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ASTR 5610, Majewski [SPRING 2020]. Lecture Notes

ASTR 5610 (Majewski) Lecture Notes


You should begin making your way through Binney & Merrifield's Chapter 5. We will be hotting most of the topics in that Chapter 6 this semester.

(Very) Brief Review of Stellar Structure and Evolution

Fundamentals of Stellar Interiors and Evolution

Theory of stellar structure and evolution obviously important to understanding stellar populations and evolution of clusters and galaxies.

Lives of stars governed by the basic principle by which larger structures, like star clusters and galaxies, also live:

Let heat flow outward so that inner regions may become denser and, therefore, even hotter.

Basic elements of standard stellar structure theory:

Vogt-Russell Theorem

Through the Vogt-Russell theorem we can theoretically predict where stars should be in the "theoretical HR diagram" of effective temperature and bolometric luminosity.

Uncertainties in the Models

The above process is responsible for the major sequences in the typical color-magnitude (or HR) diagram of a stellar population.

However, there are several details that lead to important variations in the character of the observed stellar spectrum and position on the CMD.

Generally each of these is poorly understood at present -- at least the theories about them are presently more rudimentary.

These create uncertainties in the true structures of stars, and these uncertainties accumulate as models evolve (i.e., once an uncertainty in the theory is introduced at a point in evolution, all subsequent phases of evolution are uncertain in the theory).

Generally these effects are not predicted, but used as free parameters:

Red Giant Branch, Mass Loss and the Horizontal Branch

The subgiant branch is occupied by stars in hydrogen shell burning, but not yet fully convective envelopes.

An important phase in the life of < 8 solar mass stars is the red giant branch.

The vertical RGB, where a star moves up the Hayashi track, is a shell hydrogen burning star that has a fully convective envelope.

(The Hayashi track in the HR diagram is a nearly vertical downward path followed by contracing pre-main-sequence stars, or upward vertical path for expanding post-main-sequence, red giant stars; the vertical track is a result of the star not being out of hydrostatic equilibrium and heavily convective.)

When a star with mass less than about 2 solar masses evolves to the tip of the RGB, it undergoes a helium flash, when the triple alpha nuclear fusion reaction is initiated.

This explosive phenomenon for lower mass stars causes an almost immediate loss of mass.

Post-HB Evolution

Stars on the HB slowly brighten above the ZAHB in the CMD as they evolve.

Once a star exhausts He in the core and transitions to He shell burning, the star evolves quickly in a second red giant-like stage, called the asymptotic giant branch.

Post-AGB Evolution:

Low Mass Stars

After reaching the top of the AGB, a lower mass star sheds almost all of its remaining hydrogen.

High Mass Stars

For stars with initial masses larger than about 8 solar masses, the carbon created in helium burning can ignite, and nuclear burning proceeds in stages (onion shell model) until iron is created in the core.

Iron is the most tightly bound nucleus, so its creation signals the end of exothermic nuclear fusion.

Runaway core implosion releases energy that may lead to supernova and formation of neutron star or black hole in the center of the star. Boom.

Summary of (Major Sequences in CMDs)=(Phases in the Evolution of a Star)
Table from Binney & Merrifield.
From Carroll & Ostlie.

Simple Numerical Relations

Though the above evolutionary description comes from large-scale computer simulations, there are some simple rule of thumb, order of magnitude approximations useful to remember.

ZAMS Mass-Luminosity Relation

On the ZAMS, the luminosity of a star goes roughly as 3.5.

ZAHB Magnitude

The luminosity of HB stars is roughly 50L (independent of mass).

This corresponds to an absolute visual magnitude of roughly +0.5.

Main Sequence Lifetime

The Main Sequence lifetime of a star is fixed by the length of time that its luminosity can be supported by thermonuclear conversion of H to He.

Horizontal Branch Lifetime

A similar argument can be used to obtain the HB lifetime.

Supergiant Lifetime

And for supergiants:

More accurate estimates for these lifetimes are obtained from evolutionary models, and are given in Binney & Merrifield.

Relative Number of Stars in Different Evolutionary Phases for Simple Stellar Population

The post-MS phases of stellar evolution are typically much shorter than the MS lifetime for that same star.

Under these circumstances, the relative number of stars, Ni , in any particular evolutionary phase, i , is given by the relative amount of time τi a star of mass (MSTO) spends in that phase.

It can also be shown (HW problem) that the contribution of phase i to the integrated light of a Simple Stellar System is proportional to the amount of fuel a star burns when it is in that phase.
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All material copyright © 2003, 2006, 2008, 2010, 2012, 2014, 2016, 2018, 202, 2020 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 551 and Astronomy 5610 at the University of Virginia.