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Edmund Stoner and white dwarf stars Edwin Thomas To cite this version: Edwin Thomas. Edmund Stoner and white dwarf stars. Philosophical Magazine, Taylor & Francis, 2011, pp.1. 10.1080/14786435.2011.586377. hal-00710060 HAL Id: hal-00710060 https://hal.archives-ouvertes.fr/hal-00710060 Submitted on 20 Jun 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Philosophical Magazine & Philosophical Magazine Letters For Peer Review Only Edmund Stoner and white dwarf stars Journal: Philosophical Magazine & Philosophical Magazine Letters Manuscript ID: TPHM-11-Mar-0088.R1 Journal Selection: Philosophical Magazine Date Submitted by the 13-Apr-2011 Author: Complete List of Authors: Thomas, Edwin; University of Leicester, Physics and Astronomy Keywords: total energy methods, electron theory, electron energy states Keywords (user supplied): cosmology, white dwarfs, Chandrasekhar mass http://mc.manuscriptcentral.com/pm-pml Page 1 of 30 Philosophical Magazine & Philosophical Magazine Letters 1 2 3 4 Edmund Stoner and white dwarf stars 5 6 7 E. Thomas, Department of Physics and Astronomy, University of 8 9 Leicester, University Road, Leicester LE1 7RH, UK 10 11 12 13 14 Abstract 15 16 The discovery ofFor a limiting Peer mass for white Review dwarf stars is today Only usually attributed to 17 Subramanian Chandrasekhar. However it appears that an article by Edmund Stoner, which 18 19 appeared in the Philosophical Magazine in 1930, was the first publication to give a 20 convincing demonstration of the existence of a limiting mass for white dwarfs. We examine 21 22 here why it is that the contributions of Stoner and others towards this discovery have been 23 largely forgotten. 24 25 26 27 28 1. Introduction 29 30 The Biographical Memoires of Fellows of the Royal Society [1] tell us that Edmund Clifton 31 32 Stoner was born in Esher in the county of Surrey in 1899. When he was in his teens his 33 parents moved to Bolton in Lancashire where he won a scholarship that enabled him to 34 attend Bolton Grammar School. From there he entered Cambridge University in 1918 35 36 graduating in 1921 with a first-class degree in the Natural Sciences Tripos. Surprisingly, 37 although the physics lectures given to undergraduates were quite mathematical in content 38 39 there was no mathematics teaching in the syllabus, students being expected to pick up what 40 they needed on their own. Stoner was conscious of this lack of formal mathematics training 41 42 throughout his career. 43 44 Between 1921 and 1924 Stoner worked for a PhD in the Cavendish laboratory with Ernest 45 Rutherford as his official supervisor. His research topic was the measurement of the 46 47 absorption of X-rays by a selected group of elements. He obtained his PhD in 1924, despite a 48 prolonged period in hospital after being diagnosed with diabetes. Towards the end of his 49 50 time at the Cavendish he wrote a paper entitled The distribution of electrons among atomic 51 energy levels . This paper, published in the Philosophical Magazine [2] preceded Pauli’s 52 53 enunciation of his exclusion principle and played a significant role in its creation: in effect it 54 contained an explicit statement of the exclusion principle. It should be noted that the 55 56 exclusion principle was to play a crucial role in the theory of white dwarfs. 57 58 After deciding that he did not wish to remain in Cambridge, Stoner successfully applied for 59 a lectureship in the Physics Department of the University of Leeds. There, where he 60 remained until his retirement in 1963, he switched to research in theoretical physics and http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters Page 2 of 30 1 2 3 embarked on pioneering work to understand the magnetic properties of matter: this is the 4 5 work for which he is best known. His interest in white dwarfs was sparked by Fowler’s paper 6 On Dense Matter [3]. Over the period 1929 to 1932 he published the pioneering papers on 7 8 white dwarfs, which are the subject of this article. In particular he deduced the existence of 9 a limiting mass for white dwarfs now known as the Chandrasekhar mass. 10 11 12 13 14 2. White dwarfs 15 16 White dwarfs areFor hot, very Peer compact, stars Review that have ceased nuclearOnly burning. Their high 17 18 temperature and low luminosity places them in the bottom left-hand corner of the 19 Hertzprung- Russell diagram [4]. The white dwarf, 40 Eridani B, recorded by William 20 Herschel in 1783 was the first to be detected [5]. By the late 1920s, when Stoner started his 21 22 investigations, the masses, luminosities and surface temperatures of a small number of 23 white dwarfs had been measured. The best-known example, Sirius B, is the faint companion 24 25 of Sirius, the brightest star in the night sky. The observational data at this time for Sirius B 26 gave its mass to be 0.85 solar masses, its surface temperature 8000 K and its radius 21 000 27 7 -3 28 km. These figures imply a mean density of about 5 X 10 kg m . At the time this density 29 exceeded that of any other known object by several orders of magnitude. For example the 30 -3 31 mean density of the Sun is about 1 400 kg m and the density of osmium metal, the densest 32 element, is 2.2 X 10 4 kg m -3. It is interesting to note that, with these values for the mass and 33 radius of Sirius B, the General Theory of Relativity predicts that light coming from its surface 34 -1 35 would have a red shift of 20 km s . A measurement of this red shift published by W S Adams 36 [6] produced a value of 19 km s -1. However, we now know that this apparent agreement 37 38 between The General Theory of Relativity and the data on Sirius B, which so delighted 39 Eddington, is coincidental. Adam’s measurement of redshift is too low by a factor of 4 and 40 41 the radius is too large by a factor of almost 4. The modern values for the mass, temperature, 42 radius and red shift of Sirius B are 0.98 Msolar , 22 000 K and 6 000 km respectively and the red 43 -1 44 shift, measured using the Hubble space telescope, is 80 km s [7]. With these 45 measurements the density of Sirius B becomes 2 X 10 9 kg m -3 or 2 tonnes cm -3. 46 47 Such high densities seemed at the time to raise a paradox: matter compressed to this 48 49 degree must be completely ionised so what happens to the star as its reaches the end of its 50 lifetime and starts to cool? In the words of Sir Arthur Eddington [8] 51 52 ‘The star could not stop losing heat, but it would not have enough energy to cool 53 54 down’. 55 56 Eddington supposed that for the star to reach a stable cold state, its nuclei and electrons 57 58 needed to recombine into atoms. But to do this the star needed to regain normal density by 59 expanding against the force of gravity, which it could not do. According to classical physics, a 60 http://mc.manuscriptcentral.com/pm-pml Page 3 of 30 Philosophical Magazine & Philosophical Magazine Letters 1 2 3 cold ionised gas cannot exert any pressure so the star was doomed to continue contracting 4 5 indefinitely, a situation that Eddington regarded as absurd. 6 7 The resolution of this paradox was provided by the newly discovered quantum mechanics 8 9 and the Pauli Exclusion Principle. The Cambridge theoretician R H Fowler realised that even 10 at the absolute zero of temperature a very dense electron gas will exert a large pressure and 11 12 that this pressure could support a white dwarf star against collapse [3]. Fowler assumed that 13 the electrons occupied the lowest energy states allowed by the Pauli Principle, which states 14 that only two electrons, one in each of two spin states, can occupy a state of volume h3 in 15 16 six-dimensionalFor phase space, Peer where h isReview the Planck constant. OnlySuch a gas is said to be 17 degenerate ; the uppermost filled state has a momentum p0 which, as a function of number 18 19 density of electrons n, is given, at absolute zero, by 20 21 3/1 3 3/1 22 p0 = h n . (1) 23 8π 24 25 So a high density of electrons in physical space implies that they have high momenta and 26 27 hence that they exert a large pressure which, for non-relativistic electrons, is given as a 28 function of the mass density ρ = µ m n by the expression 29 e H 30 3/5 2 3/2 31 h 3 ρ P = , (2) 32 5 8 33 me π µe mH 34 35 where me is the mass of an electron, mH the mass of hydrogen and µ the average atomic 36 e 37 weight per electron.
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