Metallicity distribution function

The metallicity distribution function (MDF) is an indicator of the enrichment history of a system. Large samples can be obtained [4,5] using low resolution... 

The metallicity distribution function (MDF) in galaxy halos contains other important clues about the process of galaxy formation. In recent years, a wealth of MDF data have been collected for the Milky Way (eg. [3], [4]), M3I (eg. [I]),... 

Fig. 8.20. Metallicity distribution function of globular clusters (crosses indicating error bars and bin widths) and halo field stars (boxes), after Pagel (1991). Copyright by Springer-Verlag.

Fig. 8.22. Metallicity distribution function for giants in the Galactic bulge, after Zoccali et al. (2003), fitted with a Simple model having a yield of Z .

Thus the mass of stars and that of the whole system steadily increase while z soon approaches 1 and the stellar metallicity distribution is very narrow (see Fig. 8.24). The accretion rate is constant in time if the star formation rate is any fixed function of the mass of gas. Other models in which the accretion rate is constant, but less than in the extreme model, have been quite often considered in the older literature (e.g. Twarog 1980), but are less popular now because they are not well motivated from a dynamical point of view, there is an upper limit to the present inflow rate into the whole Galaxy of about 1 M0yr 1 from X-ray data (Cox Smith 1976) and they do not provide a very good fit to the observed metallicity distribution function. 

The Hull cell cathode has a continuous variation of current density along its length, and there are equations which give the primary current density at any point not too near the end. If the local thickness is measured at two points for which P is known, Tcan be calculated. The real current distribution is a function of cathode and anode polarisation as well as of the resistance of the electrolyte. The metal distribution ratio will be... 

In the discussion of hypoelectronic metals in ref. 4, the number of ways of distributing Nv/2 bonds among NL/2 positions in a crystal containing N atoms with valence v and ligancy L was evaluated. The number per atom is the Nth root of this quantity. Structures for which the number of bonds on any atom is other than v-l,v, orv + l were then eliminated with use of the binomial distribution function [only the charge states M+, M°, and M are allowed by the electroneutrality principle (5)]. In this way the following expression for rhypo, the number of resonance structures per atom for a hypoelectronic metal, was obtained ... 

In this paper we have endeavored to present a review of some characterization methods of metal nanoclusters, focusing, among the extremely vast array of methods and techniques, on two of them, XRD and TEM, on which we have direct experience, and emphasizing also some recent developments, like the radial distribution function in XRD and EH in TEM. 

The distribution function for globular clusters is somewhat more complicated, as there appear to be two (probably overlapping) distributions corresponding to the halo and the thick disk, respectively. These have been tentatively fitted in Fig. 8.20 with a Simple model truncated at [Fe/H] = —1.1 for the halo and a model for the thick disk clusters with an initial abundance [Fe/H] = —1.6 (the mean metallicity of the halo) and truncated at [Fe/H] = —0.35. The disk-like character of the more metal-rich clusters is supported by their spatial distribution (Zinn 1985). Furthermore, there is a marginally significant shortage of globular clusters in the lowest... 

Errors in the use of the instantaneous recycling approximation need to be considered, depending on the assumed history of star formation and mass ejection. After long times, e.g. 15 Gyr, low-mass stars eject relatively metal-poor material and modify the distribution in a similar way to what happens in some of the inflow models discussed below. However, it is still rather doubtful whether any Simple model can explain the abundance distribution function as well as satisfying other constraints. 

This generates a series of abundance distribution functions with M as a parameter (Fig. 8.25). As M increases, the distribution becomes more like a Gaussian (i.e. a parabola on this logarithmic plot) on the low-metallicity side of the peak (although there is still always a low-metallicity tail), and the peak itself shifts to lower metallicities in units of the yield. 

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