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Schwarzschild, Martin

SCHWARZSCHILD, MARTIN

(b. Potsdam, Germany, 31 May 1912; d. Princeton, New Jersey, 10 April 1997), astrophysics, galaxy evolution, stellar constitution, interiors, and evolution.

Schwarzschild, a leading practitioner of the theory of stellar structure and evolution for much of the twentieth century, made enormous contributions not only to astronomical knowledge but to the professional development of the American astronomical community. His mentoring and textbook writing trained generations, and his personality and social sensibilities inspired colleagues and students alike.

Life and Family in Germany Born to the famed director of the Potsdam Astrophysical Observatory, Karl Schwarzschild, and Else Rosenbach, the daughter of a professor of medicine and surgery at the University of Göttingen, he was the middle of three children. His father died in 1916, and so the family returned to Göttingen, where Martin was raised and trained in astronomy by Hans Kienle, the director at Göttingen. Martin and his siblings grew up in a protected, narrow social stratum surrounded by family and his parents’ colleagues and friends. Of them, Martin counted the physicist Carl Runge as one of his earliest influences and mentors in mathematics and physics. Robert Emden, the author of the famous Gaskugeln, was an uncle by marriage.

After completing classical secondary school training, Schwarzschild entered the University of Göttingen in 1931, studying mainly mathematics and physics, at Kienle’s direction, under Richard Courant and Otto Neugebauer. He also studied in Berlin, and was in fact there when the Reichstag burned and Adolf Hitler became chancellor. At that point, in February 1933, his mother decided that conditions were turning too threatening and called him back to Göttingen, urging him to complete his studies through to the PhD as quickly as possible, which he did, sympathetically encouraged and protected by Kienle through tutorials and directed reading.

Schwarzschild had acquired an interest in the pulsation theory of a class of variable stars called Cepheids, renowned for their utility in calculating distances to stars. But largely through reading Arthur Stanley Eddington’s books and learning there that the mechanism through which the stars vary in luminosity was not at all well understood in terms of its varying structure, Schwarzschild set himself the task of understanding how Cepheids pulsate as they do. He was interested in a theoretical study, but Kienle required observational work as well, which took much longer than expected, mainly because of the antiquated equipment and poor weather conditions. In consequence Martin was still at work on his thesis when persons of Jewish descent were barred from any of the university buildings. So Kienle had the janitor of the observatory take the needed measuring equipment each night to Schwarzschild’s mother’s apartment so that he could finish the work as rapidly and invisibly as possible.

Completing his PhD exam in December 1935, and his thesis soon after, “Zur Pulsationstheorie der delta Cephei-Sterne” (On the pulsation theory of delta Cepheid stars), Schwarzschild still had to finish his observations, and as he was doing this, Kienle searched for a way to get him out of Germany. Svein Rosseland of Oslo quickly offered him a one-year postdoctoral position at his institute starting in the spring of 1936, which allowed him to study pulsation theory, the theory of the stellar interior, and stellar rotation.

Postdoctoral Fellowship in Oslo Research in Oslo centered around stellar structure calculations aided by one of Vannevar Bush’s mechanical analogue computing machine known as a differential analyzer. Rosseland encouraged Schwarzschild and others to use it collectively and even though Schwarzschild was initially skeptical he found it useful enough to do publishable work with it on pulsation, the first astronomical publication to appear based upon its application. During his tenure in Oslo, he also explored observational constraints on possible sources of energy production in stars.

Move to the United States Schwarzchild was barely in Oslo when Harlow Shapley invited him to a three-year appointment at Harvard University. He arrived at Harvard in the summer of 1937, finding a vibrant company of European refugee scientists and American astronomers and physicists. He continued to work on Cepheid pulsation, analyzing how the pulsation characteristics could be used to determine the phase relationship between the light and velocity variations.

In the summer of 1938, during a visit to Stockholm and the General Assembly of the International Astronomical Union, Schwarzschild argued that pulsations were limited to the outer envelope of stars, and so were not a good indicator of what went on in the stellar core. Thus they were comparatively less interesting as tests or constraints on energy sources. Nevertheless, he carried on with his Cepheid work, all the while becoming more and more involved with problems of the deep stellar interior. His visit to Stockholm also gave him the opportunity to visit his mother in Germany, which was the last time they were together. By then his older sister had moved to England for study, and his younger brother, in deteriorating health, remained behind.

At Harvard Schwarzschild became acquainted with people such as Subrahmanyan Chandrasekhar and Lyman Spitzer. Both would play central roles in the course of Schwarzschild’s career. Through Shapley and Bart Bok, he responded to a job offer from Columbia University, and acquired his first permanent position. In a two-person department working for Jan Schilt, Schwarzschild found at his disposal a legacy created by Wallace J. Eckert, who had pioneered the use of punched-card-fed computing machines for astronomy. With support from Thomas J. Watson, Eckert had secured an array of IBM machines and staff in what was called after 1937 the Thomas J. Watson Astronomical Computing Bureau. Schilt’s students used the machines for statistical studies of stellar motions, and Schwarzschild applied them to his Cepheid research with the invaluable aid of a machine operator named Lillian Feinstein. She taught Schwarzschild how to use the machines, and then assisted in the actual calculations. These were all mechanical and electrical devices, without logical electronics, but they were so much more capable than Rosseland’s Oslo machine that Schwarzschild was able to reevaluate his pulsation models, accurate to far more decimal places. Recent statistical studies of Cepheid periods suggested to Schwarzschild that this class of variable star exhibited the characteristics of harmonic oscillators and so he explored them with this well-known technique.

During his eighteen months at Columbia, Schwarzschild had considerable contact with senior physicists such as Enrico Fermi, as well as Isidor I. Rabi and Harold Urey. He knew that the physicists could not talk about their secret work, so lunches were devoted to astrophysics. Fermi in particular was very helpful and insightful, supplying data that were otherwise difficult to obtain, such as estimates for cross sections for collisions between electrons and hydrogen atoms. These helped Schwarzschild calculate levels of collisional ionization in the hydrogen convection zones in the stellar interiors of red giants, finding them more important than photoionization effects for creating equilibrium conditions.

At Columbia in 1941, following up conversations with Gunnar Randers in Oslo, and continued contact with Chandrasekhar, who was then a visiting professor at Princeton University, Schwarzschild began to look seriously at the importance of stellar rotation, basically to find equilibrium configurations for stars that possessed angular momentum. He was working on this problem as well as teaching when the attack on Pearl Harbor changed his life for he decided then and there to enlist in the army. As a German Jew, he felt he could not avoid active service when the American students he was teaching were all headed that way.

War Service After basic training and a short assignment to an antiaircraft gunnery unit, Schwarzschild transferred to the Aberdeen Proving Ground in Maryland for ballistics research, but chafed at the assignment, wanting to see action at the front. He was now a citizen, so he applied for Officers’ Candidate School, specifically the antiaircraft gunnery officers’ school, which brought a special assignment with the Twelfth U.S. Air Force in Italy, performing operations analysis with a front line ordnance unit to assess the types of ordnance needed to carry out such tactical missions as knocking out bridges and railroad lines. With the end of the war, Schwarzschild was discharged as a first lieutenant, receiving the Legion of Merit and a Bronze Star for his services, mainly for producing a simplified fire control system that could be used in the field to operate antiaircraft batteries.

Returning from the war, back at Columbia, Schwarzschild married Barbara Cherry. They had met at Harvard when Barbara, a Radcliffe University student, took graduate astronomy courses. They corresponded throughout the war and married immediately after the war, just as Barbara was finishing her work at the Massachusetts Institution of Technology’s Radiation Laboratory. Barbara also became Martin’s collaborator and professional associate, engaging in astronomical research, especially the observational aspects, supporting him in his interests, and managing the affairs of the family. They could not have children.

By the time he returned in late 1945 he was already working on stellar rotation again as well as a related study of the solar helium content. As one of the most promising young theorists in America, he soon had offers from major astronomical centers that were reorganizing and strengthening their theoretical expertise in astrophysics. Ultimately Schwarzschild chose Princeton, mainly because Spitzer had been called there as the new director, and his contacts with Spitzer through the Neighbors’ meetings, a periodic conference of East Coast astronomers, convinced him that their scientific philosophies and outlook were very similar and that Spitzer would provide just the environment he needed. Both were basically theoreticians, but both knew that they could not work independent of observational constraints, and in fact both wanted to remain active in observational work. Spitzer had, in fact, accepted the directorship with the understanding that a second senior professorship would be provided, and that both would be allowed leaves of absence on a regular basis for observational work. Schwarzschild remained at Princeton for the remainder of his career and life.

Princeton Years Schwarzschild and Spitzer set about rebuilding Princeton astronomy. They centered their graduate program around a strong theoretical core, creating a two-year cycle of four one-semester graduate astronomy courses, requiring that their students take the rest of their training in physics. Gradually they added staff, mainly through new research programs. In particular Schwarzschild became involved in Spitzer’s large project to design and develop a stable fusion reactor called the “Stellerator,” an adjunct to Project Matterhorn, John

Wheeler’s nuclear weapons program. Both men were stimulated to get involved in such work when the Korean War broke out. Both developed strong connections with staff and graduate students at the combined Mount Wilson and Palomar Observatories. This cross-institutional pattern established one of the most robust programs in stellar astrophysics in the world, which led to, among other things, the modern view of how stars age.

Stellar Structure and Evolution Schwarzschild had always been interested in stellar structure, as the central theme in stellar astronomy. He was keenly aware of attempts by others to build models of the Sun and stars, based largely upon Eddington’s idea that the source of energy causing a star to shine was distributed throughout its interior, and that the energy itself was transported to the stellar surface chiefly by radiation, not by the transfer of matter (convection). By the late 1930s, however, Schwarzschild was among a small but growing circle of theoretical astrophysicists who knew that that Eddington’s “standard model” had to be modified in a number of significant ways: first by arguments that thermonuclear energy sources had to lie at the very centers of stars, and that this created huge temperature gradients and hence convection in stellar cores. Further, the fusion processes would cause chemical inhomogeneities that would change the interior structure. With the appearance and rapid acceptance of Hans Bethe and Karl F. von Weizsäcker’s specific nuclear mechanisms, the proton-proton (PP) and the carbon-nitrogen-oxygen (CNO) cycles, which confirmed the need for a high temperature gradient to produce helium from hydrogen, by the early 1940s everyone knew that stratified, composite models would be necessary to explore the evolution of stars. But just at that time, Chandrasekhar and Mario Schönberg had shown that there was an upper limit to the amount of hydrogen within a star available for fusion. Once that fraction was consumed, the core would become isothermal (a single temperature throughout) and beyond that there seemed to be no stable equilibrium configurations for stars. The problem became: how to model stars with varying compositions but isothermal cores, especially at a stage after hydrogen was exhausted in the core? The physicist George Gamow had the idea that increased temperatures in the inner portion of the outer envelope would stimulate a new source called shell burning. Chandrasekhar rejected this idea and Gamow’s techniques, arguing that they were not mathematically rigorous.

Chandrasekhar and Gamow’s differences destabilized the field somewhat in the 1940s, and Schwarzschild cautiously explored how stars might change in structure in response to chemical and physical changes. Schwarzschild’s first stellar model for the Sun in 1946 was homogeneous with a convective core. He adjusted composition to match the solar luminosity and radius and employed the CNO process. He tried for more realism in 1949, collaborating first with Li Hen and later with J. Beverly Oke, constructing red giants that were static and inhomogeneous and at first nonevolving, but soon, with convective cores, they could be made to evolve, through a series of laborious computational exercises. In hindsight, at this time one can see Schwarzschild beginning a series of connected studies leading to a way to overcome the Schönberg-Chandrasekhar limit, and to explore what happens to stars once they exhaust hydrogen in their cores.

The great question at the time was: where do stars “go” on the Hertzsprung-Russell (HR) diagram?, which was then, as now, the heuristic playing field for stellar evolution studies. Since the first elucidation of the HR diagram, a graphical plot of a star’s physical characteristics, mainly its temperature against its intrinsic brightness, by Ejnar Hertzsprung and Henry N. Russell independently between 1908 and 1913, astronomers had used the HR diagram to explore how these characteristics of a star change as the star ages. Do they become white dwarfs or red giants? Gamow and almost everyone else had for decades assumed that it had to be toward the white dwarf stages because that was the time-honored direction of gravitational contraction. But observational and theoretical evidence had been mounting since the early 1930s that such was not the case. Schwarzschild’s strategy was to test theory against the best observational evidence. The latter was facilitated by his connections with Walter Baade and the Mount Wilson–Palomar–California Institute of Technology staff. Essentially, Schwarzschild and Baade joined forces to solve the stellar evolution problem. The details of this episode are in David H. DeVorkin (2006).

Baade’s goal in 1951 was to find, using HR diagrams of globular clusters, just where and how stars in these clusters, all believed to be of the same age, and evolving at rates highly dependent upon their relative masses, ceased being common “main sequence” types and began moving to the red giant range, in other words, where and when in their lives did they “turn off” the main sequence to become giants? Baade coordinated observations in the West, and Schwarzschild the theory in the East, and both visited back and forth, cross-fertilizing students and staff.

Observed cluster “turn-off” points were not fully reconciled with theoretical models of shell burning until Schwarzschild collaborated with Fred Hoyle in the spring of 1953. By then Schwarzschild had the assistance of Richard Härm, who was exceptionally adept at numerical computational techniques. Working also with William Baum and then with Hoyle, who brought in new perspectives from nuclear physics, Schwarzschild had assembled a wealth of talents and insights to combine computational and heuristic techniques to make the final push. Hoyle refined the models Schwarzschild had constructed earlier with Allan Sandage, finding that stellar turnoffs occurred after the envelope of the star went from radiative equilibrium to convective equilibrium with the onset of shell burning. The now-accepted idea of a hydrogen-burning shell migrating outward through the envelope worked sufficiently well to match observations, right up into the giant realm in the upper right-hand corner of the HR diagram. Thus by 1955 the forty-year-old picture of red giants as young stars in formation was finally reversed by Schwarzschild, Baade, and their compatriots, establishing them as old, evolved stars.

Schwarzschild continued on exploring the fine structure of postmain sequence stellar evolution well into the 1970s and to retirement. But a watershed came in 1958 when he published the first advanced textbook that explicitly led students through the process. Structure and Evolution of the Stars was considered a central source of instruction and inspiration soon after its publication. It was a straightforward book, designed to be affordable and disposable, and was written in a conversational tone that became an inspiration to generations of advanced students, laying out the processes of stellar evolution on the eve of access to high-speed electronic computers. It described the problems yet to solve, and gave hints on how to solve them. Schwarzschild recalls knowing that it would not be a definitive work; in fact, he intended it to be a stimulus to attract new talent to the field.

Other Lines of Research Schwarzschild will be most remembered for his contributions to stellar structure and evolution, but he was also keenly interested in the closely related problem of sorting out and interpreting the meaning of Baade’s stellar populations and in the nature and importance of convection in the atmospheres of the Sun and stars. There were links between all three.

During the war, at Mount Wilson Baade announced his revolutionary concept that the stellar content of galaxies could be divided into distinct populations with characteristic colors and luminosities. Population I stars were found in the disk of the galaxy, mainly single stars and stars in open galactic clusters, whereas Population II were in the bulge and halo, characteristic of the stars found in globular clusters, the nuclei of spiral galaxies and in elliptical galaxies. He called upon astronomers to figure out why these differences existed. In 1950 Martin and Barbara Schwarzschild made one of their periodic visits to Mount Wilson to take a series of high-dispersion spectra to compare the chemical characteristics of high-velocity and low velocity F-type stars. These velocity classes were thought to be an indicator of age, and indeed, they found a correlation: the metal to hydrogen ratio was higher in the low-velocity Population I stars, and higher in the Population II high-velocity stars. This association between heavy-metal Abūndance and population helped to establish the evolutionary significance of the populations. Schwarzschild continued this line of work, collaborating with Spitzer and Rupert Wildt, to further explore the origins of these chemical differences in terms of evolutionary differences in the interstellar medium. Again Schwarzschild was most interested in how the stellar populations revealed element-building processes in stellar evolution, whereas Spitzer was more interested in how conditions in the interstellar medium promoted star formation, using his expertise in the physics of plasmas. Schwarzschild continued his interest in stellar populations through the 1950s, in collaboration with students and staff from Mount Wilson.

The second related area he engaged in his postwar career dealt with theories of convection and the importance of element mixing and rotation in an evolving star. After a summer of solar observing at Mount Wilson in 1950 with Robert S. Richardson, trying to examine convective phenomena in the solar photosphere, Schwarzschild became frustrated by limitations of Earth’s atmosphere. Back in Princeton, Schwarzschild complained to Spitzer and others about this seemingly insuperable limitation, and, encouraged by Spitzer and James Van Allen, who was then part of Project Matterhorn, decided to pursue building a telescope that could be lofted by balloon into the transparent upper stratospheric layers. Spitzer was thinking about the ultimate use of satellites for astronomy, and even Schwarzschild’s father had flown solar instruments on a zeppelin years back. So Martin Schwarzschild, with Spitzer’s guidance, eventually created Project Stratoscope, funded by the Office of Naval Research and later by the National Science Foundation (NSF) and finally by the National Aeronautics and Space Administration (NASA).

The first stratoscope was highly successful: a 12-inch photographic reflector on a stabilized platform flew under huge plastic balloons in 1957 and, in an improved form, in 1959 to produce the clearest images of the solar photosphere known to exist at that time. They were in fact sufficiently clear to help Schwarzschild discriminate between competing theories of convection in the outer solar envelope and spurred him to return to convection theory in the 1960s.

In the post-Sputnik era, Spitzer committed his department to building a large spaceborne telescope. Allied with this institutional effort, Schwarzschild continued Project Stratoscope, expanding its scope with NASA funding to build a 36-inch balloon-borne system, Stratoscope 2, capable of performing a range of spectroscopic and visible-range imaging studies requiring precise pointing and stability. As he recalled years later, “We always looked at the balloons as an exercising ground, for scientific results, before the satellites. All of which took more time than we then thought” (Schwarzschild oral history, 19 July 1979, p. 162, American Institute of Physics). It was indeed a time-consuming and deeply frustrating experience for Schwarzschild, who loyally continued with the program well through the 1960s. His mistake, he later felt, was to stick with photographic imaging, which required pointing and stability precision beyond what was feasible at the time.

Beyond his immediate duties of research and teaching, Schwarzschild participated in NSF funding panels and later, as a member of the National Academy of Sciences, was invited to become a member of the Space Science Panel of the President’s Science Advisory Committee (PSAC), serving for some eight years during the Apollo era, 1959 through 1967. After that he served on NASA’s Astronomy Missions Board from 1967 though 1969. His most active participation on the PSAC panel centered on preparing arguments for the White House, and later for congressional testimony in 1962, regarding a scientific role for Project Apollo. Schwarzschild never felt that science could justify the expense of the Apollo program, but did testify that good science could be done as a consequence of a human lunar landing. However, he always argued that its real value was to help stimulate and boost science education in the United States, as well as the nation’s overall technology capability.

Schwarzschild was active in the International Astronomical Union, serving as a vice president; and in the American Astronomical Society, serving as vice president, president-elect, and president between 1967 and 1972. This was a time of profound change in the society as it formed large specialty-related divisions and managed the transfer of arguably the most important astronomical journal of the time, the Astrophysical Journal, to society ownership.

Retirement Schwarzschild formally retired from Princeton in 1979 but remained active in the profession and in research. Characteristically modest, he later recalled that his retirement was stimulated by the retirement of his longtime associate Richard Härm, who had contributed so much to his effectiveness in stellar structure and evolution calculations. Upon retirement Schwarzschild also switched his research focus from stellar interiors to the study of galactic structure, which had been a longtime interest. Taking a middle course between those interested in the astrophysics of galaxy structure and evolution, and those who examined galaxies dynamically, Schwarzschild decided to perform a series of computational experiments that would create numerical models for the structure of the nuclei of elliptical galaxies that could be tested against observation. His goal was to test an assumption that others had always made: that galaxy nuclei were rotationally symmetric. What he found was that deviations from rotational symmetry fit the observations better than those constrained by symmetry, which, as Jeremiah Ostriker (1997) put it, “revolutionized our understanding of elliptical galaxies,” showing them to be triaxial.

Schwarzschild was the recipient of many awards and honors. He was Russell Prize Lecturer of the American Astronomical Society for 1960, and received the Bruce Medal of the Astronomical Society of the Pacific (1965) and the Gold Medal of the Royal Astronomical Society (1969). He was elected a foreign member of the Royal Society in 1996, and was a posthumous recipient of the U.S. National Medal of Science in 1997. Martin and Barbara lived a quiet but full life, on a wooded street between the Princeton campus and the Institute for Advanced Study. They shared many interests beyond astronomy, including skiing, cross-country snowshoe treks, gardening, mineral and rock collecting, and birding. They arranged their backyard to accommodate their interests and there enjoyed being a part of nature.

BIBLIOGRAPHY

Much of the material in this essay is based upon oral histories, Martin Schwarzschild “Oral History” American Institute of Physics Center for History of Physics: 10 March 1977; 3 June 1977; 16 December 1977; 19 July 1977; 18 June 1982; 20 April 1983; 26 August 1991. There is also an interview with Schwarzschild concentrating on computational techniques at the Charles Babbage Institute, University of Minnesota. Martin Schwarzschild’s private papers are housed at Princeton University’s Firestone Library, Manuscript Division.

WORKS BY SCHWARZSCHILD

“Zur Pulsationstheorie der delta Cephei-Sterne.” Veröffentlichungen der Universitäts-Sternwarte Göttingen, Nr. 45. Zeitschrift für Astrophysik 11 (1936): 152–180. His thesis.

“Über die Energieerzeugung in den Sternen.” Zeitschrift für Astrophysik 13 (1937): 126.

“Zur Pulsationstheorie.” Mitteilung aus dem Institut für theoretische Astrophysik, Oslo. Zeitschrift für Astrophysik 15 (1938): 14–31.

“Overtone Pulsations for the Standard Model.” Astrophysical Journal 94 (1941): 245–252.

With Lillian Feinstein. “Automatic Integration of Linear Second-Order Differential Equations by Means of Punched-Card Machines.” Review of Scientific Instruments 12 (1941): 405–408.

With Lyman Spitzer Jr., and Rupert Wildt. “On the Difference in Chemical Composition between High- and Low-Velocity Stars.” Astrophysical Journal 114 (1951): 398–406.

With I. Rabinowitz, and Richard Härm. “Inhomogeneous Stellar Models. III. Models with Partially Degenerate Isothermal Cores.” Astrophysical Journal 118 (1953): 326–334.

With Richard Härm. “Inhomogeneous Stellar Models. IV. Models with Continuously Varying Chemical Composition.” Astrophysical Journal 121 (1955): 445–453.

With Fred Hoyle. “On the Evolution of Type II Stars.” Astrophysical Journal 121 (1955): 776. Brief summary of the following paper.

———. “On the Evolution of Type II Stars.” Astrophysical Journal Supplement 2 (1955): 1–40.

With William A. Baum. “A Comparison of Stellar Populations in the Andromeda Galaxy and Its Elliptical Companion.” Astronomical Journal 60 (1955): 247–253.

Structure and Evolution of the Stars. Princeton, NJ: Princeton University Press, 1958. Reprinted, New York: Dover, 1965.

With John B. Rogerson Jr., and J. W. Evans. “Solar Photographs from 80,000 Feet.” Astronomical Journal 63 (1958): 313.

With Richard Härm. “Evolution of Very Massive Stars.” Astrophysical Journal 128 (1958): 348–360.

With J. D. R. Bahng, R. E. Danielson, and J. B. Rogerson Jr. “Sunspot Photographs from the Stratosphere.” Astronomical Journal 64 (1959): 323.

“Convection in Stars.” Astrophysical Journal 134 (1961): 1–8. 1960 Henry Norris Russell Prize Lecture.

“Astronomical Photography from the Stratoscope.” In Annual Report of the Smithsonian Institution. Washington, DC: U.S. Government Printing Office, 1963.

“Prepared Statement on the Space Program.” Publications of the Astronomical Society of the Pacific 75 (1963): 527. Reprint (from Congressional Record) of statement to the Senate Committee on Aeronautical and Space Sciences, 11 June 1963.

“Stellar Evolution in Globular Clusters.” Quarterly Journal of the Royal Astronomical Society 11 (1970): 12–22. 1969 George Darwin Lecture, RAS.

With E. S. Light and R. E. Danielson. “The Nucleus of M31.” Astrophysical Journal 194 (1974): 257–263.

“Triaxial Equilibrium Models for Elliptical Galaxies with Slow Figure Rotation.” Astrophysical Journal 263 (1982): 599–610.

OTHER SOURCES

Arny, Thomas. “The Star Makers: A History of the Theories of Stellar Structure and Evolution.” Vistas in Astronomy 33, no. 2 (1990): 211–233.

Burbidge, E. Margaret, and Geoffrey Burbidge. “Stellar Evolution.” In Handbuch der Physik. Vol. 51: Astrophysik II: Sternaufbau, edited by S. Flügge. Berlin: Springer, 1958.

DeVorkin, David H. Henry Norris Russell: Dean of American Astronomers. Princeton, NJ: Princeton University Press, 2000.

———. “The Changing Place of Red Giants in the Evolutionary Process.” Journal for the History of Astronomy 37 (2006): 429–469.

Emden, Robert. Gaskugeln: Anwendungen der mechanischen Wärmetheorie auf kosmologische und meteorologische Probleme. Leipzig, Germany: B. Teubner, 1907.

Henyey, Louis G. “Award of the Bruce Gold Medal to Martin Schwarzschild.” Publications of the Astronomical Society of the Pacific 77 (August 1965): 233–236.

Merritt, David. “Martin Schwarzschild’s Contribution to Galaxy Dynamics.” In Galaxy Dynamics: A Rutgers Symposium: Proceedings of a Symposium Held at Rutgers University, Piscataway, New Jersey, USA, 8–12 August 1998, edited by David Merritt, J. A. Sellwood, and Monica Valluri. Astronomical Society of the Pacific conference series, vol. 182. San Francisco: Astronomical Society of the Pacific, 1999.

Mestel, Leon. “Martin Schwarzschild, a Tribute.” Bulletin of the Astronomical Society of India 25 (1997): 285–287.

Osterbrock, Donald. Chapter 5. In Walter Baade: A Life in Astrophysics. Princeton, NJ: Princeton University Press, 2001.

Ostriker, Jeremiah P. “Martin Schwarzschild, (31 May 1912–10 April 1979).” Nature 388 (31 July 1997): 430. Reprinted in the Proceedings of the American Philosophical Society 143 (September 1999): 487–489.

Sandage, Allan. Centennial History of the Carnegie Institution of Washington. Vol. 1, The Mount Wilson Observatory. Cambridge, U.K.: Cambridge University Press, 2004.

Tassoul, Jean-Louis, and Monique Tassoul. A Concise History of Solar and Stellar Physics. Princeton, NJ: Princeton University Press, 2004.

Trimble, Virginia. “Martin Schwarzschild (1912–1997).” Publications of the Astronomical Society of the Pacific 109 (December 1997): 1289–1297.

David H. DeVorkin

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