5.10.2. Ejection from galaxies
The observation that the intracluster medium contains a significant abundance of heavy elements shows that it cannot be entirely due to the infall of primordial gas (Sections 4.3.2 and 5.2). The only way known for producing reasonable quantities of heavy elements is through nuclear reactions in stars. Since there is no significant luminous stellar population outside of galaxies at present, there are two possibilities. First, there may have been an early generation of pregalactic stars (Carr et al., 1984), or second, it may be that some portion of the intracluster gas was ejected from galaxies. This section considers the second possibility.
Are the present rates of mass loss from stars in galaxies sufficient to produce the required amount of gas if all the stellar mass loss is added to the intracluster gas? Let us assume that the intracluster gas is chemically homogeneous (Section 5.4.5), so that the inferred heavy element abundance is about half of the solar value. Then, since this is comparable to the present abundances in the stars in elliptical galaxies in clusters, ejection from galaxies would have to supply a significant portion of the observed intracluster gas. The total mass of intracluster gas is at least as large as the total mass of stars in galaxies in a luminous X-ray cluster ( 10% of the virial mass). Now the current rate of mass loss expected from the stellar populations seen in elliptical or S0 galaxies is
Thus, only a few per cent of the intracluster gas could be supplied in a Hubble time 1010 yr at the current rate.
In doing estimates of this sort, it is very important to remember that mass loss from stars is due to their evolution as they exhaust their nuclear fuel, and thus the mass loss from a stellar population is primarily due to the most luminous stars. In estimating the rate of mass loss, the rate per luminous star should be multiplied by the mass of luminous matter, and not the total (virial) mass. Another way of stating this is that the rate of mass loss is proportional to the luminosity of a stellar population and not to its mass; thus the rate of mass loss per unit mass varies inversely with the mass-to-light ratio (Section 2.8).
The rate of mass loss from stars in galaxies must have been higher in the past, if stellar mass loss has contributed significantly to the intracluster medium. One simple way this can have occurred is for elliptical and S0 galaxies to have contained more massive stars in the past, since massive stars have higher rates of mass loss. At present, these galaxies have only relatively low mass stars M* 0.8 M (Fall, 1981). Since stellar lifetimes decrease with mass, and the presently observed stars have lifetimes comparable to the Hubble time, any higher mass stars produced at the time of galaxy formation would no longer exist. High mass stars tend to die as supernovae which are very effective in producing and dispersing heavy elements, so these stars might provide the heavy elements in the intracluster gas and in the stars seen in the galaxies today without leaving any very low abundance stars (Carr et al., 1984). Moreover, the supernovae could aid in the removal of gas from the galaxies into the intracluster medium.
It is often suggested that all the stars in an elliptical or S0 galaxy formed at one time during the formation of the galaxy itself. Stars with a wide range of masses are usually assumed to have been made in protogalaxies, and the present stellar population is only those lower mass stars whose lifetimes exceed the age of the galaxy. Usually, the distribution of the masses of stars that form (the initial mass function or IMF) is taken to be a power-law, and the star formation rate is assumed to decline exponentially with the age of the galaxy:
where N* is the number of stars formed of mass M*, the lower and upper limits to the IMF are ML and MU, and t* is the time scale for star formation. A power law with a = 2.35 is called the 'Salpeter IMF' (Salpeter, 1955) and fits the current star formation in the disk of our galaxy. The time scale for star formation is often taken to be comparable to the dynamical time in a galaxy, t* 3 × 108 yr. The resulting model for the gas loss from a galaxy depends on the IMF assumed and on the values of t* and tst, the time scale for the removal of gas from the galaxy.
Larson and Dinerstein (1975) calculated the properties of the intracluster gas based on this model. They assumed a Salpeter IMF. The only gas loss process they considered was supernova heating from the same stellar population; this may underestimate the ejected mass if collisions or ram pressure ablation also contribute. Based on this model, they found that the majority of the gas was not removed in galaxies more massive than about 1010 M. The total gas mass ejected from galaxies in a cluster was about 30% of the mass in stars in galaxies, and the ejected mass had roughly solar abundances. Because these calculations preceded the detection of the iron X-ray lines in clusters, they successfully predicted that nearly solar abundances would be found.
Fairly similar results were found by Ikeuchi (1977), Biermann (1978), De Young (1978), and Sarazin (1979). Biermann assumed most of the galaxies were spirals that were stripped by collisions and ram pressure; this resulted in a more complete removal of interstellar gas, but over a longer time (tst t*). Biermann found somewhat lower heavy element abundances of 0.1 to 0.5 of solar, with the gas mass ranging from 1 to 0.1 of that of the stars. De Young noted that the supernova energy was sufficient to unbind the gas produced by stellar mass loss in galaxies, and thus assumed that nearly all the gas was ejected quite rapidly (tst < t*). He also considered a wider range of IMFs, and generally found heavy element abundances that were larger, 1-3 times solar. This was primarily sensitive to the exponent a in the IMF. The ejected gas masses were 0.15 to 0.5 of the stellar mass. One exception to the agreement among these authors was Vigroux (1977), who claimed that galaxies could not make enough iron during the course of their normal evolution. The account he gave of his calculations was rather sketchy, so it is difficult to compare them to the others. With this exception, the general conclusion was that galaxies could eject an amount of gas about half the stellar mass with roughly solar abundances during their normal stellar evolution. If this gas were diluted with roughly an equal amount of unprocessed primordial gas, either within the forming galaxies or in the cluster, the observed mass and heavy element abundances in the intracluster gas would be reproduced.
In most of these models, the time scale of star formation is assumed to be short, t* 109 yr. During this time, most of the stars in the galaxy are formed, and the more massive and luminous stars live and die explosively in supernovae. As a result, it is expected that the newly formed galaxies would be very bright during this era (De Young, 1978; Bookbinder et al., 1980).
The evolution of the intracluster gas in models with ejection from galaxies depends on the length of time it takes the newly enriched gas to be stripped, tst. De Young (1978) noted that the energy input from the supernovae produced by a stellar population which would give the needed iron abundance would be sufficient to unbind the interstellar gas. This assumes that the supernova energy is efficiently converted to kinetic energy in the gas.
On the other hand, if the supernovae energy is radiated away, the gas may remain bound to the galaxy. Norman and Silk (1979) and Sarazin (1979) showed that this was likely to be the case, because the large quantity of intracluster gas in clusters implies that there was a large density of gas in protogalaxies. At high densities the gas cools rapidly, and individual supernova remnants radiate away their energy before they overlap. Under these circumstances, the galaxies may retain their gas. Norman, Silk, and Sarazin suggested that galaxies retain much of their initial gas content as extended hot coronae. If this gas cannot be removed by supernovae, then collisions or ram pressure remain as stripping mechanisms (Section 5.9). They further assumed that galaxy formation is very efficient, in the sense that nearly all the gas in a cluster was initially contained in galaxies. Then, there would be very little intracluster gas at first, and ram pressure ablation would not be effective. The galaxies would first lose gas slowly through collisions, and when the intracluster density was high enough, ram pressure stripping would start. Because ram pressure ablation both increases the gas density and increases with increasing gas density, this leads to a runaway stripping of cluster galaxies. The evolution of the gas in a cluster would then occur in two extended stages, with a rapid transition between them. First, all the gas would be bound to galaxies. Then, it would be rapidly stripped and remain distributed in the intracluster medium after that time. This was proposed as an explanation of the Butcher-Oemler effect (Section 2.10.2); the Butcher-Oemler clusters were still in this first stage. Unfortunately, this model predicts that these clusters have very little intracluster gas, when in fact they were subsequently observed to be luminous X-ray sources (Section 4.8). Larson et al. (1980) argued that the disks of spiral and S0 galaxies are produced by infall from coronae of gas bound to galaxies, and that a spiral galaxy becomes an S0 when the corona is stripped and the gas supply to the disk stops. In this way, there would be a longer interval between the stripping of the corona and the cessation of star formation in the disk. Perhaps Butcher-Oemler clusters are within this interval. One problem with these models for gaseous coronae is that they require a rather delicate and unstable balance between supernova heating and cooling.
Biermann (1978) proposed a similar model in which gas produced by disk galaxies is stored in their disks, and is eventually stripped by collisions and ram pressure. Himmes and Biermann (1980) gave a somewhat more detailed model, in which elliptical galaxies in a cluster lose their interstellar gas rapidly by supernova heating and provide an initial amount of intracluster gas, which begins the process of ram pressure stripping of spiral galaxies. They argued that this model can reproduce the present intracluster gas masses, iron abundances, and dependence of the galactic population on X-ray luminosity (Section 4.6). In this model, the spiral fraction in cluster decreases continuously with time, and the variation from a redshift of z 0.4 to the present is consistent with the Butcher-Oemler effect.
One general feature of these models in which gas is ejected from galaxies over a long period of time is that the luminosities of X-ray clusters are expected to increase with time. Unfortunately, this is the same prediction made by Perrenod's infall models with deepening cluster potentials, as discussed in the previous section.
A number of one-dimensional, spherically symmetric, hydrodynamic simulations have been made of the evolution of intracluster gas, including ejection from galaxies. Cowie and Perrenod (1978) calculated models with a fixed cluster potential and assumed that the rate of gas ejection from galaxies varied inversely with time * >1 / t. There was no primordial intracluster gas in these models. The gas was ejected at zero temperature (Section 5.3.3) and assumed to mix immediately with the intracluster gas. When the gas ejection rate is large, the models evolve to steady-state cooling flows (Cowie and Binney, 1977; Section 5.7.1). In models with lower ejection rates, the X-ray luminosity either is roughly constant (no thermal conduction) or increases by about a factor of two (thermal conduction) from a redshift z = 1 to the present. Perrenod (1978b) calculated ejection models in a varying cluster potential; the results were very similar to those described above for infall models. He found a better fit to the present gas distributions with these models than with infall models, and the ejection models were less sensitive to the assumed initial conditions and model parameters. These models showed a rapid increase in X-ray luminosity with time, as did the infall models.
Ikeuchi and Hirayama (1980) ran hydro models with no primordial gas, in which gas is ejected from all the galaxies simultaneously and very rapidly (tst 107 yr). This seems rather unlikely, since this time scale is less than the sound crossing time for a single galaxy. Because of this assumption of rapid ejection, they chose the following initial conditions: at the start of their calculation, the ejected gas was placed in the cluster in a nonhydrostatic distribution determined by their ejection model, and then 'let go'. The gas then adjusted to the cluster potential on a sound crossing time (Section 5.5). These models have very large X-ray luminosities 1048 erg/s during this initial relaxation time t 3 × 108 yr. It seems very unlikely that such high luminosities would be realized, since the actual gas ejection must take considerably longer than was assumed.
It has generally been assumed that the ejected gas mixes rapidly (both chemically and thermally) with the intracluster gas (De Young, 1978). However, Nepveu (1981b) argues that this will not occur (although the only mechanism he considers is turbulent mixing), and that the ejected and intracluster gases must be treated as two separate fluids.
Hirayama (1978) and Nepveu (1981b) have given hydrodynamic models for the evolution of the intracluster medium including both gas ejected from galaxies and primordial gas. In both cases, the primordial gas is initially relaxed, and galaxy gas is injected at a constant rate. In both of these calculations, the ejected gas is concentrated to the cluster center (R 2 Mpc), and there is a large gradient in the heavy element abundance across the cluster. As noted previously (Sections 5.4.5 and 5.5.6), such a concentration of heavy elements to the cluster center will increase the strengths of the X-ray lines from these elements. Thus the abundances derived from the X-ray spectra of clusters could overestimate the real abundances. However, because most of the X-ray emission in these models comes from radii of less than 2 Mpc, this effect is not very serious. Spatially resolved X-ray spectra across a cluster might detect such a gradient, and this would allow one to deduce the proportions of ejected and intracluster gas.