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Publications of the Astronomical Society of the Pacific 97:1058-1064, November 1985

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Publications of the Astronomical Society of the Pacific 97:1058-1064, November 1985 Publications of the Astronomical Society of the Pacific 97:1058-1064, November 1985 IMPLICATIONS OF THE DWARF SPHEROIDAL GALAXY MASS-METALLICITY RELATION GRAEME H. SMITH Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, 5071 West Saanich Road, Victoria, BC V8X4M6, Canada The presence of a mass, metallicity relation among the dwarf spheroidal galaxies is taken to mean that these systems were able to support a degree of chemical enrichment. The properties of this relation are discussed in terms of a model which assumes that internal chemical evolution of the dwarf spheroidals was promoted by supernova activity, which at the same time, however, caused a gradual loss of mass from these galaxies. Such a model, which was first proposed by Hartwick to explain the metal abundance distribution among the Galactic globular clusters, can account for the dwarf spheroidal mass, metallicity relation if it is assumed that the present mass of these systems is proportional to their initial masses Síl as 3¾ ^ â)î7/4. By assuming a power-law dependence of 3ft on the proto-cloud radius it is inferred that the most massive dwarf spheroidals formed from the densest clouds. This is in accord with the observation that the present surface brightness of dwarf spheroidals increases with increasing mass. The observed slope of the dwarf spheroidal mass, metallicity relation is significantly different from current estimates of this slope for elliptical galaxies. It is suggested that this difference implies that dwarf spheroidals and ellipticals had different formation histories, in accord with Kormendy's observation that these two types of systems exhibit different trends between surface brightness and luminosity. Key words : dwarf spheroidals-elliptical galaxies-chemical evolution models I. Introduction model is used to provide possible inferences about some The presence of heavy-element variations within some of the properties of the proto-clouds from which the dwarf of the dwarf spheroidal (Dsph) galaxies, e.g., Draco (Zinn spheroidals formed, while in Section V the dwarf 1978; Kinman, Kraft, and Suntzeff 1980; Stetson 1984; spheroidals are compared with elliptical galaxies. Smith 1984; however, see Bell 1985), Fornax (Zinn and II. The Data Persson 1981; Buonanno et al. 1985), and Sculptor (Norris and Bessell 1978; Smith and Dopita 1983; Da Costa 1984), Data on the mean metal abundances and integrated suggests that these objects have undergone some level of magnitudes of the dwarf spheroidal companions to the internal chemical enrichment. Measurement of the metal Galaxy, as well as NGC 147 and NGC205, have been abundances of the dwarf spheroidals has been an active taken from the literature and collected in Table I, along area of recent research, and it is now apparent that a luminosity, mean metallicity correlation exists among Table I Luminosity and Metallicity Data for Dwarf Galaxies these galaxies (see, e.g., Aaronson and Mould 1985; Zinn 1985; for a review of this material). The existence of such a relation adds further support to the hypothesis of dwarf Galaxy M [Fe/H] spheroidal self-enrichment. The Galactic globular clus- NGC 205 -16.5 1 -0.85 0.282 ters by contrast show no such correlation, a fact which has NGC 147 -15.1 1,2 -1.20 0.126 been taken as evidence that the majority of clusters did Fornax -12.9 3 -1.4 0.079 not produce their own metals, but merely acquired them Leo I -11.4 3 -1.85 as a consequence of forming from preenriched halo gas. 0.028 Hartwick (1976, 1983), and Searle and Zinn (1978), have Sculptor -10.8 3 -1.85 0.028 demonstrated that relatively simple models of chemical Leo II -10.2 3 -1.95 0.022 evolution can account for the abundance distributions Carina -9.2 3 -1.9 0.025 among Galactic halo stars and globular clusters (see Bond Ursa Minor 7 -2.25 0.011 (1981), however, for an alternative conclusion). Following Draco 7 -2.24 0.011 from these comparisons, the present paper aims to com- pare the predictions of these models with a mass, metal- References 1) Mould, Kristian, and Da Costa (1984). licity relation derived in Section II for the dwarf 2) Mould, Kristian, and Da Costa (1983). 3) Aaronson and Mould (1985). spheroidals. A review of these models, together with a 4) Buonanno et al. (1985). 5) Da Costa (1984). mention of some of their implications for dwarf spheroidal 6) Mould and Aaronson (1983). evolution that have been previously discussed in the 7) Zinn (1985). 8) Suntzeff et al. (1983). literature, is given in Section III. In Section IV a compari- 9) Adopted by Zinn (1985) as the average of spectroscopic abundance measurements from Kinman, Kraft, and Suntzeff (1980); Stetson (1984); son between observations and the chemical enrichment and Smith (1984). 1058 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System THE DWARF SPHEROIDAL GALAXY MASS-METALLICITY RELATION 1059 with the source references. A plot of [Fe/H] against Mv is well be too low, however, the critical assumption made shown in Figure 1, and illustrates the good correlation about [3W/L]V in the current work is that it is independent previously drawn attention to by Aaronson and Mould of Mv. This assumption directly affects the slope derived (1985), and Zinn (1985). Zinn in particular has empha- for the mass-metallicity relation. At present there is no sized the fact that the scatter about a line of best fit can be observational basis to either support or disprove it, and so accounted for entirely by observational uncertainty. Ear- the following discussion proceeds upon the simplest as- lier versions of this diagram with fewer data points but sumption that [Tt/L]v is constant among the dwarf which nonetheless reveal the correlation, have been dis- spheroidals. cussed by Mould, Kristian, and Da Costa (1983), and To provide some idea as to the stability of the least- Buonanno et al. (1985). Least-squares fits of [Fe/H] squares fit of equation (1) with regard to the composition against Mv, and Mv against [Fe/H], were made to the data of the data sample used, the most discrepant point, corre- in Table I, and the coefficients averaged to give the sponding to Carina, can be excluded from the sample and relation the fit repeated. The result is [Fe/H] -3.654 - 0.169MV (1) [Fe/H] = -3.756 - 0.175 Mv , This line is also shown in Figure 1. To convert this to a which differs by only Δ [Fe/H] = 0.05 from equation (1) at mass, metallicity relation the magnitudes have been con- My = -10. verted to total (stellar) masses 33¾ by adopting a globular cluster-like mass-to-light ratio of [5ÎJi/L]v = 2. Therefore, III. The Chemical-Enrichment Model with M ν,Θ ■ 4.79, A. Evolution Within a Closed System My = 5.54 — 2.5 log10 3KS A cloud which is initially gaseous and of total mass is and considered to form stars at a rate F. It is assumed that there is no delay between the formation of a massive star [Fe/H] = -4.590 + 0.423 log1() (2) and the ejection of its newly synthesized heavy elements, Equation (1) is very similar to the fit and that furthermore this enriched ejecta is immediately dispersed throughout the entire cloud. For a closed sys- [Fe/H] = -3.60 - 0.16MV tem the equations governing mass conservation, and the obtained by Zinn (1985) from a slightly different set of buildup of the heavy-element abundance within the in- parameter values for the same objects listed in Table 1. terstellar medium (ISM) are The value of [23í/L] used here is quite uncertain. v s = (ι - ß)F = -m Recent observations (Aaronson 1983; Faber and Lin 1983; G (3) Lin and Faber 1983) suggest that the dwarf spheroidals j^zTlc) = (Y + ßz)F - zF (4) may have mass-to-light ratios dissimilar from those of globular clusters. The value of 2 used in equation (2) may where S and 3WG are the instantaneous stellar and gas masses, respectively, 2: is the ISM heavy element abun- dance by mass fraction, β is the fraction of mass returned by stars to the ISM, and Y is the total mass of heavy elements returned to the ISM per mass of stars formed. The solution of equations (3) and (4) is well known to be (Searle and Sargent 1972; Pagel and Patchett 1975; Lyn- den-Bell 1975) 2;-^= -i/ In (SKg/ÏIÎ) (5) [Fe/H] where 2: is the metal abundance of stars forming when a mass fraction of the system is still gaseous, is the initial abundance, and y = Y/(l—β) is the yield, i.e., the mass of heavy elements returned to the ISM per mass of material remaining in long-lived stars. The frequency distribution of metal abundance among the stars is -10 -15 Mv f(z) = ds/dz = (l/y) expizjy) exp{—zly) , Fig. 1-The metallicity, luminosity relation for the dwarf spheroidal and dE galaxies listed in Table I. A least-squares-fitted line is also shown. where s = S/ so that the mean metal abundance is © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 1060 GRAEME H. SMITH <z) = J fzf(z)dz/ / '¡(zjdz a model well represents the abundance distribution within the Galactic halo. Following Hartwick's precepts, it is assumed that the rate of loss of gas from a system, Sí, = Zi + y(\ + In [I - ss]- In [1-S/]) ; (6) sf is proportional to the rate of star formation, F, i.e., Zf being the metal abundance of the youngest stars M = cF = -A .
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