# Galaxies Lecture 13

Now we’re going to back up a little bit and talk some more about the components of galaxies. We start with stellar evolution.

• Main Sequence
• H${\displaystyle \to }$He via pp chain or CNO cycle
• Convection mixes H and He.
• He is heavier and sinks to center
• HR diagram
• He flash only happens in low mass stars when He core becomes degenerate before He can ignite.
• Pre-MS branch (Hiyashi strip) varies L and R to maintain constant T.
• ${\displaystyle M_{V}\left({horizontal \atop branch}\right)=0.17\left({Fe \over H}\right)+0.82}$, so higher metallicity means dimmer stars.
• Tip of the Red Giant Branch (RGB) changes little with stellar type, so it can indicate an approximate distance.
• Initial Metallicities
• Set via Big Bang nucleosynthesis theory.
• Observationally, a star hot enought ot excite He will also create He.
• Using young, low-mass stars, we have measured ${\displaystyle Y={He \over H}=0.228\pm 0.005}$, and ${\displaystyle {dM_{bol} \over dY}=3}$ (bolometric magnitude = integrated over frequency) for fixed z, T (metallicity temperature).
• We can measure Y in the ISM via radio recombination lines: ${\displaystyle n=110\to n=108}$ in H and ${\displaystyle He^{+}}$.
• ${\displaystyle t_{life}={\alpha mc^{2} \over L}}$, where ${\displaystyle \alpha }$ is a fudge factor.
• ${\displaystyle H\to He}$ takes ${\displaystyle 10Gyr{{M \over M_{\odot }} \over {L \over L_{\odot }}}}$.
• ${\displaystyle H\to Fe}$ takes ${\displaystyle 0.18Gyr{1 \over {L \over 1000L_{\odot }}}}$. This is independent of mass because stars only burn up to the Chandrasekhar limit.
• Horizontal Branch (He burning) takes 0.1 Gyr.
• Instability Strip
• ${\displaystyle \kappa }$ (opacity) instability sets a vertical strip of instability in HR diagram, which covers a wider range of temperatures at higher luminosities.
• Normally, as temperature increases, opacity decreases, allowing the extra heat out.
• Near the ionization limit, opacity increases with temperature, causing heating, which builds up pressure and expands the star.
• The period of this expansion is roughly ${\displaystyle {r_{*} \over c_{s}}}$.
• ${\displaystyle P\left({\rho \over \rho _{0}}\right)^{\frac {1}{2}}=Q\sim {1 \over {\sqrt {G\rho _{0}}}}\sim 1hr}$, where ${\displaystyle Q}$ is a constant.
• The fundamental mode of expansion is lowest mode: the whole star expands. However, there are harmonics to radial expansion, and interior zero points, so that only the outer layers of the star expand.
• Solar Oscillations are not large scale, and are sensitive to conditions inside the star.
• Cepheids have both fundamental and overtone oscillations. The period-luminosity rlation is tight in K-band, but wider at B, V.
• Nuclear Physics
• There are more neutrons in heavier elements
• ${\displaystyle ^{56}Fe}$ is the most stable, but can get heavier elements with fusion as well.
• ${\displaystyle \alpha +\alpha }$ makes it easiest to get an even mass-number.
• neutron capture in high-mass stars give other elements.
• S process (slow) absorbs ${\displaystyle n^{0}}$ and then ${\displaystyle \beta }$-decays into the next element up
• R process (rapid) absorbs lots of ${\displaystyle n^{0}}$ and the ${\displaystyle \beta }$-decays.
• the number of elements depends on initial metallicity, neutron cross-section, and radioactivity.
• Heavy elements are dispersed into the ISM via stellar winds, PNe, SN (Type II, also Ib, Ic) core collapse, and SN Type Ia
• Population Evolution
• Can use known ages of stars to study population ages and histories.
• Age and metallicity can be indicators of the historical star formation rate.
• In the Local Group:
• dSp, dE have no evidence of recent star formation; old populations
• Carina has 3 episodes of star formation; how was the gas replentished?
• Irr have on-going star formation and young populations; how is gas maintained when SN winds eject it?