................................... 13 3.3.2 Rotational period ......................................................................... 15 3.4 Magnetars ........................................................................................... 16 4 MAGNETISM, THE HEISENBERG MODEL AND ARGONNE V14 POTENTIAL ...... 18 4.1 Magnetism .......................................................................................... 18 4.2 The Heisenberg model........................................................................ 19 4.3 Argonne v14 potential ......................................................................... 23 5 A NEW MODEL FOR THE PULSAR MAGNETIC FIELD ........................................ 26 5.1 The Theory ......................................................................................... 26 5.2 The physics behind ............................................................................. 27 5.2.1 The neutron ................................................................................. 27 5.2.2 Spin ............................................................................................. 27 5.3 Calculations ........................................................................................ 28 5.3.1 Number of neutrons .................................................................... 28 5.3.2 The total magnetic field strength ................................................ 28 5.3.3 The interchange constant, J ......................................................... 29 6 CONCLUSIONS AND DISCUSSION ................................................................... 31 7 REFERENCES ................................................................................................ 33 7.1 Books & articles ................................................................................. 33 7.2 Figures ................................................................................................ 34 v vi 1 Introduction There is an “orthodox” model for the magnetic field of neutron stars that for many years have been more or less accepted within the astronomical society (Manchester, Taylor, 1977). There are, however, a few problems with it; It does not explain: the strong magnetic fields satisfactorily; the stability of the magnetic field; how the magnetic field can be misaligned with the rotational axis. In this thesis a different model is presented and it will be shown that the strong magnetic fields of e.g. the magnetars, the stability and the misalignment can be understood with this model. In chapter two the stellar evolution will be explained briefly. In the third chapter neutron stars and pulsars will be reviewed and the theories of today will be examined. After this, ferromagnetism and the Argonne v14 potential will be presented in the fourth chapter. In the fifth chapter a new theory for the magnetic fields of neutron stars and pulsars will be constructed and compared to known observational properties. And in chapter six the results and my own conclusions will be presented. 1.1 Task The model that will be presented in this thesis suggests that the pulsar is a giant nucleus with all spins, and therefore all magnetic moments, directed in the same direction. This model would explain the strong and stable magnetic field of the pulsars which has not yet been done satisfactorily. The task at hand is to investigate whether or not this model can be valid or not. So the spin-dependent part of the binding energies will be examined as well as the Heisenberg Hamiltonian for ferromagnetism. 1 1.2 Method Some simplifying assumptions will be made. These will be presented in chapter five. We will look at the Heisenberg Hamiltonian for ferromagnetism and the Argonne v14 potential, which describes the nucleon-nucleon potential in a nucleus, and hence is a possible model for the nucleons in a neutron star. 2 2 Stellar evolution Our universe is vast, and the number of stars one can see in the sky is uncountable. But where do these stars come from? There are something called nebulas, some of which can be seen with the naked eye, like the Orion nebula in Orion’s sword. There are different kinds of nebulas, emission, reflection and dark nebulas just to mention some. Stars are most often formed in the dark nebulas. The dark nebulae consist of dust grains and un-ionized atoms, there are also heavier atoms in the clouds, but dust grains and hydrogen are there in abundance. The reason why they are dark is because they are so opaque that they block any visible light coming from behind them and they are so cold that they do not emit any light themselves and hydrogen atoms may form molecules. Because of the vastness of the nebulas, several light-years across, many stars are formed simultaneously. The star formation starts when the gravitational forces between the grains and molecules in the nebula overwhelm their kinetic energy. It starts to contract and since the gravitational forces are getting stronger the denser the cloud becomes, the more it contracts. It will continue to form a protostar, which will then become a main sequence star after several thousand years. A main sequence star is an
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