Dwarf elliptical galaxies clearly once had gas and formed stars, and therefore must at some time in their past have looked like dwarf irregular galaxies. Could dE's simply be highly evolved irregulars? The secular evolution of irregulars to dE's, with evolutionary time scale being controlled by the environment, could plausibly account for the different clustering properties of dE and irregular galaxies (see Sect. 6). There are, in fact, many intermediate-type (dE/Irr) dwarf systems in the Virgo cluster and around massive field giants where we may be witnessing the conversion of an irregular to a dE (Sandage and Binggeli 1984; Vigroux et al. 1986; Sancisi et al. 1987; Sandage and Hoffmann 1991; Sandage and Fomalont 1993). In this section we review processes that could bring about such a conversion.
7.6.1. Sweeping
Gas will be stripped from a galaxy moving through a hot medium if the ram pressure exceeds the restoring force per unit area due to the galaxy's own gravity (Gunn and Gott 1972). For a spherical galaxy, ram pressure will be effective if
where 
h is the density of the hot gas, and v,
M, R, and g
are the velocity, mass, radius, and mean gas density of the galaxy
(Takeda et
al. 1984).
Complete stripping of the central regions
requires that
v2 exceed the maximum binding force, which
for a King model is 
3.5 g 
2, where
is the galaxy velocity dispersion. To get a rough idea of the importance
of ram-pressure sweeping, consider a galaxy with = 25 km s-1
and a density nH = 1 cm-3 moving through an
external medium at 700 km s-1. According to the above formula,
complete sweeping would require a density in the external medium
n > 4 x 10-3 cm-3, something that is achieved
only within the central 100 kpc of the Virgo cluster core.
In addition to ram pressure,
evaporation, turbulent viscous stripping, and laminar stripping will
also act to remove the ISM from an infalling dwarf galaxy
(Cowie and
Songaila 1977;
Nulsen 1982).
Nulsen (1982)
estimates a typical mass loss rate of
for a galaxy of radius r in a cluster of velocity dispersion
with
a gas density h, for all of these transport processes
(different ones acting in different regimes of galaxy velocity relative
to the sound-speed in the external medium). In more convenient units,
this becomes
where rkpc is the galaxy radius in kpc,
which suggests a stripping timescale of 2 x 109 yr for
a galaxy with a mass in gas of M = 108
M
in a cluster with mean gas density
n = 10-4 cm-3 and velocity dispersion
= 700 km s-1.
Such densities are attained within 300 kpc of M87
(Fabricant and
Gorenstein 1983).
(Timescales are significantly shorter for the Coma cluster.)
The above arguments suggest that in clusters such as Virgo, gas removal will be relatively slow except in the central regions of the cluster. Galaxies on orbits that do not pass through the central ~ 0.5 Mpc will probably retain gas for several times 109 years. Galaxies that orbit beyond the central Mpc could retain their gas for a Hubble time. Unless the orbits are predominantly radial, we should expect to see a large variation in the gas content of dwarf galaxies over the central few Mpc of the Virgo cluster. Observationally, dE's are the dominant dwarf-galaxy population over this entire region, and there are no obvious systematic variations in their properties with position in the cluster, other than the frequency of nucleation (Sect. 6).
We conclude, purely on the basis of these arguments, that stripping
was probably not the dominant gas-removal mechanism in environments
such as the Virgo and Fornax clusters.
A similar argument suggests
that stripping is probably not the major gas removal mechanism
for the Milky Way companions. For a galaxy of radius 1 kpc to
lose 2 x 107 M in less than 10 Gyr would require
n > 10-4 cm-3, averaged over the orbit of
the galaxy. ROSAT observations probably exclude > 106 K gas
at the required densities for normal spiral galaxies
(Pietsch 1992).
However, these simple arguments neglect the fact that the interstellar media of galaxies are multi-phase. Low-density diffuse gas will be much more easily stripped than the high-density gas that is directly associated with star formation. What effect this has on the evolution of a galaxy therefore depends on how gas circulates from dense to diffuse phases - a process that is stopped by sweeping at densities much lower than required for removal of the entire ISM. If sweeping by an external medium is the dominant gas-removal mechanism (i.e. if all dE's pass through high density regions at some time during their lives), the natural consequence is that the metallicity-luminosity relation should not exist, or should be modulated by environment. While the stripping timescale depends on galaxy mass, leading to some correlation, it also depends on galaxy orbit and the time when the galaxy encountered a dense external medium, both of which are probably independent of mass, but may introduce correlations of metallicity with position. No such correlations have been identified, but they have not been ruled out either.
Independent of this discussion, there are four classical arguments against a pure stripping scenario for dE's brighter than about MB = -14 (Davies and Phillipps 1988; Binggeli 1994a): (1) bright dE's have nuclei and irregulars do not, (2) bright dE's have surface brightnesses that are too high compared to irregulars (see Fig. 3), (3) bright Im's are flatter than bright dE's, (4) dE's are more metal-rich than Im's (Zinnecker and Cannon 1986; Thuan 1985). Of these, argument (3) now appears considerably weaker (Sect. 2.2.3), and argument (2) has not been demonstrated explicitly for complete samples, controlling for the underlying luminosity-metallicity correlation.
Even if interaction with a surrounding medium does not remove all the gas, it is possible that it influences the star formation histories of dE galaxies in other ways. Episodic encounters of dE's with dense gas, either in galaxy halos or in clusters, could provide a mechanism for forming multiple, distinct generations of stars, thus enhancing surface brightness and metallicity, and for forming the nuclei. In this regard, the effect of pressure confinement by the external medium may be more important than the gas removal processes discussed above.
7.6.2. Pressure confinement
Pressure confinement by the intracluster medium has been
considered by
Fabian et
al. (1980) and by
Babul and Rees
(1992)
in the context of dwarf galaxies. For a gas cloud of mean density
ng and temperature Tg to be in pressure
equilibrium with a surrounding medium of density nh
and temperature
Th, we require that ng
Tg nh Th (ignoring gravity).
A galaxy with a Tg = 100 K ISM of star-forming
density ng 1
cm-3 encountering a medium of
T 4 x 107 K
(the approximate temperature of the Virgo cluster gas found
by
Fabricant and
Gorenstein (1983),
will be pressure confined at densities
nh
10-6 cm-3. A galaxy falling into the cluster
for the first time at the present epoch encounters such densities
at a relatively low (subsonic) velocity, and may consequently have its ISM
compressed long before ram pressure and other gas removal mechanisms become
efficient. If the star-formation rate scales with some power
of the ISM density, such pressure confinement provides a natural
explanation for the existence of blue compact dwarf galaxies
(dwarf galaxies with enhanced central star formation) at the peripheries
of clusters
(Hoffmann et
al. 1989),
and also provides a mechanism for
converting Irr to higher-surface-brightness dE galaxies through a
period of enhanced star formation prior to gas stripping, similar
to the scenario proposed by
Davies and
Phillipps (1988).
On the other hand,
White and Frenk
(1991) and
Cole et al. (1994)
argue that star formation will be self-regulated (see
Sect. 7.5.1),
with dwarf galaxies maintaining a large reservoir of gas at the
virial temperatures of their halos by injection of energy
from a roughly constant of star formation.
Interaction with the ICM will increase the
density, and hence shorten the cooling time of the gas.
Once the external pressure dominates, the cooling time
scales roughly as tcool 
nh-1 for a galaxy
moving through an isothermal cluster halo. The effect once again
will be to increase the star-formation rate during infall into
the cluster.
7.6.3. Tidal Shaking
Since cooling and star formation (presumably) depend on density, in principle any mechanism that can perturb the density of gas in a quiescent dwarf irregular can increase the star formation rate. If gas is subsequently expelled either by winds or stripping, the galaxy can complete its transition from an irregular to a dE. One possible mechanism that does not require an external gaseous medium is ``tidal shaking'' (Miller 1988). Tidally induced star formation has been invoked in the context of hierarchical models (Lacey and Silk 1991; Lacey et al. 1993), where the details of the mechanism were not specified. The process has never really been quantified for dwarfs. However, Icke (1985) carried out hydrodynamical simulations for rotating disk galaxies that indicate that even distant encounters can cause shocks in the ISM without significantly perturbing the stars. The development of shocks depends on the mass of the perturber and the mass ratio of the perturber to the perturbed galaxy. Icke's scaling relations imply that for a perturber/perturbed galaxy mass ratio of 1000, shocks will develop if perigalacticon is less than ~ 30 perturbed galaxy scale radii. For dE scale radii of ~ 1 kpc, this requires rather close (i.e. rare) passages, and is therefore probably not very effective on the outskirts of clusters (where pressure induced star formation might be). However, shocks per se may not be necessary to influence the star-formation rate, which in some models is determined by a delicate balance of cooling and supernova heating. Tidal shaking may be enough to superimpose on this feedback cycle an environment-dependent modulation in the star formation efficiency, which may help explain the environmental variations in the dE fraction, and the episodic bursts of star formation seen in local dE's.
However, we must emphasize that mechanisms such as pressure induced star formation and tidal shaking can only provide a viable way to form the large dE populations of clusters if a suitable reservoir of galaxies exists. The mass function of field dwarf irregulars and HI clouds must therefore have roughly the same slope as the dE mass function. The data are really too sparse to tell whether this is the case. The comparison of the dE and Irr luminosity functions certainly does not support such a transition, as the Irr LF appears to be flat (Binggeli et al. 1988). The slope of the HI mass-function from blind surveys is perhaps somewhat steeper (Kerr and Henning 1987; Weinberg et al. 1991; Schade and Ferguson 1994).
An obvious consequence of induced star formation is that dE galaxies may have formed many of their stars after the collapse of galaxy clusters. As this occurs rather late in hierarchical models, dE galaxies should contain significant components of stars with ages less than ~ 5 Gyr.
7.6.4. Stochastic Star Formation
A final link between dwarf irregulars and dwarf ellipticals is the possibility that star formation in gas-rich dwarf galaxies is stochastic, with short bursts followed by long periods of dormancy (Gerola et al. 1980; Tyson and Scalo 1988). Such a mechanism is not viable as an explanation for most dE's because they should have large reservoirs of HI. However, only a few dozen dE's have actually been searched for HI, leaving open the possibility that some could be dormant dwarf irregulars. Particularly attractive candidates are bright non-nucleated dE's, which show the same spatial distribution in clusters as the dwarf irregulars (see Sect. 6.1). Only a few have been observed in HI, and none detected.