Abundance distribution function

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. 

Fig. 8.25. Theoretical abundance distribution functions according to Lynden-Bell s Best Accretion Model for different values of M, after Pagel (1989b).

Fig. 8.26. Oxygen abundance distribution function for disk stars. Data deduced from observation are shown by the boxes (same as in Fig. 8.23, after Sommer-Larsen 1991a) and by the dotted line and curve at lower left (after Beers Sommer-Larsen 1995). The solid curve shows the distribution given by the model of Pagel and Tautvaisiene (1995).

Fig. 8.40. Magnesium abundance distribution functions for the thick and thin disks. Histograms Fe/H distributions from Wyse and Gilmore (1995) converted to Mg/H from the relations found by Fuhrmann (1998). Curves dashed, simple inflow model (Eqs. 8.46 to 8.52) for the thick disk dotted, prompt initial enrichment model plus inflow for the thin disk short-dash-dotted, inflow model without PIE long-dash-dotted, PIE without inflow. After Pagel in E. Vangioni-Flam et al. (2001). Copyright by World Scientific.

Neglecting the variation in the denominator of Eq. (8.39), show that the abundance distribution function in Clayton s inflow model peaks in the neighbourhood of z = 1. 

Show that in Larson s extreme inflow model with initial abundance Z0 = 0, the abundance distribution function is given by... 

Regardless of the details concerning self-enrichment and winds, the existence of isolated star formation bursts will also affect the iron-oxygen and iron-a relations, introducing scatter in Fe/O and possibly gaps in the iron abundance distribution function. When the interval between successive bursts exceeds the evolution time for SN la (maybe about 1 Gyr), iron will build up in the ISM resulting in an enhanced Fe/O ratio in the second burst so that one can end up with [Fe/O] > 0 (Gilmore Wyse 1991) see Fig. 8.7. 

Unlike the age-abundance relation, the distribution function of stellar abundances of primary elements is independent of past rates of star formation as long as instantaneous recycling holds, and this makes it a potentially powerful clue to the evolutionary histories of stellar populations. 

Figure 8.19 shows an estimate of the distribution function of oxygen abundances among field stars of the Galactic halo and Fig. 8.20 shows the iron abundance... 

Fig. 8.19. Distribution function of oxygen abundances among halo field stars taking [Fe/H] from Fig. 8.15 and assuming an Fe-O relation similar to those in Fig. 8.5, after Pagel (1992b). With kind permission from Kluwer Academic Publishers.

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... 

Besides the carbon cluster ions, carbide cluster ions are formed in different plasmas with remarkably high ion intensities. The abundance distribution of these carbide cluster ions as a function of cluster size has been observed to be very similar using the different sohd-state mass spectrometric methods, with higher intensities for cluster ions with even numbered carbon atoms than for neighbouring... 

Proteomics Proteins Yes Measures abundance, distribution, posttranslational modifications, functions, and interactions of cellular proteins... 

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