To be published in "Vulcano Workshop: Chemical Enrichment of
Intracluster and Intergalactic Medium", May 14 - 18 2001,
eds. F. Matteucci and F. Giovannelli, ASP Conference Series;
Abstract. An attempt is made to guess the overall cosmic abundance of "metals" and the contribution made by the energy released in their production to the total intensity of extragalactic background light (EBL). With a comparable or somewhat larger amount coming from white dwarfs, and a probably quite modest contribution from AGNs, one can fairly easily account for the lower end of the range of existing estimates for the total EBL intensity (50 to 60 nwt m-2 sterad-1), but it seems more difficult should some higher estimates (90 to 100 in the same units) prove to be correct.
Table of Contents
There are certain more or less well or badly determined integral constraints on the past history of star formation in the universe. These include
A useful starting point is the cosmic baryon budget drawn up by Fukugita, Hogan & Peebles (1998), hereinafter FHP, shown in the accompanying table. The total from Big Bang nucleosynthesis (BBNS) adopted here agrees quite well with the amount of intergalactic gas at a red-shift of 2 to 3 deduced from the Lyman forest, but exceeds the present-day stellar (plus cold gas) density by an order of magnitude. (1)
|All baryons from BBNS|
|(D/H = 3 × 10-5 a)||0.04 h70-2|
|Stars in spheroids||0.0026 h70-1 b|
|Stars in disks||0.0009 h70-1 b|
|Total stars||0.0035 h70-1 b|
|Cluster hot gas||0.0026 h70-1.5 b|
|Group/field hot gas||0.014 h70-1.5 b (0.004h75-1 in O VI systems c)|
|Total stars + gas||0.021 h70-1.5 b|
|Machos + LSB gals||?? b|
|Z (stars, Z = 0.02 d)||7 × 10-5 h70-1|
|Z (hot gas, Z = .006)||1.0 × 10-4 h70-1.5 b|
|1.2 × 10-4 h70-1.3 e|
|Yield Z / *||0.051 h70-0.3 ( 3Z!)|
|Damped Ly- (H I)||0.0015 h70-1 b, f|
|Ly- forest (H+)||0.04 h70-2 b, g|
|Gals + DM halos|
|(M/L = 210 h70)||0.25 b, h|
|(fB = .056 h-1.5)||0.37 h70-0.5 b, i|
|a O'Meara et al 200l; but see also Pettini & Bowen 2001; b Fukugita, Hogan & Peebles 1998; c Tripp, Savage & Jenkins 2000; d Edmunds & Phillipps 1997; e Mushotzky & Loewenstein 1997; f Storrie-Lombardi, Irwin & MacMahon 1996; g Rauch, Miralda-Escudé, Sargent et al 1998; h Bahcall, Lubin & Dorman 1995; i White & Fabian 1995.|
FHP pointed out that a dominant and uncertain contribution to the baryon budget comes from intergalactic ionized gas, not readily detectable because of its high temperature and low density. The number which I quote is based on the assumption that the spheroid star-to-gravitational mass ratio and baryon fraction are the same in clusters and the field, an assumption that had also been used previously by Mushotzky & Loewenstein (1997). The resulting total star-plus-gas density is within spitting distance of B from BBNS, but leaves a significant-looking shortfall which may be made up by some combination of MACHOs and low surface-brightness galaxies; it is not clear that a significant contribution from the latter has been ruled out (cf O'Neil 2000).
1 The stellar density taken here from FHP is based on B-luminosity density estimates and might be revised upwards by 50 per cent in light of SDSS commissioning data (Blanton et al 2000) or downwards by 20 per cent in light of 2dF red-shifts plus 2MASS K-magnitudes (Cole et al 2000); in either case we are following FHP in assuming the IMF by Gould, Bahcall & Flynn (1996), which has 0.7 times the M / LV ratio for old stellar populations compared to a Salpeter function with lower cutoff at 0.15 M. Back.
We now have the tricky task of estimating the total heavy-element content of the universe. Considering stars alone, it seems reasonable to adopt solar Z as an average, but the total may be dominated by the still unseen intergalactic gas, which Mushotzky & Loewenstein argue to have the same composition as the hotter, denser gas seen in clusters of galaxies, i.e. about 1/3 solar. (2) It could be the case, though, that the metallicity of the IGM is substantially lower in light of the metallicity-density relation predicted by Cen & Ostriker (1999) and in that of the low metallicities found in low red-shift Ly- clouds by Shull et al (1998). Against this, we have neglected any metals contained in LSB galaxies or whatever makes up the shortfall between IGM and B, so we are being conservative in our estimate of Z.
The mass of heavy elements in the universe is related to that of stars through the yield, defined as the mass of "metals" synthesised and ejected by a generation of stars divided by the mass left in form of long-lived stars or compact remnants (Searle & Sargent 1972). The yield may be predicted by a combination of an IMF with models of stellar yields as a function of mass, or deduced empirically by applying a galactic chemical evolution (GCE) model to a particular region like the solar neighbourhood and comparing with abundance data. E.g. Fig 1 shows an abundance distribution function for the solar neighbourhood plotted in a form where in generic GCE models the maximum of the curve gives the yield directly, and it is a bit below Z. Similar values are predicted theoretically using fairly steep IMFs like that of Scalo (1986). In Table 1, on the other hand, if we divide the mass of metals by the mass of stars, we get a substantially higher value, corresponding to a more top-heavy IMF.
Figure 1. Oxygen abundance distribution function in the solar neighbourhood, after Pagel & Tautvaisiene (1995).
There are two other indications for a top-heavy IMF, one local and one in clusters of galaxies themselves. The local one is an investigation by Scalo (1998) of open clusters in the Milky Way and the LMC, where he plots the IMF slopes found as a function of stellar mass. The scatter is large, but on average he finds a Salpeter slope above 0.7M and a virtually flat relation (in the sense dN / dlogm 0) below, which could quite easily account for the sort of yield found in Table 1. The other indication is just the converse of the argument we have already used in guessing the abundance in the IGM: the mass of iron in the intra-cluster gas is found (Arnaud et al 1992) to be
where LV is the luminosity of E and S0 galaxies in the cluster. As has been pointed out by Renzini et al (1993) and Pagel (1997), given a mass:light ratio less than 10, we then have
The argument is very simple; the issue is just whether such high yields are universal or confined to elliptical galaxies in clusters.
2 This refers to iron abundance, the relation of which to the more energetically relevant quantity Z is open to some doubt. Papers given at this conference indicate an SNIa-type mixture in the immediate surroundings of cD galaxies with maybe a more SNII-like mixture in the intra-cluster medium in general; for simplicity I assume the mixture to be solar. Back.
The deduction of past star formation rates from rest-frame UV radiation in the Hubble and other deep fields as a function of red-shift is tied to "metal" production through the Lilly-Cowie theorem (Lilly & Cowie 1987):
where (1 + a) 2.6 is a correction factor to allow for production of helium as well as conventional metals and (probably between about 1/2 and 1) allows for nucleosynthesis products falling back into black-hole remnants from the higher-mass stars. is the fraction of total energy output absorbed and re-radiated by dust and H is the frequency at the Lyman limit (assuming a flat spectrum at lower frequencies). The advantage of this formulation is that the relationship is fairly insensitive to details of the IMF.
Eq (7) is the same as eq (13) of Madau et al (1996), so I refer to the metal-growth rate derived in this way as Z(conventional).
Assuming a Salpeter IMF from 0.1 to 100 M with all stars above 10 M expelling their synthetic products in SN explosions, one then derives a conventional SFR density through multiplication with the magic number 42:
In general, we shall have
where is some factor. E.g., for the IMF adopted by FHP, = 0.67, whereas for the Kroupa-Scalo one (Kroupa et al 1993) = 2.5.
Finally, the present stellar density is derived by integrating over the past SFR and allowing for stellar mass loss in the meantime, and the metal density is related to this through the yield, p:
(where is the lockup fraction), whence (if a = 1.6)
which can be compared with Z 1/60. It was pointed out by Madau et al (1996) that the Salpeter slope gives a better fit to the present-day stellar density than one gets from the steeper one - a result that is virtually independent of the low-mass cutoff if one assumes a power-law IMF.
Eq (8), duly corrected for absorption, forms the basis for numerous discussions of the cosmic past star-formation rate or "Madau plot". Among the more plausible ones are those given by Pettini (1999) shown in Fig 2 and by Rowan-Robinson (2000), which leads to similar results and is shown to explain the far IR data. Taking = 0.62 (corresponding to a Salpeter IMF that is flat below 0.7M) rather than Pettini's value of 0.4 (for an IMF truncated at 1M), and = 0.7, we get the data in the following table.
Figure 2. Global comoving star formation rate density vs. lookback time compiled from wide-angle ground-based surveys (Steidel et al. 1999 and references therein) assuming E-de S cosmology with h = 0.5, after Pettini (1999). Courtesy Max Pettini.
Table 2 indicates that the known stars are roughly accounted for by the history shown in Fig 2 (or by Rowan-Robinson) and the metals also if is close to unity, i.e. the full range of stellar masses expel their nucleosynthesis products. At the very least, has to be 1/2, to account for metals in stars alone. The other point arising from the table, made by Pettini, is that at a red-shift of 2.5, 1/4 of the stars and metals have already been formed, but we do not know where the resulting metals reside.
|z = 0||z = 2.5|
|* = *(conv.) dt||3.6 × 108 M Mpc-3||9 × 107 M Mpc-3|
|* = * / 1.54 × 1011 h702||.0024h70-2||6 × 10-4 h70-2|
|Z = p * = * / (42 )||2.0 × 107 M Mpc-3||5 × 106 M Mpc-3|
|Z (predicted)||1.3 × 10-4 h70-2||3.2 × 10-5 h70-2|
|Z (stars, Z = Z)||7 × 10-5 h70-1|
|Z (hot gas, Z = 0.3Z)||1.0 × 10-4h70-1.5|
|-> 0.5 1.3|
|Z (DLA, Z = 0.07Z)||2 × 10-6 h70-1|
|Z (Ly. forest, Z = 0.003Z)||1 × 10-6 h70-2|
|Z (Ly. break gals, Z = 0.3Z)||?|
|Z (hot gas)||?|
Figure 3. Spectrum of extragalactic background light, based on COBE data after Hauser 2001 (diamonds with error bars, dotted and short-dash curves), Madau & Pozzetti 2000 (squares), Totani et al 2001 (crosses), Bernstein, Freedman & Madore 2001 (triangles) and Armand et al 1994 (asterisk). The broken-line curve (Biller et al 1998) and horizontal dash-dot line (Hauser 2001) show upper limits based on lack of attenuation of high-energy -rays from AGNs and the solid curve is from the model by Pei, Fall & Hauser (1999). The arrow showing an upper limit at 10µm is from unpublished thesis work by A. Barrau, cited by Gispard, Lagache & Puget (2000).
Fig 3 shows the spectrum of extragalactic background light (EBL) with the model fit by Pei, Fall & Hauser (1999). Gispert, Lagache & Puget (2000) have estimated the total EBL I d based on observation to lie within the following limits:
|6µm:||20 to 40||nwt||m-2||sterad-1|
|> 6µm:||40 to 50||"||"||"|
|Total:||60 to 90||"||"||"|
(The total from the model of Pei, Fall & Hauser (1999) is 55 in these units.)
We use the estimates of stellar and metal densities in Tables 1 and 2 together with eq (7) and an assumption about the mean red-shift of metal formation to derive the EBL contributions from:
Here we use eq (6) without the (1 + a), since most of the nuclear energy is already released on reaching this stage. Assuming most stars to belong to an old population so that
Madau & Pozzetti (2000) and Brusa, Comastri & Vignali (2001) have made estimates of the AGN contribution to EBL based on the the abundance of massive black holes and that of obscured hard X-ray sources, respectively. They agree that the contribution is quite small, of order 5 nwt m-2 sterad-1.
The upshot is that these readily identifiable contributions add up to 48 nwt m-2 sterad-1, well within range (given the obvious uncertainties in mean z and other parameters) of the lower estimate given at the beginning of this section. It is interesting to note that white dwarfs and intergalactic metals come out as the major contributors, either one predominating over metallicity in known stars. To reach the higher estimate may involve some more stretching of the parameters.
I thank Richard Bower, Jon Loveday and Max Pettini for helpful information and comments.