MacTutor
With the death of Professor Thomas George Cowling FRS on 16 June 1990, one day before his 84th birthday, the Society lost one of its most distinguished and well-loved Fellows. Cowling was a second-generation theoretical astrophysicist who entered the subject when Eddington and others had already established the discipline on a firm foundation. He made very important contributions to the subject of stellar structure, but above all he was one of the first to stress the importance of magnetic fields in astronomical problems.
Tom Cowling was born in Hackney, London on June 17, 1906. He was the second of four sons of George and Edith Cowling and attended Sir George Monoux Grammar School, Walthamstow from 1917 to 1923. He won an open mathematics scholarship to Brasenose College, Oxford, where he was a student from 1924 to 1930. He was awarded a University Junior Mathematical Exhibition in 1925 and a scholarship in 1926, and he graduated with first-class honours in mathematics in 1927. His scholarship at Brasenose was not adequate to finance his course, and additional support from the Department of Education carried the expectation, if not the obligation, that he would become a school teacher. As a result, when he was awarded a three-year postgraduate scholarship at Oxford, he spent the first year taking a diploma in education before becoming Professor E.A. Milne's first research student at Oxford from 1928 to 1930 Subsequently, he was a demonstrator in Professor Sydney Chapman's department at Imperial College before holding an Assistant Lectureship at Swansea (1933–37), lectureships at Dundee (1937–38) and Manchester (1938–45), and professorships at Bangor (1945–48) and Leeds (1948–70), where he remained as an Emeritus Professor until his death. Cowling spent his entire career in mathematics departments, and the number of moves he made will seem remarkable to young academics today.
Cowling was elected to Fellowship of the Society on January 9, 1931. He was a member of Council from 1939–44, 1950–55, and 1965–68, being President from 1965–67 and Vice-President from 1952–54 and 1967–68 He was awarded the Gold Medal of the Society in 1956 for his distinguished contributions to theoretical astrophysics and particularly for his work on the stability of stars. He was elected to Fellowship of the Royal Society in 1947, and other awards he received included the Bruce Gold Medal of the Astronomical Society of the Pacific in 1985 and the Hughes Medal of the Royal Society in 1990. The latter award was made two days before he died, and he did not learn of it. In the International Astronomical Union, he was President of Commission 35, Stellar Constitution, from 1955 to 1958, and of Commission 43, Magnetohydrodynamics and the Physics of Ionized Gases, from 1964 to 1967.
Throughout his research career, Cowling tackled difficult problems, most of which required a combination of mathematical skills and physical insight. His total list of publications is not very long by current standards, but almost all of his papers contain an important point, many of which have survived to the present day. He was not only self-critical but he was critical of the work of others. If any young scientist learnt that Cowling approved of some of his work he knew that he had succeeded. I came under his influence early in my career because he refereed my first papers both on stellar structure and on magnetohydrodynamics. His demand for high standards was combined with a warm personality and a dry sense of humour which endeared him to all who knew him. His great height meant that one could always catch his eye in the middle of a boring introductory speech at a conference reception.
His first two publications set the scene for his life's work, one being on the solar magnetic field and the other on stellar structure. In the first, he criticized some recent work by Chapman and independent work by Ross Gunn, which suggested that the magnetic field of the Sun was limited in its radial extent, the idea being that the motion of charged particles in the magnetic field produced a current and an additional magnetic field which caused the limitation. Cowling showed that the treatment was not self-consistent and that the Sun must possess open field lines. This criticism by Chapman did him no harm because, once he had completed his doctorate, Chapman offered him a junior post in his department and later asked him to collaborate in the production of their treatise The Mathematical Theory of Non-Uniform Gases. Published in 1939, this became a classic text with second and third editions appearing in 1952 and 1970. In 1950, Cowling published an elementary book Molecules in Motion on the same subject
In 1932, Cowling wrote his first paper on the electrical conductivity of an ionized gas in the presence of a magnetic field, and he showed that the motion of the gas perpendicular to the field was rapidly dampened. Although the paper did not explicitly refer to the frozen-in-field, a concept later particularly associated with the name Alfvén, the germ of the idea was there. Cowling returned to this problem in 1956. By then, it was known that the electrical conductivity of a gas in directions perpendicular to a magnetic field was much less than the conductivity parallel to the field, but there was dispute about what the effective value of the conductivity should be used in the formula for the dissipation of energy. Cowling obtained an expression for the dissipation similar to one also obtained by Piddington, which indicated that cosmic magnetic fields could be much less long-lived than if the conductivity had its standard value. Shortly afterward, his introductory book, Magnetohydrodynamics, was published by Interscience Together with an accompanying book, The Physics of Fully Ionized Gases by Lyman Spitzer, it gave a clear introduction to the new subjects of magnetohydrodynamics and plasma physics, which were developing rapidly in response to attempts to produce controlled thermonuclear reactions in the laboratory and to the start of space exploration of the solar system.
The piece of Cowling's work, which is probably known at least by name to the greatest number of scientists, appeared in a paper entitled 'The Magnetic Field of Sunspots' in 1933. It was then realized that some cosmic magnetic fields, including those of sunspots and the Earth, could not be slowly decaying primeval fields. They must be maintained, and Sir Joseph Larmor had proposed that the sunspot fields were regenerated by dynamo action involving axisymmetric motions in the conducting gas. Cowling proved that no axisymmetric field could be self-maintained. For a second time, Cowling had found a clear error in a paper by one of the leaders in his subject. Cowling's anti-dynamo theorem had a very significant influence and it was about 20 years before the topic of dynamo maintenance of magnetic fields recovered from the blow. Then numerical calculations by Bullard and Gellman suggested that non-axisymmetric dynamos could exist and a conceptual non-axisymmetric dynamo was invented by Herzenberg.
The solar magnetic field, and in particular sunspots, was a subject to which he returned frequently. Sometimes it was to criticize the work of others, as in a 1935 paper in Monthly Notices in which he cast strong doubt on current ideas about the cooling of sunspots, or in a 1946 paper in the same journal in which he showed that Alfvén's theory of sunspots was inconsistent internally and with observations. He concluded that there were some ideas of permanent value in Alfvén's work, but that the theory as a whole must be discarded. In the same year, he had shown that the observed behaviour of sunspot magnetic fields could not be due to growth or decay of the field, which would take about 300 years. Observed field changes that take place in days must be produced by the moving around of a pre-existing field.
Another topic with which Cowling's name is always associated is that of the lifetime of magnetic fields in stellar interiors In a paper entitled 'On the Sun's general magnetic field' he studied the decay of a primeval magnetic field in the radiative interior of a star and he showed that in relatively massive stars the lifetime of the field could exceed the main sequence lifetime. This led to the realisation that while some stellar magnetic fields, such as those in the solar atmosphere, must be maintained by dynamos, other fields such as the surface fields of the strongly magnetic stars may be decaying fossil fields or may at least have been produced by past dynamo action. Cowling's interest in stellar magnetic fields led to three important and influential review articles, 'General magnetic fields in the Sun and stars' with Horace Babcock in Monthly Notices in 1953, 'Solar electrodynamics' in The Sun, edited by G.P.Kuiper also in 1953 and 'Magnetic stars' in Stellar Structure, edited by L.H.Aller and D.B.McLaughlin in 1965.
In an early paper in 1931, Cowling showed that models of stars with degenerate interiors could not represent ordinary stars, thus giving support to Eddington's models composed of a perfect gas throughout. Following Eddington's work on stellar structure, it was generally accepted that the main mechanism of energy transport in stars was radiation, but Cowling introduced a model that was for years afterwards known as the Cowling model, in which convection was the principal mechanism of energy transport in the deep interior, with the outside being in radiative equilibrium. It was not possible to determine which stars would have convective cores until energy generation in stars was elucidated by Bethe and von Weizsäcker in 1938/39. Meanwhile, Cowling had indicated that convection would occur in stars with Kramer's opacity if the energy release increased with temperature more rapidly than .
A concern about stars with energy release strongly dependent on temperature was that they would be vibrationally unstable. A small rise in temperature would lead to a large increase in energy release. Although this would cause expansion and cooling, when the star subsequently contracted the temperature might be higher than at the previous contraction leading to an oscillation of increasing amplitude. Jeans believed that this was a serious objection to Eddington's stellar models and Eddington himself found vibrational instability if the energy release was highly temperature sensitive. In two papers Cowling showed that vibrational instability was very unlikely. He proved that instability required that in radiative stars the ratio of specific heats be less than 1.38 and that in convective regions either the ratio of specific heats be very close to 4/3 or the temperature exponent of energy generation be much greater than the critical value previously suggested. Ledoux subsequently showed that these conditions are met in very massive stars.
Stellar models were constructed with the simplifying assumption that temperature and density vanished at the surface, but problems arose for lower main-sequence stars like the Sun with convective exteriors. With the simplified boundary conditions, there is a free parameter in the models. Cowling, and independently Biermann, showed how an improved boundary condition, taking into account the need for energy transport to be by radiation close to the stellar surface, enabled this ambiguity in the models to be removed. Although this work was done in the 1930s, its consequences only received prominence in 1961 when Hayashi showed that the behaviour of pre-main-sequence stars was crucially dependent on taking account of the correct boundary condition. Biermann and Cowling corresponded about their work, and this led to a close friendship, although they did not meet until after the Second World War. Their correspondence also led to one joint paper on the "Chemical composition and vibrational stability of stars" published in Zeitschrift für Astrophysik in 1939
A characteristic piece of work was a single paper published in 1938, 'On the Motion of the Apse Line in Close Binary Systems.' He realized that the previous discussions of the manner in which the elliptical orbit rotates by Russell, Walter, and Kopal were all incorrect because they all assumed that the stars would behave to a greater or lesser extent as rigid bodies during their motion. When he took full account of the lack of rigidity of the stars, he obtained a formula for the advance of periastron which was generally similar to that of Russell but which had different numerical factors in some of the terms
Probably Cowling's paper on stellar structure that receives greatest attention today is his 1941 paper "The Non-Radial Oscillations of Polytropic Stars." In this, he identified two series of non-radial oscillations: the -modes driven by pressure variations and the -modes, or gravity modes. In addition, there was a single -mode, or fundamental mode. At that time, there did not seem to be much prospect of observing this wealth of oscillations, even if they were excited in real stars. Now it is possible to observe a complete spectrum of p-modes at the surface of the Sun and to use them as a probe of the properties of the Sun's interior through solar seismology.
That paper was Cowling's last really important one on stellar structure, although he wrote four further papers on rotating and magnetic stars. These were early studies of oscillations and convection in rotating stars, a demonstration that it was very unlikely that the observed magnetic variable stars were oscillating and a proof that a published model of a star containing a magnetic field was unstable but that the effect of the instability was likely to be a readjustment of the field structure rather than an explosion.
Cowling's active research career was cut short by illness. In 1957 he suffered from a bad back and in 1960 he had a heart attack, which though not very serious in the long run restricted his activities for some years. He told me that he found it difficult to believe that he would ever be able to undertake further responsibilities outside Leeds and that he was very grateful to his two predecessors as Presidents of the Society, Bill McCrea and Dick Woolley, for persuading him to let his name go forward for the presidency in 1965. As President he gave addresses on 'The development of the theory of stellar structure' and 'Interstellar and interplanetary magnetic fields'. He wrote a number of review articles and revised his books and also published three articles on various topics relating to mathematics, astronomy, astrology and religion, one being the 1977 Brodetsky Memorial Lecture at Leeds and another the 1981 Milne Lecture at Oxford. His last important astronomical paper was 'The present status of dynamo theory' in the 1981 Annual Review of Astronomy and Astrophysics.
As I mentioned earlier, Cowling's entire career was spent in mathematics departments, and he had few colleagues or students with whom he collaborated; Leon Mestel as a research fellow and Eric Priest as a research student were the notable exceptions. He also had neither formal education in astronomy himself nor taught astronomy as a faculty member. He recognized that this was not the way astronomy should be done in the future, and he actively encouraged plans for a National Institute of Theoretical Astronomy. Although the National Institute did not come into being, the idea led to the Institute of Astronomy at Cambridge and the Astronomy Centre at Sussex. By that time, Cowling did not feel strong enough to contemplate a move to an astronomical environment.
Tom Cowling married Doris Marjorie Moffatt on August 24, 1935, and he is survived after a long and happy marriage by his wife, two daughters, a son, and grandchildren. He was a lifelong active member of the Baptist church.
R.J. Taylor
Tom Cowling was born in Hackney, London on June 17, 1906. He was the second of four sons of George and Edith Cowling and attended Sir George Monoux Grammar School, Walthamstow from 1917 to 1923. He won an open mathematics scholarship to Brasenose College, Oxford, where he was a student from 1924 to 1930. He was awarded a University Junior Mathematical Exhibition in 1925 and a scholarship in 1926, and he graduated with first-class honours in mathematics in 1927. His scholarship at Brasenose was not adequate to finance his course, and additional support from the Department of Education carried the expectation, if not the obligation, that he would become a school teacher. As a result, when he was awarded a three-year postgraduate scholarship at Oxford, he spent the first year taking a diploma in education before becoming Professor E.A. Milne's first research student at Oxford from 1928 to 1930 Subsequently, he was a demonstrator in Professor Sydney Chapman's department at Imperial College before holding an Assistant Lectureship at Swansea (1933–37), lectureships at Dundee (1937–38) and Manchester (1938–45), and professorships at Bangor (1945–48) and Leeds (1948–70), where he remained as an Emeritus Professor until his death. Cowling spent his entire career in mathematics departments, and the number of moves he made will seem remarkable to young academics today.
Cowling was elected to Fellowship of the Society on January 9, 1931. He was a member of Council from 1939–44, 1950–55, and 1965–68, being President from 1965–67 and Vice-President from 1952–54 and 1967–68 He was awarded the Gold Medal of the Society in 1956 for his distinguished contributions to theoretical astrophysics and particularly for his work on the stability of stars. He was elected to Fellowship of the Royal Society in 1947, and other awards he received included the Bruce Gold Medal of the Astronomical Society of the Pacific in 1985 and the Hughes Medal of the Royal Society in 1990. The latter award was made two days before he died, and he did not learn of it. In the International Astronomical Union, he was President of Commission 35, Stellar Constitution, from 1955 to 1958, and of Commission 43, Magnetohydrodynamics and the Physics of Ionized Gases, from 1964 to 1967.
Throughout his research career, Cowling tackled difficult problems, most of which required a combination of mathematical skills and physical insight. His total list of publications is not very long by current standards, but almost all of his papers contain an important point, many of which have survived to the present day. He was not only self-critical but he was critical of the work of others. If any young scientist learnt that Cowling approved of some of his work he knew that he had succeeded. I came under his influence early in my career because he refereed my first papers both on stellar structure and on magnetohydrodynamics. His demand for high standards was combined with a warm personality and a dry sense of humour which endeared him to all who knew him. His great height meant that one could always catch his eye in the middle of a boring introductory speech at a conference reception.
His first two publications set the scene for his life's work, one being on the solar magnetic field and the other on stellar structure. In the first, he criticized some recent work by Chapman and independent work by Ross Gunn, which suggested that the magnetic field of the Sun was limited in its radial extent, the idea being that the motion of charged particles in the magnetic field produced a current and an additional magnetic field which caused the limitation. Cowling showed that the treatment was not self-consistent and that the Sun must possess open field lines. This criticism by Chapman did him no harm because, once he had completed his doctorate, Chapman offered him a junior post in his department and later asked him to collaborate in the production of their treatise The Mathematical Theory of Non-Uniform Gases. Published in 1939, this became a classic text with second and third editions appearing in 1952 and 1970. In 1950, Cowling published an elementary book Molecules in Motion on the same subject
In 1932, Cowling wrote his first paper on the electrical conductivity of an ionized gas in the presence of a magnetic field, and he showed that the motion of the gas perpendicular to the field was rapidly dampened. Although the paper did not explicitly refer to the frozen-in-field, a concept later particularly associated with the name Alfvén, the germ of the idea was there. Cowling returned to this problem in 1956. By then, it was known that the electrical conductivity of a gas in directions perpendicular to a magnetic field was much less than the conductivity parallel to the field, but there was dispute about what the effective value of the conductivity should be used in the formula for the dissipation of energy. Cowling obtained an expression for the dissipation similar to one also obtained by Piddington, which indicated that cosmic magnetic fields could be much less long-lived than if the conductivity had its standard value. Shortly afterward, his introductory book, Magnetohydrodynamics, was published by Interscience Together with an accompanying book, The Physics of Fully Ionized Gases by Lyman Spitzer, it gave a clear introduction to the new subjects of magnetohydrodynamics and plasma physics, which were developing rapidly in response to attempts to produce controlled thermonuclear reactions in the laboratory and to the start of space exploration of the solar system.
The piece of Cowling's work, which is probably known at least by name to the greatest number of scientists, appeared in a paper entitled 'The Magnetic Field of Sunspots' in 1933. It was then realized that some cosmic magnetic fields, including those of sunspots and the Earth, could not be slowly decaying primeval fields. They must be maintained, and Sir Joseph Larmor had proposed that the sunspot fields were regenerated by dynamo action involving axisymmetric motions in the conducting gas. Cowling proved that no axisymmetric field could be self-maintained. For a second time, Cowling had found a clear error in a paper by one of the leaders in his subject. Cowling's anti-dynamo theorem had a very significant influence and it was about 20 years before the topic of dynamo maintenance of magnetic fields recovered from the blow. Then numerical calculations by Bullard and Gellman suggested that non-axisymmetric dynamos could exist and a conceptual non-axisymmetric dynamo was invented by Herzenberg.
The solar magnetic field, and in particular sunspots, was a subject to which he returned frequently. Sometimes it was to criticize the work of others, as in a 1935 paper in Monthly Notices in which he cast strong doubt on current ideas about the cooling of sunspots, or in a 1946 paper in the same journal in which he showed that Alfvén's theory of sunspots was inconsistent internally and with observations. He concluded that there were some ideas of permanent value in Alfvén's work, but that the theory as a whole must be discarded. In the same year, he had shown that the observed behaviour of sunspot magnetic fields could not be due to growth or decay of the field, which would take about 300 years. Observed field changes that take place in days must be produced by the moving around of a pre-existing field.
Another topic with which Cowling's name is always associated is that of the lifetime of magnetic fields in stellar interiors In a paper entitled 'On the Sun's general magnetic field' he studied the decay of a primeval magnetic field in the radiative interior of a star and he showed that in relatively massive stars the lifetime of the field could exceed the main sequence lifetime. This led to the realisation that while some stellar magnetic fields, such as those in the solar atmosphere, must be maintained by dynamos, other fields such as the surface fields of the strongly magnetic stars may be decaying fossil fields or may at least have been produced by past dynamo action. Cowling's interest in stellar magnetic fields led to three important and influential review articles, 'General magnetic fields in the Sun and stars' with Horace Babcock in Monthly Notices in 1953, 'Solar electrodynamics' in The Sun, edited by G.P.Kuiper also in 1953 and 'Magnetic stars' in Stellar Structure, edited by L.H.Aller and D.B.McLaughlin in 1965.
In an early paper in 1931, Cowling showed that models of stars with degenerate interiors could not represent ordinary stars, thus giving support to Eddington's models composed of a perfect gas throughout. Following Eddington's work on stellar structure, it was generally accepted that the main mechanism of energy transport in stars was radiation, but Cowling introduced a model that was for years afterwards known as the Cowling model, in which convection was the principal mechanism of energy transport in the deep interior, with the outside being in radiative equilibrium. It was not possible to determine which stars would have convective cores until energy generation in stars was elucidated by Bethe and von Weizsäcker in 1938/39. Meanwhile, Cowling had indicated that convection would occur in stars with Kramer's opacity if the energy release increased with temperature more rapidly than .
A concern about stars with energy release strongly dependent on temperature was that they would be vibrationally unstable. A small rise in temperature would lead to a large increase in energy release. Although this would cause expansion and cooling, when the star subsequently contracted the temperature might be higher than at the previous contraction leading to an oscillation of increasing amplitude. Jeans believed that this was a serious objection to Eddington's stellar models and Eddington himself found vibrational instability if the energy release was highly temperature sensitive. In two papers Cowling showed that vibrational instability was very unlikely. He proved that instability required that in radiative stars the ratio of specific heats be less than 1.38 and that in convective regions either the ratio of specific heats be very close to 4/3 or the temperature exponent of energy generation be much greater than the critical value previously suggested. Ledoux subsequently showed that these conditions are met in very massive stars.
Stellar models were constructed with the simplifying assumption that temperature and density vanished at the surface, but problems arose for lower main-sequence stars like the Sun with convective exteriors. With the simplified boundary conditions, there is a free parameter in the models. Cowling, and independently Biermann, showed how an improved boundary condition, taking into account the need for energy transport to be by radiation close to the stellar surface, enabled this ambiguity in the models to be removed. Although this work was done in the 1930s, its consequences only received prominence in 1961 when Hayashi showed that the behaviour of pre-main-sequence stars was crucially dependent on taking account of the correct boundary condition. Biermann and Cowling corresponded about their work, and this led to a close friendship, although they did not meet until after the Second World War. Their correspondence also led to one joint paper on the "Chemical composition and vibrational stability of stars" published in Zeitschrift für Astrophysik in 1939
A characteristic piece of work was a single paper published in 1938, 'On the Motion of the Apse Line in Close Binary Systems.' He realized that the previous discussions of the manner in which the elliptical orbit rotates by Russell, Walter, and Kopal were all incorrect because they all assumed that the stars would behave to a greater or lesser extent as rigid bodies during their motion. When he took full account of the lack of rigidity of the stars, he obtained a formula for the advance of periastron which was generally similar to that of Russell but which had different numerical factors in some of the terms
Probably Cowling's paper on stellar structure that receives greatest attention today is his 1941 paper "The Non-Radial Oscillations of Polytropic Stars." In this, he identified two series of non-radial oscillations: the -modes driven by pressure variations and the -modes, or gravity modes. In addition, there was a single -mode, or fundamental mode. At that time, there did not seem to be much prospect of observing this wealth of oscillations, even if they were excited in real stars. Now it is possible to observe a complete spectrum of p-modes at the surface of the Sun and to use them as a probe of the properties of the Sun's interior through solar seismology.
That paper was Cowling's last really important one on stellar structure, although he wrote four further papers on rotating and magnetic stars. These were early studies of oscillations and convection in rotating stars, a demonstration that it was very unlikely that the observed magnetic variable stars were oscillating and a proof that a published model of a star containing a magnetic field was unstable but that the effect of the instability was likely to be a readjustment of the field structure rather than an explosion.
Cowling's active research career was cut short by illness. In 1957 he suffered from a bad back and in 1960 he had a heart attack, which though not very serious in the long run restricted his activities for some years. He told me that he found it difficult to believe that he would ever be able to undertake further responsibilities outside Leeds and that he was very grateful to his two predecessors as Presidents of the Society, Bill McCrea and Dick Woolley, for persuading him to let his name go forward for the presidency in 1965. As President he gave addresses on 'The development of the theory of stellar structure' and 'Interstellar and interplanetary magnetic fields'. He wrote a number of review articles and revised his books and also published three articles on various topics relating to mathematics, astronomy, astrology and religion, one being the 1977 Brodetsky Memorial Lecture at Leeds and another the 1981 Milne Lecture at Oxford. His last important astronomical paper was 'The present status of dynamo theory' in the 1981 Annual Review of Astronomy and Astrophysics.
As I mentioned earlier, Cowling's entire career was spent in mathematics departments, and he had few colleagues or students with whom he collaborated; Leon Mestel as a research fellow and Eric Priest as a research student were the notable exceptions. He also had neither formal education in astronomy himself nor taught astronomy as a faculty member. He recognized that this was not the way astronomy should be done in the future, and he actively encouraged plans for a National Institute of Theoretical Astronomy. Although the National Institute did not come into being, the idea led to the Institute of Astronomy at Cambridge and the Astronomy Centre at Sussex. By that time, Cowling did not feel strong enough to contemplate a move to an astronomical environment.
Tom Cowling married Doris Marjorie Moffatt on August 24, 1935, and he is survived after a long and happy marriage by his wife, two daughters, a son, and grandchildren. He was a lifelong active member of the Baptist church.
R.J. Taylor
Thomas George Cowling's obituary appeared in Journal of the Royal Astronomical Society 32:2 (1991), 201-205.