the evolution of galaxies and its significance for cosmology

13
THE EVOLUTION OF GALAXIES AND ITS SIGNIFICANCE FOR COSMOLOGY* Beatrice M. Tinsleyt Department of Astronomy The University of Texas at Austin Austin, Texas 78712 and Instirute of Physical Sciences The University of Texas at Dallas Richardson, Texas 75080 This paper will describe some effects on observational cosmology of the evolu- tion of stars in ordinary galaxies. Such evolution proceeds on leisurely time scales of billions of years and is not necessarily related to the spectacular high- energy evolutionary phenomena discussed elsewhere in this monograph. “Normal” galaxies are used as probes of the kinematic and gravitational properties of the universe. All the information we receive from them comes at the finite speed of light, so increasingly distant galaxies are seen as they were increas- ingly long ago. Thus, any evolution of their luminosities and colors must system- atically affect the trends with distance that are supposed to yield cosmological information. FIGURE 1 shows that look-back times that correspond to the greatest galactic redshifts yet established (z - 0.5) are a significant fraction of the age of the oldest stars in our galaxy. We therefore expect that the most distant galaxies have somewhat different stellar populations from nearby ones and so their inte- grated photometric properties must be different. We cannot treat galaxies as stan- dard candles. To illustrate possible evolutionary effects, it will be sufficient to consider here only the Friedman models with zero cosmological constant; in steady-state models, the effects must, of course, be zero on the average for a sufficiently large sample of galaxies. A thorough discussion of possible observational tests to discriminate among these models was given by Sandage’ and of look-back times and possible effects of evolution by the same author.2 The present status of observations will not be reviewed here; recent studies are those of Sandage and Hardy,’ Brown: Gott ef a!.,’ and Gunn and Oke,6 among others. A full understanding of galactic evolution is still far from reach. It would be satisfying to have, for instance, a complete theory of how the Hubble sequence of galactic types has evolved from perturbations in the primeval cosmic gas; this theory would ideally include details and explanations of the variety of stellar populations in the HR diagram, chemical compositions, and the quantity and composition of interstellar matter within and among galaxies. Luckily, progress in the context of observational cosmology can be made with very partial under- *Supported in part by National Science Foundation Grant MPS 73-04673 AOI. tPresent address: Astronomy Department, Yale University, New Haven, Conn. 06520. 436

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Page 1: THE EVOLUTION OF GALAXIES AND ITS SIGNIFICANCE FOR COSMOLOGY

THE EVOLUTION OF GALAXIES AND ITS SIGNIFICANCE FOR COSMOLOGY*

Beatrice M. Tinsleyt

Department of Astronomy The University of Texas at Austin

Austin, Texas 78712 and Instirute of Physical Sciences The University of Texas at Dallas

Richardson, Texas 75080

This paper will describe some effects on observational cosmology of the evolu- tion of stars in ordinary galaxies. Such evolution proceeds on leisurely time scales of billions of years and is not necessarily related to the spectacular high- energy evolutionary phenomena discussed elsewhere in this monograph.

“Normal” galaxies are used as probes of the kinematic and gravitational properties of the universe. All the information we receive from them comes at the finite speed of light, so increasingly distant galaxies are seen as they were increas- ingly long ago. Thus, any evolution of their luminosities and colors must system- atically affect the trends with distance that are supposed to yield cosmological information. FIGURE 1 shows that look-back times that correspond to the greatest galactic redshifts yet established ( z - 0.5) are a significant fraction of the age of the oldest stars in our galaxy. We therefore expect that the most distant galaxies have somewhat different stellar populations from nearby ones and so their inte- grated photometric properties must be different. We cannot treat galaxies as stan- dard candles.

To illustrate possible evolutionary effects, it will be sufficient to consider here only the Friedman models with zero cosmological constant; in steady-state models, the effects must, of course, be zero on the average for a sufficiently large sample of galaxies. A thorough discussion of possible observational tests to discriminate among these models was given by Sandage’ and of look-back times and possible effects of evolution by the same author.2 The present status of observations will not be reviewed here; recent studies are those of Sandage and Hardy,’ Brown: Gott e f a!.,’ and Gunn and Oke,6 among others.

A full understanding of galactic evolution is still far from reach. It would be satisfying to have, for instance, a complete theory of how the Hubble sequence of galactic types has evolved from perturbations in the primeval cosmic gas; this theory would ideally include details and explanations of the variety of stellar populations in the HR diagram, chemical compositions, and the quantity and composition of interstellar matter within and among galaxies. Luckily, progress in the context of observational cosmology can be made with very partial under-

*Supported in part by National Science Foundation Grant MPS 73-04673 AOI. tPresent address: Astronomy Department, Yale University, New Haven, Conn. 06520.

436

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Tinsley: Evolution of Galaxies 437

FIGURE I . Look-back times, scaled to a Hubble constant of 50 km sec-l Mpc-I, as a function of redshift in two Friedman cosmological models with A = 0.

REDSHIFT

standing. To compute the evolution of colors and luminosities of galaxies, we “only” need to know the stellar birthrate [including its initial mass function (IMF)] up to the present time and the chemical composition of stars that dominate the light of each type of galaxy.

The sequence of normal galaxies can apparently be understood, as a first approximation, in terms of a naive extrapolation from our Galaxy: let us assume simply that stars in all galaxies have compositions similar to those in the solar neighborhood, that star formation began at the same time in all galaxies, that it has always proceeded with the same IMF (the local galactic function), and that galaxies differ only in the time dependence of their stellar birthrate. Then, from sets of stellar evolutionary tracks and relations between effective temperatures, colors, and so on, we can compute the colors and luminosities as a function of age for a series of model galaxies. FIGURE 2 shows the two-color diagram of such a

h I I I I I I

-0.2- \ m

-

0.0 -

U - 8 -

0.2 -

-

0.4 -

06

0 4 0 6 0 8 10

FIGURE 2. Two-color diagram for galaxies. Solid line is drawn through the mean points given for each Hubble type by de Vaucouleurs and de V a u c o ~ l e u r s . ~ ~ Open and closed circles are colors of models, computed by the method de- scribed in Tinsley,’ at age l l x lo9 yr. Models are labeled by the time constant T (in lo9 yr) for the birthrate, which varies as exp (-t/?). Dashed lines show the evolution of two models, from 5 x lo9 yr at the top cross mark, through 8 x lo9 y r at the next cross, and reach- ing I I x lo9 yr at the closed circle. (To avoid confusion, evolutionary tracks are not shown for the models with open circles.)

i

B -V

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438 Annals New York Academy of Sciences

series of models at age 11 x lo9 yr, with birthrates that vary as exp(-t/T), as indicated. There is very close agreement with the mean two-color relation for normal galaxies: at the red end, models with a rapid decline in the birthrate have the colors of elliptical galaxies, and the bluest models, with constant birthrate, have the colors of Magellanic irregulars. Combined wit‘h the observed increase in gas content up this sequence, these results suggest that the Hubble sequence is one of time scales for converting gas into stars (although no explanation is offered for its defining characteristic, a sequence of morphologic types). (For further discus- sion, see the papers by T i n ~ l e y , ~ . ~ Searle el al..’ Larson and Tinsley,” Sargent and Tinsley,” and Talbot and Arnett.”)

Although it would be consistent with results like these to use very simple- minded galactic models for cosmology, there are important reservations. There are neither necessary nor sufficient reasons to believe that such a simple set of models adequately describes stellar evolution in real galaxies. Problems include the fol- lowing: 1. In the absence of very detailed data, there is no unique model (birthrate, IMF, composition, age) that yields a given set of colors and gas content. The evolutionary tracks in FIGURE 2 show, for instance, that a few billion years’ reduc- tion in age mimics a similar change in the time constant T. 2. It is known that differences of stellar metal abundances exist within and among galaxies, and they affect their colors and rates of evolution. 3. Even so-called normal galaxies exhibit a considerable spread of colors about the mean line.

Faced with the complexity and variety of galaxies, we can adopt the following approach: estimate the nature of evolutionary effects on observational cosmology on the basis of the simplest consistent models; then, if the effects appear to be important, study the galaxies and models in detail to resolve ambiguities.

THE MAGNITUDE-REDSHIFT RELATION

The determination of q,, from the rn-z relation for giant elliptical galaxies has been the main subject of evolutionary studies. Following the approach just outlined, I shall describe the general reasons for believing that the evolutionary correction is extremely important and then (in NUMERICAL MODELS FOR ELLIPTI- CAL GALAXIES) discuss the progress that is being made toward accurate estimates.

The results presented in FIGURE 2 and below show that a very good first ap- proximation is simply to assume that all stars in giant elliptical galaxies were formed in a single initial burst. The population then evolves through stages that resemble a rich open cluster of increasing age, as illustrated in FIGURE 3. (A globular cluster HR diagram would not be appropriate, because metal-poor stars are not important contributors to the light of these ga1a~ies.I~) Stars were formed all along the main sequence, but after 5 x lo9 yr (roughly the age of a galaxy with z - 0.5), all massive stars have evolved away, and there is a main sequence up to a mid-F spectral type, a subgiant branch (dashed line), and an extended red giant branch, including the “clump” (horizontal branch) of early K giants. The giant branch is like that of the old-disk population (e.g. Eggen14), more extended than those of open clusters because of their small total populations. After 10 x lo9 yr, the main-sequence turnoff has evolved down to early G , the subgiants are fainter

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Tinsley: Evolution of Galaxies 439

L Log -

Lo

SPECTRAL TYPE

FIGURE 3. Schematic H R diagram for a single generation of stars, as described in the text.

and redder, but the same giant branch is populated. The integrated light of a galaxy like this will be dominated by early K giants, turnoff stars, and G dwarfs in the blue; a t longer wavelengths, the light will come from later giants and dwarfs, in proportions that depend on how thickly the lower main sequence is populated compared to the turnoff that feeds the giant branch. The colors will clearly get redder with time, most rapidly at short wavelengths. The luminos- ity will get fainter unless there is such a steep IMF (steep luminosity function on the main sequence) that the number of giants is increasing, a possibility that will soon be shown unlikely on spectroscopic grounds.

The effect of evolution on the determination of qo is illustrated schematically by FIGURE 4: the curves exaggerate the difference between theoretical m-z relations for two values of qo; these relations are applicable to standard candles. Brighter magnitudes at a given redshift imply a greater value of qo. Now, suppose there were a set of data points lying along the line for qo = 1; because the distant galaxies are seen as they were when intrinsically brighter than local ones, evolution must be taken out by moving each point t o a fainter magnitude (to the right) by an

FIGURE 4. Very schematic representa- tion of m-z relations in two Fried- man models (A = 0). one open (40 = 0 ) and one closed (90 = I ) . Magnitudes become fainter to the right, and redshifts increase upward.

log z

"e - KV

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440 Annals New York Academy of Sciences

amount that increases with z . The corrected set of points will clearly correspond to a smaller value of 4,.

It is instructive to make a preliminary estimate of this correction by means of a series expansion of the theoretical m - z relations in powers of z . (Of course, such an expansion cannot be used in practice t o solve for q,.) The relation for broad- band visual magnitudes is

+ o(z’) + constant, (1)

where Kv is the usual K term, and H , is Hubble’s constant (which enters signifi- cantly only as the time scale for evolution; its role as the distance scale is absorbed into the constant term). The zero-order term is just Hubble’s law. The first-order term contains the deceleration parameter qo and evolution of the absolute magni- tude a t wavelengths that are redshifted into the observer’s V band. A slightly different relation applies i f magnitudes are obtained at fixed wavelengths of emission, as by the spectrophotometric technique of Gunn and Oke! there is no K term, and evolution is evaluated a t that fixed wavelength. Equation 1 shows that i f evolution were not allowed for, the shape of the observed m-z relation would be interpreted in terms of an apparent value of qo that would exceed the true value by

1 d M A M Aq, - --I - H , d t z

where A M is the absolute value of the evolution of magnitude in look-back time At = z / H , ( z << 1 ) . Incidentally, this equation shows the extreme sensitivity of qo to any systematic change with z of the absolute magnitude of galaxies sampled, because any change will cause a n error Aq, - A M / z . For example, because the intrinsic dispersion in the magnitudes ohfirst-ranked cluster galaxies is about 0.3 mag., systematic selection effects must be very carefully avoided.

Three factors that determine d M / d t were originally considered by Humason et al.,I5 and I shall discuss the present situation along the same lines; I shall not review the rather rapid historical evolution of estimates of these three factors and A40.

Evolution of Color (originally the “Stebbins- Whitford effect”)

FIGURE 5 illustrates the spectral energy distribution of a nearby galaxy ( z =

0.0) and of one that is redshifted ( z = 0.3). Observations in the observer’s V band sample a shorter-wavelength region at emission for the distant galaxy, and the usual K term allows for this difference with the assumption that the redshifted galaxy has the same spectral energy distribution (in its proper coordinates) as well- studied nearby giant ellipticals. Because we expect the distant (younger) galaxy to be bluer, this term must underestimate its luminosity a t the wavelengths sampled. However, spectrophotometry of galaxies out to the largest redshifts used in the

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Tinsley: Evolution of Galaxies 44 1

WAVELENGTH ( F )

FIGURE 5 . Illustration of types of data used for the m-z relation. Apparent magnitude is plotted versus log wavelength; the vertical scale is marked in I-mag. intervals for mono- chromatic absolute units (erg cm-* sec-’ Hz-’), with arbitrary zero points for the two curves. The lower spectral energy distribution is for a nearby galaxy (typical of those studied by Oke and S a ~ ~ d a g e ~ ~ and Gunn and Oke6); in the upper part, the same spectral energy distribution has been redshifted by a factor of 1.3 and extended schematically to short wavelengths. The observer’s V band is marked to show the part of the spectrum that would be observed for each galaxy; also, the equivalent wavelength of the V band at emis- sion is marked for each galaxy.

m-z relation now directly demonstrates that this error is negligible.6*’6 Of course, i f magnitudes are measured at a fixed wavelength of emission (e.g., a t X v marked in FIGURE 5) , the question of color evolution is not directly relevant. The use of empirical limits on the rate of color evolution as a constraint on the rate of luminosity evolution will be discussed in NUMERICAL MODELS FOR ELLIPTICAL GALAXIES.

Unevolving Dwarf Stars

If nearly all the light a t visual and somewhat shorter wavelengths comes from unevolving stars below the main-sequence turnoff, d M / d t will clearly be very small. But, if the light is giant dominated, d M / d t will depend on the changing rate a t which stars peel off the main sequence, that is, on the stellar mass-lifetime relationsand on the I M F at turnoff. There is now much evidence for the latter alternative.

The blue-uv spectra of elliptical galaxies were classified as K giant by Morgan and Mayall.” Thus, even at short wavelengths, G dwarfs just below turnoff are not dominant.

O’Connell’* measured several luminosity-sensitive spectral features in the red (Nal 8190, CaII 8542, Ti0 8880) with a spectrum scanner and found that all indi-

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442 Annals New York Academy of Sciences

cated dominance of giant stars in the light. Because, it is the weakness of the fea- ture for NaI 8190 that supports this conclusion, there should be no serious con- fusion with metallicity effects.

Whitford" was unable to detect the Wing-Ford band (9910 A) in similar scan- ner observations of elliptical galaxies. This feature is very strong in M dwarfs and appears only weakly in the photometric index for M giants (where it is due to TiO, not the Wing-Ford feature itself). Whitford's powerful data appear to be consis- tent only with essentially no contribution to the light a t 9910 A from late dwarfs; they even place constraints on the contribution of very late giants.

found strong CO bands (at 2.3 p m ) in the central regions of many elliptical galaxies, which again indicates that late K-M giants must be far more important than dwarfs, from which the CO band is absent.

Observations a t long wavelengths d o not entirely exclude the possibility that late K-M giants provide the ir light, while, for example, early K dwarfs are domi- nant enough in the visual region to slow down d M / d t significantly. But any rea- sonable IMF and giant luminosity function, together with the constraints set by continuum colors, demand that if there are enough late giants to account for the ir spectral features, earlier giants should provide most of the visual light.?

Most of the above criteria refer to rather more central regions of elliptical galaxies than are included in the magnitudes for the m-z relation, so we must worry about possible gradients in the stellar population. Generally, colors get bluer and spectral features get weaker as observations a re made through larger apertures, a fact that suggests a declining metal ab~ndance .~ ' - " The changes are small, and no tendency t o increasing dwarf dominance (at least outside a small nucleus) is established.$

Frogel et

Stellar Evolution

Finally, d M / d t depends on evolution of stars from the main-sequence turnoff. A quick estimate (cf. FIGURE 3) shows that the turnoff magnitude itself evolves a t a rate Ifo-' d M / d t - 4! But, of course, this is not directly reflected as a magnitude change in the integrated light, which depends rather on the rate a t which stars enter the giant branch.

For an initial estimate, suppose there is a power law IMF, so that stars with masses in the interval (m,m + dm) were formed with relative numbers d N a m-( '+X)dm, and that stars have main-sequence luminosities a mu and lifetimes a m-'Iv. Then, with additional simplifying assumptions, it can be

?These remarks are based on the models by the above authors and on current studies by Whitford, G u m , and Tinsley?L

§Frogel er a/.'' comment on a possible decrease of CO band strength with increasing aperture and remark that in individual stars, the strength should be very insensitive to abundance. However, if the entire stellar population moves to lower metallicity, its giant branch is bluer, and fewer of the very cod stars have strong CO. Thus, I believe that lower abundances will lead to weaker CO in the integrated light, and it is therefore not yet clear whether the gradient, if real, is one of metallicity or increasing dwarf richness.

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Tinsley: Evolution of Galaxies 443

shown that the integrated luminosity evolves a t the rate

C + ( y - 1)- 1 + G ’ (3)

where G is the ratio of light from giants to light from dwarfs.” This approxima- tion applies to the light a t any wavelength, as long as the appropriate coefficients are used. Because 0 < G/(I + G ) < I , and for visual light, y - 1.3, a - 4, we have from Equation 2 that Aqo - (1.3 - 0 .3x) /Hot , where t is the age of the galaxies. But, t < t o , the age of the universe, and in the cosmological models being considered, H , to < 1. Therefore, as a first approximation,

(4)

Note that this formula includes both the effects of stellar evolution and the reduc- tion of d M / d t by unevolving dwarfs.

It should be understood that the second term in Equation 3 is unimportant, because the relative contribution of giants changes slowly. Giant stars may, in- deed, dominate the light (C > I) , so that Equations 3 and 4 reflect mainly their changing numbers; in fact, it can be shown, in the framework of this simple model, that Aq, is directly proportional to C.26 All of the above results hold if x < a, which the detailed models discussed in the next section will verify.

If, for example, elliptical galaxies had the I M F derived by Salpeter” with the slope x = 1.35, this analytic approximation would predict an evolutionary correc- tion A9, ,> 0.9. The local I M F near the turnoff mass (- I M,) is, in fact, much shallower (x - 0.25), which would give Aq, I .2. Thus, from the first approxk mation, we learn that the evolutionary correction depends mainly on the slope of the I M F at turnoff, and, because the spectra of elliptical galaxies show that late dwarfs are not important contributors to the light, we expect that the slope must be shallow, so Aqo will be large.

Aq, ,> 1.3 - 0 . 3 ~ .

NUMERICAL MODELS FOR ELLIPTICAL GALAXIES

Numerical models, which give integrated colors and luminosities of evolving stellar populations, must be used for a more precise estimate of the correction Aq, consistent with all the data. Equation 4 shows that to determine qo t o an accuracy of, for example, 0.2, we must know the slope of the I M F t o better than 0.7. Unfortunately, whereas the rate d M / d t in models depends almost entirely on the slopex of the I M F at turnoff, the spectral energy distributions that must be studied to determine x depend also on the age, metallicity, possible presence of stars formed after the initial burst, luminosity function on the giant branch, and departures from a power law IMF; no doubt, problem parameters could be multi- plied beyond this list.

Dynamical Evolution

Larson and Tinsley” have considered possible effects of later generations of stars on the evolution of elliptical galaxies. In Larson’sZ8 dynamical models, star

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444 Annals New York Academy of Sciences

formation can (formally) continue at all radii up to the present time, a t first from the primeval gas and later from gas shed by evolving stars. Because this gas tends to fall inward, star formation reaches a maximum in the nucleus rather later than over most of the galaxy, and it remains relatively more important there; the same effect creates a metallicity gradient, since central stars are mostly formed from gas that has been processed through earlier generations further out. It is possible that supernovae soon establish a galactic wind, so that star formation is cut off after about lo9 yr.29*30 If so, the density profile that Larson2' matches so well to observations and the metallicity gradient would have already been established, be- cause most of the gas is turned into stars before that time.

Some predictions of color gradients in these models are shown in FIGURE 6 (for further details, see Larson and Tinsleyl'). The horizontal line is for a popula- tion all formed within lo9 yr and all with solar metal abundance. The model with a red nucleus shows the effect of allowing for the composition gradient; the most important influence is on the effective temperatures and line-blanketing of the giant stars. The model with a blue nucleus exhibits the additional (and dominant) effect of allowing the gas to turn into new stars continuously rather than being blown out. Because most elliptical galaxies have red nuclei, we conclude that their colors cannot be greatly influenced by late generations of stars. The con- straints imposed by colors d o not permit late star formation to affect d M / d t (for a given IMF) significantly a t any radius. However, a small contribution from young stars could cause the confusion mentioned above with other effects, most seriously in that bluer colors mimic a shallower IMF. Careful syntheses based on detailed spectrophotometric scans," combined with the constraints provided by the red-ir spectral features discussed in THE MAGNITUDE-REDSHIFT RELATION, should enable the various possibilities to be distinguished.

8-v

/YOUNG S T A R S

o.9i

1.1 I I I I 0 5 10 15 20

R A D I U S ( k p c )

FIGURE 6. Effects of a metallicity gradient and of continued star formation on the color- radius relation of a model elliptical galaxy." See text for explanation.

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Tinsley: Evolution of Galaxies

0 7 I 1

I I 5 10 15 20

445

FIGURE 7. Evolution of the absolute V magnitude (arbitrary zero point) and two colors of a single-generation model with x = I and with a luminosity function on the giant branch derived in part from the old-disk giants.

Detailed SingleGeneration Models

Larson and Tinsley’s results suggest that stars born within the first billion years dominate the light of elliptical galaxies and that the effects of later generations will a t most be seen only at the shortest wavelengths. Therefore, I return to single- generation models and summarize some results of T i n ~ l e y , * ~ * ~ ~ Rose and T i n ~ l e y , ~ ~ and work in progress.32a

The stellar content of these models is an empirically calibrated lower main sequence; an evolving main sequence, subgiant branch, and lower giant branch based on theoretical tracks for solar-composition stars; and an empirically cali- brated “clump” and later giant branch. It is especially important t o use appro- priate giant stars in the synthesis, because we know that they dominate the light. Their position in the HR diagram is assumed, for now, to be that of the oldest- disk giants in the solar n e i g h b ~ r h o o d ; ’ ~ their luminosity function is incompletely known from theory and difficult to derive from the empirical sample and therefore must contain several parameters that are allowed t o vary over the range of uncer- tainty. This creates some confusion with changes of IMF in the values of red-ir spectral indices, in particular.

For some sample results, FIGURE 7 illustrates the evolution of M , , B-V, and R-I of a model with a power-law IMF (x = 1 in this case). Its colors evolve no faster than permitted by the observations of distant galaxies by Oke and San- dage,” Oke,I6 and Gunn and Oke;6 this is the case largely because giant stars dominate and their relative numbers scarcely change during the look-back time: if x were as great as 3, color evolution would be faster than allowed. The spectrum obtained with this IMF is (at all plausible ages) somewhat too dwarf rich in terms of the spectral indices mentioned above, agreement cannot be forced by arbitrarily adjusting the giant luminosity function because of constraints provided by the continuum colors, so it appears that we need x < I . The model shown in FIGURE 7

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446 Annals New York Academy of Sciences

has dMv/dlnt = 1.0, which implies a first-order correction Aqo 2 I . And, because this model is already too dwarf rich, we seem to be faced with evolutionary correc- tions even greater than unity. (Paradoxically, the giant-rich models needed to agree with the observed slow evolution of color are those that evolve fastest in luminosity.)

More detailed comparisons with spectral energy distributions of galaxies, from 3300 t o 10,700 A, have been made by Tin~ley*~~’* and by Rose and Tin~ley .~’ With relatively low-resolution scans (bandpasses of 80 and 160 A), it is all too easy to obtain excellent continuum fits for various combinations of age, giant luminosity function, and IMF. New data with four times that resolution (recently obtained by Gunn) will provide far more stringent constraints.’’

At present, it seems fairly safe to conclude that if the I M F can be approximated by a power law, it has x < I , independently of the uncertainties. This implies that Aqo > 1 as a first estimate; the detailed procedure used by Gunn and Oke6 results in a somewhat greater downward correction to qo for a given IMF.

A necessary caution is that we are actually synthesizing only the present-day population of elliptical galaxies, which gives us no direct information about the number of giant stars there in the past. I t is conceivable that there were very few stars above the present turnoff, because elliptical galaxies might have a curved I M F that turns over sharply a t just the present turnoff mass. In this case, the effec- tive value of “x” for present colors and spectra could be small, whereas the effec- tive value for dM/dr could be very large; there were few giants that contributed to the past luminosity. If so, the current models should predict incorrect spectral energy distributions when compared to distant galaxies. There is no evidence for such a discrepancy (e.g.. see FIGURE 2 of Tinsley2’). The extreme similarity of the spectral energy distributions of galaxies a t different red shifts (e.g., Okei6) is strong evidence against a sharp change in the giantldwarf ratio during the look- back times relevant t o the m-z relation. Increasingly detailed comparison of younger models with more distant galaxies will continue to provide very useful constraints and should eventually reveal bluer colors a t short wavelengths as direct evidence of evolution of the turnoff point.

REMARKS O N OTHER COSMOLOGICAL OBSERVATIONS

Luminosity evolution of elliptical galaxies also affects the relation between isophotal diameters and redshifts, which is another of the possible ways of deter- mining q0.’*35 If the galaxies a t larger z are intrinsically brighter, a larger proper diameter is reached at a given isophote than one would predict from the effects of redshift alone. The result is that qo is overestimated by an amount that, to first order, happens to be the same as the evolutionary correction to the m-z relation.36

The situation is far more complicated for the number-magnitude relation, because spiral galaxies contribute more than half of the total counted. This rela- tion is anyway very insensitive to qo. as noted by Sandage,’ chiefly because in a series expansion, qo cancels out of the first-order term. Problems with the inter- pretation of number counts are discussed by Brown and Tinsley.” Evolution, of all types of galaxies, enters in the first order; a first estimate suggests that a t

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Tinsley: Evolution of Galaxies 447

magnitude B = 22, evolution may mimic a decrease in qo of about I .O. It appears that this relation will be useful as a test of cosmological models only if the evolution of all types of galaxies is understood to great look-back times and if extremely well-calibrated limiting magnitudes, as a function of galaxy type, are avaihble for the counts. Various authors have noted that the number-magnitude relation may be most useful as a test of large-scale homogeneity, chiefly be- cause it is insensitive t o qo. For the same reason, it may place useful constraints on the evolution of late-type galaxies.

Even further complications are involved in interpretation of the diffuse back- ground because light from the initial burst of star formation in primeval galaxies might be redshifted into the observer’s bandpass. If the epoch of galaxy formation is right for this phenomenon to occur, the detection of individual primeval galaxies might be feasible.4245 On the other hand, dust in the primeval galaxy itself might have absorbed the light and reradiated it in the infrared. It seems likely on the basis of Larson’s28 models that primeval galaxies will appear as condensed objects, ,< I arcsec across, not readily distinguishable a t any wave- length from nearer galaxies46 In any case, the diffuse background light must carry information about galactic evolution from very early epochs; the cosmological parameter to which it is most sensitive is likely to be the redshift (or range of red- shifts) of first star formation in galaxies.

CONCLUSIONS

The field of galactic evolution is clearly full of unexplored pathways that will lead to useful information for cosmology and to a better understanding of galaxies themselves. We are beginning to disentangle evolutionary from cosmological ef- fects in observations of giant elliptical galaxies alone, because these luckily seem to have had a very simple history of star formation. This cannot be true for later types of galaxies, with their wide variety of dynamical and photometric proper- ties. Observations that involve all types of galaxies out to great look-back times are likely to reveal as much about the processes of galaxy formation and evolution as about the large-scale structure of the universe.

ACKNOWLEDGMENTS

It is a pleasure to thank Drs. J . E. Gunn, J. A. Frogel, R . B. Larson, S. E. Persson, and A. E. Whitford for valuable discussions. I am also very grateful for the use of data prior to publication from the papers by Brown,4 Gunn and Oke,6 Frogel et and Whitford.”

REFERENCES

1. 2. 3.

SANDAGE, A. R. l961a. Astrophys. J . 133: 355. SANDAGE, A. R . 1961b. Astrophys. J . 134: 916. SANDAGE, A. R. 8~ E. HARDY. 1973. Astrophys. J . 183: 743.

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4. 5 .

6. 7. 8. 9.

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21.

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