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Author name code: schwarzschild-martin
ADS astronomy entries on 2022-09-14
author:"Schwarzschild, Martin" 

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Title: Jeans and Boltzmann solutions for oblate galaxies with flat
    rotation curves
Authors: de Zeeuw, P. T.; Evans, N. W.; Schwarzschild, M.
1996MNRAS.280..903D    Altcode: 1995astro.ph.12082D
  A general solution of the Jeans equations for oblate scale-free
  logarithmic potentials is given. This provides all possible second
  velocity moments that can hold up a stellar population of flattened
  scale-free density against the gravity field. A two-parameter subset
  of second moments for the self-consistent density of Binney's model
  is examined in detail. These solutions have the desirable property
  that the observable dispersions in the radial and proper motions
  can be given explicitly. In the spherical limit, the potential of
  these models reduces to that of the singular isothermal sphere. The
  Jeans solutions for scale-free densities of arbitrary flattening that
  can correspond to physical three-integral distribution functions are
  identified. The problem of finding distribution functions associated
  with the Jeans solutions in flattened scale-free logarithmic potentials
  is then investigated for Binney's model. An approximate solution of
  the collisionless Boltzmann equation is found which provides a third
  (partial) integral of good accuracy for thin and near-thin tube
  orbits. It is a modification of the total angular momentum. This
  enables the construction of many simple three-integral distribution
  functions. The kinematic properties of these approximate DFs are shown
  to agree with a subset of the Jeans solutions --- which are thereby
  confirmed as good approximations to physical solutions.

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Title: Self-consistent Models for Galactic Halos
Authors: Schwarzschild, Martin
1993ApJ...409..563S    Altcode:
  Richstone has pioneered the use of the scale-free logarithmic potential
  for the study of the dynamics of galactic halos. Now modern computers
  make it practical to exploit that potential in its exact form without
  central softening. The orbital structure of the potential, which differs
  significantly from that of the separable Stackel potentials, has been
  explored systematically with the help of 2-D start spaces. Six triaxial
  nonrotating density models representative of various axis ratios have
  been selected. For each model 600 orbits have been integrated over
  a time interval equivalent to about 55 orbital periods, or 1 Hubble
  time. Of these orbits, half are defined in the x-z start space (mostly
  S-tubes, O-tubes, and I-tubes) and the other half in the stationary
  start space (mostly boxlets such as bananas but also many unstable
  stochastic orbits). From these orbits self-consistent equilibrium models
  have been constructed by the usual methods, with the help of a 48 cell
  grid on the reference sphere and by employing long sequences of Lucy
  iterations. The main result of these numerical constructions is that in
  all six cases self-consistent solutions exist. For the rounder models
  (with density axis ratios c/a >= 0.5) solutions involving only stable
  orbits exist, although solutions also involving stochastic orbits may
  be preferred by the halo formation processes. For the flatter models
  (with density axis ratios c/a ~ 0.3) stochastic orbits have to be
  included in the solution-a consequence of the replacement of box orbits
  by boxlets in halo potentials. The inclusion of unstable stochastic
  orbits in self-consistent equilibrium models raises the question
  of the persistence of these models. The rate of such impersistence
  has been estimated and found not threatening under the conditions
  prevailing in halos where only about 50 orbital periods occur in a
  Hubble time. It is concluded that equilibrium considerations alone,
  without the consideration of possible instabilities and without the
  consideration of halo formation processes, do not suffice to constrain
  the overall shape of galaxy halos.

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Title: The Orbital Structure of Galactic Halos
Authors: Lees, Joanna F.; Schwarzschild, M.
1992ApJ...384..491L    Altcode:
  Numerical experiments have been carried out to investigate the
  restrictions on triaxial models for the halos of galaxies. Some of
  the conclusions drawn from the numerical experiments are: (1) the
  dominant occurrence of boxlets may be a fairly general phenomenon in
  triaxial galactic halos; (2) most of the tube orbits in the halo are
  not affected by the higher resonances; and (3) triaxiality truncations
  favor the existence of self-consistent equilibria in galactic halos.

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Title: The Ring Instability in Radially Cold Oblate Galaxy Models
Authors: de Zeeuw, Tim; Schwarzschild, Martin
1991ApJ...369...57D    Altcode:
  Goodman's indicator has been employed to investigate the stability
  of self-consistent perfect oblate spheroids built exclusively with
  thin tube orbits. Guided by the results of recent N-body simulations,
  we have experimented with a variety of axisymmetric perturbations
  which leave the flattening of the model constant, but change the
  radial density distribution. Goodman's indicator has been calculated
  by combination of the orbital indicators with the exact and unique
  phase-space distribution function of the thin-orbit model. This confirms
  that strongly flattened thin-orbit models are unstable against a ring
  perturbation, in agreement with the classical result for circular disks,
  and recent N-body simulations. The transition to stability occurs at
  an axis ratio of 0.33 +/- 0.02. Perturbations that are concentrated in
  the center are most destabilizing. The limitations of the application
  of Goodman's indicator are discussed.

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Title: Prolate Galaxy Models with Thin Tube Orbits
Authors: Hunter, C.; de Zeeuw, P. T.; Park, C.; Schwarzschild, M.
1990ApJ...363..367H    Altcode:
  We consider the construction of self-consistent distribution functions
  for prolate Stackel models. The orbits are confined by three independent
  integrals of motion and form two different families, the inner and
  outer long-axis tubes. The models constructed are built exclusively
  with infinitesimally thin orbits, and orbits of both families
  are needed. Once the density of the model has been split into two
  components, one for each family, two phase-space distribution functions
  can be found uniquely by solving one-dimensional integral equations
  of Abel type. But the models are not unique, because a variety of
  splits of the density is possible at all except extreme values of
  the axis ratio. Except at these extremes, physical models require
  that both families of orbits are populated. We have constructed a
  range of models for perfect prolate spheroids of all axis ratios, and
  have computed several of their other basic physical properties such as
  mean-streaming velocities, dispersions, angular momenta and the relative
  masses of their two orbit families. The mean- streaming motions exceed
  the circular velocity in the inner regions of these models.

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Title: Orbital Contributions to the Stability of Triaxial Galaxies
Authors: de Zeeuw, Tim; Schwarzschild, Martin
1989ApJ...345...84D    Altcode:
  Goodman's indicator is employed to investigate the stability of
  perfect ellipsoids, which are prototypical nonrotating triaxial galaxy
  models. The contributions of the individual stellar orbits to the
  indicator are presented for three specific adiabatic perturbations,
  which change the axis ratios of the ellipsoids but leave the density
  profile invariant. It is found that for barlike perturbations, in
  which one axis is elongated and another is compressed, box orbits
  are predominantly destabilizing, while outer long-axis tubes are
  invariably stabilizing. Short-axis tubes and inner long-axis tubes
  may be both stabilizing and destabilizing. These results for the
  contributions by individual orbits have been combined with Statler's
  (1987) results for the distribution functions of self-consistent perfect
  ellipsoid models. This combination, though still numerically insecure,
  permits tentative estimates of Goodman's indicator for these models,
  with the following results. The occurrence of a bar instability
  appears to be confirmed for triaxial models in which box orbits are
  heavily occupied. Nearly prolate models seem to suffer from the same
  instability. In strongly elongated triaxial models nearly all orbits
  are stabilizing, so that these systems are likely to be stable against
  barlike perturbations, in agreement with recent N-body simulations. The
  results for an adiabatic perturbation in which all three axes of the
  ellipsoid are changed in the same direction indicate--but by no means
  prove-- the existence of a possible core instability.

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Title: Stability of Selfconsistent Galaxy Models
Authors: de Zeeuw, P. T.; Schwarzschild, M.
1989BAAS...21.1012D    Altcode:
  No abstract at ADS

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Title: On the Orbit Structure of the Logarithmic Potential
Authors: Miralda-Escude, Jordi; Schwarzschild, M.
1989ApJ...339..752M    Altcode:
  The consequences of replacing centrophilic box orbits with
  centrophobic boxlets in the scale-free logarithmic potential are
  examined. Particular attention is given to the possibility that exact
  triaxial self-consistent dynamical models do not exist for density
  figures corresponding to the logarithmic potential. It is suggested
  that the central cusp of the logarithmic potential destroys the
  box orbits at high energy and replaces them with boxlets which are
  too wide to reproduce the triaxial density figure of the model in a
  self-consistent manner.

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Title: Nonuniqueness of Self-consistent Equilibrium Solutions for
    the Perfect Elliptic Disk
Authors: de Zeeuw, P. T.; Hunter, C.; Schwarzschild, M.
1987ApJ...317..607D    Altcode:
  The uniqueness or nonuniqueness of the physical solution for the
  self-consistent dynamical equilibrium of a perfect elliptic disk is
  investigated. A physical solution is defined as one that corresponds
  to a distribution function in action space that is not only nonnegative
  everywhere but also smooth. A specific solution is constructed for the
  perfect elliptic disk by using the elliptic closed orbits exclusively
  to provide the density of the model along the short axis beyond the
  focus. The specific solution, consisting of boxes and elliptic closed
  orbits, turns out to have the maximum possible angular momentum. It
  is shown that a band of nonclosed tubes provides the same density
  as a properly chosen combination of elliptic closed orbits and box
  orbits. This result permits a more general solution to be derived from
  the specific one. This general solution is found to be not unique.

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Title: Galactic Models with Moderate Stochasticity
Authors: Schwarzschild, Martin
1987NYASA.497...16S    Altcode:
  No abstract at ADS

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Title: Galactic Models with Moderate Stochasticity
Authors: Schwarzschild, M.
1987cpa..work...16S    Altcode:
  Contents: 1. Separable potentials. 2. Potentials for elliptical
  galaxies. 3. Central scatterer. 4. Figure rotation. 5. Galactic systems
  with more chaos.

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Title: Dynamical Models for Galactic Bars: Truncated Perfect
    Elliptic Disk
Authors: Schwarzschild, Martin
1986ApJ...311..511S    Altcode:
  de Zeeuw's perfect ellipsoid has been truncated on a surface of constant
  density. This truncation preserves the internal potential. A strongly
  triaxial case is considered, and the truncation is placed inside the
  bifurcation points (foci of the relevant ellipsoidal coordinates). Then
  the ellipsoid is projected into a two-dimensional perfect elliptic
  disk. The self-consistent dynamics of such disks involves only one major
  orbit family (box orbits) since all tube orbits reach beyond the foci,
  i.e., outside the truncation surface. The dynamical models for two
  samples of these disks have been derived numerically. The occupation
  frequencies are found to be positive everywhere. The dynamical solutions
  for these disks appear to be unique, owing to the limitation to one
  major orbit family. The limit of the truncated perfect elliptic disks
  (for the truncation approaching the center) is Freeman's disk, which
  itself is the projection of a uniform ellipsoid. The uniqueness of the
  dynamical solution for a highly triaxial truncated perfect elliptic
  disk suggests that the dynamics of a thin elongated nonrotating
  galactic bar with little density beyond the bifurcation points may
  be completely determined by its density figure. The same may well be
  true for corresponding bars with nonzero figure rotation, but this
  extension is outside the scope of this study.

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Title: An analysis of observations of the streaming velocities in
    the bulge of M 31.
Authors: Teuben, P.; Turner, E. L.; Schwarzschild, M.
1985ApJ...289...58T    Altcode:
  McElroy (1983) has recently provided an extensive set of radial
  velocity measurements for the stellar mean motions in the bulge
  of M31. These velocities show a surprisingly bumpy pattern. It is
  frequently postulated that the absorption clouds in the bulge are the
  cause of these observed velocity bumps. If this postulate is correct,
  further improvements of the velocity measurements will be futile and
  their use as a dynamical diagnostic minimal. To test this pessimistic
  hypothesis, the effects of the observed dust clouds on the velocity
  observations have been analyzed. Fortunately the observed clouds cannot
  be the main cause of the bumps in the observed velocities. Furthermore,
  a statistical analysis of the present velocity observations strongly
  suggests the existence of unidentified systematic errors which might
  explain the apparent bumps.

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Title: An approximate numerical model for a nonrotating galactic bar.
Authors: Schwarzschild, M.
1984BAAS...16..720S    Altcode:
  No abstract at ADS

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Title: Stellar orbits in angle variables
Authors: Ratcliff, S. J.; Chang, K. M.; Schwarzschild, M.
1984ApJ...279..610R    Altcode:
  Following recent basic developments by Binney and Spergel, the equations
  of motion for a star in a galactic potential have been transformed from
  time to angle variables. A numerical procedure has been devised to solve
  the transformed equations for two-dimensional box and loop orbits in the
  equatorial plane of a triaxial potential. In this procedure an orbit
  is specified not by its starting values in phase space, but either by
  its frequencies or by its action values. A substantial set of orbits
  has been derived by this procedure for one potential. The results
  for their physical and geometrical characteristics are displayed in
  action diagrams.

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Title: Analysis of box orbits in a triaxial galaxy
Authors: Vietri, M.; Schwarzschild, M.
1983ApJ...269..487V    Altcode:
  It is pointed out that box orbits appear to play a key role for triaxial
  hot self-consistent stellar systems, just as the near-circular orbits
  do for cool fast-rotating disk systems. Since elliptical galaxies and
  possibly also the bulges of spiral galaxies may be triaxial in many
  cases, the present investigation is concerned with a further study of
  box orbits. Binney and Spergel (1982) have suggested a qualitative model
  for box orbits, taking into account the basic fact that box orbits are
  quasi-periodic with as many independent periods as dimensions. The
  current investigation has the objective to derive an approximate,
  reasonably simple representation of two-dimensional box orbits. The
  considered representation exploits directly the quasi-periodic character
  of the box orbits. In the incomplete second order development described,
  the coordinates X and Y of a two-dimensional box orbit in a triaxial
  potential are each represented by the sum of several terms.

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Title: Triaxial equilibrium models for elliptical galaxies with slow
    figure rotation
Authors: Schwarzschild, M.
1982ApJ...263..599S    Altcode:
  An earlier numerical construction of a triaxial model for a stellar
  system in dynamical equilibrium has been extended, first by adding
  a slow figure rotation, and second by adding rotational streaming
  on Z-tube orbits. The figure rotation was kept low so that the main
  resonances, including the outer edge of Binney's instability strip,
  fall outside the model. This figure rotation induces weak rotational
  streaming, prograde on box orbits and retrograde on X-tube orbits. The
  resulting net streaming has a very low velocity (although substantially
  higher than the figure rotation by itself) and a complicated pattern,
  prograde in the inner portion and retrograde in the outer portion. The
  addition of prograde Z-tube orbits, circling around the short (Z)
  rotation axis, introduces strong rotational streaming on these
  orbits. The net effect of this streaming is, however, substantially
  diluted by the box orbits, which are needed for the support of the
  triaxial figure. The maximum net rotational streaming velocity thus
  permitted for the figure here used (1:1.25:2) appears sufficient to
  model the observed rotation of most giant ellipticals.

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Title: Retrograde closed orbits in a rotating triaxial potential
Authors: Heisler, J.; Merritt, D.; Schwarzschild, M.
1982ApJ...258..490H    Altcode:
  Four closed periodic orbit sequences are determined numerically, and
  their stability is investigated by the standard Floquet method, for the
  case of a specific, triaxial rotating potential. The sequences comprise
  (1) stable anomalous orbits that are tipped to the long axis which they
  circle, so that they also circle the short rotation axis, (2) unstable,
  anomalous orbits circling the intermediate axis, otherwise behaving
  like (1), (3) stable, normal retrograde orbits lying in the equatorial
  plane, which become unstable against perpendicular perturbations
  in Binney's instability strip, and (4) Z-axis orbits lying on the
  rotation axis, which, although stable in their inner section, become
  unstable to perturbations parallel to the intermediate axis farther
  out, and to the long axis farther out still. The entire set contains
  one composite sequence which is stable over the entire energy range,
  consisting of the outer section of the normal retrograde orbits, the
  sequence of the anomalous orbits, and the inner section of the Z-axis
  orbits. It is suggested that the composite sequence may be relevant
  to the dynamics of gas masses captured by rotating triaxial galaxies.

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Title: A model for elliptical radio galaxies with dust lanes.
Authors: van Albada, T. S.; Kotanyi, C. G.; Schwarzschild, M.
1982MNRAS.198..303V    Altcode:
  The stationary states of motion of gas in a triaxial stellar system
  which rotates about one of its principal axes are described. It is
  noted that four dynamically different situations are possible and that
  in two of these the gas layer is warped. The morphology of elliptical
  radio galaxies with dust lanes, such as NGC 5128 (Cen A) and M84, can
  be understood through this model; transient phenomena are not required.

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Title: Semistochastic orbits in a triaxial potential
Authors: Goodman, J.; Schwarzschild, M.
1981ApJ...245.1087G    Altcode:
  The numerical investigation of stellar orbits in a specific triaxial
  potential, which was previously described, has been extended. The
  local stability has been tested for box orbits for one representative
  energy. Of these box orbits, 27% were found to be unstable. The
  stationary points of the unstable orbits fall in an area mostly near
  the minor axis but also extending to the intermediate axis. This
  situation is related to the characteristics of the special periodic
  orbits along the principal axes. The orbit along the major axis is
  stable, the one along the minor axis is unstable, and the one along
  the intermediate axis is unstable in one out of two independent
  perturbation directions. These results, which can be interpreted
  in terms of resonances between an orbit and its perturbations, may
  extend to a wider class of triaxial nonharmonic potentials. <P />Seven
  box orbits-three stable ones and four unstable ones-were further
  investigated by integrating each orbit over a full Hubble time and
  recording the velocity vector each time the orbit crossed through
  a small cell at the center of the figure. For each stable orbit
  the velocities for all central crossings were identical within the
  numerical uncertainty, except for an eightfold multiplicity with the
  same reflection symmetries as the potential. This reemphasizes that
  the majority of orbits in the chosen potential have three effective
  integrals. On the other hand, for each unstable orbit the velocities for
  central crossings scatter around a mean value. However, the scatter
  is much less than one expects for a truly stochastic orbit. Each
  of the four unstable orbits visited only a small subregion of the
  total velocity domain visited by all unstable box orbits of the same
  energy. Accordingly these orbits are here referred to as semi stochastic
  rather than truly stochastic. The cause of this semistochasticity is
  not understood. To test whether the gross features of semistochastic
  orbits are more sensitive to perturbations than those of orbits
  with three effective integrals, three box orbits one stable and two
  unstable-were rerun with the application of perturbations at regular
  intervals. The perturbation strength varied between runs from the low
  level expected from stellar encounters to much stronger levels. Though
  strong perturbations increased the velocity dispersion for central
  crossings, the semi stochastic orbits proved no more sensitive
  than the stable one. <P />It is concluded that in the specific case
  investigated no truly stochastic orbits exist and that, for the purpose
  of constructing numerical self-consistent equilibrium configurations,
  the semistochastic orbits may be considered in much the same way
  as regular orbits with three effective integrals. if the absence of
  truly stochastic orbits should prove to be a general phenomenon for
  potentials relevant to galaxies, the variety of equilibrium figures
  for galaxies should be larger than otherwise might be expected.

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Title: Shapes of unperturbed galaxies
Authors: Schwarzschild, M.
1981seng.proc...43S    Altcode:
  The shapes of galaxies not perturbed by a nearby important companion
  or large-scale spiral structure are considered in order to ascertain
  the relative importance of present equilibrium conditions and formation
  history in determining galactic shape. The differences between the three
  possible levels of symmetry of a galactic shape - spherical, axial
  and triaxial - with respect to their implications for the dynamics
  of stellar systems are examined, and the existence of nonclassical
  effective integrals corresponding to an isolating function of the six
  phase-space coordinates which is essentially constant on an orbit
  for the relevant time, is demonstrated. A numerical procedure for
  the construction of self-consistent equilibrium models is outlined to
  illustrate the role played by orbits with three effective integrals,
  and the behavior of stochastic orbits, which have no effective
  integrals other than the energy integral, is considered. Finally,
  the qualitative properties of the major orbit families in a triaxial
  potential are reviewed and the probable existence of hot triaxial
  equilibrium configurations is noted.

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Title: Tri-axial dynamics in the core of normal galaxies.
Authors: Schwarzschild, M.
1980HiA.....5..205S    Altcode:
  No abstract at ADS

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Title: On the nonexistence of three-dimensional tube orbits around
    the intermediate axis in a triaxial galaxy model.
Authors: Heiligman, G.; Schwarzschild, M.
1979ApJ...233..872H    Altcode:
  A specific triaxial model for a galaxy was previously investigated
  by numerical methods. In that investigation tube orbits around the
  major axis (X), as well as tube orbits around the minor axis (Z),
  had been found, but no tube orbit around the intermediate axis (Y)
  had been encountered. The present paper shows, again by numerical
  methods, that Y-tube orbits nearly certainly do not exist in the
  adopted model. Instead, a new family of 'shell orbits' has been
  found. The existence of X- and Z-tube orbits and the replacement of
  Y-tube orbits by shell orbits are made understandable by a numerical
  determination of the stability or instability, respectively, of the
  relevant two-dimensional closed resonance orbits in the three symmetry
  planes of the model.

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Title: A photometric determination of twists in early-type
    galaxies. II.
Authors: Williams, T. B.; Schwarzschild, M.
1979ApJS...41..209W    Altcode:
  In continuation of previous work, detailed photometric data have been
  obtained for two elliptical galaxies by using the Mount Lemmon 1.5-m
  telescope and a large SEC television camera. As before, the aim of this
  photometry is to gain additional information on the occurrence of twists
  in such galaxies; i.e., on the change of the position angle of the major
  axes of the isophotes from the center outward. No significant twist
  was found in NGC 1052. However, NGC 584 was found to have a securely
  observed twist of about 10 deg within 10 kpc from its center. These
  data strengthen previous indications that many ellipticals contain
  twists in their inner, bright portions.

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Title: A numerical model for a triaxial stellar system in dynamical
    equilibrium.
Authors: Schwarzschild, M.
1979ApJ...232..236S    Altcode:
  A sample numerical model has been computed for a triaxial stellar system
  in dynamical equilibrium. A four-step procedure was employed. (1) A
  density distribution with a modified Hubble profile - to approximate
  elliptical galaxies - and axis ratios of 1:25:2 was chosen. This figure
  was further chosen not to rotate. (2) The potential corresponding to the
  chosen density distribution was computed. (3) About 1500 orbits were
  computed with this potential, one at a time, each covering typically
  100 oscillations through the system; i.e., about 1 billion years. These
  orbits belong to two families, viz., box orbits and tube orbits around
  the long axis of the system. (4) A reproduction of the chosen density
  distribution - in terms of its mass in 285 cells in each octant -
  was sought by superposition of a subset of the available orbits,
  each populated by an appropriate nonnegative number of stars. The
  application of linear programming led to a numerical solution. The
  main results are: First, the majority of the orbits computed in step
  3 turned out to have three effective integrals; i.e., two nonclassical
  ones in addition to the energy integral. Second, the existence of the
  numerical solution found in step 4 suggests the existence of triaxial
  self-consistent systems in dynamical equilibrium with density profiles
  fitting elliptical galaxies.

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Title: Large area CCD image sensors for space astronomy
Authors: Schwarzschild, M.
1979puobsrept.....S    Altcode:
  The Defense Advanced Research Projects Agency (DARPA) has a substantial
  program to develop a 2200 x 2200 pixel CCD (Charge Coupled Device)
  mosaic array made up of 400 individual CCD's, 110 x 110 pixels
  square. This type of image sensor appeared to have application in space
  and ground-based astronomy. Under this grant a CCD television camera
  system was built which was capable of operating an array of 4 CCD's to
  explore the suitability of the CCD's to explore the suitability of the
  CCD for astronomical applications. Two individual packaged CCD's were
  received and evaluated. Evaluation of the basic characteristics of the
  best individual chips was encouraging, but the manufacturer found that
  their yield in manufacturing this design is two low to supply sufficient
  CDD's for the DARPA mosaic array. The potential utility of large mosaic
  arrays in astronomy is still substantial and continued monitoring of
  the manufacturers progress in the coming year is recommended.

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Title: A photometric determination of twists in three early-type
    galaxies.
Authors: Williams, T. B.; Schwarzschild, M.
1979ApJ...227...56W    Altcode:
  Detailed photometric data have been obtained for three early-type
  galaxies by using the Cerro Tololo 1.5-m telescope and an SEC
  television camera. The aim of this photometry is to gain further
  accurate information on the occurrence of twists in such galaxies; i.e.,
  on any variations with radius of the position angle of the major axes
  of the isophotes. The results of the photometry are: (1) the finding
  of no detectable twist within the bulge of the S0 galaxy NGC 5102;
  (2) confirmation of a substantial twist (about 10 deg) in the inner
  portion of the E3 galaxy IC 1459; and (3) determination of a moderate
  twist (about 5 deg) within the E4 galaxy NGC 4697, possibly too small
  to have been previously detected. If such moderate twists should turn
  out to be common in elliptical galaxies, the suspicion of triaxiality
  for most such galaxies would be enhanced.

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Title: Surface Photometry of Two Elliptical Galaxies.
Authors: Williams, T. B.; Schwarzschild, M.
1978BAAS...10..422W    Altcode:
  No abstract at ADS

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Title: Conference Summary
Authors: Schwarzschild, M.
1978sfsn.conf..273S    Altcode:
  No abstract at ADS

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Title: The study of stellar structure.
Authors: Schwarzschild, M.
1978tpar.book....1S    Altcode:
  The physical principles and processes introduced into the study
  of stellar structure during the past 100 years are reviewed,
  emphasizing those processes that dominate the simplest stars in
  their various evolutionary phases. Attention is given to hydrostatic
  equilibrium, stellar energy transport, nuclear and gravitational
  energy sources, quiet mass ejection, violent dynamical phases, and
  nucleosynthesis. Investigations of radiative and convective energy
  transport are discussed along with the derivations of pressure-density
  relations for white dwarfs and neutron stars, the Hayashi limit, the
  first analyses of hydrogen fusion and inhomogeneous stellar models, the
  discovery of evolutionary transitions powered by gravitational-energy
  release, and mass loss from the sun, hot giants and supergiants, and
  red giants and supergiants. Studies of stellar pulsation, contraction to
  the main sequence, violent mass ejection, and stellar nucleosynthesis of
  heavy elements are also summarized. The lack of a theory for turbulent
  convection and the problem of missing solar neutrinos are identified
  as two flagrant deficiencies in the study of stellar structure.

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Title: An instability due to the local mixing-length approximation.
Authors: Kruskal, M.; Schwarzschild, M.; Haerm, R.
1977ApJ...214..498K    Altcode:
  The basic equations normally used for the study of dynamical phases in
  stellar evolution are shown to lead to short-wavelength instabilities
  when they are applied to convective envelopes in which the density
  decreases inward. This instability results from the standard local
  approximation for the mixing-length theory, which has unphysical
  consequences for small-scale perturbations. The instability disappears
  when a nonlocal mixing-length approximation is used.

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Title: Robert E. Danielson (1931-1976)
Authors: Schwarzschild, Martin; Spitzer, Lyman
1977Icar...30..601S    Altcode:
  No abstract at ADS

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Title: SEC TV Surface Photometry of Three Southern Galaxies.
Authors: Williams, T. B.; Schwarzschild, M.
1977BAAS....9..319W    Altcode:
  No abstract at ADS

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Title: Mixing between burned core material and surface layer.
Authors: Schwarzschild, M.
1977saif.conf..205S    Altcode:
  No abstract at ADS

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Title: An Approximate Dynamical Model for Spheroidal Stellar Systems
Authors: Ruiz, Maria Teresa; Schwarzschild, M.
1976ApJ...207..376R    Altcode:
  A simple dynamical model is derived for axisymmetric stellar systems in
  which the density is constant on spheroids with fixed eccentricity. The
  model is given as a tool for the analysis of the relations between
  the brightness distribution, the rotational velocity, and the
  velocity dispersion in the inner portions of an observed spheroidal
  system. Subject headings: galaxies: internal motions - galaxies:
  structure - stars: stellar dynamics

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Title: Transition from a Red Giant to a Blue Nucleus after Ejection
    of a Planetary Nebula
Authors: Harm, R.; Schwarzschild, M.
1975ApJ...200..324H    Altcode:
  The evolution of two stars, with 0.65 M0 and 1.00 M0, respectively,
  has been computed through the transition phase following the rapid
  dynamical ejection of a planetary nebula by a red giant. This ejection
  phase was mimicked by a sequence of hydrostatic red-giant models with
  steadily decreasing mass. The sequence was terminated at the moment of
  rapid decrease of the previously high pulsational instability. With
  the starting model thus derived, the constant-mass transition phase
  was found to last about 6000 years. This time interval is just short
  enough that the star can start providing the ultraviolet radiation
  in time to excite the ejected nebula before the nebula completely
  disperses. Subject headings: interiors, stellar - late-type stars -
  planetary nebulae - stellar evolution

---------------------------------------------------------
Title: Absolute spectrophotometry in M31 and M32.
Authors: Oke, J. B.; Schwarzschild, M.
1975ApJ...198...63O    Altcode:
  For a number of places in the bulge of M31, and for two places in
  M32, photometric scans from lambda = 3300 A to lambda = 10,600 A
  have been obtained with the multichannel spectrometer on the 5-m Hale
  telescope. The scans show that in both objects the color temperature
  (particularly shortward of 5000 A) decreases toward the center,
  and that the strength of the CN bands increases toward the center in
  both objects, in agreement with other earlier observations. The new
  data can all be interpreted in terms of an increase of heavy-element
  abundance toward the center in both objects by a factor probably less
  than 2, and by an excess of heavy elements in M31 compared with M32
  by a factor probably greater than 2, in qualitative agreement with
  earlier conclusions of other observers.

---------------------------------------------------------
Title: Photoelectric speckle interferometry of the solar granulation.
Authors: Harvey, J. W.; Schwarzschild, M.
1975ApJ...196..221H    Altcode:
  Using the Mc Math solar telescope on a morning of average seeing
  it has been found possible, with the help of photoelectric speckle
  interferometry, to detect securely the existence of details in the
  quiet solar granulation up to a wavenumber of 240 x 10-6 km-1, i.e.,
  a wavelength of one-third of an arc second. Subject headings: granules
  and supergranules, solar - image processing

---------------------------------------------------------
Title: On the scale of photospheric convection in red giants and
    supergiants.
Authors: Schwarzschild, M.
1975ApJ...195..137S    Altcode:
  An attempt is made to estimate the sizes of the convective elements
  which dominate the brightness variations on the photospheres of red
  giants and supergiants. The data assembled permit the extreme hypothesis
  that these dominant convective elements are so large that only a modest
  number of them exists at any one time on the entire surface of such
  a star - in contrast with two million granules on the sun.

---------------------------------------------------------
Title: The nucleus of M31.
Authors: Light, E. S.; Danielson, R. E.; Schwarzschild, M.
1974ApJ...194..257L    Altcode:
  The nucleus of M31 was photographed at a resolution of 0.2 sec with the
  91-cm balloon-borne Stratoscope II telescope. At the half-intensity
  level, the nucleus was observed to be elliptical with its major axis
  lying in position angle of 63 (plus or minus 5) deg. The peak surface
  brightness was 12.7 plus or minus 0.3 V mag per square second of arc
  assuming B - V = 1.0. The nucleus appears to be a separate feature
  from the bulge with a scale height of approximately 0.5 pc. The mass
  of the nucleus is of the order of 100 million solar masses, and the
  apparent visual mass-to-light ratio is of the order of 20.

---------------------------------------------------------
Title: Concluding Remarks
Authors: Schwarzschild, M.
1974IAUS...66..256S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Absolute spectrophotometry in M31 and M32
Authors: Oke, J. B.; Schwarzschild, M.
1974STIN...7510879O    Altcode:
  For a number of places in the bulge of M31 and for two places in M32
  photometric scans from 3300 A to 10,600 A have been obtained with the
  multichannel spectrometer on the 5-meter Hale telescope. The scans show
  that in both objects the color temperature (particularly shortwards of
  5000 A) decreases towards the center and that the strength of the CN
  bands increases towards the center in both objects in agreement with
  earlier observations. The new data can all be interpreted in terms
  of an increase of heavy element abundance towards the center in both
  objects by a factor probably less than 2 and by an excess of heavy
  elements in M31 compared to M32 by a factor probably greater than 2,
  in qualitative agreement with earlier conclusions.

---------------------------------------------------------
Title: Stability of the Sun against Spherical Thermal Perturbations
Authors: Schwarzschild, M.; Harm, R.
1973ApJ...184....5S    Altcode:
  In view of the serious solar neutrino discrepancy, the stability of
  the Sun against spherical thermal perturbations has been investigated
  by detailed computations. It was found that the Sun is stable against
  perturbations of this class, thus confirming the usual assessment based
  on approximate physical arguments. Subject headings: instabilities -
  interiors, solar

---------------------------------------------------------
Title: An Upper Limit to the Angular Diameter of the Nucleus of
    NGC 4151
Authors: Schwarzschild, Martin
1973ApJ...182..357S    Altcode:
  During the seventh flight of Stratoscope II, a 36-inch balloon-borne
  telescope, five photographs of the nucleus of the Seyfert galaxy
  NGC 4151 as well as four equivalent photographs of a comparison star
  were obtained. These photographs show high definition and are well
  exposed. From a densitometric analysis a safe upper limit to the
  half-intensity diameter of the nucleus of O'!O8 is derived. This
  new upper limit is less than half the upper limit previously
  determined. Subject headings: galactic nuclei - galaxies individual -
  Seyfert galaxies

---------------------------------------------------------
Title: INVITED PAPER - Convection in Stars.
Authors: Schwarzschild, M.
1973BAAS....5....1S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Oscillatory Thermal Instabilities at the Onset of Helium
    Shell Burning.
Authors: Härm, R.; Schwarzschild, M.
1972ApJ...172..403H    Altcode:
  The onset of thermal instability has been investigated in detail
  for globular-cluster stars in the evolutionary phase during which
  the helium-burning shell is just forming. The investigation shows
  that (a) the main unstable phase ("second red-giant phase" or
  "asymptotic branch") is preceded by a short and inconsequential
  preliminary unstable phase during which the instability is weak and
  of an oscillatory character, (b) the main unstable phase generally
  commences not with a simple exponential instability (real eigenvalue),
  but with an oscillatory instability (complex eigenvalue), (c) this
  oscillatory instability appears to be caused by an interaction between
  the driving layer containing the helium shell source and a reacting
  layer below the driving layer, and (d) the oscillatory instability
  gives way (after a quite limited time span) to a simple exponential
  instability which causes the repetitive helium-shell flashes described
  in earlier investigations.

---------------------------------------------------------
Title: High Resolution Photographs of the Nuclei of M31 and M32
    Obtained by Stratoscope II.
Authors: Danielson, R. E.; Light, E. S.; Schwarzschild, M.; Tomasko,
   M. G.
1971BAAS....3Q.445D    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Points noirs dans la théorie de l'évolution stellaire
Authors: Schwarzschild, M.
1971LAstr..85..277S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: High Resolution Photographs of the Nucleus of NGC 4151.
Authors: Schwarzschild, M.
1971BAAS....3..243S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: High-Resolution Photographs Obtained by Stratoscope II
Authors: Danielson, R. E.; Savage, B. D.; Schwarzschild, M.;
   Tomasko, M.
1970BAAS....2Q.307D    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the Evolutionary Phase of Cepheids in Globular Clusters
Authors: Schwarzschild, M.; Härm, R.
1970ApJ...160..341S    Altcode:
  The beginning of the helium shell burning phase has been computed
  through the first flash cycle for each of nine globular-cluster
  stars (differing in mass and initial composition). While seven of
  thesestarsremained on the red-giant branch throughout the cycle, two
  stars did not. The latter passed, after each flash, through a loop in
  the H-R diagram reaching well into the strip occupied by Population II
  Cepheids. It is suggested that the occurrence of these evolutionary
  loops might be the reason for the occurrence of Cepheids in globular
  clusters.

---------------------------------------------------------
Title: Stellar Evolution in Globular Clusters
Authors: Schwarzschild, Martin
1970QJRAS..11...12S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: An Upper Limit to the Angular Diameter of the Nucleus of
    NGC 4151
Authors: Danielson, R.; Savage, B. D.; Schwarzschild, M.
1968ApJ...154L.117D    Altcode:
  From an analysis of images of the nucleus of the Seyfert galaxy NGC
  4151 obtained during a recent ifight of Stratoscope II, a 36-inch
  balloon-borne telescope, we conclude that a safe upper limit to the
  half-intensity angular diameter of the nucleus is O~'18. This diameter,
  which refers to the non-thermal continuum, is several times as small
  as the lower limit to the half-intensity diameter of the region giving
  rise to the emission lines

---------------------------------------------------------
Title: Stratoscope II Integrating Television System.
Authors: Cope, A. D.; Luedicke, E.; Danielson, R.; Schwarzschild, M.
1968AJS....73....9C    Altcode:
  An integrating television system has been developed as part of the
  Stratoscope II program, and will be flown in place of photographic
  film in later flights. The TV camera, which is capable of operating
  with either an image orthicon or an image isocon tube, can integrate
  for more than 1 h when cooled to - 200C. The isocon scan is superior to
  the orthicon scan because a single setting of the isocon beam current
  will suffice to read from threshold to full target while the orthicon
  beam current must be carefully adjusted for each level of exposure to
  obtain the best signal to noise ratio. The resolution of a diffraction
  limited image will not be significantly degraded if the sine wave
  response of the imaging device is at least 50% at the spatial frequency
  for which the response of the optics becomes zero. The television tube
  which has been most fully tested contained an S20 photo- cathode and
  a wide spaced MgO target. The sine wave response for first scan read
  out of this isocon tube is 50% at 2.5 cycles/mm and 30% at 5 cycles/
  mm. The above criterion would require that the tube be operated in
  conjunction with optics at f/800, a prohibitively large focal ratio. An
  integrating image isocon tube with a close- spaced Elcon glass target
  has just been developed by RCA. Preliminary measurements on this
  tube indicate that the 50% response for first scan readout occurs at
  about 10 cycles/mm. It thus appears that this integrating TV tube,
  operated atf/200, is a satisfactory substitute for 103aG film at f/100
  as presently used by Stratoscope II. Project Stratoscope of Princeton
  University is sponsored by NSF, ONR, and NASA.

---------------------------------------------------------
Title: On the Blue End of the Horizontal Branch in Globular Clusters
Authors: Hartwick, F. D. A.; Härm, R.; Schwarzschild, M.
1968ApJ...151..389H    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Oscillatory Thermal Instability of Helium-Burning Shells.
Authors: Schwarzschild, Martin; Harm, R.
1968AJS....73R..35S    Altcode:
  All recent investigations on stellar models containing helium- burning
  shells have shown these models to be thermally unstable. Thus thermal
  instability appears to be a general characteristic of helium-shell
  models. In view of this fact the onset of this instability has
  been reinvestigated. It was found that in some cases the thermal
  instability does not set in as a simple exponential runaway, but as
  an oscillatory instability (corresponding to "over- stability" in
  dynamical problems). This result runs contrary to the usual experience
  in problems of thermal flow in hydrostatic systems. It does not vitiate
  the conclusions drawn from detailed computations of evolutionary model
  sequences. It does, however, complicate the study of the onset of this
  instability since it necessitates the search for complex eigenvalues,
  rather than for the simple real eigenvalues usually characteristic
  for thermal flow problems.

---------------------------------------------------------
Title: An Upper Limit to the Angular Diameter of the Nucleus of
    NGC 4151.
Authors: Danielson, R.; Savage, B. D.; Schwarzschild, M.
1968AJS....73Q.173D    Altcode:
  The most recent launch of Stratoscope II, a 36-in. balloon-borne
  telescope, occurred on 18 May 1968. The telescope operated reliably
  during the entire night at an altitude of 80 000 ft, but the diffraction
  limited performance of the optics (0'.' 1 limiting resolution)
  was degraded by a quasisteady convection pattern set up in the main
  telescope tube. The stellar images (X =3800- 5800 A) recorded during
  the flight were elongated with angular dimensions generally less than
  0'.'3 by 0'.'8. However, in spite of the degraded images, an average
  guidance jitter as low as 0 "03 rms was achieved on 6th to 8th magnitude
  guide stars. Photoelectric tracings of two weakly exposed images of the
  nucleus of the Seyfert galaxy NGC 4151 give a width (at the half maximum
  intensity) of 0 "20 for the narrowest dimension. Taking account of the
  probable error of this measurement as well as the broadening effects
  of the telescope diffraction and the microdensitometer slitwidth, we
  conclude that a safe upper limit to the half maximum intensity diameter
  of the nucleus of NGC 4151 is 0 `118 (about 9 pc). This upper limit
  refers to the nonthermal continuum which, according to Oke and Sargent
  (Astrophys. J. 151, 807,1968), comprises most of the energy radiated by
  the nucleus. In contrast, the observations of Oke and Sargent indicate
  that the volume in which the emission lines arise has a half maximum
  intensity diameter of at least 016. Project Stratoscope of Princeton
  University is sponsored by NSF, ONK, and NASA.

---------------------------------------------------------
Title: Hydrogen Mixing by Helium-Shell Flashes
Authors: Schwarzschild, M.; Härm, R.
1967ApJ...150..961S    Altcode:
  Numerical calculations have been carried out which cover the first
  4 million years of those evolution phases in which helium burning
  occurs in a shell in a star of 1 solar mass and of a Population
  II composition. The thermal instability previously found to
  occur in these helium-shell-burning phases leads to relaxation
  oscillations-just as has already been shown by other authors for
  other types of stars. Thirteen consecutive relaxation cycles are
  covered by the present computations. In each cycle the main helium-
  shell flash causes a convective xone to stretch outward from the helium
  shell. In the initial relaxation cycles this convection xone does not
  reach the hydrogen-containing layers. However, cycle after cycle the
  main helium-shell flash increases in strength and, in consequence,
  causes a larger and larger convection xone. Mter about nine cycles
  the convection xone finally reaches the hydrogen-containing layers
  and from then on, for a short while in each cycle, hydrogen is mixed
  into the hot carbon-rich interior. This physical situation with its
  likely importance for nucleosynthesis we had searched for originally in
  connection with the helium-core flash, with, however, negative results;
  while now, in connection with the helium-shell flashes, the results
  seem to be encouragingly positive.

---------------------------------------------------------
Title: The Sun as a Star
Authors: Schwarzschild, M.
1967easp.book...14S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Red Giants of Population II. IV
Authors: Härm, R.; Schwarzschild, M.
1966ApJ...145..496H    Altcode:
  The evolutionary phases of a Population II star through the helium
  flash have been recomputed with improved representations for several
  of the relevant physical processes. The new computations show that
  the helium flash is less extreme than indicated by the earlier, less
  accurate computations; the nuclearenergy release reaches only 1011
  LQ at the peak, and the rate of evolutionary changes now appears
  to be too slow for major hydrodynamic effects. On the other hand,
  the new computations confirm the earlier results indicating that the
  convective core at its greatest extent (after the flash) misses the
  hydrogen-rich region by about two density scale heights. Accordingly,
  in view of the very small overshooting from convective cores found
  in a recent separate investigation, it now appears highly likely that
  the helium flash does not lead to mixing in the star.

---------------------------------------------------------
Title: New impetus to astrometry
Authors: Schwarzschild, Martin
1966VA......8....3S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Overshooting from Stellar Convective Cores.
Authors: Saslaw, W. C.; Schwarzschild, M.
1965ApJ...142.1468S    Altcode:
  The possible extent by which the motions in a convective core might
  overshoot into the surrounding stable layers has been investigated by
  a fundamental mode analysis as well as by the method of following the
  entropy excess of a rising element. The fact that a great number of
  convective motions occur consecutively in a relevant evolution time
  has also been taken into account. The results indicate that the usual
  procedure of neglecting all overshooting from convective cores will
  generally be a good approximation.

---------------------------------------------------------
Title: Thermal Instability in Non-Degenerate Stars.
Authors: Schwarzschild, M.; Härm, R.
1965ApJ...142..855S    Altcode:
  In the numerical investigation of the evolution of a star of 1 Mo
  through the phases in which it contains a helium-burning shell as well
  as a hydrogen-burning shell, an unexpected type of thermal instability
  has been encountered. This instability is somewhat reminiscent of
  the helium flash even though degeneracy plays no role in the models
  considered. The existence of the instability has been made reasonably
  certain both by a physical analysis and by a direct mathematical
  derivation. The new instability appears to have the character of
  a thermal runaway in a non-degenerate shell containing a highly
  temperature-sensitive nuclear-energy source. Such a shell will be
  unstable only if it is sufficiently thin not to affect the over-all
  hydrostatic structure of the star noticeably. Under this condition the
  pressure within the shell cannot greatly increase during the thermal
  runaway, and hence cooling by an adiabatic expansion cannot stabilize
  the shell. Some speculations are presented regarding whether this
  instability could have substantial consequences for a star's evolution.

---------------------------------------------------------
Title: Structure and evolution of the stars
Authors: Schwarzschild, Martin
1965ses..book.....S    Altcode: 1965QB801.S35......
  No abstract at ADS

---------------------------------------------------------
Title: Infrared Spectra of Red-Giant Stars.
Authors: Woolf, N. J.; Schwarzschild, M.; Rose, W. K.
1964ApJ...140..833W    Altcode:
  The second flight of Stratoscope II was carried out during the night
  of November 26,1963. The telescope was equipped with an infrared
  spectrometer with a useful sensitivity range from 1 to 3 M The balloon
  operations were carried out without difficulty. The telescope was
  operated from 6 P.M to 6 A.M. Spectral tracings were obtained for
  ten objects. This paper reports on the observations of six nearby
  red- giant stars. The spectra of the hotter objects showed that the
  terrestrial atmosphere above the balloon had no disturbing effects
  on the measurements. The only terrestrial band weakly indicated in
  the spectra is that of carbon dioxide at 2.7 . The spectrum of a Tau
  (KS) shows practically no bands but has a clear intensity peak around
  1.6 where bound-free and free-free absorption of H- and H2- leaves
  a relatively transparent region in the continuous absorption . The
  same phenomenon is shown in the spectra of the cooler stars although
  complicated by band structure. Water-vapor absorption bands at 1.4
  and 1.9 appear distinctly in the spectrum of the supergiant a Ori
  (M2). These bands occur with a similar strength in the spectrum of p
  Per (M4), but are weaker in M Gem (M3). In the spectrum of R Leo (M8,
  m = 7.9) and particularly of o Cet (M9, m = 8.4) the water-vapor bands
  at 1.4,1.9, and 2.7 are extremely strong.

---------------------------------------------------------
Title: SYMPOSIUM ON INSTRUMENTAL ASTRONOMY: Mars observations from
    Stratoscope II
Authors: Danielson, R. E.; Gaustad, J. E.; Schwarzschild, M.; Weaver,
   H. F.; Woolf, N. J.
1964AJ.....69..344D    Altcode:
  On 1 March 1963 Stratoscope II, a balloon-borne telescope, was flown
  for the first time with the aim of investigating the infrared spectrum
  of Mars. A series of technical difficulties arose during the flight and
  severely restricted the number and quality of the spectrometer scans
  that were obtained. Nevertheless, the following results could be deduced
  from these scans: (1) It is improbable that the water vapor content
  of Mars is greater than 40 (2) If the total pressure at the surface
  of Mars is assumed to be 87 mbar, the amount of CO2 in the atmosphere
  of Mars amounts to about 6000 cm-atm rather than 3000 cm-atm as pre-
  viously estimated.

---------------------------------------------------------
Title: Red Giants of Population II. III.
Authors: Härm, H.; Schwarzschild, M.
1964ApJ...139..594H    Altcode:
  The question whether the helium flash causes mixing of hydrogen into
  the helium core is examin' computing detailed model sequences for
  three stars differing in mass and composition. These sequ derived by
  the Henyey method, cover the entire helium-flash phases. The numerical
  results indicatc the convective core, though greatly extended during the
  later cooling phases after the helium misses reaching the hydrogen-rich
  layers, but only by a very narrow margin. In view of the narro of this
  margin and because of the fact that a number of physical complications
  have not yet been 1 into account in these computations, we still cannot
  answer the question regarding mixing caused b helium fla .

---------------------------------------------------------
Title: Variation of the Gravitational Constant and the Evolution of
    the Sun.
Authors: Pochoda, P.; Schwarzschild, M.
1964ApJ...139..587P    Altcode:
  Evolutionary model sequences have been computed for the Sun under
  various assumptions for the variation of the gravitational constant
  G. For these computations G was taken to vary to the reciprocal of the
  power n of the time. For the age of the Universe, T, values ranging from
  15 billion years were used. It was assumed that 4.5 billion years ago
  the Sun was in its initial mainuence state. It was found that a mild
  variation of G, corresponding to n = 0.2, produces no difficulty the
  representation of the observed Sun as the end product of an evolution
  starting with the initial in-sequence state and lasting for 4.5 billion
  years. In contrast, a strong variation of G, corresponding =1.0,
  permits a satisfactory representation of the present Sun only if the
  age of the Universe is ut 15 billion years or more. This limitation
  arises from the circumstance that with a shorter age of Universe the
  initial main-sequence state of the sun falls relatively earlier in the
  history of the Universe a G, under the present assumptions, was still
  rather high; this causes so large an initial luminosity .he Sun as to
  lead to an exhaustion of the hydrogen in the solar core and an evolution
  off the main uence before 4.5 billion years would have elapsed.

---------------------------------------------------------
Title: New Infrared Observations with Stratoscope II.
Authors: Danielson, R. E.; Rose, W. K.; Schwarzschild, M.; Woolf, N. J.
1964AJ.....69Q.539D    Altcode:
  The second flight of Stratoscope II was carried out during the night
  of 26 November 1963. The telescope was again equipped with an infrared
  spectrometer, this time employing indium arsenide detectors with a
  useful sensitivity range from 1 to 3 P. The balloon operations were
  carried out without difficulties from the launch at Palestine, Texas,
  to the landing at Kosciusko, Mississippi. The telescope was operated
  from the ground station near Ruston, Lousiiana, from 6 p.m. until
  6 a.m. Spectral tracings were obtained for ten objects: Jupiter,
  the moon, Aldebaran, Mu Cephei, Betelgeuse, Mira, Sirius, R Leonis,
  Rho Persei, and Mu Geminorum. The spectra of the moon, Aldebaran,
  and Sirius showed that the terrestrial atmosphere above the balloon
  (80 000 ft) had no disturbing effects on the measurements; the only
  terrestrial band weakly indicated in the spectra is that of carbon
  dioxide at 2.7 P. The spectrum of the moon shows an increasing albedo
  from 1 to 2 P. Above 2 P the intensity increases rapidly in accordance
  with the expected thermal emission of the moon. The spectrum of Jupiter
  shows deep methane bands at 0.85, 0.99,1.16,1.37, and 1.7 P and the
  ammonia fundamental band at 3.0 P. A very broad feature in Jupiter's
  spectrum from 2.0 to 2.5 P is probably caused by combination bands
  of methane with the possibility of a contribution from the hydrogen
  molecule. The spectrum of Aldebaran (KS) shows practically no bands
  but has a clear intensity peak around 1.6 P where the bound-free and
  the free-free absorption of Ii- and H2- leave a relatively transparent
  region in the continuous absorption coefficient; the same phenomenon
  is also shown by the spectra of the cooler giants through complicated
  by band structure. Betelgeuse (M2) clearly shows the water vapor
  bands at 1.4 and 1.9 P as well as indications of a band at 2.7 P;
  also the carbon monoxide band at 2.3 P is fairly strong. The spectra
  of R Leonis (M8) and particularly of Mira at minimum (M9) show the
  water vapor bands at 1.4 and 1.9 P with extreme strength. Finally,
  the spectrum of Mu Cephei permits the determination of an upper limit
  for the absorption of interstellar ice grains in the band at 3.1 ~
  this upper limit turns out rather smaller than the expected value.

---------------------------------------------------------
Title: Professor Svein Rosseland
Authors: Randers, Gunnar; Schwarzschild, Martin
1964ApNr....9....7R    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Prepared Statement on the Space Program
Authors: Schwarzschild, M.
1963PASP...75..527S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Hydrodynamic Oscillations in the Solar Chromosphere.
Authors: Bahng, J.; Schwarzschild, M.
1963ApJ...137..901B    Altcode:
  Compression waves in the chromosphere, with the motions assumed vertical
  and of standing-wave character, are studied with the aim of accounting
  for the 5-minute oscillations recently discovered. For such waves the
  photosphere is found to provide an effectively solid bottom, while the
  corona can provide a free, largely reflective surface. The temperatures
  and depths in the chromosphere required to fit the observed period are
  not in discord with other evidence for the chromospheric temperature
  profile.

---------------------------------------------------------
Title: Book Review: Structure and Evolution of the stars
Authors: Schwarzschild, M.
1963SvA.....6..600S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Red Giants of Population II. II.
Authors: Schwarzschild, M.; Härm, R.
1962ApJ...136..158S    Altcode:
  In continuation of the work described in Paper I of this series,
  a sequence of 70 core models has been constructed for a red giant of
  population II, covering the helium flash. This phenomenon occurs when
  helium-burning starts in the contracting core. Because of the high
  degeneracy in the core, the new energy source causes heating, not an
  expansion. The rise of the temperature accelerates the helium-burning,
  and thus a thermal runaway occurs, which terminates only when the
  core becomes non-degenerate. Subsequent helium-burning causes rapid
  expansion and cooling. At the peak of the helium flash the temperature
  reaches over 300 million degrees. The rate of energy liberation at this
  peak corresponds to about 1012 solar luminosities. Practically none
  of this energy penetrates the thermal blanket of the non-degenerate
  outer layers of the helium core. The evolution at the peak is so fast
  that the time interval between successive numerical models had to be
  reduced to as low as 2 seconds.

---------------------------------------------------------
Title: Hydrodynamic Oscillation of Solar Chromosphere.
Authors: Bahng, J.; Schwarzschild, M.
1962AJ.....67..267B    Altcode:
  Standing compression waves in a plane parallel atmosphere are studied
  with the aim of accounting for the oscillations recently discovered by
  Leighton (1960, 4th IAU-IAUTAM Symposium on Cosmical Gas Dynamics)
  in the solar atmosphere. An idealized model consisting of three
  isothermal layers with temperature discontinuities at the interfaces is
  considered. The bottom layer, representing the photosphere, is assumed
  to be at 60000 K. Because of its steep density gradient, this layer
  acts as a reflector and the amplitude of the oscillation in this bottom
  layer decreases very rapidly with increasing depth. The top layer,
  with a temperature of the order of 10~ 0K or higher, acts also as a
  reflector, similar to the action of a free surface. This reflection
  is however, not perfect, and some energy leaks out in the form of
  progressive waves traveling upwards'. The corresponding energy loss
  is small enough to fit the observed oscillation decay rate if the top
  temperature is not substantially below 10~ 0K. In the middle layer
  the oscillation has essentially the character of a standing wave. The
  period of the oscillation is largely determined by the temperature and
  depth of the middle layer. To explain the observed 5-min period a depth
  between 1200 and 1700 km is required for a temperature between 80000
  and 300000K. This depth range is of the right order of magnitude for the
  depth of the chromosphere. This work is a part of Project Stratoscope,
  which is sponsored by the ONR, NSF, and NASA.

---------------------------------------------------------
Title: Stellar Evolution Phases with Mass Ejection
Authors: Schwarzschild, M.
1962dmim.conf..266S    Altcode: 1972dmim.conf..266S
  No abstract at ADS

---------------------------------------------------------
Title: Book Review: Structure and Evolution of the stars
Authors: Schwarzschild, M.
1962AZh....39..770S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Stellar Evolution
Authors: Schwarzschild, M.
1962IAUTB..11..137S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The Temperature Fluctuations in the Solar Granulation.
Authors: Bahng, J.; Schwarzschild, M.
1961ApJ...134..337B    Altcode:
  A new measurement of the root-mean-square intensity fluctuation in the
  granulation has been made from a photograph obtained on the Stratoscope
  flight of September 24, 1959. After correcting this measurement for the
  effects of the instrumental profile, the root-mean-square temperature
  fluctuation in the granulation is found to be +920 K.

---------------------------------------------------------
Title: Lifetime of Solar Granules.
Authors: Bahng, J.; Schwarzschild, M.
1961ApJ...134..312B    Altcode:
  A time sequence of high-definition photographs of the solar granulation
  was obtained on the Stratoscope flight of August 17,1959 The correlation
  function in time for the photospheric intensity variations has been
  determined from these photographs. The correlation function was found to
  be well represented by a simple exponential decay with a time constant
  of 6 27 minutes. If the average lifetime of granules is defined as
  twice the time interval in which the correlation drops to hall, then
  this lifetime is found to be 8.6 minutes.

---------------------------------------------------------
Title: Convection in Stars.
Authors: Schwarzschild, Martin
1961ApJ...134....1S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The Helium Flash in Population II Giants.
Authors: Härm, R.; Schwarzschild, M.
1961AJ.....66R..45H    Altcode:
  The evolution of a star of 1.2 solar masses has been followed through
  the phase in which the helium burning begins, with the following
  results. The helium burning sets in when the temperature in the
  contracting core reaches about 80 million degrees. Owing to the
  high degeneracy in the core the new energy source does not cause an
  expansion but rather heating. The rise of the temperature further
  accelerates the helium burning and thus a thermal runaway occurs,
  as predicted by Mestel. This runaway terminates only when the core
  becomes nondegenerate. Subsequent helium burning causes rapid expansion
  and cooling. At the peak of the helium flash the temperature reaches
  approximately 300 million degrees. The energy liberated at this peak
  corresponds to about 1012 solar luminosities. Practically none of this
  energy penetrates the thermal blanket of the nondegenerate outer layers
  of the helium core. The evolution at the peak is so fast that the time
  interval between successive numerical models had to be reduced to as
  low as 2 sec. It appears uncertain whether the neglect of dynamical
  effects remains a reasonable approximation in this phase. In the Hertz
  sprung-Russell diagram the star slides down the red-giant branch while
  the helium flash goes on,in the interior.

---------------------------------------------------------
Title: Die Theorie des inneren Aufbaus der Sterne
    (Karl-Schwarzschild-Vorlesung)
Authors: Schwarzschild, M.
1961MitAG..12...15S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the Spectrum of Turbulent Convection.
Authors: Ledoux, P.; Schwarzschild, M.; Spiegel, E. A.
1961ApJ...133..184L    Altcode:
  A procedure is described by which, under certain assumptions, the
  turbulence spectrum can be derived for the motions in a convectively
  unstable layer. The energy input from the buoyancy forces is assessed
  in this procedure by deriving the growth rates of the laminar modes
  obtained from the relevant linearized equations On the other hand,
  the exchange of energy between modes is assumed to follow Heisenberg's
  elementary theory of turbulence. The procedure is carried through for
  an exceptionally simple case for which a closed solution was found for
  the spectrum. The results, though not strictly applicable, are applied
  to the convection in the solar photosphere for purposes of orientation.

---------------------------------------------------------
Title: On the Periods of Long-Period Variables in Globular Clusters.
Authors: Stothers, Richard B.; Schwarzschild, M.
1961ApJ...133..343S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Lifetime of Solar Granules.
Authors: Baling, J. D. R.; Schwarzschild, M.
1960AJ.....65..481B    Altcode:
  A sequence of high-definition photographs of the solar granulation was
  obtained on the Stratoscope flight of August 17, 1959. The sequence
  covers a time interval of eight minutes. The correlation function in
  time for the photospheric intensity variations has been determined
  frnm these photographs, with the help of an optical method proposed by
  Kovasznay. The resulting correlation function can be closely represented
  by an exponential decay: R(At)= exp(-~t/6.3 minutes). If the average
  lifetime of granules is defined as twice the time interval in which
  the correlation drops to Si one half, then this lifetime is found to be
  8.6 minutes with an internal probable error of ~0.2 minutes. This new
  value is approximately twice as long as the classical determination
  by Ten Bruggencate and Grotrian based on low-definition plates. It
  is in general agreement with the more recent approximate estimates by
  Macris, Rbsch and Hugon, and Bray and Loughhead. Project Stratoscope
  is supported by the Office of Naval Research and by the National
  Science Foundation. % CO2, 22- 25% N2, and 0-3% H2O. The additional
  assumptions of adiabatic equilibrium below the cloud cover and
  isothermal equilibrium above the clouds were made. These conditions
  imply an average temperature gradient of 90K/km below the clouds,
  a cloud height of 33 km, a scale height of 6.86 km, and a pressure
  at the cloud level of 0.038 of the surface pressure. The mechanism of
  absorption results from the collision-induced dipole moment in CO2 and
  N2 and the rotational lines of H2O. The optical depth at any height
  has been computed and the radio brightness calculated from that. A
  surface pressure of 30 (terrestrial) atmospheres for 0% H2O or 10 atm
  for 3% H2O is needed to match the radio data. Thus, assuming a surface
  temperature of 6000K, fairly high surface pressures are indicated
  unless an unknown atmospheric constituent is a strong absorber of
  microwave energy. Further millimeter measurements are indicated, and
  these could be coupled with the possible detection of other molecules
  by their radio spectral lines. These include O2 at 5 and 2.53 mm, CO
  at 2.6 and 1.3 mm, NO at 1.99 and 1.20 mm, NO2 at 1.13 cm, and N2O at
  1.19 cm, 5.97, 2.98, and 2.39 mm.

---------------------------------------------------------
Title: Note on the brightness fluctuation in the solar granulation
Authors: Gaustad, J.; Schwarzschild, M.
1960MNRAS.121..260G    Altcode:
  On photographs of the solar granulation obtained with a balloon-borne
  telescope, Blackwell, Dewhirst and Dollfus (i) measured a
  r.m.s. brightness fluctuation of per cent. From this measurement they
  deduced a true r.m.s. brightness fluctuation of i8 per cent. This
  deduction was based on an accurate measurement of the contrast
  transmission function of their instrument, but on an approximate
  application of this transmission function to the granulation. This
  note alms to show that, using the same observed r.m.s. brightness
  fluctuation, the same measured instrumental transmission function, and
  the same value of I 4 seconds of arc for the average granule diameter,
  a more detailed analysis gives a true r.m.s. brightness fluctuation
  not of i8 per cent, but of only about 7 per cent. The overestimate by
  Blackwell et al. appears to have resulted from their identifying the
  granule diameter with a wave-lenght rather thin half a wave-length.

---------------------------------------------------------
Title: Photographs of the Solar Granulation Taken from the
    Stratosphere.
Authors: Schwarzschild, Martin
1959ApJ...130..345S    Altcode:
  A 12-inch solar telescope equipped with a photoelectric pointing
  mechanism and an automatic camera has been flown by unmanned balloons
  to an altitude of 80000 feet. A number of photographs of the solar
  granulation obtained with this telescope are of very high definition
  and show the granulation to have the character of non-stationary
  convection. The bright granules, ranging in diameter from about 300
  to about 1800 km, are of highly irregular, often polygonal, shape and
  are separated from one another by dark, often very narrow, lanes. The
  root-mean-square temperature fluctuation, uncorrected for instrumental
  smoothing, is found to be only + 60 . The analysis suggests that the
  true root-mean-square temperature fluctuation is probably not larger
  than * 100 .

---------------------------------------------------------
Title: Balloon Astronomy
Authors: Schwarzschild, Martin; Schwarzschild, Barbara
1959SciAm.200e..52S    Altcode: 1959SciAm.200e..52M
  No abstract at ADS

---------------------------------------------------------
Title: On the Maximum Mass of Stable Stars.
Authors: Schwarzschild, M.; Härm, R.
1959ApJ...129..637S    Altcode:
  Following an earlier investigation of Ledoux, the coefficient of
  pulsational stability has been recomputed for massive stars on the
  basis of the detailed models just published. From the homogeneous models
  representing the initial main-sequence state it is found that (assuming
  a helium content of 22 per cent) stars are pulsationally stable if
  they are lighter than 60 solar masses and unstable if they are heavier
  than this critical mass. From the inhomogeneous models representing
  subsequent evolution phases it is found that a star gains in pulsational
  stability as it evolves. For stars just above the critical mass, in
  the range from 60 to 65 solar masses, pulsational stability is gained
  so quickly after the initial main-sequence state that the pulsational
  instability can hardly have serious consequences. For stars heavier than
  65 solar masses, however, the instability is of sufficient duration and
  e-folding speed to have probably major effects. As already suggested
  by Ledoux, the existence of a critical mass for pulsational stability
  of mainsequence stars makes it appear probable that pulsational
  instability is indeed the mechanism which determines the upper limit
  for stellar masses. To bridge the gap between the theoretical value
  of 65 solar masses and the observed limit of about 95 solar masses,
  one might assume that in this mass range the pulsational instability,
  though not yet strong enough to cause immediate disruption, is already
  sufficiently strong to cause continuous shell ejection, as indicated
  by the P Cygni phenomenon.

---------------------------------------------------------
Title: Sunspot photographs from the stratosphere.
Authors: Bahng, J. D. R.; Danielson, J. B.; Rogerson, J. B., Jr.;
   Schwarzschild, M.
1959AJ.....64Q.323B    Altcode:
  The i~-inch telescope used during the balloon flights in 1957 has
  been modified by adding a television link so that the astronomer
  on the ground can see what the telescope is photographing, and by
  adding a radio command so that the astronomer can focus the telescope
  and direct it to any place on the solar disk during the flight. On
  the first flight this season the television and command links worked
  satisfactorily but instrumental vibrations and dust on optical surfaces
  limited the number and usefulness of the high- definition photographs
  obtained. However, before the next flight both these disturbances
  were greatly reduced and on the second flight (Aug. 17, 1959) a large
  number of high quality photographs was obtained. Time sequences were
  taken, both of granulation far from sunspots and of sunspots with their
  immediate surroundings. The time variations of the granules as well as
  of the penumbral filaments are clearly visible. A highly preliminary
  inspection of the photographs suggests that the granulation directly
  adjacent to sunspots does not seem to differ strikingly in size or
  lifetime from those in undisturbed regions. Project Stratoscope is
  sponsored jointly by the Office of Naval Research and the National
  Science Foundation. Princeton University Observatory Princeton, N. J.

---------------------------------------------------------
Title: Theoretical interpretation of the Hertzsprung-Russell diagram
    (Introductory paper)
Authors: Schwarzschild, M.
1959IAUS...10...79S    Altcode: 1959SAnAp...8...79S
  No abstract at ADS

---------------------------------------------------------
Title: Evolution of Very Massive Stars.
Authors: Schwarzschild, M.; Härm, R.
1958ApJ...128..348S    Altcode:
  Models for the initial state and for the early evolution phases of stars
  with masses between 30 and 200 solar masses have been constructed It
  was found that, as evolution proceeds in these very massive stars,
  the convective instability moves outward. This effect is caused by
  the low values of produced by the radiation pressure. In consequence,
  an intermediate semiconvective zone develops in which the convection
  is so slow that it does not contribute to the energy transport but is
  fast enough to modify the composition, so that convective neutrality is
  maintained in every layer of this zone throughout the early evolution
  phases. The resulting models show that these very massive stars will
  use up as much as two-thirds of their total initial hydrogen content
  before exhaustion in the core occurs. Accordingly, the evolution
  proceeds somewhat more slowly for these stars than had previously been
  estimated; even a star of 200 solar masses spends over two million
  years in the evolutionary phases before its core gets exhausted

---------------------------------------------------------
Title: Solar photographs from 80,000 feet.
Authors: Schwarzschild, M.; Rogerson, J. B., Jr.; Evans, J. W.
1958AJ.....63..313S    Altcode:
  During the summer of 1957 three unmanned balloon flights have been
  carried out with the aim of obtaining direct solar photographs with
  high definition, undisturbed by atmospheric seeing. The first flight
  had the purpose of testing the pointing mechanism and carried only a
  dummy telescope. The full telescope, constructed by Perkin-Elmer Co.,
  carried on the second and third flights, consisted of a parabolic
  mirror of ~~-inch aperture, f/8, an enlarging lens which produced an
  effective focal length of 200 feet, and a 35-mm movie camera taking an
  exposure each second with exposure time 0~.00I. The focus was scanned
  over a range of 10 to 20 times the focus tolerance. In the pointing
  control which was constructed by the Research Service Laboratories
  of the University of Colorado, photo- diodes were employed to find
  the sun and center on it. Motor-driven magnetic clutches were used
  to move the telescope with the motion in azimuth being accomplished
  by rotating against a heavy flywheel carrying the batteries. In
  the execution of the flights, carried out by General Mills, Inc.,
  no serious difficulties were encountered in the launching, tracking
  and recovering of the equipment. The cost of repairs for launching
  damage averaged for each of the three flights about 5 per cent
  of the construction cost. *Presented at the 99th A.A.S. meeting,
  Indianapolis, Ind., December 27-30, 1957. Several exposures of very
  high definition were obtained, both of the center of the solar disk
  and of the limb. These exposures show that the solar granulation has
  a cellular though highly irregular character. The bright cells appear
  separated from each other by dark, often very sharp lines. The sizes
  of the elements seem to range from 2" down to 0'.'3. This project was
  sponsored by the Office of Naval Research and the Geophysics Research
  Directorate of the Air Force. Princeton University Observatory,
  Princeton, N. J., and Sacramento Peak Observatory, Sunspot, N. M.

---------------------------------------------------------
Title: Theory of Stellar Evolution and the Age Sequence of Stellar
    Populations
Authors: Schwarzschild, M.
1958RA......5..204S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Structure and evolution of the stars.
Authors: Schwarzschild, Martin
1958ses..book.....S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Inhomogeneous Stellar Models. V. a. Solar Model with Convective
    Envelope and Inhomogeneous Interior.
Authors: Schwarzschild, M.; Howard, R.; Härm, R.
1957ApJ...125..233S    Altcode:
  A model for the sun has computed in which account has been taken both
  of the deep hydrogen convection zone and of the internal inhomogeneity
  in composition caused by the transmutation of hydrogen during the last
  five billion years. The model is found to permit good agreement with
  the analysis of the solar photosphere as regards chemical composition
  and as regards the depth of the hydrogen convection zone. Furthermore,
  the model indicates that the sun must have become brighter by nearly
  2 mag. during the five billion years.

---------------------------------------------------------
Title: A Spectroscopic Comparison Between - and Low-Velocity K Giants.
Authors: Schwarzschild, Martin; Schwarzschild, Barbara; Searle, L.;
   Meltzer, A.
1957ApJ...125..123S    Altcode:
  High-dispersion spectra of six high-velocity and ten low-velocity
  K giants were taken with the coude' spectrograph of the 100-inch
  telescope at Mount Wilson. Central depths were measured for 78 lines
  and profiles for 3 lines in the region X 4100-4500 The high-velocity
  giant # Ori was found to deviate from the low-velocity giants in an
  appreciable strengthening of CH relative to Fe I, a slight weakening
  of CN relative to Fe I, and a weakening of the Fe 1 lines-all in
  agreement with previous estimates. The amounts of these deviations can
  be explained by a deficiency of the metals in # Ori by a factor of 4 and
  by a deficiency of carbon, nitrogen, and oxygen by a similar amount. The
  same type of deviations, though to a lesser degree, were found for the
  high-velocity giants 14 And and a Boo, while no significant deviations
  were found for HD 39853, HD 154733, and a Sct Regarding the abundance of
  barium and the rare earths relative to iron, no significant difference
  was observed between any of the high- and low-velocity giants

---------------------------------------------------------
Title: Stellar Structure and Evolution
Authors: Schwarzschild, M.
1956SCoA....1..177S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the Colors of Subdwarfs.
Authors: Schwarzschild, M.; Searle, L.; Howard, R.
1955ApJ...122..353S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: A comparison of stellar populations in the Andromeda galaxy
    and its elliptical companion
Authors: Baum, W. A.; Schwarzschild, M.
1955AJ.....60..247B    Altcode:
  . For selected fields in the Andromeda Galaxy, M 31, and in its
  elliptical companion, NGC 205, the resolved stars were counted and the
  surface brightnesses measured photoelectrically. The count-brightness
  ratio thus obtained was found to be significantly higher for the
  companion than for the Andromeda Galaxy. The count-brightness ratio
  for the companion agrees with that for globular clusters, whereas
  the ratio for the Andromeda Galaxy agrees with that for the solar
  neighborhood. This indicates that the bulk of the light of the Andmmeda
  Galaxy is contributed not by extreme Population II stars but likely
  by old Population I stars.

---------------------------------------------------------
Title: Note on the Mass of M92.
Authors: Schwarzschild, M.; Bernstein, S.
1955ApJ...122..200S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the Evolution of Type II Stars.
Authors: Hoyle, F.; Schwarzschild, M.
1955ApJS....2....1H    Altcode:
  The evolution of the stars in globular clusters has been followed from
  the main sequence to the top Qf the red giant branch. In the initial
  phases the relevant models consist of partially degenerate isothermal
  helium cores and radiative hydrogen envelopes. These models show the
  well-known turnoff from tile main sequence in the Hertasprung-Russell
  diagram of globular clusters. The helium core steadily increases
  in mass because of the hydrogen-burning. When the core has reached
  approximately 20 per cent of the total stellar mass, tile envelope
  has reached an appreciable extent, and it is found necessary to
  take into account explicitly the photospheric boundary condition
  and the hydrogen convection zone. During the subsequent phases this
  convection zone steadily deepens while the luminosity increases; the
  star evolves in the Hertxsprung-Russell diagram along the observed red
  giant sequence. During these phases the internal temperature steadily
  rises so that the carbon cycle can keep in balance with the increasing
  luminosity. At the top of the red giant sequence the temperature in the
  hydrogen-burning shell at the edge of the core reaches about 40,000,000
  , while the helium core reaches approximately 50 per cent of the stellar
  mass. The model sequence thus computed appears to be' in satisfactory
  agreement with the observations in globular clusters. In addition,
  the difference between the red giants of population I and \ II can,
  it seems, be explained by the difference in the metal abundance of the
  two populations if this abundance difference is taken account of in the
  photospheric boundary condition; for the relevant evolution phases,
  a larger metal content produces a larger extent of the envelope and
  hence later spectral types. It is estimated that near the top of
  the red giant sequence the more and more rapid contraction of the
  core will heat the center until it reaches the temperature necessary
  to start helium-burning. The onset of this process is believed to
  terminate the red giant sequence by eliminating the degeneracy in the
  core. Preliminary computations suggest that this change in the stellar
  model will rather suddenly lower the luminosity and put the star on the
  beginning of the horizontal branch in the Hertxsprung-Russell diagram.

---------------------------------------------------------
Title: On the Evolution of Type II Stars.
Authors: Hoyle, F.; Schwarzschild, M.
1955ApJ...121..776H    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Inhomogeneous Stellar Models. IV. Models with Continuously
    Varying Chemical Composition.
Authors: Härm, R.; Schwarzschild, M.
1955ApJ...121..445H    Altcode:
  Nine sample models are constructed in which the mean molecular weight
  varies from the center to the surface by a factor of 2.5 and in which
  this variation occurs continuously inside an intermediate zone. These
  models are compared with simpler models in which the same composition
  variation occurs discontinuously at an interface. The comparison shows
  that the simpler, discontinuous models may be used to compute the
  luminosity with satisfactory accuracy but that they tend to exaggerate
  the radii-in certain cases by an order of magnitude.

---------------------------------------------------------
Title: Additional Data for Turbulence Spectrum of Solar Photosphere
    at Long Wave Lengths.
Authors: Frenkiel, F. N.; Schwarzschild, M.
1955ApJ...121..216F    Altcode:
  A plate showing the granulation with exceptional deflnition was
  selected from the regular Mount Wilson solar program. On this plate
  8000 intensity measurements were made. The measurements were analyzed
  in terms of a turbulence spectrum of photospheric intensities. The
  spectrum, when corrected for the flnite resolution of the photograph, is
  found to be fairly constant in the wave-length band from 2000 to 30,000
  km. This result for the turbulence spectrum of photospheric intensities
  is similar to the earlier indications found for the turbulence spectrum
  of velocities, in showing that the spectrum contains much energy in
  the wave-length band around 15,000 km, but disagrees with them in
  not showing in the corrected spectrum a large decrease from 15,000 to
  4000 km.

---------------------------------------------------------
Title: Mass distribution and mass-luminosity ratio in galaxies
Authors: Schwarzschild, M.
1954AJ.....59..273S    Altcode:
  . The observational data bearing on the mass distribution and
  mass-luminosity ratio in galaxies are rediscussed and assembled. The
  observations on the mass distribution indicate, contrary to earlier
  suggestions, that the data now available permit the assumption of
  identical spacial distribution of mass and luminosity. The results for
  the mass-lumi- nosity ratio are summarized in Table 7. In agreement
  with earlier investigations, the elliptical galaxies are found to
  have a mass4uminosity ratio much larger than that of pure population
  I systems. The Andromeda nebula is found to have an intermediate
  mass-luminosity ratio, suggesting that the body of the Andromeda nebula
  may consist of a mixture of population II and old population I stars.

---------------------------------------------------------
Title: Inhomogeneous Stellar Models. III. Models with Partially
    Degenerate Isothermal Cores.
Authors: Schwarzschild, M.; Rabinowitz, I.; Härm, R.
1953ApJ...118..326S    Altcode:
  A search was made for conditions under which models with partially
  degenerate isothermal cores could give radii as large as those of red
  giants. Special conditions were found for which detailed computations
  gave, indeed, models fitting well the red giants in radius and
  luminosity. But it has not been investigated whether the special
  conditions are likely to be realized in the evolution of a star.

---------------------------------------------------------
Title: The Possible Influence of Interstellar Clouds on Stellar
    Velocities. II.
Authors: Spitzer, Lyman, Jr.; Schwarzschild, Martin
1953ApJ...118..106S    Altcode:
  The increase with time of random stellar velocities, as a result of
  gravitational encounters with interstellar cloud complexes, has been
  recomputed, taking into account the presence of differential galactic
  rotation. As a result of such nonuniform rotation, the clouds will have
  velocities relative to one another even if their random velocities
  are zero; the gravitational potential of these clouds will he a
  fluctuating function of time; and the stars will gain kinetic energy
  from the clouds. To explain the increase of velocity dispersion with
  advancing spectral type along the main sequence, the mass of a typical
  cloud complex must be in the neighborhood of 106m0, the value found
  previously; but the random velocity of a cloud complex, as a whole,
  is irrelevant and may be vanishingly small. Since inhomogeneities
  of density with the required scale of some 300 parsecs or more seem
  indicated by the extinction observations, it seems not unlikely that
  star-cloud encounters are, in fact, responsible for the greater velocity
  dispersion of the later-type, older stars of population type I.

---------------------------------------------------------
Title: On the evolution of stars and chemical elements in the early
    phases of a galaxy
Authors: Schwarzschild, M.; Spitzer, L.
1953Obs....73...77S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Inhomogeneous Stellar Models. II. Models with Exhausted Cores
    in Gravitational Contraction.
Authors: Sandage, A. R.; Schwarzschild, M.
1952ApJ...116..463S    Altcode:
  Seven shell-source models with exhausted, gravitationally contracting
  cores have been computed in detail. The models form an evolutionary
  sequence starting from a confignration whose isothermal core
  contains the -Chandrasekhar limitating mass. It is found that, as the
  cores contract, the envelopes greatly expand. Thus from the initial
  confignration, which is near the main sequence, the stars evolve rapidly
  to the right in the H-R diagram, amply covering the giant region. In
  this evolution the gravitational contraction contributes less than
  4 per cent to the total luminosity. A comparison of this theoretical
  evolution with the observed H-R diagram for globular clusters appears
  to explain the sudden turnoff from the main sequence to the giant
  region at about Mb = +3.5.

---------------------------------------------------------
Title: Preliminary Analysis of the Turbulence Spectrum of the Solar
    Photosphere at Long Wave Lengths.
Authors: Frenkiel, F. N.; Schwarzschild, M.
1952ApJ...116..422F    Altcode:
  The available data on the velocities of granules are analyzed according
  to the methods of the statistical theory of turbulence. The analysis
  indicates that the turbulence spectrum of the solar photosphere may not
  be of a simple form but may have-in addition to the suspected primary
  maximum at wave lengths of the order of 300 km-a secondary maximum at
  long wave lengths of about 15,000 km.

---------------------------------------------------------
Title: Inhomogeneous Stellar Models. I. Models with a Convective
    Core and a Discontinuity in the Chemical Composition.
Authors: Oke, J. B.; Schwarzschild, M.
1952ApJ...116..317O    Altcode:
  A number of stellar models with a discontinuity in chemical composition
  have been computed through in detail. An arbitrary, but fixed,
  hydrogen-poor composition was used for the interior of all models,
  and a fixed hydrogen-rich composition was similarly used for all
  envelopes. The position in the star at which the change in chemical
  composition occurs was varied over a wide range. The computed models
  were found to cover well the observed red giants, as far as radii and
  luminosities are concerned. The masses of the theoretical red-giant
  models, however, fall systematically somewhat below the standard
  massluminosity relation-a circumstance not necessarily in discordance
  with observation.

---------------------------------------------------------
Title: Note on the color-magnitude diagram of Messier 3
Authors: Schopp, John; Schwarzschild, Martin
1952AJ.....57...61S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Perigalactic and apogalactic distances of high-velocity stars
Authors: Schwarzschild, Martin
1952AJ.....57...57S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Inherited and acquired characteristics of stars
Authors: Schwarzschild, Martin
1952AJ.....57....5S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The Possible Influence of Interstellar Clouds on Stellar
    Velocities.
Authors: Spitzer, Lyman, Jr.; Schwarzschild, Martin
1951ApJ...114..385S    Altcode:
  Gravitational encounters between stars and interstellar clouds produce
  a much shorter relaxation time of the galaxy in the solar neighborhood
  than do star-star encounters. This result is caused by much larger
  masses of the interstellar clouds as compared with stars. In the
  extreme case that the largest cloud complexes acting as gravitational
  units should have masses of the order of a million solar masses it is
  found that low-velocity stars may have been speeded up appreciably by
  star-cloud encounters during 3 X lO years. This speedup of the stars,
  which is the same for stars of all masses, arises from the tendency of
  the encounters to act toward equipartition of energy between clouds
  and stars, though at the present time equipartition must be far from
  reached. If the masses of the large cloud complexes are, in fact,
  high enough to make the star-cloud encounters sufficiently effective,
  one may suppose that all low-velocity population I stars have been
  formed from interstellar clouds with initial average velocities equal
  to those of the present clouds and that the present differences in the
  velocity dispersions of population I stars have been caused entirely
  by star-cloud encounters. Under this assumption, the encounters would
  have increased the average velocity of older groups (late dwarfs
  and red giants) by about a factor of 2, while they would not have
  had time to affect the velocities of the younger stars (early main
  sequence). Even under extreme assumptions the star-cloud encounters
  are found to be incapable of changing noticeably the velocities of
  the fast population II stars. This may indicate that all population
  II stars were formed from the interstellar matter at an early stage,
  when the velocities of the primeval clouds were still high.

---------------------------------------------------------
Title: On the Difference in Chemical Composition Between - and
    Low-Velocity Stars.
Authors: Schwarzschild, M.; Spitzer, L., Jr.; Wildt, R.
1951ApJ...114..398S    Altcode:
  The spectroscopic peculiarities of highwelocity of the CH bands and
  weakening of the CN bands and of the metal lines-can tentatively be
  explained by a general reduction in the abundance of the heavy elements
  and a somewhat lesser reduction in the abundance of the medium-heavy
  elements, relative to the abundances for low-velocity stars. As a
  working hypoQhesis, it is proposed that such a general difference in
  chemical composition between stars of populations I and II stems from
  the preferential accumulation of grains in the denser interstellar
  clouds from which the star of population I might be formed. The
  astrophysical discussion indicates that the dissociation energy of
  the molecules N2 and CO should be close to 9.5 e.v.; the considerably
  lower or higher values still advocated by some spectroscopists are
  not supported by the astronomical evidence.

---------------------------------------------------------
Title: On the Color-Magnitude Diagram for M 15.
Authors: Johnson, Harold L.; Schwarzschild, Martin
1951ApJ...113..630J    Altcode:
  Magnitudes and colors determined for 251 nonvariable stars in the
  globular cluster M 15. The resulting color-magnitude diagram indicates
  that the brighter stars in M 15 may belong to two sequences. The first
  sequence consists of red giants and supergiants and may possibly be
  the bright end of the subdwarf sequence. The second sequence consists
  of the horizontal branch characteristic of globular clusters. This
  branch appears to bend downward at its blue end and may thus possibly
  be the bright continuation of the regular main sequence.

---------------------------------------------------------
Title: A Spectroscopic Comparison Between - and Low-Velocity F Dwarfs.
Authors: Schwarzschild, Martin; Schwarzschild, Barbara
1950ApJ...112..248S    Altcode:
  High-dispersion spectrograms were obtained with the coud spectrograph
  of the l(iO4nch telescope at Mount Wilson for nine F stars, including
  three high-velocity and three low-velocity,'dwarfs. On the spectrograms,
  depths were measured for seventy-eight lines, equivalent widths for'
  thirteen lines, and profiles for four lines. The relative temperatures
  and pressures of the nine stars were analyxed with the help of the
  photoelectric color indices determined by Dr. Eggen and the degrees of
  ionixation derived from the line depths, and the various measurements
  were discussed as functions of temperature and pressure. The final data
  showed no difference between the high-velocity and the low-velocity
  F dwarfs, with the following exceptions: The CH features were found
  somewhat stronger relative to the Fe I lines in the highvelocity dwarfs
  than in the low-velocity dwarfs, indicating that the abundance ratio of
  C to Fe is probably approximately 2.5 times higher in the high-velocity
  dwarfs than in the low-velocity dwarfs. A second, though extremely
  uncertain, difference appeared in the equivalent widths of the Fe I
  lines, which indicated that possibly the abundance ratio of H to Fe
  might be larger in the high-velocity dwarfs by about a factor of 2 as
  compared with the low-velocity dwarfs.

---------------------------------------------------------
Title: Zeeman Shifts for Stellar Dipoles and Quadrupoles with
    Inclined Axes.
Authors: Schwarzschild, Martin
1950ApJ...112..222S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the Turbulent Velocities of Solar Granules.
Authors: Richardson, R. S.; Schwarzschild, M.
1950ApJ...111..351R    Altcode:
  With the 150-foot solar tower of the Mount Wilson Observatory, a
  spectrum of the solar granulation was obtained, showing individual
  granules with good definition. The Doppler shifts shown by this
  plate were measured and the corresponding turbulent velocities
  determined. From these data, together with the turbulent velocities
  determined from other solar observations, a tentative turbulence
  spectrum is derived for the solar photosphere. This spectrum suggests
  the possible existence of turbulent elements only 10(Y 200 km in
  diameter, with velocities of the order of 2 km/sec and brightness
  contrasts much exceeding those of the directly observable larger
  granules.

---------------------------------------------------------
Title: On the Abundance of C<SUP>13</SUP> in the Solar Atmosphere
Authors: Greenstein, J. L.; Richardson, R. S.; Schwarzschild, M.
1950PASP...62...15G    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Book Reviews: The Pulsation Theory of Variable Stars
Authors: Schwarzschild, Martin
1949Sci...110...21S    Altcode: 1949Sci...110...21R
  No abstract at ADS

---------------------------------------------------------
Title: Anharmonic Pulsations of the Standard Model.
Authors: Schwarzschild, Martin; Savedoff, Malcolm P.
1949ApJ...109..298S    Altcode:
  The anharmonic pulsations of the standard model are investigated. It
  is found that for the amplitude of characteristic cepheids, anharmonic
  pulsations yield practically the same period as harmonic pulsa- tions
  do. Furthermore, the anharmonic pulsations are found to produce an
  appreciable skewness in the radial velocity-curve; however, this
  skewness is still smaller than that observed

---------------------------------------------------------
Title: Red-Giant Models with Chemical Inhomogeneities
Authors: Hen, Li; Schwarzschild, M.
1949MNRAS.109..631H    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The Interior of the Sun
Authors: Schwarzschild, Martin
1949ASPL....5..392S    Altcode: 1949ASPL..248.....S
  No abstract at ADS

---------------------------------------------------------
Title: The Energy Source in the Interior of the Sun
Authors: Schwarzschild, Martin
1949ASPL....5..400S    Altcode: 1949ASPL..249.....S
  No abstract at ADS

---------------------------------------------------------
Title: Magnetic oscillations of a highly idealized star
Authors: Schwarzschild, Martin
1949AnAp...12..148S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: A Stellar Model for Red Giants of High Central Temperature.
Authors: Richardson, Robert S.; Schwarzschild, Martin
1948ApJ...108..373R    Altcode:
  The assumption is made that the turbulence in the convective core of
  a red giant emits acoustical noise of such strength that the entire
  energy flux is carried solely by the noise through the layers sur-
  rounding the core. According to this assumption, a stellar model is
  computed which consists of a con- vective core, an isothermal zone,
  and a radiative envelope. It is found that a star built according to
  this model may have a central temperature high enough for the carbon
  cycle to operate and have simul- taneously a radius as large as that
  of the biggest red giant

---------------------------------------------------------
Title: On the Pulsation in the Atmosphere of η Aquilae.
Authors: Schwarzschild, M.; Schwarzschild, B.; Adams, W. S.
1948ApJ...108..207S    Altcode:
  On twenty spectra of ~ Aquilae, taken with the coudé spectrograph of
  the 100-inch telescope with a dispersion of 2.9 A/mm and covering the
  entire pulsation cycle, forty-three lines of iron were selected for
  measurement. The radial-velocity variations of these lines were found
  to indicate that the selected lines of Fe i and Fe ii arise essentially
  from the same atmospheric layers. From the depth measurements of these
  lines the variations of the excitation temperature and of the electron
  pressure were determined. The equivalent widths, determined for a few
  iron lines at mid-descending branch, showed that the hydrogen-metal
  ratio in ~ Aquilae can differ from that in the sun by only a small
  factor. The curve of growth at the same phase gave turbulent velocities
  much smaller than the velocities determined from line profiles, which
  may possibly indicate the existence of a fast turbulence with very large
  elements. From the above data the density variation was computed. The
  comparison of this variation with that of the velocity suggests that
  possibly in the atmosphere of ~ Aquilae the kinetic temperature in-
  creases greatly with height and that in the highest layers the pulsation
  has the character of a simple pro- gressive wave. I. INTRODUCTIO

---------------------------------------------------------
Title: On Noise Arising from the Solar Granulation.
Authors: Schwarzschild, Martin
1948ApJ...107....1S    Altcode:
  It is shown that the mechanism which maintains the high temperature
  of the corona may consist of a stream of acoustical noise which is
  produced-by the granulation and which transports mechanical energy
  into the corona

---------------------------------------------------------
Title: On Stellar Rotation. II.
Authors: Schwarzschild, M.
1947ApJ...106..427S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The new photometer of the Rutherfurd Observatory
Authors: Eichner, L. C.; Hett, J. H.; Schilt, J.; Schwarzschild, M.;
   Sterling, H. T.
1947AJ.....53...25E    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the Helium Content of the Sun.
Authors: Schwarzschild, Martin
1946ApJ...104..203S    Altcode:
  Under the assumption that the sun consists of hydrogen, helium, and
  Russell mixture, it is shown that the sun contains approximately 40
  per cent of helium

---------------------------------------------------------
Title: Symposium: Intrinsic Stellar Variation. Recent studies of
    the pulsation theory
Authors: Schwarzschild, Martin
1946PAAS...10..117S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On Stellar Rotation.
Authors: Schwarzschild, Martin
1942ApJ....95..441S    Altcode:
  In section I the general problem of stellar rotation is discussed,
  and a special formulation, taking ac- count of the viscous forces in a
  restricted form, is given. The corresponding equations are set down in
  section II, and the first-order perturbation method for their solution
  is discussed in section III. For the special case of the standard model
  in slow rotation the equations are given in section IV and solved in
  sections V and VI. The solution is found to be unique and to correspond
  to a solid-body rotation

---------------------------------------------------------
Title: Note on the ionisation in the hydrogen convection zone
Authors: Schwarzschild, Martin
1942MNRAS.102..152S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Overtone Pulsations for the Standard Model.
Authors: Schwarzschild, Martin
1941ApJ....94..245S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: On the variables in Messier 3
Authors: Schwarzschild, Martin
1940HarCi.437....1S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: The Harvard Conference on Cepheid Variables
Authors: Gaposchkin, S.; Menzel, Donald H.; Mohr, Jenka; Norman, D.;
   Schwarzschild, M.; Shapley, Harlow; Sterne, T. E.; Thorndike, S. L.;
   Whipple, Fred L.
1938PA.....46..378G    Altcode: 1938PA.....46..378.; 1938HarRe.148....1G
  No abstract at ADS

---------------------------------------------------------
Title: On the Light Curves of Cepheids.
Authors: Schwarzschild, Martin
1938HarCi.429....1S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Zur Pulsationstheorie. (Mitteilung aus dem Institut für
    theoretische Astrophysik, Oslo. ) Mit 2 Abbildungen.
Authors: Schwarzschild, M.
1938ZA.....15...14S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Über die Energieerzeugung in den Sternen.
Authors: Schwarzschild, M.
1937ZA.....13..126S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Improved elements of BB Centauri
Authors: Schwarzschild, M.
1936BAN.....7..337S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Zur Pulsationstheorie der δ
    Cephei-Sterne. (Veröffentlichungen der Universitäts-Sternwarte
    Göttingen, Nr. 45. ) Mit 2 Abbildungen.
Authors: Schwarzschild, Martin
1936ZA.....11..152S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Die Schwankung der Farbtemperatur von α Ursae
    minoris. (Veröffentlichungen der Universitäts-Sternwarte Göttingen,
    Nr. 46). Mit 2 Abbildungen.
Authors: Schwarzschild, M.
1936ZA.....12..171S    Altcode:
  No abstract at ADS

---------------------------------------------------------
Title: Zur Pulsationstheorie der δ Cephei-Sterne 

---------------------------------------------------------
Title: Zur
Pulsationstheorie der δ Cephei-Sterne 

---------------------------------------------------------
Title: On the pulsation theory
    of cepheid stars;
Authors: Schwarzschild, Martin
1936PhDT........19S    Altcode:
  No abstract at ADS