Beatrice M Tinsley Publications


We give a list of some of Beatrice Tinsley's publications beginning with her thesis in 1967 and continuing until her death in 1981. For the thesis we give the Acknowledgements and Abstract, and for each of the following publications we give the Abstract to the paper. We note that some of the papers are joint publications but we have not listed Tinsley's co-authors. This list is only a sample of the papers Tinsley published. We give a larger sample of her papers from the earlier years, giving only one or two of the 10-15 papers she published in each of the later years.

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  1. Evolution of galaxies and its significance for cosmology

  2. Evolution of the Stars and Gas in Galaxies

  3. Distribution of redshifts of quasars

  4. Possibility of a large evolutionary correction to the magnitude-redshift relation

  5. Evolution of the M31 disk population

  6. The luminosity function of old-disk red giants compared with theoretical rates of evolution

  7. The color-redshift relation for giant elliptical galaxies

  8. Possibility that the Far Ultraviolet Excess in M31 is Due to Main-Sequence Stars

  9. Post-Main Sequence Evolution of Low Mass Old Disk Stars

  10. Galactic Evolution

  11. Stellar Evolution in Elliptical Galaxies

  12. Effects of Evolution on the Diameter-Redshift Relation

  13. A First Approximation to the Effect of Evolution on \q0 \\

  14. The Magnitude-Redshift Relation in Brans-Dicke Cosmology

  15. The Possible Line Feature in the X-ray Background

  16. Analysis of the Magnitude-Redshift Relation Including Possible Effects of Evolution

  17. On the evolution of evolutionary corrections

  18. The magnitude-redshift relation in Hoyle-Narlikar cosmology

  19. Dependence of the Integrated Background Light on Cosmology, Galactic Spectra, and Galactic Evolution

  20. Analytical Approximations to the Evolution of Galaxies

  21. A Critique of Hoyle and Narlikar's New Cosmology

  22. An unbounded universe?

  23. Constraints on models for chemical evolution in the solar neighborhood

  24. Photometric Properties of Model Spherical Galaxies

  25. On Stellar Birthrates and Age Distributions

  26. Evolution of the Nearby Stellar Population and Its Kinematics

  27. Galaxy counts as a cosmological test

  28. Predetonation lifetimes of Type II supernovae

  29. Possible influence of comets on the chemical evolution of the galaxy

  30. On the Correlation Between M/L and Colour for Spiral Galaxies

  31. An accelerating Universe

  32. Interpretation of Stellar Metallicity Distribution

  33. What stars become supernovae?

  34. Is deuterium of cosmological or of galactic origin

  35. Synthesis of stellar populations

  36. On the Origin of SO Galaxies

  37. Evolution of galaxies and its significance for cosmology

  38. Will the Universe Expand Forever?

  39. The cosmological constant and cosmological change

  40. Accelerating Universe revisited

  41. The Evolution of Galaxies: Evidence from Optical Observations

  42. HR Diagrams of Galaxies: Ages and Stages of Evolution

  43. Galactic Evolution with the Space Telescope

  44. Cosmology and galactic evolution

  45. On the interpretation of galaxy counts

  46. Correlation of the dark mass in galaxies with Hubble type

1967.

1. Evolution of galaxies and its significance for cosmology.
Presented to the Faculty of the Graduate School of the University of Texas in partial fulfilment of the requirements for the Degree of Doctor of Philosophy. The University of Texas, Austin, Texas. January, 1967.

Acknowledgements.

I wish to thank my Supervising Professor, Dr Rainer K Sachs, whose advice, stimulating questions, and encouragement have enabled me to undertake and continue this research. It is also a pleasure to thank Dr Harlan J Smith, Dr Neville J Woolf, and Dr Gerard de Vaucouleurs for their interest and suggestions.

To my husband, Brian A Tinsley, I wish to express my deepest gratitude for the most essential encouragement, support, and cooperation he has given me throughout my association with The University of Texas.

This research has been sponsored by the Office of Aerospace Research, United States Air Force, and was carried out during the tenure of a University of Texas Fellowship.

Abstract.

Evolution of the content and light of galaxies are studied to determine their significance for cosmology.

A numerical computation of evolution starts from gas with Population I composition; then stars are formed at all times, at rates which are functions of stellar mass and mass of gas in the galaxy. Discrete time steps of 10910^{9} years are used, and 13 stellar masses. The stars are placed on the H-R diagram according to their masses and ages; each star finally becomes a white dwarf, while its excess mass enriches the interstellar gas. Different evolutionary sequences are constructed by adjusting four parameters of a stellar birthrate function. Then 'galaxies' resulting from each sequence of 10 to 12 ×109\times 10^{9} years are compared with observed local galaxies, with respect to colours in Johnson's 8-colour (UBVRIJKL) system, mass/light ratio, relative mass of gas, and types of stars contributing to the light.

'Galaxies' closely resembling all normal types, Im to E, can be formed with a stellar birthrate proportional to the inverse square of stellar mass, and to the mass of gas in the galaxy; the types differ in initial rate of gas consumption and in the birthrate of very low mass stars. These types can all have the same age, and do not form an evolutionary sequence.

Theoretical magnitude-redshift relations (mzm-z) are constructed, for a variety of cosmological models, using the computed past history of giant elliptical systems. Three values of Hubble's constant are considered, since effects of evolution are greater if this is small. The colour-redshift relation is also discussed, but effects of evolution are small in the range observed. Inclusion of galactic evolution greatly reduces the differences in mzm-z relations between models. This is because those models with the greatest luminosity distance at a given redshift also have the greatest light travel-time, so the galaxies would be seen earlier when they were brighter.

Many cosmological models are found to be consistent with the observed mVzm_{V}-z relation, including models also consistent with empirical limits on the mean density of matter, with the minimum age of the universe inferred from evolution of star clusters, and with a steep number-flux density relation for radio sources.

Equivalent widths of interest for studies of the composition and evolution of galaxies
1968.

2. Evolution of the Stars and Gas in Galaxies.
A numerical computation of evolution starts from gas with Population I composition; then stars are formed at all times, at rates which are functions of stellar mass and mass of gas in the galaxy. Discrete time steps of 10910^{9} years are used, and 13 stellar masses. The stars are placed on the H-R diagram according to their masses and ages; each star ends as a white dwarf, while its excess mass enriches the interstellar gas. Different evolutionary sequences are constructed by adjusting four parameters of a stellar birth-rate function. Then "galaxies" resulting from each sequence of 10-12 ×109\times 10^{9} years are compared with observed local galaxies with respect to colours, mass-to-light ratio, relative mass of gas, and types of stars contributing to the light.

"Galaxies" closely resembling all normal types, Im to E, can be formed with a stellar birth rate proportional to the inverse square of stellar mass and to the mass of gas in the galaxy; the types differ in initial rate of gas consumption and in the birth rate of very low-mass stars. These types can all have the same age, and do not form an evolutionary sequence.

It is shown that giant elliptical galaxies may have been so much brighter at short wavelengths a few billion years ago that the observed magnitude-redshift relation can be interpreted in terms of cosmological models that do not suffer from the high density and small age of the conventionally preferred model.
1969.

3. Distribution of redshifts of quasars.
The observed complex distribution of quasar redshifts has been interpreted by Barbieri, Bonometto and Saggion (1968) as due to a combination of simple distributions of cosmological and gravitational redshifts. An error in their analysis is noted which invalidates their conclusions.
1970.

4. Possibility of a large evolutionary correction to the magnitude-redshift relation.
Galactic evolution may be rapid enough to reconcile the observed magnitude-redshift relation with cosmological models of acceptably great age and low density, in spite of recent evidence to the contrary. Previous treatments of this subject have suffered from use of wrong quantities as the evolutionary correction, and from lack of generality in galactic models. A range of giant elliptical galaxies can be synthesised which are compatible with the available photometry, including Oke and Sandage's (1968) observations of a slow rate of change of colour B-V. One such model galaxy is discussed which evolves sufficiently rapidly at short wavelengths to provide an evolutionary correction of several tenths of a magnitude at redshift 0.46.
1971.

5. Evolution of the M31 disk population.
An evolutionary model for the M31 inner disk population is described, which at age 12 billion years agrees closely with the narrow-band colours and line indices recently measured by Spinrad et al. (1971), and with the broad-band colours from 0.36 to 3.4 μ\mu. Assuming that gE galaxies have the same stellar population as the M31 inner disk, this model is used to derive evolutionary effects in cosmology. Interpretation of the magnitude-redshift relation is substantially affected, since the evolutionary correction to V magnitudes at redshift 0.2 may be 0.09 mag. if H0=100kms1Mpc1H_{0} = 100 km s^{-1} Mpc^{-1}, or ≥ 0.25 mag. if H0=50.H_{0} = 50. Changes in some line strengths may be observable at redshift 0.46, showing the younger stellar population at earlier times. Our results differ from estimates by other authors, also based on the assumption that the gE and disk populations are identical, that the photometry of Spinrad et al. (1971) precludes a significant rate of evolution. One reason for the difference is that our model has an unexpectedly shallow luminosity function just below the main sequence turnoff; another reason is that authors in the past have used the change in absolute V magnitude as the evolutionary correction, whereas the appropriate quantity is the change in absolute magnitude at the emitted wavelengths, and evolution is more rapid at these shorter wavelengths.
6. The luminosity function of old-disk red giants compared with theoretical rates of evolution.
A rich sample of low-mass old-disk giants is obtained from six very similar groups discovered by Eggen. Their combined luminosity function is compared with Iben's theoretical track for a population I star of 1.25 solar masses, which ends at Mbol=3.2M_{bol} = -3.2, at core helium ignition. It is found, after allowance for selection effects and statistical uncertainty (~25 per cent), that the distribution of subgiants and giants up to Mbol=3.2M_{bol} = -3.2 is compatible with evolution at the theoretical rate , except that about half the giants in the 'clump' at +1 > MbolM_{bol} > 0 must be in a later stage lasting ~50 million years. The 23 known group members brighter than the theoretical track must be in later stages totalling 5 million years. It appears that about 70 per cent of the nuclear energy available to the star is consumed by the end of the main-sequence and red-giant stages of evolution.
7. The color-redshift relation for giant elliptical galaxies.
The colours of giant elliptical (gE) galaxies in clusters out to redshift z=0.2z = 0.2, observed by Oke and Sandage (1968), are studied for systematic colour-redshift effects. To reveal any intrinsic changes, the K term is subtracted from each colour, after correction for galactic reddening and the resulting (BV)cKBV(B-V)_{c} - K_{B-V} versus zz relation analysed. If the Oke and Sandage KK terms (relevant to nuclear colours) are used, the best fitting linear relation shows negligible change with zz. But if the Whitford (1970) KK terms (relevant to integrated colours) are used, there is a trend to bluer colours, by 0.07 mag. at z=0.2z = 0.2 if higher weight is given the better observed clusters. An upper limit, of ±0.08 mag. at z=0.2z = 0.2, is set to possible systematic aperture effects, by the total change between nuclear and integrated BVB-V and UBU-B of nearby gE galaxies.

The colour-redshift trends, interpreted as evolutionary changes, are related to evolution in the magnitude-redshift relation by means of models of stellar evolution in a gE galaxy. If one uses the linear fit to the colour-redshift relation obtained with Whitford K terms and neglect of any aperture effects (which is the appropriate case if Oke and Sandage used large enough apertures), and if one adopts plausible limits to the ratio between colour and magnitude evolution, the effect of evolution in the magnitude-redshift relation results in a negative value of q0q_{0}. There are still substantial observational and theoretical uncertainties affecting this conclusion.
8. Possibility that the Far Ultraviolet Excess in M31 is Due to Main-Sequence Stars.
The far ultraviolet (UV) excess in the central region of M31, observed by OAO-2, could be due to young main-sequence stars. More than enough such stars are present in the model for the M31 inner disk population derived by Tinsley and Spinrad (1971) to match line- and colour-indices at longer wavelengths. If the far UV radiation of typical galaxies arises from young stars, the theoretical UV background is enhanced greatly by evolutionary effects. For evolution at the rate of Tinsley and Spinrad's model for M31, or of Arnett's (1971) "linear" model for our galaxy, the enhancement is a factor 2.5 to 14, depending on the Hubble constant and the spectrum at wavelengths below 1700 Å.
9. Post-Main Sequence Evolution of Low Mass Old Disk Stars.
A rich sample of low-mass old disk giants and subgiants is obtained by combining the six very similar groups discovered by Eggen (1958).
1972.

10. Galactic Evolution.
A program is described for studying the evolution of galaxies. Some initial results are presented. suggesting future applications of the program.

In the models, stars are formed from interstellar gas, and the evolution of each star is followed from the main sequence to death. Semi-empirical tracks based on old open clusters and old-disk moving groups are used for the later stages of low-mass stars. Properties of the models that can be calculated at times from 1 to 11 × 10910^{9} years (in discrete time steps of 10910^{9} years) are: the detailed stellar population at 566 points of the H-R diagram; the mass of gas and its helium and metal content; the bolometric magnitude; integrated broad-band colours and magnitudes on Johnson's 8-colour system; the mass to light ratio; the UV flux at 1700 Å integrated intermediate-band colours on McClure and van den Bergh's system: narrow-band colours on Wood's system; and narrow-band scanner colours and indices on Spinrad and Taylor's system.

The models studied to date are homogeneous and contain solar-composition stars only. Metal-poor and super-metal-rich stars can be added (as integrated globular clusters and SMR K giants) to a computed population before its photometric properties are found. Stellar birthrates used include a variety of initial luminosity functions and functions of time or gas mass. These functions provide a set of models with which to survey the potentialities of the method. Future studies will use birthrate functions based on theories of star formation in various types of galaxies.

Models discussed here were not planned to match any galaxy precisely, but the types of birthrate required for various typical galactic populations, and their overall evolution, are clearly indicated. Some results of interest are: (I ) Models evolve redwards along the observed galactic 2-colour relation, so UBV colours cannot tell if a galaxy contains only, or just predominantly, young stars. (2) The observed far ultraviolet flux could arise from young main sequence stars, in galaxies with a finite present birthrate. (3) Super-metal-rich stars are probably formed in elliptical galaxies and the central regions of spirals. (4) The infrared light of galaxies is predicted to be dominated by late giants, even in systems with a high mass-to-light ratio, (5) The Spinrad-Taylor indices are far the most sensitive of the properties studied to the distribution of stellar temperatures, luminosities, and abundances in a population. Use of broad-band colours alone can be seriously misleading.
11. Stellar Evolution in Elliptical Galaxies.
Elliptical galaxies are described by models in which the evolution of stars is followed for 12 billion years. Stellar birthrates chosen are mainly power laws in stellar mass, cut off after 10910^{9} years; effects of these oversimplifications are discussed. Integrated magnitudes, broad-band colours, narrow-band scanner spectral energy distributions, and strengths of spectral features are derived as a function of time.

Comparison of computed with empirical energy distributions sets limits to the galactic age for each initial mass function (IMF). Unless the Universe is extremely young, a fairly shallow IMF is required. There are then few late dwarfs to provide unchanging light, so significant evolution toward fainter luminosities must occur. The magnitude-redshift relation is affected in such a way that q0q_{0} appears larger than its true value by at least 0.5. The colours of models with a shallow IMF evolve very slowly, however, because much of their light comes from low-mass giants whose colours depend very weakly on mass; this result agrees with colours of galaxies observed at large redshifts.

The possibility of continued star formation in the nuclei of some ellipticals, from gas shed by stars dying throughout the galaxy, can explain the occurrence of Balmer absorption lines and emission lines from H II regions.

Production of metals during the first 10910^{9} years is calculated, leading to an explanation of the observed increase in stellar metal abundance and redness toward the centre. The computed abundances are lower than observed, however. If a preceding short burst of very massive stars has occurred, these can produce enough metals, leave in visible stellar remnants to provide the observed high mass-to-light ratios, and radiatively ionise the intergalactic medium at the epoch of galaxy formation.
12. Effects of Evolution on the Diameter-Redshift Relation.
The relation between redshift and metric angular diameters is unaffected by evolution of the light of galaxies, but the relation using isophotal diameters is subject to an evolutionary correction. At small redshifts, the required correction to the indicated value of q0q_{0} is identical to that required in use of the magnitude-redshift relation. An apparent discrepancy, approximately equal to that found between Sandage's preliminary value (q0q_{0} ~ 1) from isophotal diameters and Baum's value q0=0.3q_{0} = 0.3) from metric diameters, is predicted.
13. A First Approximation to the Effect of Evolution on q0q_{0}.
Because the spectral energy distributions of nearby giant elliptical galaxies are inconsistent with a very steep initial luminosity function, their rate of evolution must be such as to move the magnitude-redshift relation to an apparent value of q0q_{0} at least 0.5 greater than its true value. This conclusion is true even at small redshifts, and it is consistent with the observed slow evolution in colour of giant elliptical galaxies.
14. The Magnitude-Redshift Relation in Brans-Dicke Cosmology.
The magnitude-redshift relation expected in a flat Brans-Dicke world is discussed. Effects of stellar evolution, both in the conventional manner and as caused by the time-variation of the gravitational constant, are included.
15. The Possible Line Feature in the X-ray Background.
This letter evaluates the effects of cosmological redshift and galactic evolution on Silk's (1971) theory of the Z-ray background due to young pulsars in supernova remnants, including the possible line feature near 7 keV due to K-line photons from iron-group elements. For any plausible cosmological time scales, galactic ages, and pulsar parameters, the strength of the redshifted continuum radiation from the supernova shells is found to obscure the red-smeared line feature in the background spectrum, so that the feature is probably undetectable. This result is insensitive to the choice of models for cosmology and galactic evolution, and holds even if the past supernova rate per unit galactic mass were the same as the present rate in our galaxy.
16. Analysis of the Magnitude-Redshift Relation Including Possible Effects of Evolution.
In this paper, we compare the magnitude-redshift data for brightest cluster galaxies with cosmological models of general relativity, including non-zero cosmological constant. Our study is parallel to that by Peach (1970). We use the same data but an independent method, and obtain somewhat different results. We also consider possible effects of evolution.
17. On the evolution of evolutionary corrections.
It is well known that if giant elliptical galaxies were brighter in the past, the value of q0q_{0} inferred from the magnitude-redshift diagram is greater than its true value; i.e., a positive correction Δq0\Delta q_{0} (apparent-real) is required. This paper demonstrates the consistency of Tinsley's recent estimates for a substantial positive Δq0\Delta q_{0} with arguments in the literature leading to negligible corrections.
18. The magnitude-redshift relation in Hoyle-Narlikar cosmology.
Because of the rapid change of the gravitational constant with time in Hoyle and Narlikar's new cosmology, the Hubble plot of galaxies predicted by this theory is much steeper than the observed plot. The colours predicted for distant galaxies are also in disagreement with observed colours.
1973.

19. Dependence of the Integrated Background Light on Cosmology, Galactic Spectra, and Galactic Evolution.
The theoretical spectrum and intensity of the integrated light of distant galaxies is studied as a function of uncertain parameters entering its calculation. These include the cosmological model, epochs of formation of galaxies, evolution of the magnitudes and colours of galaxies of different types, the ultraviolet radiation of galaxies, and the local luminosity density of the universe. It is found that the background light is affected strongly by all of these factors, in such a way that even highly penetrating observational data could yield little firm information for either cosmology or galactic evolution. If better estimates of these parameters than those presently available are obtained from other considerations, measurements of the background light could provide an important test of their consistency.
20. Analytical Approximations to the Evolution of Galaxies.
Analytical expressions are derived for the evolution of the luminosity, mass of stars, mass of invisible remnants, rate of ejection of gas from stars, and yield of heavy elements in idealised model galaxies. The equations are based on simple assumptions concerning the mass function of star formation and stellar evolution, and they apply to an arbitrary time-dependence of the stellar birthrate. Especially simple and instructive forms are derived for the expressions in the cases where star formation occurs uniformly and where it occurs in an initial burst. These results are used to show how certain properties of elliptical galaxies, globular clusters, and late-type galaxies depend on parameters characterising their rate of star formation and the initial mass function. In spite of the severe limitations of this approach to galactic evolution, it sheds light on the results obtained from detailed numerical models, and it predicts a number of useful general relationships among galactic properties.
21. A Critique of Hoyle and Narlikar's New Cosmology.
The magnitudes of spiral and elliptical galaxies, and colours of distant ellipticals, predicted by Hoyle and Narlikar's new cosmology, are derived on the assumption that the variation of the gravitational constant GG affects only the stellar temperatures and luminosities. The galaxies are predicted to be much brighter and bluer than observations allow. Changes of the stellar content with time, or the possibility of a convective dwarf population for ellipticals (as suggested by Hoyle), are found to be implausible. It appears very difficult to reconcile this theory with observations of galaxies unless it can be shown that a strong increase in GG results in fundamental changes in stellar structure which counteract the effects considered here.
1974.

22. An unbounded universe?
A variety of arguments strongly suggest that the density of the universe is no more than a tenth of the value required for closure. Loopholes in this reasoning may exist, but if so, they are primordial and invisible, or perhaps just black.
23. Constraints on models for chemical evolution in the solar neighborhood.
Chemical evolution in the local region of the Galaxy is described by analytical approximations to models based on a variety of hypotheses that have been proposed to account for the observed abundances in stars, interstellar gas, and the solar system. There are many alternative (although not always mutually exclusive), physically plausible models to be considered, and many parameters related to nucleosynthesis, star formation, gas flows, etc., which cannot be reliably determined a priori. In spite of these uncertainties, it is found that very few types of models are consistent with several important empirical constraints. These are the paucity of metal-poor stars, the small difference between the mean metal abundances of the oldest and youngest disk stars, and the lack of observable change in certain isotopic abundance ratios during the last 4.5 billion years. Unless there is an unknown Galactic site of deuterium production, the production rates in supernovae of other light elements relative to deuterium appear to restrict the class of viable models further to those in which a significant fraction of primordial deuterium has not been processed through stars. Either metal-enhanced star formation or the infall of primordial gas leads to evolutionary models consistent with all these constraints. It is found that the ratio between s-process abundances and stellar production factors is nearly model-independent, but that the relative importance of the big bang or red-giant stars as the source of 3He depends on details of the evolutionary history.
24. Photometric Properties of Model Spherical Galaxies.
This paper presents the results of detailed calculations of the photometric properties of the dynamical models for the formation and evolution of spherical galaxies recently computed by Larson. The models that were found in Paper I to have radial density distributions closely matching those of elliptical galaxies are found to resemble elliptical galaxies also in their colours, mass-to-luminosity ratios, and narrow-band spectral energy distributions. However, the residual star formation activity in the nuclei of these models makes the nuclear colours bluer than normal, suggesting that most elliptical galaxies have lost their residual gas and do not experience current star formation. The effect of the metal abundance gradient of Paper I on the colours has been estimated, and (in the absence of current star formation) it causes the nucleus of a galaxy to appear redder than the outer regions, as is generally observed. The models with expanding boundaries, in which star formation continues to be important at the present time, have colours and mass-to-luminosity ratios which resemble those of spiral galaxies, showing that differences in the photometric properties of different types of galaxies can be understood in terms of different dynamical histories. The evolution of the photometric properties of the models is discussed, and it is concluded that continuing star formation in elliptical galaxies is not likely to affect significantly the rate at which they evolve in colour and luminosity. The predicted supernova rates in models whose UBV colours resemble those of different Hubble types of galaxies agree with the observed supernova rates in these types of galaxies.
25. On Stellar Birthrates and Age Distributions.
A general relationship is derived between the age distribution of A-F stars and the time-dependence of their birthrate. Depletion of these stars by death, which is relatively more severe in older generations, means that their present age distribution is not directly proportional to the birthrate. Two recently derived age distributions, each for several hundred nearby evolving stars, are shown to be consistent with a birthrate that has decreased over the past 7 billion years, with e-folding time about 5 billion years.
26. Evolution of the Nearby Stellar Population and Its Kinematics.
Following the discovery of a great number of low-velocity M dwarfs (Weistrop, 1972 and others), Biermann (1973) formulated the idea that the velocity dispersions of stars are a property largely given to the stars at formation and modified over galactic timescales. Using the ideas and formalism of Tinsley (1972), a quantitative model of the stellar population in the solar neighbourhood is investigated which includes the evolution of stellar kinematics. The model is able to account for all major properties of the stellar disk population (halo stars excluded). The tentative conclusion is drawn that the spiral arm inclination and/or shock strength was considerably greater in the past history of the Galaxy.
27. Galaxy counts as a cosmological test.
Analytical approximations and numerical calculations are given for the number-magnitude relation for galaxies. It is shown that this relation is no more sensitive to the cosmological model (in particular, to the value of q_0 in the standard Friedmann models without cosmological constant) than to effects of galactic evolution and possible intergalactic absorption. Counts are expected to be dominated by spiral galaxies. The number-magnitude relation is thus not a straightforward cosmological test, since its interpretation will require a good knowledge of the luminosity functions, spectra, and evolution of all types of galaxies.
28. Predetonation lifetimes of Type II supernovae.
Since Type II supernovae tend to occur near the inner edges of spiral arms (Moore 1973), an upper limit to the precursor lifetimes, and hence a lower limit to the precursor masses, can be set. Moore derived a limit of 35 solar masses, on the assumption of constant stellar velocity across the arm; this mass is too great to agree with supernova statistics or theoretical predictions. Here we consider the motion of the stars across the arm under the influence of the spiral gravitational field, and find a limit of about 8 solar masses, which does agree with other estimates. However, the computed stellar orbits make it difficult to believe that supernovae are as tightly clustered to the inner edges as claimed by Moore.
29. Possible influence of comets on the chemical evolution of the galaxy.
It has been suggested by Cameron that a cloud of comets containing a mass of condensable elements, comparable to the mass of such elements in the sun, formed on the outskirts of the solar system. If the formation of such comet clouds is a general feature of star formation, they constitute a significant sink of elements heavier than helium. It is shown here that this process provides a possible explanation for the very slow rate at which the mean metal abundance of disk stars has increased during the lifetime of the Galaxy.
30. On the Correlation Between M/L and Colour for Spiral Galaxies.
The correlation between M/L and B-V found for spiral galaxies by Nordsieck is compared with theoretical relations for model galaxies with the same initial mass function (IMF). There is evidence that the observed relation is steeper, suggesting that the lower IMF may be enhanced in earlier types of galaxies, but more data are needed to confirm this possibility.
1975.

31. An accelerating Universe.
New data on the Hubble diagram, combined with constraints on the density of the Universe and the ages of galaxies, suggest that the most plausible cosmological models have a positive cosmological constant, are closed, too dense to make deuterium in the big bang, and will expand for ever. Possible errors in the supporting arguments are discussed.
32. Interpretation of Stellar Metallicity Distribution.
The dispersion in metal abundances of stars of a given age is similar to that in the abundance distribution of dwarfs with lifetimes greater than the age of the Galaxy. Thus the latter distribution cannot be correctly interpreted unless the former dispersion is taken into account. With this consideration, dynamical models for the formation of the Galaxy by collapse, and models for chemical evolution that consider accretion of gas shed by halo stars, no longer predict too few moderately metal-poor G-K dwarfs in the solar neighbourhood.
33. What stars become supernovae?
This paper assembles a variety of empirical lines of evidence on the masses and stellar-population types of stars that trigger supernova (SN) explosions. The main theoretical motivations are to determine whether type I supernovae (SN I) can have massive precursors and whether there is an interval of stellar mass between the masses of precursors of pulsars and white dwarfs that is disrupted by carbon detonation. Statistics of stellar birthrates, SN, pulsars, and SN remnants in the Galaxy show that SN II (or all SN) could arise from stars with masses greater than about 12 to 49 solar masses. Several methods of estimating the masses of stars that become white dwarfs are consistent with a lower limit of about 5 solar masses, so carbon detonation may be avoided. Studies of the properties of galaxies in which SN occur, and their distributions within galaxies, support the usual views that SN I have low-mass precursors and SN II have massive precursors. The restriction of known SN II to Sc and Sb galaxies is shown to be statistically consistent with massive stars in other galaxies also dying as SN II. Possible implications of the peculiarities of some SN-producing galaxies are discussed.
34. Is deuterium of cosmological or of galactic origin.
If deuterium is made primarily in stars, then according to current models of galactic evolution it should have a higher abundance in the metal-rich parts of the Galaxy. If it is produced only in the initial big bang, then astration causes a decrease in D abundance with increasing metal abundance 2. Since the sign of the galactic metal abundance gradient is known (dzdr<0\Large\frac{dz}{dr}\normalsize < 0), we propose that a determination of the sign of the deuterium abundance gradient would indicate the probable origin of this isotope. In particular it appears possible that the ratio of the radio recombination line strengths (D/H) from dense H II regions might be measurable with realisable equipment and determine, relatively unambiguously, the ratio of abundances in various parts of the Galaxy.
35. Synthesis of stellar populations.
Lectures by Beatrice M Tinsley given at the Scuola di Astronomia, "Stellar Populations," Erice, Sicily, May 20-31, 1974.
36. On the Origin of SO Galaxies.
We discuss the hypothesis that SO galaxies are former spirals, in which star formation has been cut off by loss of gas. Observed UBV colours, compiled from the literature, are compared with those of model galaxies; they are consistent with the cutoff hypothesis, with the reddest SO's having ceased star formation at a very early epoch, and the bluest having made stars up to 1 or 2 10910^{9} years ago. The mass of the gas that has been shed by evolving stars, between the cutoff epoch and now, is estimated. This is greater than the upper limits observed for H I, implying that there is some continuing mechanism for ridding SO galaxies of their gas. Several mechanisms for cutting off star formation are mentioned, and it is suggested that galaxies classified as SO may have a variety of origins.
37. Evolution of galaxies and its significance for cosmology.
Possible effects on observational cosmology of star evolution in ordinary galaxies are described. Only Friedman models with zero cosmological constants are considered. Numerical models for elliptical galaxies are discussed.
1976.

38. Will the Universe Expand Forever?
The recession of distant galaxies, the average density of matter, the age of the chemical elements and the abundance of deuterium together suggest that the expansion cannot be halted or reversed.

Cosmological inquiry is ancient, but only in the past 50 years or so have we begun to understand how the universe began and what its ultimate fate may be. The crucial perception came in the 1920's, when Edwin P Hubble demonstrated that the spiral nebulas are not local objects but independent systems of stars much like our own, and thereby showed that the universe is a much larger place than had been imagined. Hubble showed further that the entire observable system of galaxies is in orderly motion. As is now well known, the nature of that motion is expansion: all distant galaxies are receding from us.

That the universe is expanding is today considered established. A question that remains unsettled is whether the expansion will continue forever or whether the receding galaxies will someday stop and then reverse their motion, eventually falling together in a great collapse. The answer to this question determines the geometrical character of the universe, that is, it determines the nature of space and time. If the expansion continues perpetually, the universe is "open" and infinite; if it will some day stop and reverse direction, the universe is "closed" and of finite extent.

In order to choose between those possibilities, astronomers construct mathematical models of the universe and then attempt to find observable features of the real universe that would confirm one of the models and exclude all others. So far no single measurement has been made with enough precision to settle the question unambiguously. Several independent tests are possible, however, and pieces of the puzzle have been supplied by many workers employing quite different techniques. It now seems feasible to assemble the pieces. Taken together, the available evidence suggests that the universe is open and that its expansion will never cease.
1977.

39. The cosmological constant and cosmological change.
Is the Universe of infinite extent, or is it a finite system? Will it expand forever, or will it reach some maximum size before turning and collapsing upon itself like an inverse Big Bang? Just a few years ago, models of the conventional Friedman types were showing consistent, albeit tentative, evidence for an open, ever‐expanding Universe. Since then, further data and theory have inevitably conspired to blur the appealing simplicity of that picture. In this article I will show how the Friedman models fare in the light of new developments - particularly the recognition of a whole new class of evolutionary corrections to the properties of distant galaxies, and a proposed reinstatement of Einstein's disinherited cosmological constant. We shall see that the basic questions, posed above, are still unanswered.
1978.

40. Accelerating Universe revisited.
There is growing evidence that the Hubble constant is of the order of 100 kms1Mpc1km s^{-1}Mpc^{-1}, rather than only half as great. The purpose of this paper is to discuss the Friedman models that are consistent with such a large expansion rate, as well as with current estimates of stellar ages and the density of the Universe. If one accepts estimates of at least 100 kms1Mpc1km s^{-1}Mpc^{-1} for the Hubble constant, and that globular clusters have ages of the order of 16,000 Myr, then the only possible Friedman models of the Universe are those with a positive cosmological constant and q0<1q_{0} < −1. Various independent tests of this conclusion are suggested.
41. The Evolution of Galaxies: Evidence from Optical Observations.
The clearest evidence that galaxies evolve comes from the Milky Way: here we see stars with ages and lifetimes differing by 4 orders of magnitude, and with chemical compositions indicating a hundred-fold enrichment in metals between the times of formation of the halo and most disc stars. the general resolution of Olbers' Paradox also gives evidence for cosmological change: the sky is dark because galaxies turned on a finite time ago (Harrison, 1974). Here I discuss some of the further evidence for galactic evolution that is emerging from observations probing billions of years in lookback time.
42. HR Diagrams of Galaxies: Ages and Stages of Evolution.
Baade (1944) based his concept of stellar populations in galaxies on the HR diagrams that he inferred from the magnitude at which their brightest stars could be resolved. His type I population had bright blue supergiants like those in the disk of the Milky Way, while the brightest stars in type II were the red giants found in globular clusters. He postulated that the Hubble sequence of galaxy types from irregulars to ellipticals contained increasing proportions of Population II relative to Population I, and that similar differences characterised nuclear bulges of spirals relative to their disks. A very important revision of this picture came with the discovery by Morgan and Mayall (1957; Morgan, 1956, 1959) that the integrated blue light of the nuclear bulges of M31 and the Galaxy is dominated by strong-lined CN giants, not by the weak-lined type found in globular clusters. On the basis of integrated spectra of galaxies, Morgan developed a revised population scheme, in which the extreme types are a young-star rich population, like Baade's extreme Population I, and a young-star deficient population, analogous to Population II but generally metal-rich. Different proportions of these two types are still thought to represent the main differences among stellar populations in different regions of galaxies.
1979.

43. Galactic Evolution with the Space Telescope.
Since almost every facet of astronomy is relevant to the evolution of galaxies, most of the topics discussed at this Colloquium are important to the field. For example, stellar populations and inter-stellar matter in galaxies are to be understood in the context of evolution, and when galaxies are used as probes in cosmological studies it is vital to know how their intrinsic properties vary with time. Some aspects of research on galactic evolution with the Space Telescope are discussed by several authors in the recent ESO/ESA Workshop (Macchetto et al., 1979). In this paper, I concentrate on "lookback" studies that compare present-day and younger galaxies directly. Many of the theoretical ideas mentioned here are quite speculative; the aim is to provide viewpoints from which ST (and related ground-based) studies can be planned, knowing that the real world billions of years ago will surely contain more surprises than verifications of any projections.
1980.

44. Cosmology and galactic evolution.
Classical global cosmological tests based on optical data for individual galaxies for the large-scale structure and dynamics of the universe are discussed, with emphasis on the effects of galactic evolution. Consideration is given to the Hubble diagram, expressing the relation between apparent magnitude and redshift for the brightest cluster galaxies, and the effects of deceleration and curvature, stellar evolution and dynamic evolution on it, and to counts of galaxies as a function of apparent magnitude and the observational factors influencing them. The two tests are shown to be sensitive to different aspects of galactic evolution and different properties of the universe, and demonstrate principles applicable to other cosmological tests.
45. On the interpretation of galaxy counts.
New models are presented for the interpretation of recent counts of galaxies to 24th magnitude, and predictions are shown to 28th magnitude for future comparison with data from the Space Telescope. These results supersede earlier, more schematic models by the author. Tyson and Jarvis found in their counts a "local" density enhancement at 17th magnitude, on comparison with the earlier models ; the excess is no longer significant when a more realistic mixture of galaxy colours is used. Bruzual and Kron's conclusion that Kron's counts show evidence for evolution at faint magnitudes is confirmed, and it is predicted that some 23d magnitude galaxies have redshifts greater than unity. These may include spheroidal systems, elliptical galaxies, and the bulges of early-type spirals and SO's, seen during their primeval rapid star formation.
1981.

46. Correlation of the dark mass in galaxies with Hubble type.
The slow increase of M/L with colour for spiral galaxies shows that the mass ratio of dark material to ordinary stars is greater in blue galaxies than in red ones; the masses referred to are those within the Holmberg radii of the galaxies. Two possible interpretations of this result are that bluer galaxies form stars with an initial mass function weighted toward low stellar masses, or that bluer galaxies have relatively more massive dark haloes. The latter hypothesis is supported by the much faster increase of M/L with radius in late- than in early-type galaxies, and by the need for a dark halo to stabilise the discs of late-type spirals. The relative dominance of dark haloes in late-type galaxies is explained tentatively, in the context of current models for galaxy formation.

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