GALAXIES, DWARF SPHEROIDAL JEREMY MOULD Physically small and intrinsically faint elliptical galaxies are known as dwarfs. The smallest and faintest of these are referred to as dwarf spheroidal galaxies. Low surface brightness is a characteristic of dwarf spheroidals, but in this and other respects the distinction from dwarf ellipticals appears to be simply a matter of degree. LOCATION Ten galaxies define the class. Seven of these are satellites of the Milky Way. They are known by the names of their home constellations: Draco, Ursa Minor, Carina, Leo I and II, Sculptor, and Fornax. The other three are satellites of M31, and are known as Andromeda I-III. Positions of all of these galaxies are given in Table 1. The radial distances of these objects from their parent galaxies are similar to those of the globular cluster systems of these galaxies. No dwarf spheroidals are known outside the Local Group of galaxies, probably because the surface brightness of dwarf spheroidals is typically *1% of that of the night sky, and because individual giant stars in these galaxies would fall below the limit of the Palomar Observatory Sky Survey beyond the Local Group. Within the Local Group, however, satellite status seems to be a real characteristic of dwarf spheroidal galaxies. LUMINOSITY The absolute visual magnitudes of dwarf spheroidals range from Mv=-8 to Mv=-13 mag. Distances assumed in calculating these values are given in Table 1. The sources for the data in Table 1 are numerous, and cannot be cited here in full. None of their known properties except their satellite status distinguish dwarf spheroidals from the dwarf ellipticals surveyed in the Virgo cluster of galaxies. In particular, dwarf ellipticals have been found in Virgo as faint as the brightest dwarf spheroidal in the Local Group (Fornax). Neither the Virgo dwarf elliptical sample nor the local dwarf spheroidal sample is well adapted to defining the luminosity distribution of galaxies at these magnitudes. The Virgo sample is very incomplete (but still seems to be rising in number) at Mv*12; the local sample is too small to define any distribution. SIZE The effective radius of a galaxy is defined to be the radius which contains half the light. The effective radii of dwarf spheroidals range from 0.2-1.0 kpc. The ellipticity of a galaxy is 1-b/a where b is the minor, and a is the major axis of an elliptical isophote. The ellipticities of dwarf spheroidals range from 0 to 0.55. These data, from the review by Paul Hodge, are contained in column 6 of Table 1. The ellipticity of Ursa Minor is high for an elliptical galaxy, but flatter dwarf ellipticals are known in the Virgo cluster. The term "spheroidal" is truly a misnomer. MASS Measurement of the Doppler velocities of stars in dwarf spheroidal galaxies allows an estimate to be made of the mass required to bind them gravitationally within a measured volume. Although the luminosities of dwarf spheroidals span almost 2 orders of magnitude, the masses measured by Marc Aaronson and his colleagues cover a smaller range from 7x10**** 13x10*** M* The mass-to-light ratios of the two smallest dwarf spheroidals, Draco and Ursa Minor, appear to be much greater than those of the larger dwarfs. The data are summarized in column 9 of Table 1. Such large mass-to-light ratios seem to require the existence of dark matter in Draco and Ursa Minor, if we suppose that matter is distributed like light. The true distribution of mass in these galaxies, however, is quite unknown. DENSITY Within the effective radius the mean density is lowest in the Fornax galaxy: P*********M* pc**. For comparison P******** M* pc*3 in the Large Magellanic Cloud. For Draco P********M* pc*3, a density comparable to the density due to stars in the solar neighborhood. STELLAR CONTENT The dwarf spheroidal companions of the Milky Way have an interesting dual character. On the one hand, galaxies such as Ursa Minor have color magnitude diagrams almost indistinguishable from those of globular clusters. On the other hand, there are systems like Carina, in which there is a considerable stellar population of intermediate age. The other five dwarf spheroidals are a blend of these characteristics-some are more like Ursa Minor, others are more like Carina. As shown in column 10 of Table 1 the fraction of the light in each galaxy that comes from a population of age between 1 and 10 billion years ranges from 5% for Sculptor up to 70% for Carina. Indicators of an intermediate age population include the presence of asymptotic giant branch (AGB) carbon stars, anomalous Cepheid variable stars, and an overluminous main sequence turnoff. Table 1 contains the latest count of anomalous Cepheids (AC) (column 11), and indicates whether or not a main sequence (MS) turnoff, more luminous and younger than that of globular clusters, is seen (column 12). THE INTERSTELLAR MEDIUM Stringent upper limits have been set on the mass of neutral hydrogen in six of the seven Local Group dwarf spheroidal galaxies (see column 13 of Table 1). These upper limits are ***** M* for Fornax and Leo I and II. For Sculptor the data of Gillian Knapp and her colleagues show a small positive perturbation in the baseline at the now accurately known heliocentric velocity (107 km s**). If this detection is real, Sculptor may contain *********** M* of neutral hydrogen. The upper limits on H I in Draco and Ursa Minor are much lower: 68 and 280 M*, respectively. Mass loss from dying stars will readily furnish an interstellar medium exceeding these limits in a billion years. However, given the measured wind velocities from the envelopes of red giants, and the shallow gravitational potential of dwarf spheroidals, it is likely that such material is able to escape the galaxy as a wind on a considerably shorter time scale. CHEMICAL COMPOSITION It is generally supposed that the chemical composition of the stellar systems of Population II is *75% hydrogen by mass, *25% helium, and less than 1% "heavy elements" (i.e., everything else). If the heavy-element mass fraction is denoted by Z,Z/Z* ranges from ** to *** in dwarf spheroidals. Individual values are given in column 14 of Table 1. There is also evidence for a modest variation in Z from star to star in these galaxies. More luminous dwarf spheroidals have higher values of (Z), and in fact the review by Aaronson shows a linear relation between absolute magnitude Mv and metallicity (i.e., log(Z)). This result is loosely termed the "mass-metallicity relation" for elliptical galaxies and smoothly connects all dwarf ellipticals studied to date. There is a plausible extension to giant elliptical galaxies. STAR FORMATION HISTORY In the chemical enrichment history of a galaxy a generation of massive stars produces heavy elements in millions of years by means of Type II supernovae, but a generation of intermediate mass stars takes characteristically a billion years to return its products to the interstellar medium. Although the spread in Z seen in all dwarf spheroidals (and also in the massive globular cluster w Centauri) may have its origin in the first few generations of massive stars, it is clear that an isolated galaxy with an escape velocity as low as 10-20 km s** cannot retain its interstellar medium for many such generations. Ejection of the gas before more than a few percent of it has been turned into stars can account for the low metallicity of dwarf spheroidal galaxies. Ejection of the interstellar medium after a few million years is inconsistent, however, with the existence of intermediate age populations in a number of dwarf spheroidals. A more acceptable possibility is to suppose that dwarf galaxies are produced by the aggregation of many gas-rich clouds (perhaps similar to the Lyman- * clouds known to exist at earlier epochs). Each merger event stimulates a little more star formation, and the galaxy grows, while at the same time the interstellar medium is enriched in heavy elements. This accumulation provides an alternative basis for a mass-metallicity relation. In this scenario we have to suppose that, for the first few billion years of a galaxy's history, gravity wins over the distruptive effect of massive star formation, but that eventually the balance is reversed, and the interstellar medium is ejected for good. STRUCTURE AND DYNAMICS Classicaly, the idealized structure of a dwarf spheroidal galaxy is an isothermal sphere whose gravitational potential is truncated by the tidal field of the Milky Way. Core radii and tidal radii of such models, which are known as King models (after Ivan R. King), are given in columns 7 and 8 of Table 1. More recently it has been noted that an exponential surface brightness distribution can also yield an acceptable fit: This is not a strong constraint on the structure of a dwarf galaxy, because the visible galaxy covers rather few scale lengths. Galaxies with exponential disks are generally supported against gravitational collapse by rotation. Rotation has only been detected, however, in the Fornax galaxy. Substructure in the star distribution has also been detected in Fornax. Dark Matter At the present time the nature of the dark matter which constitutes most of the mass of spiral galaxies is quite unknown. Conceivably it is baryonic (e.g., Jupiters); alternatively, it could be self-gravitating elementary particles of either known or unknown form. If the particles are massive neutrinos, for example, the Pauli exclusion principle of quantum mechanics prescribes a maximum number density for a given velocity dispersion, *. A lower limit on the mass of the neutrino follows from the mass that they contribute to bind the galaxy. This lower limit scales like ****. Therefore dwarf galaxies place the strongest lower limit. If the measured velocity dispersion of Draco and Ursa Minor is due to the presence of such dark matter, the mass of such hypothetical neutrinos must exceed **500 eV. Such large masses violate a number of other constraints. Additional Reading Aaronson, M.(1986). The older stellar population in dwarf galaxies. In Star Forming Dwarf Galaxies and Related Objects, D. Kunth, T.X. Thuan, and J. Tran Thanh Van, eds. Editions Frontieres, Gif-sur-Yvette. Aaronson, M.(1986). Local group dwarf galaxies: The red stellar population. In Stellar Populations, C. Norman, A. Renzini, and M. Tosi, eds. Space Telescope Science Institute Symposium Series, Vol.1. Cambridge University Press, Cambridge, p. 45. Aaronson, M. and Olszewski, E.(1987). The search for dark matter in Draco and Ursa Minor: A three year progress report. In Dark Matter in the Universe, J. Kormendy and G.R. Knapp eds. Reidel, Dordrecht, p. 153. Hodge, P.(1971). Dwarf galaxies. Ann. Rev. Astron. Ap. 9 35. Knapp, G., Kerr, F., and Bowers, P.(1978). Upper limits to the H I content of the dwarf spheroidal galaxies. Astron. J. 83,360. Sandage, A., Bingelli, B., and Tammann, G.(1985). Morphological and physical characteristics of the Virgo cluster: First results from the Las Campanas photographic survey. In The Virgo Cluster of Galaxies, ESO Conference and Workshop Proceedings No. 20, O.-G. Richter and B. Bingelli, eds. European Space Observatory, Garching bei Munchen, p. 239. See also Galaxies, Elliptical; Galaxies, Local Group.