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To begin at the beginning… (Thomas 1954). Or at least, almost the beginning. The theory of the synthesis of deuterium, helium and a little 7Li during the period of a few seconds to perhaps three minutes after the Big Bang is well developed and it occurs under conditions that, while they are indeed hot (1010–109 K), are not really extreme. The density is of the order of that of water, not enough to push the nuclear reactions even as far as carbon, as later happens in the cores of stars. The fragile deuterium abundance is an interesting case. So far no-one has managed to invent a plausible synthesis site (other than this primordial synthesis) that can produce significant amounts of deuterium and deliver it to the interstellar medium without seriously overproducing other light elements – a situation that hasn't really changed in the nearly 30 years since the definitive paper of Epstein et al. (1976). Deuterium remains probably the best indicator of the baryonic mass density in the universe – its production relates simply to the number density of protons available for reaction during the universe's early expansion, when the timescale was set by radiation-dominated dynamics. The subsequent evolution of the deuterium abundance will be discussed below.

Element synthesis then probably stopped during the early “dark ages” as density dropped with expansion until the nonlinear growth of small inhomogeneities under gravitational attraction provided regions of high enough mass density for stars to start to form. Superb illustrations of structure growth (Jenkins et al. 1998) have been computed, particularly in the CDM (cold dark matter) cosmology. The pancake and filamentary structure can, I suspect, be understood by the Lin–Mestel–Shu theorem (1965, simply demonstrated by Lynden-Bell 1979) that under gravity incipient structures collapse most rapidly along their shortest axis.

Details of this era (Bromm and Larson 2004) are as yet delightfully unconstrained by hard observational evidence. What were the first stars like? Probably mainly massive. At what redshift did they begin to form? Certainly greater than 7, since galaxies are known at least as early as Z = 6.5–6.6 (Hu et al. 2002, Kodaira et al. 2005).

The Three Commandments

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

For the epochs that follow this initial “Population III” era of stars when heavy-element abundances were essentially zero, I insist on Three Commandments of Galactic Chemical Evolution for the “simple” model and its elementary extensions:

  • 1
    Thou shalt not change the stellar initial mass function.
  • 2
    The interstellar medium shall be well mixed.
  • 3
    The products of nucleosynthesis shall be instantaneously recycled into the interstellar medium.

I will deal with these in reverse order. Instantaneous recycling is a good approximation so long as the lifetimes of the stars becoming metal-producing supernovae are short compared with the overall star-formation rate (i.e. gross evolution time) of the system. The relevant stars have masses of 10 M or above, with main-sequence lifetimes of order 108(M/10M)−2 years, and the instantaneous recycling approximation is quite reasonable even during the early galaxy formation stages (timescale of a few 108 years). A lot of emphasis – perhaps too much – has been placed on the possibility that the relative evolutionary timescales of Type Ia and Type II supernovae (108–3×109 and 106–3×107 years respectively) may explain systematic variations of some element ratios, in particular [O/Fe] – but we will not probe further here into this interesting area. Mixing we discuss below.

The initial mass function (IMF), a statistical relation specifying the average number of stars born in different mass intervals, is critical in determining the overall amount of heavy elements that will subsequently be produced by the formation of a generation of stars. Most heavy elements are produced in the supernova explosion of the rare fairly massive (∼8–100 M) stars. The “yield” of heavy elements – i.e. what mass of heavy elements is produced per mass of raw initial interstellar medium going into stars – is sensitive to the ratio of high-mass stars formed relative to the much more numerous low-mass stars. So far as I can judge, from a reasonably prejudiced view of the literature, it is still not in conflict with observation to hold the view that the (averaged) initial mass function is reasonably constant in both time and space. Since it is possible to mimic almost any astronomical phenomena by altering the IMF, here is my first plea for elementary simplicity – in terms of power of explanation the best strategy is to stick to the First Commandment and only abandon it as a really last resort. I must admit that the sin of variation might be considered merely venal rather than mortal for the first generation of Population III stars – and forgiven as a youthful indiscretion, because the usual dominant effects on cooling and opacity from heavy elements are not present. Once the massive stars of the “first generation”– whatever that really means – have rapidly produced some carbon and heavier products, the opacity of star-forming ISM probably increases sufficiently for the normal IMF-setting-physics to dominate.

The IMF also nominally sets the relationship between star-formation rate and the (time dependent) luminosity of the stellar population that is produced. Since a certain amount of element synthesis also results, it follows that there is a relation between the production of elements and the production of radiation (the “fuel consumption theorem”, Renzini 1981). Strictly speaking, the light output and element production can also be a function of the instantaneous metallicity – which (as we shall see) can vary in different ways if inflow and outflow of gas to the system is allowed. Detailed numerical modelling can attempt to follow the subtleties in population synthesis, but the concept of the correspondence of a given amount of element production per total energy output (radiation, and mechanical from stellar winds and supernovae) may be useful.

The stage is set for the formation of galaxies and their evolution. In some senses the details of this process do not affect the overall production of heavy elements in the universe – that is set by star formation and the IMF. But the details of galactic evolution will strongly affect the distribution of those elements. It seems that there are still two basic contenders for a theory of galaxy formation. The “monolithic collapse” picture in which the mass and morphology of a galaxy is set by the interplay between its star-formation rate and the dynamics of its gas, in particular the orbital angular momentum content, with galaxies essentially evolving as fairly isolated systems. Elliptical galaxies would be regarded as systems that collapsed early and rapidly used up (or lost) their remaining gas. The “hierarchical clustering” picture – which may sit better with structure formation within a dark-matter-dominated cosmology – assumes the gradual merging of smaller “building block” systems of stars and gas into larger galaxies. Elliptical galaxies would then be regarded as rather lately formed. The merging history of the smaller systems and the relative violence of the star-formation bursts triggered by their interactions would ultimately determine their particular masses and morphologies. Reality may well lie in between the two extreme models – a history of a rapid set of strong mergers followed by a few weak ones could easily mimic the global properties (but perhaps not the fine detail, for example the kinematics and metallicity of stellar subsystems) of monolithic collapse. An example is shown in figure 1.

image

Figure 1 : . An example of a galaxy-formation model in which early merging substructure is on its way to produce a long-lived spiral galaxy. The figure represents the gas component and is taken from Williams and Nelson 2001. A video of formation and evolution can be viewed at http://www.astro.cf.ac.uk/computing/parallel/gal2/Sbc.html

A great aid to understanding the evolution of the heavy elements remains the so-called “simple” model (Pagel and Patchett 1975, Pagel 1997) and its variants and, in particular, the lessons to be learnt from its breakdown! We have already mentioned the three basic rules. A particular strength of the simple model and its variants is that they contain no explicit reference to time, freeing them from uncertainties over star-formation rates. Habit makes me follow Edmunds (1990) in notation. For an interstellar gas mass g, the basic equation governing the change in the fraction z of the mass which is heavy elements (the “metallicity”) is given by, when a mass ds of the ISM is formed into stars:

  • d(zg)=p′ds-(1-α)zds-zds-o(s)ds(1)

The first term on the right-hand side represents freshly synthesized heavy elements, the second term is elements that go into stars but come out unchanged in stellar winds, the third term is the elements that are lost from the ISM into the forming stars, and the fourth term represents any gas outflow from the system. For the “simple” or “closed box” model, o(s) is set to zero. In this somewhat arcane, but convenient, notation α represents the fraction of each generation of stars that essentially remains locked up in stars or stellar remnants over a Hubble time (its value is believed to be about 0.7), and p′ is a measure of the nucleosynthesis, often expressed as the “yield”p=p′/α.

To complete the model, we also need to account for the loss of gas when stars form:

  • dg=-αds+i(s)ds-o(s)ds(2)

where i(s) accounts for any inflow of unenriched gas into the system, and again for the closed box model i(s) and o(s) are set to zero.

The evolution of deuterium can followed simply by setting the first two terms of equation 1 to zero, since essentially no net deuterium is created during normal stellar evolution, and any that goes through stars (“astration”) is destroyed, giving

  • d(zDg)=-zDds(3)

The closed box solution of equations 2 and 3 gives the well-known simple relation

  • image(4)

where f is the gas fraction, defined as gas mass/total mass of the system.

Figure 2 shows some recent measurements of D/H in the local galactic disc from Wood et al. 2004, together with what looks like the current best “primordial” value D/H = 2.2 ± 0.2 ×10−5 from three damped Lyman-α absorption line systems by Pettini and Bowen 2001. A rational interpretation of this diagram is that a local value D/H = 1.56 ± 0.04 ×10−5 can be defined in the galactic disc within a few tens of parsecs of the Sun, and the depletion of deuterium by a factor 0.63–0.8 from a primordial value of 2.2 ± 0.2 ×10−5 is consistent with the depletion factor of 0.44–0.67 predicted from equation 4 with a current galactic disc gas fraction of 0.15–0.20 and α between 0.7 and 0.8, particularly as the simple-model estimates must be upper bounds on the extent of depletion if inflows or outflows have occurred (Edmunds 1994). Primordial nucleosynthesis calculations suggest that a primordial D/H of 2.2 ± 0.2 ×10−5 is consistent with WMAP CMB predictions of baryon density. All very neat, although a slight worry may be the spread of D/H values evident in figure 2 for longer sightlines through the galactic ISM. Such variation would require too large differences in astration, so either there is some differentiation mechanism, perhaps dust or molecule related (which would be worrying, since absolute levels would then be hard to pin down), the galactic disc is poorly mixed (but see below) or the observational values will magically reduce in scatter as time passes!

image

Figure 2 : . Deuterium abundance measurements in the galactic disc, taken from Wood et al. 2004. The red arrow shows the primordial deuterium abundance D/H = 2.2 ± 0.2 ×10−5 from Pettini and Bowen (2001), illustrating the destructive effect of stellar evolution on the deuterium.

Time dependence can be built in by additional elementary assumptions, for example that the star-formation rate is proportional to some function F(g) of the gas density (assuming the box size is not changing):

  • image(5)

or simply enforcing a parameterized rate. Feedback is a popular addition to evolutionary models, and it would be physically reasonable that this feedback should depend fairly directly on the star-formation rate, since it will probably involve supernovae and other short-lived phenomena whose energy input will follow the star-formation rate. If we simply assume proportionality with a constant K, i.e.

  • image

then rearranging:

  • image(6)

Comparing equations 5 and 6 implies the obvious result that the primary effect of feedback is to slow down the star-formation rate (just altering the rate constant) rather than having any major effect on the functional dependence of the rate on parameters such as the gas density. There may be gas outflow from the system – but the effects of this can largely be taken account of in the chemical models without explicit time dependence.

Most galaxies are evidently not closed boxes, and inflow of gas during formation still proves the neatest way to explain the stellar metallicity distribution of the galactic disc – i.e. the relative numbers of stars with different metallicities. The associated observational evidence – the so-called “G-dwarf” problem – was historically the first motivation for relaxing the closed nature of the simple model. It was also clear (e.g. Hartwick 1976) that outflow of gas might also be important for particular parts of galaxy evolution, and I want to consider three of these areas – areas where it has long been suspected that outflow is at work, but where a satisfactory full explanation of how and when has yet to be given. These are (i) the metallicity distribution of globular cluster systems, (ii) the mass–metallicity (or metallicity–luminosity) relation for galaxies and (iii) apparent yields and the composition of intracluster gas. Explanations for all of these have been invented by varying the IMF, but I want to press on to see if it really is necessary to resort to this last refuge for scoundrels.

Globular cluster systems in galaxies

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

Many globular cluster systems appear to have bimodal metallicity distributions (e.g. Eerik and Tenjes 2005) – i.e. a plot of number of clusters against their metallicity has two peaks. I struggled for a long time trying to reproduce this bimodality with elementary galaxy formation models involving various forms of inflow of unenriched gas, but nearly always found only a broad single peak.

Enlightenment came with the realization that an easy way to produce two peaks is to have a galaxy evolve with a considerable outflow of gas and then, at some point, reduce or stop the outflow and let the system continue to form stars. My naive model is a box, initially open but later closed, almost the complete opposite of a two-inflow model of VanDalfsen and Harris (2004). A crude analytical example using a flow that is simply proportional to the star-formation rate (i.e. o(s) first constant, later zero) is shown for two flow rates in figure 3. Would galaxies really form like this? The metallicity distributions seem so suggestive that the model is worth further investigation in the future.

image

Figure 3 : . Elementary models for the chemical evolution of a system of globular clusters, allowing gas outflow from the galaxy which is then stopped – giving a clear bimodal structure to the metallicity distribution.

An observant reader would have noticed that the second peak is centred around solar metallicity – i.e. the yield assumed here – and this may be rather a high value for many globular cluster systems. A simple fix would be not to shut the box completely later on, but to significantly reduce the late outflow rate relative to the star-formation rate, leaving a lower mean abundance for the second peak. This model, however, would then have three parameters – and perhaps a rule for convincing “elementary” models should be that they have at most two parameters, and preferably only one! Obviously a considerable amount of gas with some (but not much) heavy elements would have flowed out into the ISM, an effect that would also be a by-product of my second point:

Mass–metallicity relations for spheroidal and elliptical galaxies

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

First consider dwarf spheroidal or elliptical galaxies that contain little or no gas. It is easy to show (Edmunds 2005) that if the Three Commandments are obeyed then the following statement must be true: If a system has lost mass so that only a fraction M of its initial mass remains when all gas has been converted into stars, the mean metallicity of its stars <z> must obey:

  • image(7)

To see the importance of this argument, invert it. A galaxy with only stars, and a mean stellar heavy-element abundance that is much less than solar must have lost a great deal of gas – as illustrated in figure 4. The gas loss is not just an explanation, it is a requirement. Of course this argument depends on the Three Commandments, and differential outflow of enriched gas from supernovae without good mixing would vitiate it. Ignoring this temptation, we note again the implications for intergalactic gas and the probable implication of a considerable dark-matter component to such galaxies to help avoid gravitational unbinding while the gas is lost. It is an obvious extension to a mass–metallicity relation by making the amount of gas lost dependent on the mass of the galaxy. This mechanism has also recently been re-invoked to explain spiral galaxy behaviour:

image

Figure 4 : . The effect of outflow of gas on the mean metal abundance (relative to the yield p) in stars in a galaxy. The curves show a lower limit on the amount of gas that must have been lost by a galaxy if its mean metal abundance reaches the given value when star formation has ceased.

Mass–metallicity relation for spirals

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

Garnett (2002) and Tremonti et al. (2004) have re-opened debate on the existence of a relationship of the metallicity of a galaxy and its mass, often known as a colour–magnitude relation from the metallicity dependence of the photometric colours of stellar populations. Tremonti et al.'s results for ISM gas phase abundances in a very large sample of galaxies from the Sloan digital survey are shown in figure 5, and – as emphasized by them – an elementary explanation in terms of gas outflow is possible.

image

Figure 5 : . Mass–metallicity relation for spiral galaxies from Tremointi et al. 2004 (their figure 6). The central blue line is our model equation 9 (essentially the same as Tremonti et al.'s fitted model shown in red). The other two blue lines show the effect of increasing and decreasing the star-formation rate constant by a factor of two.

To follow this though, think first about the time dependence of ISM abundances. For a closed box model from equation 2, and supposing the simplest linear star-formation rate dependence on gas density ds/dt=kg, then it is easy to show from equations 1 and 2 that there is a linear increase in metallicity with time:

  • image(8)

Now open the box, and consider the effect of introducing an outflow at a rate λ times the star-formation rate (i.e. o(s) =λ). Then

  • image

This metallicity is just as before in equation 8! The reduced gas mass compensates for the loss of metals. Obviously no use if we want a mass–metallicity relation at time t. We can adopt two possible approaches, both using (like Tremonti et al.) a simple two-parameter dependence of the outflow on the galaxy mass λ/α= (M/MC)−0.6, chosen because it will fit the observations well, as seen in figure 5 using MC= 5 ×109 M. The first approach is a complete fudge, and supposes that the star-formation rate (SFR) parameter k depends on the mass of the galaxy, with lower mass galaxies having have SFR slower like k/(1 +λ/α). Then systems will evolve so that at time t we have z= (p/[1 + (M/MC)−0.6])αkt. Since this allows essentially three parameters, it is not surprising that it fits quite well. A more physical explanation might be to take the “observed” star-formation/gas-density dependence due to Kennicutt (1998)ds/dt=kg1.4, which gives

  • image

We must still assume that SFR in lower mass galaxies is slower by (1 +λ/α) so that this factor cancels in the term inside the brackets giving

  • image

and taking a fixed time implies

  • image(9)

If we did not make the slower SFR rate assumption for lower mass galaxies, the mass–metallicity relation would be far too shallow. So is this apparently simple explanation correct? It has good features – we saw above that gas outflow must have occurred for low-metallicity galaxies if we are to retain our belief in the “basic assumptions”. It provides a rational explanation for the existence of metals in intergalactic and intracluster space. The star-formation rate constraints are not too bad either, if we put αkt= 3, MC= 5 ×109 M then the ratio of gas mass to total baryonic mass in the galaxy (the gas fraction) f varies nicely between f= 0.65 at M= 108M, to f= 0.2 at M= 1011M, which are not unreasonable for observed galaxies with gas in them. But how do galaxies know what star formation rate to adopt? A variation in rates by even a factor of two would begin to introduce significant scatter, as implied by the models shown by the two outer blue lines in figure 5.

One prediction is clear, though. Assuming any reasonable galaxy luminosity function, and summing up what is ejected, the metal abundances in the intergalactic gas will be sub-solar, perhaps of order 1/5 solar or less. I am so far unconvinced that this limit has been violated by X-ray observations of intracluster gas. The mixing timescales and processes out into the intergalactic medium remain an interesting area for speculation (e.g. Ferrara et al. 2000, Scannapieco 2005). An outflow explanation of the mass–metallicity relation need not be incompatible with the situation in our own galactic disc, where inflow provides the neatest explanation for the (G-dwarf) stellar metallicity distribution (Lynden-Bell 1975, Pagel 1997), since by equation 9 the outflow would be fairly small by M= 1011M, and the global effect of time-decreasing inflow on the overall metallicity may also be small (Edmunds 2005).

Global star-formation rate and metallicity

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

From the simplest star formation law ds/dt=kg, and from equations 1 and 2 starting at time to we would expect:

  • image(10)

It is not difficult to build more complicated models using, for example, the Kennicutt star-formation law, but even this very simple form is not a bad fit to the observed variation of star-formation rate (see figure 6), acknowledging the observational problems of compensating for dust-enshrouded star formation. In the figure time has been converted to redshift Z by assuming a ΩM= 0.3, ΩL= 0.7 cosmology, and star formation is assumed to start at a redshift of 5. Figure 7 shows how the mass in stars builds up, here showing how small the overall effect is of starting star formation earlier. With greater certainty and detail in the observations (e.g. Heavens et al. 2004) more careful fitting may perhaps be justified, with two or more galaxy types of different start redshifts and star-formation rates.

image

Figure 6 : . Star-formation rate as a function of redshift and lookback time, from Ivison et al. 2002 (figure 14), fitted quite well by the elementary model ds/dt=kg implying ds/dt=kemath image. The lines are for different values of star-formation constant k, all models starting at redshift Z= 5.

image

Figure 7 : . The fraction of stars formed (relative to today) as a function of redshift Z for the best-fit model in figure 6. The second curve shows the very small effect of effect of starting star formation at an earlier epoch than Z= 5.

The build up of metal abundance of the elementary model is compared in figure 8 with the history of metallicities of damped Lyman-α systems (from Rao at al. 2005), simply scaling the pαk in equation 10 to fit. The explanation of the general trend seems fine, although of course individual systems will have individual histories. Great care should really be taken, though, in relating the theoretical heavy-element abundances to observations. In assessing the overall abundance of metals in the universe, account must be taken of where the elements are, and how accessible that “where” is to observation. Controversy still rages about the extent of dust opacity effects in hiding metal-rich damped Lyman-α systems. In groups of galaxies very significant baryonic mass may still be present (Fukujita, Hogan and Peebles 1998) as warm (∼105 K) rather than hot-X-ray bright (∼106 K) intracluster gas, and remain difficult to detect and analyse for chemical composition. This component could be critical in determining the present-day mean metal abundance of the universe. Nevertheless it seems that a “pleasantly Copernican” result of a mean abundance that is around solar (Edmunds and Phillipps 1997) may not be too far from the truth (Calura and Matteucci 2004)

image

Figure 8 : . The metal abundance of damped Lyman-α systems as a function of redshift Z. The observations are from figure 6 of Rao et al. (2005). The curves are the elementary model of our figure 6, with star formation starting at redshifts (from top curve downwards) Z= 9,7,5.

Mixing in the interstellar medium

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

Comparatively little work seems to have been done on the Second Commandment. This may have been because of the apparent complexity of the problem. It is possible to make a few back-of-the envelope calculations on likely mixing processes (e.g. Edmunds 1975, Roy and Kunth 1995) mainly involving random walks of material pushed around by interstellar turbulence and supernova remnants, and shear mixing in discs. More recently computer simulations of supernova remnant mixing have been reported (Nakasato and Shigeyama 2000, De Avillez and Mac Low 2002), and interesting arguments presented by Elemegreen (1998), Scalo and Elmegren (2004), Karlsson (2004), and Karlsson and Gustaffson (2001, 2005).

A reasonable summary would be that on a small scale (perhaps 200–300 pc) chemical homogeneity to within perhaps 10% is not surprising in the galactic disc at the present epoch, although on the large radial scale of a galaxy (i.e. tens of kiloparsecs) there can be inhomogeneity – for example the apparently exponential radial gradient over a factor of 10 in abundance across the disc of M101 (Kennicutt et al. 2005). In our galactic disc, the expected local homogeneity would conflict with the deuterium depletion variation shown for path lengths over 100 pc in figure 2, but concur nicely with the uniformity of local values within 50 pc. To explain the deuterium variation by poor mixing would imply large (and unobserved) variation in ISM metallicites. At earlier epochs when only a few supernovae have contributed to the chemical composition of the interstellar medium a much more “grainy” behaviour might indeed be expected – with local variations even displaying the nucleosynthetic peculiarities of individual supernovae. Indeed, one might hope that observation of variations in particular element ratios might give a more reliable handle on supernova element production ratios (i.e. individual element yields as a function of progenitor mass, Karlsson and Gustaffson 2005) than methods that rely on fitting rather uncertain galactic evolution models (Francois et al. 2004). The surprise is that for the bulk of elements (excluding elements from comparatively rare events such as r-process nuclei) the composition of old galactic stars indicates a remarkable degree of homogeneity. For example Arnone et al. (2005) show a sample of stars between 1/1000 to 1/100 of solar abundance that have a spread of element ratios that must be smaller than the (quite respectable) uncertainties in analysis. This implies remarkable homogeneity and must be implying efficient mixing over and above the effects of turbulence and supernova remnant shells. An obvious mechanism is large-scale stretching and folding of the ISM followed by the small-scale diffusion processes – like the mixing of a blob of ink into a turbulent fluid illustrated by figure 1 of Scalo and Emegreen (2004, and reproduced from Jullien, Castiglione and Tabeling 2000). The novelty is the global velocity field – whose scale size would presumably be at least a substantial fraction of the size of the system, and the timescale that of a few free-fall collapse times – implying the large-scale flows are contemporary with violent relaxation. Thus a galactic system may actually start fairly chemically homogeneous. It is not clear whether large-scale abundance gradients start at around the same time or develop later.

Dust

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

Interstellar dust is made of heavy elements and some quite useful insight can be gained simply by following the consequences of this obvious statement. The assumption that a constant fraction of the heavy elements in the ISM is in solid form provides an elementary model which to some extent explains (Eales and Edmunds 1996) the submillimetre observation of very dusty galaxies at high redshifts. Indeed, as shown in figure 9 (based on Dunne, Eales and Edmunds 2005), at redshifts around 2–3 the heavy elements in the universe are mostly in the ISM in galaxies – and perhaps nearly half of them in solid form. By the present epoch galaxies have evolved such that most of the heavy elements now reside in stars or in the extragalactic medium. There remains an interesting problem, though. Can the dust be made rapidly enough to be present in high-redshift galaxies? The traditional view has tended to be that dust condenses in the atmospheres of late-type giant stars. If we follow the heavy elements necessary for this dust formation it is evident that the elements must be synthesized in previous generations before incorporation into the dust-making stars, which in turn may have a fairly long evolutionary time to reach their cool giant phase. The dilemma is avoided if freshly synthesized heavy elements are directly incorporated into dust in supernovae explosions. An elementary model of the “dust cycle” in galaxies (see figure 10) can be developed (Edmunds 2001) which captures the essential features of more complicated computer simulations (Dwek 1998). For the refractory cores of dust grains, the “simple” model heavy-element equation 1 (without outflow) above can be modified, where y is the fraction of the ISM heavy elements in solid form, to:

  • d(yg)=p′χ1ds-(1-α)χ2ds-yds(11)
image

Figure 9 : . The location of metals at the present day and at redshift 2.5, from the data in Dunne et al. (2005). The IGM and IGM+ represent gas outside galaxies in clusters and groups. The concentration of metals in the ISM at Z= 2.5 indicates the potential for large dust masses.

image

Figure 10 : . The dust cycle in galaxies. The black arrows show the evolution of refractory grain cores. Non-refractory mantles may accrete in dense molecular clouds, but be stripped in the harsher environment of the warm/hot ISM. It is possible that the composition of the cores themselves may evolve (Gray and Edmunds 2004), but without wholesale destruction.

The details of dust production are parameterized by the two χ coefficients, which represent the fraction of heavy elements emerging in solid dust, a “condensation” factor. The first term with χ1 represents the dust directly made from fresh elements in supernova, but could also represent carbon condensation from freshly made triple-α processed material in giant stars. The second term with χ2 represents dust made in giant star atmospheres from heavy elements incorporated at star formation. Figure 11 shows how the abundance of the dust cores would evolve, relative to the heavy-element abundances in the ISM. Without the “prompt” supernova dust it is very difficult to produce sufficient dust early on, unless star-formation rates are very high (Morgan and Edmunds 2005), since the heavy elements have to build up in the ISM before going into the dust-producing stars. Indeed, as seen from figure 11, using just condensation in stellar atmospheres (the long-dashed curve) to build up the dust in the galactic disc today would imply a rather implausibly high condensation factor (χ2 ∼ 0.8). The detailed modelling (including grain mantle growth) shows that a fixed ratio of dust to heavy metals in the ISM – perhaps about 40%– would indeed occur over a fairly wide range of galaxy evolution, provided both supernovae and giants contribute to the dust. By the present epoch much of the new dust in our galaxy probably is coming from giant star atmospheres. But do supernovae actually produce dust? Undoubtedly yes! Individual grains bear isotopic signatures of supernova origin (e.g. Choi et al. 1998), but the real issue is how much? Recently we have been able to show directly the presence of considerable quantities of cool dust in the Cas A and Kepler supernova remnants, where it cannot have just been swept up from pre-existing dust in the ISM (Dunne et al. 2005, Morgan et al. 2005). The Cas A results have been criticized because a foreground interstellar cloud may confuse (Krause et al. 2004), but we have detailed CO mapping which implies that there could still be significant supernova dust in the Cas A remnant, and no such confusion is occurring for Kepler. The issue remains controversial, but I'd put money on supernovae (or at least the late stages of evolution of massive stars) being the dust source that dominates in the early universe.

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Figure 11 : . The evolution of dust cores. The horizontal axis is the gas mass fraction, f, giving a measure of the stage of evolution of the galaxy from pure gas to all stars. The models are normalized at f= 0.15, corresponding to current conditions in the galactic disc near the Sun. The curves represent a model with only supernova grains (short dash, χ1= 0.20, χ2= 0.0), an “equal chi” mixture (solid line, χ1= 0.16, χ2= 0.16), a different mixture (dash-dot, χ1= 0.10, χ2= 0.39), and a model with only giant-star grains (long dash, χ1= 0.785, χ2= 0.0). (Edmunds 2001, figure 2)

Back to basics – and Baker Street

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture

I hope I have shown that we can gain an encouraging mechanistic insight into aspects of the evolution of the universe simply by following the abundances of chemical elements by simple models. All this might be seen as an attack on the extensive numerical modelling of galaxies and structure formation in the universe that has mushroomed in the past 20 years. It is no such thing. What I want to emphasize is the parallel need for clear thought and “elementary” methods that enable us to grasp what is going on, on the basis of a few basic physical or mathematical principles. The symbiosis is evident when simulations show where systematic behaviour is occurring and analytical arguments demonstrate what is the major physical effect causing that behaviour. “Understanding” craves a simple physical explanation for, and not just a demonstration of, why the universe behaves in the way it does. Simulators sometimes still beat the analysts – a really convincing physical explanation of the transition from main-sequence star to red giant still eludes us over 50 years after it was demonstrated numerically. Perhaps there are no “simple” explanations for some behaviour.

I wonder if George Darwin would have felt the same dichotomy in the relationship between sophisticated harmonic analysis for tidal prediction, and the explanatory power of dynamical tidal theory. Clutching tide tables as I board my tiny sailing cruiser, I am grateful for their accuracy – but musing on the ebb and flood needs more than raw numbers for satisfactory explanation. In our cosmic voyages of thought to distant times and places in the universe we might well echo Sherlock Holmes' advice on the best approach: “Elementary, my dear Watson.”

References

  1. Top of page
  2. The Three Commandments
  3. Globular cluster systems in galaxies
  4. Mass–metallicity relations for spheroidal and elliptical galaxies
  5. Mass–metallicity relation for spirals
  6. Global star-formation rate and metallicity
  7. Mixing in the interstellar medium
  8. Dust
  9. Back to basics – and Baker Street
  10. References
  11. The George Darwin Lecture