Future Improvements

In order to apply the corrections derived here, the stellar age distribution needs to be roughly known; ideally this approach should be applied to combined colour– magnitude diagrams and chemical abundance data. While these corrections elim- inate/alleviate some degree of the bias present in observed metallicity distribu- tions, there is one main potential source for inaccuracy in the above analysis: determining the HB and BL cutoff point and the separation of the RGB from AGB stars. In other words, how to relate the models to the observed sample. As outlined in Section 2.3, the HB, RC, BL, AGB and PAGB phases were excluded from the sample, while keeping as many RGB stars included as possible. Since the position on the CMD of the HB varied with both age and metallicity, it was not plausible to employ one magnitude limit for every simulation. The colour– magnitude cutoffs are shown in the simulated CMDs available online, and visibly spread out at younger ages and higher metallicity, increasing the uncertainty in the analysis of these simulations in the dimmer magnitude range. Whenever gi- ant star samples are analysed to produce chemical evolution models, the stellar lifetime biases should be analysed using identical selection criteria to the data sample.

The equations derived to RGB stars from the simulations were determined through visual inspection of the separation between the RGB and AGB tracks,

2.5. DISCUSSION 55 as well as the locations of any BL, RC and any PAGB stars, for each CMD. To maintain consistency, the separation equations were all given as polynomial or logarithm functions. The separation between the AGB and RGB was less pronounced at younger age ranges (0–1 and 1–2 Gyr), but at higher metallicities, the older stars on the AGB overlapped the younger RGB stars for each age limit (see Appendix A for CMD plots of the simulations).

Identifying under– and over–represented populations of red giants in observa- tions will help to improve future chemical evolution models, both for individual stars and galaxies. The stellar number distributions calculated here are used to estimate CFP evolutionary rates across different ages and metallicities in the following Chapter.

Chapter 3

Red Giant Evolutionary Rates

There are many factors to consider when mapping stellar structure and evolution: the initial conditions of the star, the complex processes that take place within the star, and the timescales on which they occur. The conditions in stellar interiors are vastly different to those we can create in a laboratory, and the effects of many stellar processes occurring are subtle and difficult to detect. As such, modelling certain rapid stages in stellar evolution can be difficult and uncertain. The relative numbers of highly evolved, low–mass stars as a function of temperature and luminosity can be analysed as a way to gauge the timescales for structural changes preceding helium ignition and the subsequent return to hydrostatic equilibrium.

As explained in Chapter 2, the position of an RGB star in the CMD depends not only on the metallicity of the star, but also on stellar age. Investigating how these factors interact within a well–defined region of the CMD can aid in determining relative stellar numbers in different stages of evolution, and thus estimate evolutionary rates. This research is expected to identify which stellar populations will provide the most likely combination of age and metallicity for CFP stars, therefore shaping the kinds of environments in which they are likely to be found.

This research combines simulated data from two separate models to investigate

CFP evolutionary rates. The first model is the parsec isochrones used in the

previous Chapter and follows on from those results. The second model used

here is a set of evolutionary tracks from mesa (see below) simulations. While

evolutionary tracks are easier to derive evolution times from, isochrones represent data much similar to what can be gleaned from observations.

3.1. MIST EVOLUTIONARY DATA 57

3.1

MIST Evolutionary Data

While parsec supplies isochrones covering the advanced stages of stellar evolu-

tion required in this analysis, it only provides stellar evolutionary tracks up to the TRGB and after the star reaches ZAHB. It is not uncommon for stellar evolution models to completely skip the CFP due to the high numerical complexity and vastly smaller timesteps required, compared with other evolutionary stages. For this reason, the open–source, online resource Modules for Experiments in Stellar

Astrophysics (mesa; Paxton et al., 2011, 2013, 2015) was employed here. Specif-

ically, evolution tracks of low–mass stars from the RGB through to HB or RC,

were generated using mesa Isochrones and Stellar Tracks (mist; Dotter, 2016;

Choi et al., 2016). The input physics for mesa (such as EoS, opacity, diffusion,

reaction rates, and boundary conditions) is organised into independent modules that generate and export data. The main advantage of this arrangement is that trialling different input physics is simple (Paxton et al., 2011).

mist uses the one–dimensional stellar evolution package MESA star to pro-

duce evolutionary tracks, and from those, isochrones (detailed in Dotter (2016)).

MESA starsolves equations for the composition and fully coupled structure simul-

taneously (Paxton et al., 2011). mistcovers an age range of 5≤log(age) ≤10.3,

a mass range of 0.1≤M/M≤300 and a metallicity range of −2≤[Z/H]≤0.5,

from PMS to either white dwarf cooling or the end of carbon–burning, depending on stellar mass (Choi et al., 2016).

Synthetic photometry data from mist version 1.1 were downloaded1 in the

form of stellar evolutionary tracks for this work. As with the isochrone data from parsec (see Chapter 2), bandpasses ACS I–band (F814W) and V–band

(F555W) from the HST ACS filter set were used here. Initial ν/νcrit was set

to zero (rather than the default of 0.4), as parsec does not include rotational

effects, and no extinction was implemented. Evolutionary tracks were created

for each metallicity [Fe/H] = −2,−1.6,−1,−0.6,0,+0.4, at mass intervals of

0.01M in the range 0.8-2 M . Currentlymistmodels are solar–scaled, meaning

that [Fe/H]≡[M/H]. Since different solar abundance values are used in _parsec

(Z =0.0152) and mist (Z =0.0142), the logarithmic values relative to solar

abundances were not changed (see Section 3.1.1 for details). Stellar evolution points within each of the six age ranges (1–2, 3–4, 5–6, 7–8, 9–10 and 11–12 Gyr) were then selected for each metallicity to form 36 evolution tracks equivalent to

1

the simulations using the _parsec ishochrones. The 0.5–1 Gyr age range was omitted in this analysis, as opposed to in Chapter 2, because low–mass stars this young would only be early–stage red giants, rather than near the onset of their CFP.