-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathnotes-lecture-Intro.html
681 lines (602 loc) · 27.6 KB
/
notes-lecture-Intro.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2025-02-06 Thu 09:04 -->
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>400A - Introduction</title>
<meta name="author" content="Mathieu Renzo" />
<meta name="generator" content="Org Mode" />
<link rel="stylesheet" href="./css/style.css" />
<link rel="stylesheet" href="./fontawesome-free-6.7.2-web/css/all.min.css">
<meta name="keywords" content="Mathieu, Renzo, Mathieu Renzo,
stellar evolution, 400A, University of
Arizona, Steward Observatory, stars,
theoretical astrophysics">
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
displayAlign: "center",
displayIndent: "0em",
"HTML-CSS": { scale: 100,
linebreaks: { automatic: "false" },
webFont: "TeX"
},
SVG: {scale: 100,
linebreaks: { automatic: "false" },
font: "TeX"},
NativeMML: {scale: 100},
TeX: { equationNumbers: {autoNumber: "AMS"},
MultLineWidth: "85%",
TagSide: "right",
TagIndent: ".8em"
}
});
</script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
</head>
<body>
<div id="preamble" class="status">
<!-- Preamble -->
<!-- The header -->
<div class="header">
<!-- The site name -->
<div class="site-name">
<a id="top" href="./index.html">Stellar Evolution</a>
</div>
<!-- The hamburger -->
<div class="hamburger">
<div id="myLinks" class="menu">
<a href="./index.html">Home</a>
<a href="./syllabus.html">Syllabus</a>
<a href="./lectures.html">Lectures</a>
<a href="./projects.html">Projects</a>
</div>
<a href="javascript:void(0);" class="icon" onclick="HamburgerMenuFunction()">
<i class="fa fa-bars"></i>
</a>
</div>
<div class="navbar">
<a href="./syllabus.html">Syllabus</a>
<a href="./lectures.html">Lectures</a>
<a href="./projects.html">Projects</a>
</div>
</div>
<!-- scripts -->
<script>
function HamburgerMenuFunction() {
var x = document.getElementById("myLinks");
if (x.style.display === "block") {
x.style.display = "none";
} else {
x.style.display = "block";
}
}
</script>
<script>
window.onload = () => {
const toggleButton = document.getElementById("light-dark-toggle");
const body = document.body;
const html = document.documentElement;
// Check localStorage for user preference
if (localStorage.getItem("theme") === "dark") {
body.classList.add("dark-mode");
html.classList.toggle("dark-mode");
}
// Toggle theme on click
toggleButton.addEventListener("click", () => {
body.classList.toggle("dark-mode");
html.classList.toggle("dark-mode");
// Save user preference
if (body.classList.contains("dark-mode")) {
localStorage.setItem("theme", "dark");
} else {
localStorage.setItem("theme", "light");
}
});
};
</script>
<!-- end scripts-->
</div>
<div id="content" class="content">
<p>
<b>Materials</b>: chapter 1 of Onno Pols' lecture notes.
</p>
<div id="outline-container-org5e9a604" class="outline-2">
<h2 id="org5e9a604"><a href="#org5e9a604">Introduction to the course</a></h2>
<div class="outline-text-2" id="text-org5e9a604">
<figure id="org11749cd">
<img src="./images/word_cloud20250116.png" alt="word_cloud20250116.png" width="100%">
<figcaption><span class="figure-number">Figure 1: </span>Word cloud of the students' expectations for what they are going to learn in this class (Spring 2025 semester).</figcaption>
</figure>
</div>
</div>
<div id="outline-container-org7bf9cf2" class="outline-2">
<h2 id="org7bf9cf2"><a href="#org7bf9cf2">Who am I?</a></h2>
<div class="outline-text-2" id="text-org7bf9cf2">
<p>
My name is Mathieu Renzo, I have been an assistant professor here at
Steward since last year. Before, I was a postdoc in New York city (at
the Flatiron institute and Columbia University), and before that I did
my PhD at the University of Amsterdam in the Netherlands – but I am
originally from none of these places!
</p>
<p>
The topic of this course is stellar evolution, which is my research
field. More specifically, I work on the evolution of massive stars in
binary systems. These are the stars that end their lives in <i>supernova
explosions</i>, that can outshine briefly an entire galaxy. During these
explosions some of the most exotic objects in the universe are formed,
neutron stars or black holes (especially if the explosion fails!). The
massive star progenitor of these objects are found most often in
binary systems, meaning there are two stars orbiting each other, and
they can, as they evolve, interact and exchange mass and sometimes
merge. My research is strongly embedded in the topic of this course
(stellar evolution) and touches on explosion physics, X-ray binaries,
gravitational waves, etc. I will try to connect the course material to
all these topics whenever possible!
</p>
<p>
Also, my research field (and more broadly the scientific topic of this
course) is <i>very computationally oriented</i>. Throughout the course, I
will try to highlight what is the result of computer models based on
necessary (but often grossly oversimplifying) approximations and what
is more solidly grounded in observations. We will do this by having
computational exercises, that's why I asked about your confidence in
your ability to make plots in the survey. We will start the course by
going over the physical foundations, but I will also ask you to use your
own computer models too.
</p>
</div>
</div>
<div id="outline-container-org2b85069" class="outline-2">
<h2 id="org2b85069"><a href="#org2b85069">Aim of the course</a></h2>
<div class="outline-text-2" id="text-org2b85069">
<p>
<b>To understand the structure and evolution of stars and their
observational properties using known laws of physics.</b>
</p>
</div>
</div>
<div id="outline-container-orge2baa14" class="outline-2">
<h2 id="orge2baa14"><a href="#orge2baa14">Expectations</a></h2>
<div class="outline-text-2" id="text-orge2baa14">
<p>
This is a core course during your 4<sup>th</sup> year, so you are approaching the
academic threshold beyond which you will be <b>expected</b> to carry out
independent work (either in your thesis, in the future as graduate
students or highly skilled professionals).
</p>
<p>
My idea for this course is to not only provide <i>content</i> regarding
stellar physics and evolution, but also to help you develop skills as
independent researchers for your future (whether in academia or
elsewhere).
</p>
<p>
For this reason also <i>I will not check your attendance</i>. However,
during the lectures I will present things in a way that complements
the textbook(s), and you will more likely have a better understanding
if you attend. Also, as we'll discuss in a moment, in-class
participation will count for up to 20% of your final grade, so if you
want more than a B you should come <b>and actively participate</b>.
</p>
<p>
An important thing to keep in mind as we go through the semester is to
have a <a href="https://en.wikipedia.org/wiki/Mindset#Fixed_and_growth_mindsets">growth mindset</a>: we are all here to learn and improve ourselves!
Grading will particularly reward improvement, so a failure at some
point (of one homework) is just an opportunity for improvement – not
a career stopping tragedy.
</p>
<p>
Similarly, I expect everyone in the class to treat each other with
respect and kindness. We don't all come from the same background, we
don't all need to be at the same exact level to learn from each other.
Ultimately, you are here to learn some science and <i>science is a team
effort</i>. It has been proven many times over that diverse teams achieve
better results. Start practicing this now: if someone is struggling
with some material that you think you have under control, help them.
They are not slowing you down, but giving you an opportunity to verify
and deepen your knowledge by engaging with them and the difficulties
they may be experiencing. You may soon be the one in difficulty
yourself and give them a chance to "repay". In the end we will
all be better thanks to this dynamics.
</p>
<p>
Stellar evolution is also a very vast topic, and there is too much to
cover in only one semester, with many bleeding edge developments. So I
will ask <b>you</b> to teach your peers some of the topics that don't fit
within the main part of the course. You will also evaluate (and be
evaluated) by your peers. This is because the ability of giving
constructive and helpful feedback is important in science and beyond:
you will work with others and need to help them improve, and you will
receive feedback yourselves for the rest of your careers whatever they
may be. We will do this through a project, that we will discuss later.
</p>
</div>
</div>
<div id="outline-container-org759af3d" class="outline-2">
<h2 id="org759af3d"><a href="#org759af3d">Discuss syllabus</a></h2>
<div class="outline-text-2" id="text-org759af3d">
<figure id="orgc7b4ff8">
<img src="./images/QR-syllabus.png" alt="QR-syllabus.png" width="50%">
<figcaption><span class="figure-number">Figure 2: </span>Link to <a href="./syllabus.html">syllabus</a></figcaption>
</figure>
</div>
</div>
<div id="outline-container-org76e76a7" class="outline-2">
<h2 id="org76e76a7"><a href="#org76e76a7">Let's start finally talking about stars!</a></h2>
<div class="outline-text-2" id="text-org76e76a7">
</div>
<div id="outline-container-org178e2f8" class="outline-3">
<h3 id="org178e2f8"><a href="#org178e2f8">What is a star?</a></h3>
<div class="outline-text-3" id="text-org178e2f8">
<ul class="org-ul">
<li>Historical definition: <i>flickering light source in the sky with no
intrinsic motion</i> (where flickering excludes planets, and no
intrinsic motion excludes planets <i>and</i> other solar system objects
such as comets and asteroids).</li>
<li>More modern definition: <i>self-gravitating amount of gas that at some
point is sufficiently hot for nuclear fusion</i>.</li>
</ul>
<p>
Note that the requirement of nuclear fusion is <b>extremely new</b>: only
about 100 years old! A lot can be learned about stars without knowing
anything about nuclear fusion, which we will treat, but much later in
the course.
</p>
<p>
<b>N.B.:</b> Definitions often try to "pidgeon-hole" nature into specific
categories, but often nature is more elusive. In the case of the
"modern" definition of star above, there is the boundary case of Brown
Dwarfs, which are self-gravitating amount of gas that early in their
life may do some deuterium burning. This burning does not release a
lot of energy (the deuterium nucleus, a proton and a neutron bound
together, has very low nuclear binding energy), thus these objects sit
at the boundary between planets and stars.
</p>
</div>
</div>
<div id="outline-container-org018c44e" class="outline-3">
<h3 id="org018c44e"><a href="#org018c44e">What determines the properties of a (single) star?</a></h3>
<div class="outline-text-3" id="text-org018c44e">
<ol class="org-ol">
<li><b>Mass</b></li>
<li>Chemical composition</li>
<li>Presence of other stellar companion(s)</li>
<li>Rotation</li>
<li>Magnetic fields</li>
</ol>
<ul class="org-ul">
<li><b>Q</b>: what is a star made of? Can you think of a star made of something
else? Mention <a href="https://en.wikipedia.org/wiki/Cecilia_Payne-Gaposchkin">Cecilia Payne-Gaposchkin</a>.</li>
</ul>
</div>
</div>
<div id="outline-container-org137dfe2" class="outline-3">
<h3 id="org137dfe2"><a href="#org137dfe2">Observations</a></h3>
<div class="outline-text-3" id="text-org137dfe2">
<ul class="org-ul">
<li>Photometry</li>
<li>Spectroscopy</li>
<li>Astrometry</li>
<li>Asteroseismology (either through photometry or spectroscopy)</li>
<li>Neutrinos</li>
</ul>
</div>
<div id="outline-container-org17d6d97" class="outline-4">
<h4 id="org17d6d97"><a href="#org17d6d97">Parallax</a></h4>
<div class="outline-text-4" id="text-org17d6d97">
<p>
In astrophysics (and in stellar physics in particular) we still use
quantities and units that have mostly a historical justification (one
could say for "backward compatibility" to borrow software development
language).
</p>
<p>
The yearly apparent motion on the sky of stars (w.r.t. to farther
stars that are too far to exhibit this behavior) due to the orbit of
the Earth around the Sun is called <i>parallax</i>. A commonly used unit of
distance in astronomy is the <i>parsec</i> = distance of a star with a
parallax of one arcsecond:
</p>
<p>
1 pc ≅ 3×10<sup>18</sup>cm ≅ 2 × 10<sup>5</sup> AU ≅ 3 light years
</p>
<p>
This is a measure of distance that can be used for stars
with relatively small distances to the Solar system.
</p>
</div>
</div>
<div id="outline-container-orgda33ce5" class="outline-4">
<h4 id="orgda33ce5"><a href="#orgda33ce5">Proper motion and radial velocity</a></h4>
<div class="outline-text-4" id="text-orgda33ce5">
<p>
We can also see how stars move in the sky, but we need two different
techniques to measure the velocity <i>on the plane of the sky</i> (so called
proper motion), and <i>towards</i> or <i>away</i> from us (so called "radial
velocity", as in the radial direction in a sphere centered on the
observer).
</p>
<p>
But even before considering those, we need to remove all the apparent
motions due to the Earth rotation:
</p>
<figure id="org79e5e1d">
<img src="./images/night_rotation.jpg" alt="night_rotation.jpg" width="100%">
<figcaption><span class="figure-number">Figure 3: </span>Long exposure picture showing circular tracks along the north direction. These are just the reflected motion due to the rotation of the Earth. Note the stars have different colors! Credits: G. Inchingolo.</figcaption>
</figure>
<p>
We also have to remove the apparent motion due to the orbit of the
Earth around the Sun, and the motion of the Sun and solar system
across the Galaxy (which includes a component of "peculiar motion",
that is a deviation from the galactic rotation curve).
</p>
<p>
Once all that cleaning is done, we can see the intrinsic projected
motion of a star on the sky, so called <i>proper motion</i> (sometimes
indicated with μ or pm). All that requires is a long timeline (since μ
≅ arcsin((v<sub>∥</sub> × Δ t)/d) with v<sub>∥</sub> transverse
velocity (i.e., on the plane of the sky), Δ t time baseline and d
distance of the star, and a reference frame.
</p>
<p>
<b>N.B.:</b> The proper motion is an <i>angle on the plane of the sky per unit
time</i>. Converting proper motions to physical velocity requires knowing
the distance d, which is usually hard! Moreover, d is very large
typically (d ≫ 1 pc), so measuring μ requires long time baselines and
very accurate instruments.
</p>
<figure id="orgb84b9de">
<img src="./images/Proper_motion.JPG" alt="Proper_motion.JPG" width="50%">
<figcaption><span class="figure-number">Figure 4: </span>Schematic representation of the proper motion</figcaption>
</figure>
<p>
For the motion orthogonal to the plane of the sky, that is the motion
away/towards the observer, that is the so called <i>radial velocity</i> (RV)
through the Doppler shift of spectral lines (we will talk more about
these later in the course). These sometimes can be periodic and thus
caused by either pulsations of the stellar atmosphere or Keplerian
orbital motion around a (possibly unseen) companion star, or they can
be constant (on timescales much shorter than the period of the orbit
of the star around the Galactic center) and thus reveal intrinsic
motion. In general, one does not look at just one spectral line, but a
"series" of lines (e.g., the series coming from all the transitions of
electrons across energy levels of a specific ion).
</p>
<figure id="orge9821ba">
<img src="./images/Halpha_shift.png" alt="Halpha_shift.png" width="50%">
<figcaption><span class="figure-number">Figure 5: </span>Schematic representation of radial velocity shifts. Credits: Y. Gotberg.</figcaption>
</figure>
</div>
</div>
<div id="outline-container-org710e2bc" class="outline-4">
<h4 id="org710e2bc"><a href="#org710e2bc">Magnitudes</a></h4>
<div class="outline-text-4" id="text-org710e2bc">
<p>
The magnitude scale is a logarithmic scale first introduces by
<a href="https://en.wikipedia.org/wiki/Hipparchus">Hipparchus</a>, who clearly was only able to do naked-eye observations.
This explains why a logarithmic scale: the sensory responses are often
logarithmic (see <a href="https://en.m.wikipedia.org/wiki/Weber%E2%80%93Fechner_law">Weber-Fechner's law</a>). The magnitude scale was
formalized by <a href="https://ui.adsabs.harvard.edu/abs/1856MNRAS..17...12P/abstract">Pogson 1856</a>.
</p>
<p>
The magnitudes measure the energy flux from a point-like source (like
a distant star) and it is a differential measure relative to some
standard source. Hipparchus was comparing the visual brightness of
various stars visible in the sky. This is still the basis of (some)
magnitude systems. In reality. typically magnitudes are provided
integrating over a range of frequencies (photometry!) accounting for
the response of a filter as a function of wavelength T(λ):
</p>
<div class="latex" id="orgbbf1d8a">
\begin{equation}
m = -2.5\log_{10}\left(\frac{\int T(\lambda)F_{\lambda}d\lambda}{\int T(\lambda) d\lambda}\right) + m_{0} \ \ ,
\end{equation}
</div>
<p>
where m<sub>0</sub> is the reference magnitude, F<sub>λ</sub> is the monochromatic
flux of the source, and the factor of -2.5 is chosen so that the
magnitudes measured this way roughly agree with Hipparchus'.
<i>An increase of 5 magnitudes corresponds to an increase in flux
of a factor of 100</i>.
</p>
<p>
The <i>bolometric</i> magnitude is the magnitude across all wavelengths for
an idealized perfect detector (T(λ) = 1 ∀ λ). If the distance of a
source is known, we can then infer its intrinsic luminosity from this.
</p>
<p>
The <i>apparent</i> magnitude m we just defined is a measure of the actual
photon flux received from a source (e.g., a star) on Earth, but that
of course depends on how far the source is from Earth (a candle in
your hand has a higher apparent magnitude than Betelgeuse in the
sky!). Therefore, astronomer also introduced the <i>absolute</i> magnitude as
the apparent magnitude a star would have if it were at a distance of
10pc from the Sun, thus the relation between apparent magnitude m and
absolute magnitude M is
</p>
<div class="latex" id="orgea84aa9">
\begin{equation}\label{eq:abs_magn}
M - m = -2.5\log_{10}\left[\left(\frac{d}{10\mathrm{pc}}\right)^{2}\right] \ \,
\end{equation}
</div>
<p>
where d is the distance, and it is assumed there is no absorption of
light by the interstellar material.
</p>
<p>
For the reference magnitude m<sub>0</sub> there are multiple choices (and there
are many different magnitude systems because of the T(λ) and m<sub>0</sub>
choices!). For instance, typically the star Vega (α Lyrae) is used as
a standard and by definition its magnitude in U, B, and V band in the
Vega-based magnitude system is zero. So for magnitude M=0 we have a
specific (i.e., per unit frequency) radiative energy flux of 3.5×10<sup>-20</sup>
erg cm<sup>-2</sup> s<sup>-1</sup> Hz<sup>-1</sup> corresponding to a photon flux of N<sub>λ</sub> ≅
10<sup>3</sup> photons cm<sup>-2</sup> s<sup>-1</sup> Å<sup>-1</sup> for the visual band.
</p>
<ul class="org-ul">
<li><b>Q</b>: why the square within the argument of the logarithm in Eq.
\ref{eq:abs_magn}?</li>
</ul>
</div>
</div>
</div>
</div>
<div id="outline-container-org1a7356f" class="outline-2">
<h2 id="org1a7356f"><a href="#org1a7356f">Relevant physical scales</a></h2>
<div class="outline-text-2" id="text-org1a7356f">
<p>
The star we can observe best is the closest one, the Sun (☉), so a
lot of quantities are scaled to those of the Sun in stellar physics
and in astronomy more generally.
</p>
</div>
<div id="outline-container-org5d6921d" class="outline-3">
<h3 id="org5d6921d"><a href="#org5d6921d">Solar radius: R<sub>☉</sub> = 6.957×10<sup>10</sup> cm ≅ 7×10<sup>10</sup> cm ≅ 10<sup>11</sup> cm</a></h3>
<div class="outline-text-3" id="text-org5d6921d">
<ul class="org-ul">
<li><b>Q</b>: How many R<sub>☉</sub> are in 1 AU?</li>
</ul>
</div>
</div>
<div id="outline-container-org4d57f4a" class="outline-3">
<h3 id="org4d57f4a"><a href="#org4d57f4a">Solar mass: M<sub>☉</sub> = 1.98×10<sup>33</sup> g ≅ 2×10<sup>33</sup> g</a></h3>
</div>
<div id="outline-container-org93a1353" class="outline-3">
<h3 id="org93a1353"><a href="#org93a1353">Solar luminosity: L<sub>☉</sub> = 3.82×10<sup>33</sup> erg s<sup>-1</sup> ≅ 2× M<sub>☉</sub> in cgs units!</a></h3>
<div class="outline-text-3" id="text-org93a1353">
<p>
This may be one of the reasons why we still use <code>cgs</code> in astronomy,
the other one being that the constants in electromagnetism are a
bit simpler.
</p>
</div>
</div>
<div id="outline-container-org3e4c74d" class="outline-3">
<h3 id="org3e4c74d"><a href="#org3e4c74d">Solar effective temperature: T<sub>☉</sub> ≅ 5900K ≅ 6000K</a></h3>
<div class="outline-text-3" id="text-org3e4c74d">
<p>
This is the "effective temperature" of the Sun, which we will discuss
in the <a href="notes-lecture-CMD-HRD.html">next lecture</a>. It is an approximation for the temperature of the
surface below which the radiation field is isotropic - that is the
stellar interior - and above which there is a net radial flux of
photons - that is the stellar atmosphere (but photons can still move
around in any direction, it's just on average there are more moving in
the positive r direction). Stars don't really have a well defined
"surface" and their spectra form in the atmospheric layers.
</p>
</div>
</div>
<div id="outline-container-org8aef887" class="outline-3">
<h3 id="org8aef887"><a href="#org8aef887">Solar metallicity: Z<sub>☉</sub> = 0.0146 ≅ 0.02 (older but still widely used value)</a></h3>
<div class="outline-text-3" id="text-org8aef887">
<p>
The "metallicity" is the fraction by mass of gas that is <i>not</i> hydrogen
nor helium. This includes many elements (e.g., C, N, O, Si) that a
chemist would not call "metals". See <a href="https://webelements.com/">here</a> for an online periodic table
of elements.
</p>
<p>
Often, for lack of better knowledge available, we assume that the
distribution of metals scales with the Solar distribution, sometimes
allowing for enhancement of α particles (e.g., carbon, oxygen, neon,
and all other elements that can approximately be thought of as N α
particles bound together where α particle = nucleus of helium 4).
</p>
<figure id="orga40a3ad">
<img src="./images/solar_abundance_pattern.png" alt="solar_abundance_pattern.png" width="100%">
<figcaption><span class="figure-number">Figure 6: </span>Solar abundance pattern from <a href="https://ui.adsabs.harvard.edu/abs/1989AIPC..183....1G/abstract">Anders & Grevesse 1989</a>. This shows the number of atoms normalized to 10<sup>6</sup> atoms of Silicon as a function of atomic number A. Often, for lack of better knowledge, this (or more recent updates to it) is the abundance pattern that is rescaled when changing the metallicity in a model.</figcaption>
</figure>
<p>
A common notation is also [X/H] = log<sub>10</sub>[(n<sub>X</sub>/n<sub>H</sub>)/(n<sub>X</sub>/n<sub>H</sub>)<sub>☉</sub>] where n<sub>X</sub>
is the number of ions of species X and n<sub>H</sub> is the number of protons
(i.e., hydrogen positive ions!). Often, [Fe/H] can be used as a proxy for
the metallicity (i.e., taking X=Fe).
</p>
<ul class="org-ul">
<li><b>Q</b>: Any idea why Fe here?</li>
</ul>
</div>
</div>
<div id="outline-container-org08e0255" class="outline-3">
<h3 id="org08e0255"><a href="#org08e0255">Lifetimes: ~3 Myr to ≫ age of the Universe (≅ 13.7 Gyr)</a></h3>
<div class="outline-text-3" id="text-org08e0255">
<ul class="org-ul">
<li><b>Q</b>: How old is the Sun? How long will it live? How do we know?</li>
</ul>
</div>
</div>
</div>
<div id="outline-container-org622c019" class="outline-2">
<h2 id="org622c019"><a href="#org622c019">Discuss projects</a></h2>
<div class="outline-text-2" id="text-org622c019">
<ul class="org-ul">
<li>Projects will cover topics that are important and or timely, but
hard to fit in the main body of the course</li>
<li>Occasion for you to dig deeper and teach to your peers</li>
<li>You should look over the <a href="projects.html#org14bd437">proposed project</a>, and give us a ranked list
of 5 projects you'd like to do (see <a href="https://d2l.arizona.edu/d2l/home/1463376">D2L</a> for updated deadline).</li>
<li>After receiving your preferences, we will assign to each a project
trying to maximize happiness (though it may not be possible to
accommodate everyone), and for each project we will assign two peer
referees.</li>
<li>Look over also <a href="projects.html#orgae97593">how the grading of the project will work</a>: in short,
we will evaluate your written summary (together with 2 of your
classmates!), your oral presentation in class (again, with your
peers!), and how you give feedback to others.</li>
</ul>
</div>
</div>
<div id="outline-container-orgb9324f1" class="outline-2">
<h2 id="orgb9324f1"><a href="#orgb9324f1">Homework</a></h2>
<div class="outline-text-2" id="text-orgb9324f1">
</div>
<div id="outline-container-org5ed08de" class="outline-3">
<h3 id="org5ed08de"><a href="#org5ed08de">General considerations</a></h3>
<div class="outline-text-3" id="text-org5ed08de">
<ul class="org-ul">
<li>As per the syllabus, homework should be your own production,
though you can discuss with your peers. Science is made of
collaborations, but you are expected to be able to do all the
homeworks yourself.</li>
<li>Always consult <a href="https://d2l.arizona.edu/d2l/home/1463376">D2L</a> for official deadlines. If you need an
extension, it should be agreed upon at least <b>one day before the
official deadline</b>.</li>
<li>Throughout the course the typology of exercises and difficulty
will vary. This is normal also when doing research: not every task
is as easy/as hard as the next. If you encounter difficulties,
keep in mind that it's only an opportunity to grow and improve!</li>
</ul>
</div>
</div>
<div id="outline-container-org2e1e5f2" class="outline-3">
<h3 id="org2e1e5f2"><a href="#org2e1e5f2">Specific assignments for today</a></h3>
<div class="outline-text-3" id="text-org2e1e5f2">
<ul class="org-ul">
<li>Calculate the average density of the Sun and compare it with the
density of something familiar on Earth.</li>
<li>Start looking over the <a href="projects.html#org14bd437">list of final projects</a>, you will need to
provide a ranked list of 5 preferences. Feel free to search
the web/literature to decide. Based on this list, I will try to
assign projects and peer-referees, but it may not be possible to
satisfy everyone. If you want, feel free to come up with different
subjects related to stellar physics as well to propose, but you need
to talk to me to get them approved before they can be on your list!</li>
</ul>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<div class="footer">
<hr>
<a href="#light-dark-toggle"><i id="light-dark-toggle"><i class="fa-solid fa-circle-half-stroke"></i></a>    <a href="index.html"><i class="fa-solid fa-arrow-left"></i></a>    <a href="#top"><i class="fa-solid fa-arrow-up" style="font-size:16px"></i></a>    <a href="notes-lecture-CMD-HRD.html"><i class="fa-solid fa-arrow-right" style="font-size:16px"></i></a>    <a href="https://github.com/mathren/stellar_phys_400A"><i class="fa-brands fa-github" style="font-size:16px"></i></a><hr>
<br>
Last updated on 6 February 2025 <br>
Made with Emacs 28.1 - Org mode 9.5.2
<br>
</div>
</div>
</body>
</html>