Dwarf Spheroidal Galaxies were first identified by Shapley, who had noticed two very diffuse collections of stars on Harvard patrol plates. Although these systems had about as many stars as a Globular Cluster, they were of much lower density, and hence much larger radius, and thus were considered distinct galaxies. These two, named Fornax and Sculptor after the constellations in which they appear, are in fact satellites to the Milky Way and are part of a family currently numbering nine that orbit the Galaxy. Studies by Baade and others showed that the stellar populations are old, based on the presence of RR Lyrae Stars and the apparent lack of star formation regions, prompting a question of link between these galaxies and the Elliptical Galaxies. The galactic dwarf spheroidals are themselves part of a larger class of galaxy called dwarf ellipticals (dE), which extend in luminosity from that of the faintest dwarf spheroidals (MV =−9) to around MV =−17, a good example being NGC 205. These galaxies are referred to as ‘spheroidals’ by some authors. The basic isolating characteristics of the class are low surface brightness and smooth light distribution. The radial light distributions tend to be exponential, which they have in common with Irregular and Spiral Galaxies and which distinguishes them from the ellipticals, which have more of a power-law light profile. Also, the surface brightness (either central or average value) decreases with decreasing luminosity, whereas for ellipticals surface brightness increases with decreasing luminosity. There is a range of luminosities for which both dwarf ellipticals and ellipticals exist—the difference in the types is then best demonstrated by the remarkable differences in structure between that of NGC 147, a dwarf elliptical, and M32, an elliptical, both of which are companions to M31 and which have similar luminosities.

dEs are very common. In the Local Group, there are 19 known (nine around M31, one unattached to a large galaxy, and the nine of the Milky Way already mentioned). The nearby group of M81 has 12 known. The largest collections of dEs, however, are found in the rich clusters. Virgo, for instance, has had over 400 dEs cataloged to the relatively bright luminosity of MV =−13, although the dwarfs as a population contribute less than 10% of the total light of the cluster. There is some indication that the relative number of dEs to giant galaxies in a group goes up as the number of giants increases. The luminosity function of dEs was shown by Sandage, Binggeli and Tammann to have an exponential form, thus entailing the exponential part of the Schechter function which represents the luminosity function of all galaxies. The slope of this function in Clusters Of Galaxies shows significant variations among clusters studied, with the interesting result that clusters with large cD galaxies have proportionately fewer dE galaxies (slope α ∼−1) than do those clusters without such a dominant galaxy (−1.4 ≥ α ≥−2.0). The conclusion here may be that cD halos are formed by the disruption of dwarfs, although the mechanism for doing so is unidentified, and it is as likely that the problem needing explaining is actually the preponderance of dEs in non cD clusters. The three dimensional shapes of dEs appear not to be disks, despite their exponential light profiles; rather, the flattening distributions indicate spheroidal or ellipsoidal shapes because of the lack of very flat systems. The lack of nearly circular galaxies argues against the galaxies being oblate, and although prolate systems are permitted by the data, it is most likely that, as a group, these galaxies are tri-axial.

Because of the intrinsic faintness of these galaxies, there is not a surfeit of kinematic information about them, although what is known has proved to be crucial to the study of Dark Matter In Galaxies. Studies of the velocities of individual stars in the galactic dwarf spheroidals have shown that the least luminous galaxies (UMi and Draco) have velocity dispersions around 10 km s−1 similar to the dispersions found in the brightest galactic dwarf spheroidal, Fornax, which is nearly 100 times more luminous. The high dispersions result most simply in total M/L values of order 100 for the faint dwarfs, and since the stellar M/L values are order unity, there is thus strong evidence for unseen matter. Modeling attempts to explain the large velocity dispersions by interactions and disruptions with the Milky Way have largely been unsuccessful, because these interactions, while disturbing the structure of dwarfs galaxies, do not significantly alter the central velocity dispersions. More detailed structural models of the galaxies, in which dark matter halos are included along with the observed luminous matter distribution, have confirmed the large M/L ratios and also shown that the central densities of dark matter can be very high, near 1 Mopc−3, much larger than the density of visible stars.

Spectral observations in integrated light of more distant galaxies have further shown that the dEs are slow rotators and are in general not rotationally flattened, thus placing them on common ground with the large ellipticals, and making them different from the low-luminosity ellipticals, which are rotationally flattened. The galactic dwarf spheroidal UMi, which is quite flat in projection (e = 0.6), has also been shown to have little rotation, the data coming from individual constituent stars in this case. The velocity dispersions obtained in integrated light of luminous dwarf ellipticals tend to indicate normal M/L ratios; i.e. the central areas are not dark matter dominated.

A salient feature in nearly half of the luminous dEs is the presence of a distinct nucleus. The most widely known nucleus is surely that of NGC 205, although this nucleus is in fact quite different from those of most other galaxies in that it is a young star cluster, part of the star formation event first noticed by Baade. The nuclei in other dEs appear to be the same age as the surrounding galaxy. For a small nucleus, it can appear simply as a star cluster, occasionally miscentered in the host galaxy; in the cases where the nucleus is large, it tends to blend in with the structure of the surrounding galaxy rather than appear as an imposed star cluster. Their luminosities range upwards to MV =−12, which is somewhat brighter than the brightest globular clusters known anywhere. The presence of a nucleus is weakly correlated with a number of other properties. They occur more frequently in more luminous galaxies. They occur more often in rounder galaxies. In clusters, the nucleated galaxies tend to be more concentrated as a group than do non-nucleated galaxies. Also, the nucleated galaxies tend to be redder than non-nucleated galaxies, although there is little color difference between the nucleus and the surrounding stars. None of these tendencies yet points to an origin of the nuclei, however, other than to support the obvious idea that the nuclei are secondary star formation events, where gaseous material fell to the center of a newly formed galaxy and built up a region of high stellar density. HST images of a nearby nucleus (which contains nearly 5% of the total galaxy luminosity) show a central density as high as that found in galactic globular clusters.

Like all types of galaxies, dEs contain globular clusters. The presence of them is directly related to the host galaxy luminosity, and the scaling factor appears to be more like the ellipticals with a relatively high number of clusters per unit luminosity (4 per unit MV =−15), rather than like the spirals which are cluster poor. The faintest known galaxy with globular clusters is still Fornax, which has 5. Colors and metal abundance measures of dE globulars indicate that they are more metal poor than the surrounding halo in the mean; a similar situation is found in ellipticals.

Ideas that the stellar populations are similar to those of globular clusters (i.e. uniformly old) have had to be modified, first because of the indirect indicators of young age such as the presence of anomalous Cepheid variable stars, the second parameter problem (a red horizontal branch in a metal-poor system) and upper asymptotic giant branch stars, and later more directly by color–magnitude diagrams (particularly of Carina), which show multiple main sequence turnoffs, indicating several discrete epochs of Star Formation. Many of the Local Group dwarf spheroidals show such evidence for star formation more recent than 10 Gyr. Direct evidence for current star formation among Local Group dEs is found only in NGC 185 and 205, however. More distant galaxies also show some signs of recent star formation, in that the integrated colors show large variations among galaxies of similar luminosity; some colors are bluer than can be explained by low metallicities. It is apparent that star formation in dEs is a more complex thing than in globular clusters. The acquisition of more star formation material can explain some cases, but others require self-regulation of star formation, via stellar winds perhaps. Galaxies such as the Phoenix dwarf and LGS3 are thought to be transition objects, in which star formation is about to end, after which time the galaxy would take on the appearance of a dE. Studies of all the dwarfs in the Local Group (including the irregulars) show that dwarf elliptical star formation histories merge smoothly into those of Dwarf Irregular Galaxies. A useful summary might be that stars began forming in dwarf ellipticals 15 Gyr ago, but that star formation may have ceased only a few Gyr ago.

dEs as a class have a number of remarkable relations between observed properties. As mentioned above, the central or mean surface brightnesses are directly related to the total luminosity, over a range of about 8 magnitudes. The central values used for this relation are extrapolated values, so that any nuclei present are ignored. This relation is not tight, however, and some have even doubted that it exists, noting that surface brightness selection effects in galaxy searches would tend to produce such a relation. The central surface brightnesses of these tidal tails of interacting galaxies, to that of Babul and Rees which is a more ab initio scheme. Babul and Rees have shown that the collapse of weak density perturbations can be delayed because of the photoionizing effects of the intergalactic UV radiation field at redshifts greater than 1. Thus star formation in dwarf galaxies may have begun relatively late and may have resulted in that class of galaxies being excessively bright at intermediate redshifts, perhaps leading to the excess number of blue galaxies apparent at those redshifts. Larson showed that the more massive dwarf precursors were better able to retain gas (which otherwise would have been lost via supernova explosions) and hence had longer-lived star formation epochs, resulting in higher central densities and higher metallicities. Since gas loss in self-gravitating systems cannot explain both the observed form of the decline in metallicity and surface brightness with luminosity in dEs, Dekel and Silk developed a model which included the presence of dark matter, wherein mass loss from supernova winds becomes important at a threshold value of mass and allows both stated conditions to be met. Being derived from hierarchical scenarios, the dwarfs should also predominate in areas of low density (i.e. voids), something for which there is much counterevidence for.

There are obvious connections between dEs and star-forming dwarfs (dIrrs)—low surface brightness, low metallicity, low luminosity and even similar flattening distributions. However, in detail there are problems with the idea that dEs are simply the extension of dIrrs—those galaxies that ran out of star forming gas first. As a class, dwarf ellipticals are smaller than dIrrs—there are many more large dIrrs than dEs. Thus it is hard to obtain all of the dEs by stopping the star formation and allowing the dIrrs to fade—the length scales would be wrong. (It would be possible to obtain some fraction of the dEs this way of course.) It has been difficult to compare the metallicities of dEs ([Fe/H] in general, from giant branch locations) with those of dIrrs ([O/H] in general, from ionized gas measures) to check the idea that at the same luminosity, corrected for fading for dIrrs, the two types have similar metallicities. Preliminary work does show that it is marginally possible for the observed L–Z relation of dEs to have come from that of dIrrs, but the amount of luminosity fading required is excessive. It is certainly true that dEs and dIrrs come from related progenitors, although the precise parameters separating those families is not yet known.