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<!DOCTYPE html>
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<head>
<!-- 2025-02-06 Thu 09:04 -->
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<title>400A - Evolution of stars</title>
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stellar evolution, 400A, University of
Arizona, Steward Observatory, stars,
theoretical astrophysics">
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<p>
<b>Materials</b>: Onno Pols' lecture notes Chapters 7-9-11, Kippenhahn's book
Chapters 22-24, 26-33, Hansen, Kawaler, Trimble book, Chapter 2,
<a href="http://user.astro.wisc.edu/~townsend/static.php?ref=mesa-web">MESA-web</a>.
</p>
<div id="outline-container-org9c944bd" class="outline-2">
<h2 id="org9c944bd"><a href="#org9c944bd">In class activity: evolution of stars</a></h2>
<div class="outline-text-2" id="text-org9c944bd">
</div>
<div id="outline-container-org79e7df1" class="outline-3">
<h3 id="org79e7df1"><a href="#org79e7df1">Aims</a></h3>
<div class="outline-text-3" id="text-org79e7df1">
<p>
In this class activity, you will work together in groups of three to
piece together all the things we have learned so far and describe the
evolution of single, non-rotating stars with <i>your</i> <code>MESA-web</code> models!
</p>
<p>
The aim is for you to be able to:
</p>
<ol class="org-ol">
<li><b>distinguish physical features from numerical artifacts</b></li>
<li>give a physical explanation for the features of the evolution of the star
(e.g., on the HR diagram), based on the interior structure and evolution</li>
<li>appreciate the timescales corresponding to the various features</li>
<li>being able to describe and explain the qualitative differences
between stars of different masses (and maybe even metallicity!)</li>
</ol>
<p>
This is often what we do with stellar models in research: we setup a
numerical experiment on the computer (in this case a crowdsourced grid
of many masses across the class), and then look at the results with a
copious dose of healthy skepticism and trying to filter out the
numerical artifacts from physical features of the models to build
understanding!
</p>
</div>
</div>
<div id="outline-container-org5d987d0" class="outline-3">
<h3 id="org5d987d0"><a href="#org5d987d0">Brief description of pgstar movies created by <code>MESA-web</code></a></h3>
<div class="outline-text-3" id="text-org5d987d0">
<p>
Since you downloaded your models from <a href="http://user.astro.wisc.edu/~townsend/static.php?ref=mesa-web-submit">MESA-web</a>, it makes sense to
start trying to understand your model using the <code>*.mp4</code> movie it
produces for you.
</p>
<figure id="org3ce8146">
<img src="./images/MESA-web_pgstar.png" alt="MESA-web_pgstar.png" width="100%">
<figcaption><span class="figure-number">Figure 1: </span>snapshot of a <code>MESA-web</code> generated movie for the evolution of a 1M<sub>☉</sub> star.</figcaption>
</figure>
<p>
There is a lot going on here! Below I describe the panels in the
movies produced by <code>MESA-web</code>. Note the clock for physical time on the
very top left, and the number of timestep marked on the top right.
</p>
<p>
<b>N.B.:</b> if you set up a full blown MESA installation you can customize
<i>all</i> of these!
</p>
<p>
<b>N.B.:</b> large excursions on a plot can take a very short physical time
(but a long computational time and many timesteps), viceversa
long-duration phases may take few large timesteps and <i>not</i> produce
large variations on these plots!
</p>
</div>
<div id="outline-container-orgae8e3f7" class="outline-4">
<h4 id="orgae8e3f7"><a href="#orgae8e3f7">Top right panel: abundance panel</a></h4>
<div class="outline-text-4" id="text-orgae8e3f7">
<p>
This shows log<sub>10</sub>(X<sub>i</sub>) with X<sub>i</sub> the mass fraction of the i-th isotope as
a function of mass coordinate (m=0 is the center, m=M the surface).
</p>
</div>
</div>
<div id="outline-container-orge86499a" class="outline-4">
<h4 id="orge86499a"><a href="#orge86499a">Bottom right panel: HR diagram</a></h4>
<div class="outline-text-4" id="text-orge86499a">
<p>
Showing absolute bolometric luminosity vs. effective temperature.
</p>
</div>
</div>
<div id="outline-container-org1ec6a3a" class="outline-4">
<h4 id="org1ec6a3a"><a href="#org1ec6a3a">Middle top panel: Kippenhahn diagram</a></h4>
<div class="outline-text-4" id="text-org1ec6a3a">
<p>
This shows the internal mixing processes and the energy generation as
a function of "time" (on the x-axis) and mass coordinate (y-axis):
each vertical line is effectively a snapshot at fixed time, the bottom
is the center, and the top is the surface.
</p>
<p>
Light blue indicates regions of the star where there is convection,
white shows convective boundary mixing (a.k.a. "overshooting",)
purple indicates thermohaline mixing, gray (if any) indicates
semiconvection. Red regions (which <i>can</i> be hidden behind the mixing)
indicate ε<sub>nuc</sub>>0, dark blue region indicate regions of strong neutrino
cooling (ε<sub>ν</sub> ≥ ε<sub>nuc</sub>). Some lines plotting M<sub>tot</sub>, and mass
of the Helium, CO etc. cores may also be ploted.
</p>
<p>
The x-axis here is actually the timestep number. <b>N.B.:</b> Δ t<sub>n</sub> can
vary a lot with n, so this is not a linear mapping between physical
time and timestep number!
</p>
</div>
</div>
<div id="outline-container-orgea3deaa" class="outline-4">
<h4 id="orgea3deaa"><a href="#orgea3deaa">Middle bottom panel: T(ρ)</a></h4>
<div class="outline-text-4" id="text-orgea3deaa">
<p>
Annotated log-log plot of the temperature and density. The line color
indicates mixing at that location in the star, the yellow/orange/red
outline indicates the level of energy generation.
</p>
<p>
The annotations behind indicate regions of Γ<4/3 (⇒ dynamical
instability), full degeneracy (⇒ ε<sub>Fermi</sub>≅ 4 K<sub>B</sub>T), and T(ρ)
lines corresponding to the ignition of various fuels.
</p>
</div>
</div>
<div id="outline-container-org9eac045" class="outline-4">
<h4 id="org9eac045"><a href="#org9eac045">Right panel: various profiles</a></h4>
<div class="outline-text-4" id="text-org9eac045">
<p>
These three panels show P, ρ, and T as a function of mass coordinate.
</p>
</div>
</div>
</div>
<div id="outline-container-org93d6707" class="outline-3">
<h3 id="org93d6707"><a href="#org93d6707">Mass-luminosity relation revisited with models</a></h3>
<div class="outline-text-3" id="text-org93d6707">
<p>
We have already discussed <i>empirical</i> L ≡ L(M) relations based on
<i>dynamical</i> mass measurements in SB2 eclipsing binaries, and you have
derived an analytic relation for fully radiative stars (see <a href="notes-lecture-ETransport.html#org48f5345">homework
on radiative energy transport</a>). Let's now see if our models agree and
if we can understand why if they don't!
</p>
<p>
Find the "beginning of the main sequence" of your star, as in the
point where gravothermal equilibrium is achieved and L<sub>nuc</sub> = L thanks
to hydrogen core burning and report on <a href="https://docs.google.com/spreadsheets/d/17HdroCGDeq5wl5l60erJ_-Vstz5JTujuxsz1BQhns0M/edit?gid=0#gid=0">this spreadsheet</a> your mass and
luminosity at that point.
</p>
<p>
<b>Hint</b>: A very simple approximate criterion we can adopt here is
<code>center_h1</code> ≤ 99% <code>center_h1</code> at the beginning of the evolution: this
imposes that a small amount of hydrogen has burned, enough to
establish equilibrium, but we are still very close to a homogeneous
initial stellar structure. You can find the variable <code>center_h1</code> in your
<code>trimmed_history.data,</code> in which every line contains a timestep.
</p>
<figure id="org67c295f">
<img src="./images/LM_crowdsourced.png" alt="LM_crowdsourced.png" width="100%">
<figcaption><span class="figure-number">Figure 2: </span>L(M) relation obtained in class. The red points assume homogeneous stars in hydrostatic equilibrium and fully radiative, the orange points are the results reported by the students based on <code>MESA-web</code> results. Deviations at large and small masses (related to violations of the theoretical assumptions) are expected.</figcaption>
</figure>
<p>
The red dots here correspond to log<sub>10</sub>[(M/M<sub>☉</sub>)<sup>3</sup>], the L(M) relation
that can be obtained assuming hydrostatic equilibrium <i>and</i> purely
radiative energy transport. Despite this assumption, which is <i>not</i>
verified for most of the stars, the agreement between these relations
is not bad! We can barely notice two expected significant deviations:
</p>
<ul class="org-ul">
<li>at low masses we have a <i>steepening</i> of the relation: the portion of
these stars being convective is progressively larger. Assuming fully
convective transport of energy (i.e., assuming an adiabatic
temperature gradient), one can in fact derive L(M) ∝ M<sup>4</sup>, steeper
than the theoretical scaling represented here</li>
<li>at the high masses we have a <i>flattening</i>: this is because for very
massive stars their luminosity L → L<sub>Edd</sub>∝ M, therefore we
expect a progressive flattening until L(M)∝ M. This may also be
implicated in the discussion for what is the maximum mass of a star.</li>
</ul>
</div>
</div>
<div id="outline-container-org4f71974" class="outline-3">
<h3 id="org4f71974"><a href="#org4f71974">Discuss with your "mass" group</a></h3>
<div class="outline-text-3" id="text-org4f71974">
<p>
Compare your model to the models of people nearby you and explore the
data you have. You probably want to start from the movie <code>MESA-web</code>
provides. Likely, you will need to play the movie over and over,
pausing it, and trying to correlate what happens in the various panels
to build physical understanding. If needed, you can also make more
plots (of <code>trimmed_history.data</code> and any <code>profile*.data</code> file available,
remember the python module available to read the data: <a href="http://user.astro.wisc.edu/~townsend/resource/tools/mesa-web/mesa_web.py"><code>mesa_web.py</code></a>).
</p>
<p>
<b>N.B.:</b> See also the <a href="http://user.astro.wisc.edu/~townsend/static.php?ref=mesa-web-output">output description</a> on the <code>MESA-web</code> site.
</p>
<p>
Pay attention to:
</p>
<ul class="org-ul">
<li>timescales <i>and</i> timestep size</li>
<li>HR diagram</li>
<li>behavior on the T(ρ) diagram</li>
<li>composition (at surface and core)</li>
<li>Kippenhahn diagram</li>
</ul>
</div>
<div id="outline-container-org2dcc748" class="outline-4">
<h4 id="org2dcc748"><a href="#org2dcc748">Some guiding questions for inspiration</a></h4>
<div class="outline-text-4" id="text-org2dcc748">
<ol class="org-ol">
<li>where does the evolution start?</li>
<li>what is the energy source providing the luminosity L before
significant nuclear burning occurs?</li>
<li>when does (significant) nuclear burning start? How long between the
start of the run and the beginning of nuclear burning (in physical time)?</li>
<li>where does H run out in the core? How long does the H-core burning
main sequence last?</li>
<li>what is the <i>structure</i> of the star during H core burning (core vs.
envelope). and why?</li>
<li>can you physically explain the behavior of L, R, and T<sub>eff</sub> during
the hydrogen core burning main sequence phase?</li>
<li>can you explain the morphology of the end of the H-core burning
main sequence?</li>
<li>where does He core burning start?</li>
<li>is there any other nuclear burning during He core burning? And before?</li>
</ol>
</div>
</div>
</div>
</div>
<div id="outline-container-org38698db" class="outline-2">
<h2 id="org38698db"><a href="#org38698db">Clean examples</a></h2>
<div class="outline-text-2" id="text-org38698db">
<p>
Because <code>MESA-web</code> is a simple configuration meant for didactic
applications, it may produce in certain configurations a lot of
numerical noise. See <a href="https://www.stellarphysics.org/research">here</a> (scroll down to "Stellar Evolution Videos")
some clean examples for a representative low-mass star (1M<sub>☉</sub>), high
mass star (15M<sub>☉</sub>). These were also produced with MESA, but likely
configured differently than <code>MESA-web</code>.
</p>
<p>
<b>Spoiler alert</b>: find <a href="./in-class-evol-wrap-up.html">here</a> some (partial) discussion of the evolution of
stars of various mass.
</p>
</div>
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