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
![]() | (5.121) |
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:
![]() | (5.122) |
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.