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00:00:01
[music]00:00:46
Good afternoon Let's get started I don't00:00:48
know if it's ringing, it's not ringing just don't00:00:50
get up for God's sake, that means I'll remind you that00:00:55
in two00:01:02
weeks we have a test according to plan. Sorry, it turns out great, so in two weeks we have a test according to00:01:06
plan, there is some00:01:08
possibility that she00:01:13
Our graduate and master's students will definitely help me out,00:01:16
but there is a certain probability that I will leave with00:01:19
faces at this moment, so don't be00:01:21
alarmed if some00:01:24
people come and solve problems for you and then00:01:26
hand out pieces of paper for you to solve;00:01:29
first, they solve some problems. Well00:01:33
or together with them we will be able00:01:35
to solve problems00:01:37
and then there will be00:01:42
30 different00:01:47
answer options and you choose, if you need to00:01:49
count, then count.00:01:52
Well, in the end, you need to choose an answer option,00:01:55
that is, you can’t forget to00:01:58
take some piece of paper on which you can count00:02:01
who needs it there? Take a calculator if00:02:04
you can’t extract the root of the third degree.00:02:07
What else00:02:09
will you be able to use notes, but you wo00:02:12
n’t be able to use the help of a neighbor00:02:15
or, conversely, a distant person,00:02:18
and you won’t be able to use00:02:22
any electrical equipment,00:02:24
smartphones, laptops, irons, I00:02:29
don’t know, some kind of00:02:31
soldering iron Yes, but this is generally common00:02:33
the examiner uses this on the contrary to00:02:35
students. Why00:02:36
can an examiner help a student00:02:38
tell something that he knew? Yes, I forgot,00:02:40
yes,00:02:43
good.00:02:46
If there are any questions, yes, now00:02:52
introduce a healthy lifestyle00:02:57
in the evening, do not drink a lot of strong tea,00:03:00
then,00:03:02
well, look, it will be because how00:03:06
I would tell it only to happiness, the00:03:10
lecture is recorded and posted for us.00:03:12
Therefore, in principle,00:03:15
after watching all this, it’s definitely enough to00:03:18
read anything separately; by00:03:21
and large, there’s no need for me to specifically00:03:23
write down on a piece of paper what I need to00:03:24
remember to say again so that I can00:03:27
include the question later. In general, we’re keeping an eye on it.00:03:31
it’s good if you ask some questions about the00:03:39
test and it kind of imitates the00:03:41
final test; the final test will be00:03:44
throughout the course, so the essence00:03:46
will be the same a little more. Therefore, the test is just very00:03:48
useful. It00:03:49
can help you00:03:52
on the test; you found yourself on the verge of a00:03:56
passing grade by a little bit. a little lower00:03:59
But my tests are well written,00:04:01
but God bless you,00:04:04
but in this sense If you come there00:04:08
Write a test of 30 questions to00:04:10
answer one correctly is quite00:04:13
strange because a random answer of 900:04:16
should almost be possible if he is lucky,00:04:19
but it happens People who manage to do so if00:04:22
you do it alone,00:04:24
it won’t hurt you in any way, that’s what I00:04:27
want to say, so in principle, you can00:04:29
come and try and probably there00:04:32
will be two pairs there too in two weeks, they will also let you00:04:34
go earlier,00:04:35
solid pluses, well, that means we00:04:39
continue to talk about the evolution of stars,00:04:41
turn off the overhead light,00:04:44
we continue talk about the evolution of stars, I’ll00:04:46
quickly remind you again, the third is00:04:49
all sorts of parameters of the sun00:04:52
further. It’s just that I will very often00:04:55
use, first of all, the mass and00:04:58
luminosity of the Sun, where it is, that’s why it’s00:05:02
useful to think about it.00:05:05
Imagine what it is; it’s00:05:08
good about the structure, we talked further,00:05:11
we’ll talk about different stars, I00:05:14
draw your attention to the fact that this is a00:05:16
three-part structure, the core where00:05:19
radiant reactions take place, the zone, the convective zone,00:05:21
this is not characteristic of all stars, many00:05:24
but not all, this structure can00:05:27
change greatly, it depends on us stars and00:05:29
depends on the evolutionary stage of the star at00:05:32
later times stages, as a rule,00:05:33
it turns out More complex00:05:36
And the sun, let me remind you that energy00:05:40
is released in the core further at the beginning, it is00:05:42
transmitted by radiation, this tangled00:05:43
line corresponds to the fact that00:05:46
the transfer of energy through the radiative zone00:05:50
takes an average of 70 thousand years,00:05:54
naturally the Photon there, you understand, this is00:05:56
not the same Photon wandering00:05:59
but in fact, this is in popular books,00:06:03
especially This is how the photo formulates: it takes00:06:05
170 thousand years for approximately00:06:08
what A person needs 170 years to achieve00:06:11
enlightenment and go to Nirvana, this is00:06:13
a little not the same00:06:14
well last time we talked about00:06:17
parallaxes, I will remind you about them from time to time, I00:06:19
just want to tell you remind you that00:06:21
prolax is 206,265 astronomical00:06:24
units Well, or about 3 per 10-1800:06:27
centimeters,00:06:30
okay,00:06:31
last time we came up with this00:06:35
wonderful equation, the00:06:38
equation of hydrostatic equilibrium and00:06:41
for simple estimates for very00:06:43
approximate estimates We will even00:06:45
use it once, you can use a very00:06:47
simple expression here the idea is that00:06:51
all sorts of derivatives Yes, and00:06:54
we change something pdr simply by dividing by the value and00:06:58
we get this simplified thing00:07:00
for some estimates. This is good00:07:02
to use, but00:07:05
I repeat that the pressure inside the star00:07:09
is provided by both gas pressure and00:07:12
radiation pressure. Both are00:07:15
important it’s just that for the sun, gas00:07:18
pressure is more important; for lighter stars,00:07:21
gas pressure is more powerful;00:07:24
for more massive stars, radiation pressure is slowly00:07:27
beginning to become more and more important,00:07:30
but until00:07:33
it reaches the limit, which00:07:36
is called00:07:37
and which is there sometime in November, you and00:07:40
I Let us deduce00:07:41
accordingly the00:07:43
stability of this gravitating gas ball00:07:49
leads to such a remarkable00:07:51
property which is called negative00:07:53
heat capacity00:07:55
which consists in the fact that if you00:07:57
end up energy in a star then its00:08:01
surface temperature will drop00:08:04
accordingly00:08:07
red giants for example which we00:08:09
will talk about are stars with very high00:08:11
luminosity B in the central part there00:08:14
is a very powerful source of energy working.00:08:16
This leads to the fact that the temperature of00:08:18
the star is now falling near the Sun to about00:08:21
6000 Kelvin in 7 billion years00:08:25
there will be a little over three thousand Elvin Although the00:08:28
luminosity will increase00:08:30
Well, And now we are starting00:08:33
today’s new piece and starting with a00:08:36
discussion of the diagram Herspang Russell,00:08:38
which I will show many times today in00:08:41
very, very different forms,00:08:43
so we will linger on this slide a little00:08:45
and00:08:48
discuss it in detail so that the diagram, as it00:08:51
were, can be found out almost everything.00:08:54
So,00:08:56
first of all, about the history of diagrams, the diagram00:08:59
appeared thanks to observations, there00:09:03
was no theory behind it, people00:09:07
learned measure the distance to stars00:09:10
or determine some other00:09:12
characteristics build spectra00:09:14
and when this happens people begin00:09:17
to draw many different diagrams and00:09:19
one often turns out to be useful and they00:09:23
begin to actively use it what00:09:24
happens in various fields of science00:09:26
what was here00:09:29
here on the one hand there was a spectral00:09:32
a classification for which at that time00:09:35
there was no special theory00:09:39
and therefore these letters denoting00:09:42
spectral classes are both f lcm they00:09:46
look like00:09:47
some kind of very strange set And I00:09:50
always wonder how many00:09:52
astronomers there are lcm is the password00:09:55
The Sun is a class star, or rather 200:09:59
for more accurate classifications, these00:10:01
spectral classes are each divided into 1000:10:04
classes00:10:06
and when the spectral00:10:10
classification was created. In principle, it was not00:10:11
obvious that it was not clear what00:10:15
physical property of the star this00:10:16
classification is associated with. Now we know00:10:19
this00:10:20
largely gives rise to temperature00:10:23
and therefore we can say that according to the00:10:26
horizontal The temperature is plotted on the axis,00:10:28
but it happened in the opposite direction, that is, the00:10:32
temperature increases to the left.00:10:34
Class O stars are the hottest stars; they have00:10:37
temperatures up to tens of thousands of degrees. The00:10:40
coldest stars are class00:10:43
M stars. And their temperature can be00:10:45
slightly below 3000. Here it is important to00:10:48
clarify the sun, I will repeat. two00:10:51
are located approximately in the middle,00:10:55
the diagram draws there on a variety of00:10:57
scales,00:10:59
which are chosen for reasons of convenience,00:11:02
but the sun really falls more or less00:11:05
into the middle there, now about the00:11:06
vertical axis, the00:11:11
luminosity in00:11:12
solar units is plotted here on this particular diagram. Here is one luminosity of00:11:14
the sun and, accordingly, the sun there are00:11:16
two from the saturated sun00:11:19
at the top of a star of higher luminosity and00:11:22
you see that massive stars here, the mass00:11:25
is indicated in general, stars can reach a00:11:27
luminosity of several million of the00:11:29
sun's luminosity.00:11:31
Well, the weakest stars reach a00:11:34
luminosity there of about one hundred thousandth00:11:37
the luminosity of the sun, but to determine00:11:40
the luminosity you need to know the distance00:11:42
usually there are all sorts of clever ways00:11:45
to determine luminosity but in the 19th century00:11:48
when they drew a diagram you needed a00:11:51
distance sign in the early 20s the00:11:55
distance was known for close00:11:57
stars the distance is known for close00:12:00
stars and so00:12:02
when you have a sample of close00:12:04
objects they fall into the most00:12:07
extreme as we will see more00:12:10
extreme objects, these are objects of00:12:12
high mass, but in one of the00:12:16
options I don’t remember there00:12:20
was actually luminosity because00:12:22
close stars with known prolaxes were taken,00:12:26
but you can put aside something else.00:12:28
For example, you can take one cluster of00:12:31
stars, it is located somewhere far away and00:12:34
therefore we believe that all the stars of the cluster00:12:36
are at the same distance from us,00:12:40
that is, it is clear when you are asked00:12:41
What is the distance to St. Petersburg, it is00:12:43
pointlessly quite asking to00:12:45
what part of St. Petersburg00:12:46
because it is approximately the same00:12:51
and then if you take the cluster you00:12:54
can simply draw the visible00:12:56
magnitude the task is terribly simplified You00:12:59
have two observational characteristics -00:13:01
spectral class and magnitude -00:13:05
apparently there are stellar magnitudes, and00:13:07
we will see such diagrams at least00:13:09
today with you. Well, for such00:13:13
illustrative purposes, they honestly draw the00:13:16
luminosity as if we had accurately measured it and00:13:18
now, thanks to Gaia,00:13:20
more is really possible put a billion stars on a00:13:24
diagram00:13:25
when it means that Russell and independent00:13:29
began to draw such00:13:32
diagrams in different ways, they were surprised to find that00:13:35
this plane is filled in not at all00:13:37
by chance, but lined up in several00:13:41
lines or groups,00:13:44
most of the stars00:13:46
fit on this line that00:13:49
goes from the upper left corner to the right at00:13:51
the bottom it is called the main sequence,00:13:52
sequentially00:13:56
looking ahead on the main00:13:58
sequence, stars spend00:13:59
most of their lives on it00:14:02
without fidgeting much, in the beginning there were hypotheses that00:14:06
the star travels along the main00:14:08
sequence during its life, it does not.00:14:09
It actually sits where it was born and00:14:13
at the top we have stars of large00:14:17
mass. they have high luminosity and high00:14:19
temperature. And below, on the contrary, red00:14:23
dwarfs stars with low mass and00:14:25
low luminosity and low00:14:27
temperature00:14:28
on the main sequence, the star00:14:31
spends on average about 90 percent of00:14:33
its life time, which is why it is so00:14:35
populated, very simple. Imagine we00:14:41
But even now with smartphones you can’t put a beacon on00:14:44
you we need to track your00:14:46
position for a long time, here is00:14:48
a map of Moscow and the00:14:51
more time you spent at some point,00:14:54
the larger the circle will be, the bolder the point where00:14:58
you spend the most time,00:15:01
in fact, the boldest point of00:15:03
Student life, it is excellent No,00:15:06
generally speaking, where you sleep00:15:11
8 hours a day But about a third of the time00:15:15
you simply spend more or less at one00:15:16
point00:15:19
So the stars have about the same That is,00:15:23
you can move a lot Yes, but00:15:25
you move there and inside00:15:26
universities somewhere else 8 hours just00:15:29
765 400:15:33
you spend more or less at one point00:15:36
well The main sequence stars00:15:40
live the longest where they move00:15:41
After00:15:44
means as you know that there good00:15:46
girls go to heaven bad girls go wherever00:15:48
they want00:15:49
means00:15:51
stars like the sun go Here in the00:15:55
region of giants sometimes they are called00:15:57
red00:15:59
these are massive stars can find themselves in the00:16:02
region of supergiants, that is, in this00:16:03
part of the diagram the stars get already00:16:07
evolved,00:16:08
they get there when they run out of00:16:11
hydrogen. In the depths of the hydrogen in the core of the00:16:14
star, some transformations begin to occur.00:16:16
But these transformations can00:16:19
be very interesting, stormy, but00:16:21
they take about 10 percent of the life of a00:16:24
star at the end of its life, massive stars00:16:27
experience core collapse, this can be00:16:29
accompanied or followed by a00:16:31
supernova explosion, it is important that at the end there is00:16:33
usually a compact remnant of a00:16:35
neutron star or a black hole, they00:16:37
especially cannot be placed on this diagram,00:16:39
they have very different parameters And00:16:42
stars like the sun turn into white00:16:44
dwarfs and are slowly settling into this00:16:46
region.00:16:48
Well, as the white dwarf cools down, it moves00:16:50
approximately as it elongatedly moves00:16:54
in this direction,00:16:58
respectively, in order to write the00:17:01
evolution of a star on the diagram,00:17:04
the most important thing is to know its mass;00:17:06
mass is the most important parameter of a star; in00:17:09
this sense, the star is really the00:17:10
structure of a star is very simple, it’s a gas00:17:13
ball; the00:17:14
chemical composition of a star is important to us, but it’s00:17:17
not very different from stars;00:17:24
we’ll talk to you about what changes the details of the chemical composition bring00:17:26
today. But this doesn’t affect much; what else does the00:17:30
star have a rotation speed; this00:17:32
can also influence;00:17:34
But this is important for very massive stars.00:17:37
Apparently, it00:17:39
cannot be said that the00:17:43
magnetic field also radically changes fate. In general, it does not have a strong00:17:46
effect, so mass00:17:47
is really the most important parameter; it depends on it. At00:17:50
what point in the00:17:52
main sequence the star is00:17:54
born. How much time it will spend there,00:17:56
where it will go. Then what everything will turn into00:17:59
is determined essentially by mass. The lightest00:18:02
stars have a mass of approximately 8 hundredths of the mass of00:18:05
the sun. This corresponds to00:18:08
the temperature in the center at which the00:18:10
reactions of converting ordinary00:18:12
hydrogen into a gel begin. The00:18:14
definition of a star includes one00:18:17
simple point: the reaction of00:18:19
converting hydrogen into a gel must take place at least at00:18:21
some stage of evolution, the00:18:25
most massive stars are a more complex00:18:27
question, now00:18:29
observation shows that in our00:18:31
Galaxy the most massive stars being formed00:18:34
have a short lifetime,00:18:35
so those that were formed a long time ago00:18:37
are still missing the most massive00:18:39
stars formed have a mass of somewhere around00:18:41
100-200 masses suns, all sorts of incidents are possible;00:18:44
stars can merge with each00:18:47
other in dense clusters; stars, as00:18:51
you remember, are formed during the00:18:53
gravitational collapse of a cloud that00:18:55
breaks into a fragment; as a result, a00:18:58
close group of stars can form; they00:19:00
can begin to merge. You can00:19:01
get a star with a mass of 400 in the00:19:05
sun of 600. But this some great rarity00:19:09
and requires an additional process in the00:19:12
distant past00:19:14
For which we may get00:19:15
somewhere there, the course00:19:18
conditions could have developed When you had a00:19:22
very large cloud during the collapse,00:19:23
one such Superstar was formed with a00:19:26
mass of about a million in the sun, but00:19:28
we have such objects in any case,00:19:30
we don’t see it now and in our Galaxy they are00:19:33
definitely not formed now, so it’s there00:19:35
for simple estimates. When you need to00:19:37
integrate something and quickly show it on the board,00:19:39
sometimes you can substitute there from00:19:43
0 1 to 100 of the sun. Well, it’s clear that the00:19:46
sun with its unit falls approximately00:19:49
middle if so logarithm00:19:52
is necessary algorithm well stars change00:19:56
stars evolve now we see the sun like00:19:58
this in the future it will turn into a00:20:01
red giant it will shed its outer layers00:20:03
it will give birth to a planetary nebula not00:20:06
necessarily so beautiful00:20:08
but maybe some kind It’s quite00:20:12
nice and the ejected matter00:20:14
returns back to the interstellar medium00:20:17
This wonderful nebula is00:20:19
exactly a dark cloud, it’s not a hole in00:20:23
the sky,00:20:25
respectively,00:20:26
the stars evolve, they distinguish different00:20:28
populations of stars,00:20:31
stars, population 1, these are modern00:20:35
stars in quotes. That is,00:20:37
the sun also gets there. This is generally all that is formed in00:20:40
our Galaxy over the last00:20:42
approximately 10 billion years 8 billions of00:20:45
years, this number is still constantly00:20:48
being refined and the boundaries are quite arbitrary;00:20:52
now the chemical composition of the Galaxy is00:20:55
of course changing; it is always changing in00:20:58
one direction; there are fewer light00:21:00
elements; more heavy elements;00:21:09
very large, but Studying the Galaxy,00:21:11
people identified a population of old stars,00:21:14
rounded up to 10 billion years old, they00:21:18
are associated with a period of very rapid00:21:21
formation of stars at the early stage of the life of00:21:24
our galaxy,00:21:26
and finally they identified another population of 3, these are the00:21:30
very first Stars that arose in00:21:32
the universe, they are fundamentally different in00:21:34
their chemical composition, they arose00:21:37
from a primary substance where there was hydrogen,00:21:41
helium and all the other elements are completely00:21:43
insignificant in the admixture. Well, the element there was00:21:46
lithium. In general, almost all of them are also00:21:50
isolated into a separate population, this is00:21:52
exactly what James Web will see,00:21:54
but maybe he won’t see you will have to00:21:56
wait for the next experiment,00:22:00
of course you can imagine, for00:22:02
example, astronomers in some00:22:04
other galaxy who will have only00:22:06
two populations, this is how the00:22:07
history of the formation of00:22:09
the galaxy works. They will have population one, these are00:22:13
their stars, and population 2, these are the very first00:22:16
Stars in the Universe, on the contrary, you can00:22:18
imagine00:22:20
astronomers in the galaxy with a very turbulent00:22:22
history and they can find many populations00:22:25
in their galaxy, but there will always be the00:22:28
first and the last. The first is what00:22:30
is being formed more or less now00:22:32
and, again, all massive stars00:22:34
end up there because they have a very00:22:36
short lifetime and the population is associated00:22:40
with the most the first stars will also always00:22:42
be this is a kind of universal thing for the00:22:44
entire universe,00:22:46
okay. Well, let's talk about the00:22:49
evolution of such a rather large piece, let's00:22:52
look at the Russell diagram again,00:22:56
temperature, luminosity, white dwarfs,00:22:59
the main sequence of the giant,00:23:01
supergiants, we will then highlight00:23:03
some interesting areas here But00:23:06
For now, such a scheme is quite enough for us; the00:23:09
evolution of a star is a change in00:23:11
combustion sources. As a rule, something00:23:14
happens to the star if one of the00:23:17
reaction cycles has ended; hydrogen turns into00:23:19
helium; hydrogen sooner or later00:23:21
ends00:23:23
in the region where reactions take place in the core;00:23:26
accordingly,00:23:28
some things will happen to the star. then Metamorphoses, if there is00:23:31
enough mass to create a00:23:34
high temperature in the center, then the00:23:37
combustion reactions of Helium will begin again, there will be00:23:39
another evolutionary stage, the first combustion00:23:42
of hydrogen, the second, some kind of transitional stage, the00:23:45
third combustion of Helium. Well, then it will go about the same way, the00:23:48
helium will end,00:23:55
carbon will begin to burn, and so on the reactions can00:23:58
reach iron if we consider a star00:24:01
like the sun, then the evolution will look00:24:04
something like this, almost from G2 it00:24:07
begins for a00:24:09
long, long, long time, we sit on the main00:24:11
sequence of not exactly one point,00:24:13
we will then move into smaller details in00:24:16
successive steps. We will00:24:18
see that the main sequence00:24:21
has a finite width and this is due to the00:24:24
slow evolution of the star, we sit on00:24:27
the main sequence, then the00:24:29
hydrogen runs out and the star00:24:31
expands. So it turns into a00:24:33
red giant. It’s not for nothing that the00:24:36
first stage of the red00:24:39
star is written here.00:24:49
consists of Helium, the core compresses and00:24:53
heats up. As you remember,00:24:55
since this is a gas object, the temperature00:24:59
rises and the burning of Helium begins,00:25:01
accordingly, this is like a conditionally00:25:05
second main sequence, now00:25:07
the burning of Helium in the core has begun, then it00:25:09
will end and a star like the sun will go to the00:25:12
second branch of giants, this will be more00:25:15
higher luminosity Let's00:25:16
remember This is the absolute00:25:19
magnitude The sun has an absolute00:25:21
magnitude five on the giant branch00:25:25
The magnitude will already be there00:25:27
somewhere minus 2 How many times00:25:29
does five give 100 times and two00:25:32
magnitudes is it still there 6 times 7 almost it00:25:35
turns out that in several hundred times the00:25:38
red giant has a luminosity greater00:25:41
than the luminosity,00:25:42
and then when it goes to the second00:25:45
second branch of giants for the sympathetic00:25:48
visa-giants, it will already be minus 5, that00:25:50
is, this is 10 thousand times more00:25:53
luminosity. The Sun00:25:56
in the distant future00:25:58
will increase its luminosity approximately 1000:26:00
thousand times00:26:01
after that the outer shell is00:26:03
discarded, the core remains, it cools down,00:26:05
it00:26:07
will lose luminosity, but look. The core is00:26:11
exposed. Here you saw the temperature of00:26:14
the hydrogen shell on the outside, it is low. The hydrogen00:26:16
shell is discarded.00:26:18
You are discarded; the inner00:26:20
core is exposed; it is hot, so an00:26:23
object hatches from this shell with not00:26:27
very high, but still more00:26:29
solar luminosity but it has a very high00:26:30
temperature; its temperature00:26:32
at birth is tens of thousands, maybe over 10000:26:35
thousand degrees.00:26:37
And after that, this object at the00:26:41
planetary nebula stage quickly cools down and00:26:43
finally becomes a classic white00:26:45
dwarf, which will continue to cool and00:26:47
move in this direction,00:26:51
we said that mass is the main parameter and00:26:53
here evolutionary tracks are drawn00:26:56
for stars of three different masses, and the00:27:00
chosen values are not extreme, I would00:27:04
say, and here I need to make a couple of00:27:07
comments.00:27:09
In principle, in such a drawing, any00:27:12
such00:27:13
squiggle line should be treated as an00:27:18
illustrative line.00:27:20
That is,00:27:21
this line, for example, does not mean that a00:27:24
star of 10 solar masses Exactly its00:27:27
evolution moves along this line.00:27:29
Firstly, we said that there are still00:27:31
additional parameters, the chemical00:27:33
composition of rotation,00:27:34
duality can be important. In general,00:27:37
some complications Taras, but secondly,00:27:40
calculations of Stellar evolution are00:27:42
quite complex and there remain many00:27:45
unclear questions, remember we said that00:27:47
we cannot calculate the tidal response of a00:27:50
star to the influence of a planet, so we00:27:53
cannot calculate in detail at what rate00:27:56
planets fall onto a star.00:27:59
Stellar evolution also has unresolved00:28:02
questions; there are fewer of them for stars of such masses.00:28:05
But for very massive stars, it’s right there there are00:28:08
really a lot of questions and sometimes00:28:10
it is not clear which direction the star will go00:28:12
on the diagram,00:28:14
but nevertheless, general things are visible here, which00:28:18
means the evolution is similar to the one00:28:22
shown in the previous figure, we are sitting00:28:24
on the main sequence, we00:28:26
are leaving, we are coming to the branch of giants, we are rising, we are climbing00:28:29
along the branch of giants, a00:28:31
gel flash is happening, we are falling there where00:28:34
helium burns in the core, we sit here for a long time,00:28:37
then we go for the second approach to the00:28:40
giant branch, this is called the asymptotic00:28:42
giants. Therefore, this is the abbreviation00:28:46
and here the star is already shedding its shell,00:28:49
turns into a white cable, its path has ended00:28:53
five masses of the sun, more or less a similar00:28:56
situation, but we start with more high00:28:59
luminosity and by the way, you can see significantly00:29:02
higher luminosity, only five00:29:05
times more massive, and on the main00:29:07
sequence, the luminosity at00:29:09
birth is already hundreds of times greater, and the00:29:12
sun is at the red giant stage, and they left the00:29:14
main sequence and reached the00:29:16
giant branch, which is not very00:29:18
pronounced here, and went to the stage Helium combustion00:29:20
went on a second run and here, too, the00:29:25
star lost its shell 10 masses of the sun are a little similar00:29:29
Evolution loops are arranged differently,00:29:31
we get into the region of supergiants and in the00:29:33
end such a star explodes a00:29:36
neutron star00:29:39
So mass is the main parameter of the problem How to00:29:42
determine mass we will at the end of00:29:44
today's lecture about We'll talk about this later;00:29:47
the mass, of course, is reliably determined00:29:50
only if we see that something is rotating around the star in00:29:52
a good way; we determine00:29:55
well the mass of binary systems if the00:29:58
star has some component; the00:30:00
second star is better when it is clearly visible and we00:30:03
can measure the speed of movement of00:30:05
both stars around the center of mass But00:30:09
after you have repeatedly performed00:30:12
this operation for a variety of stars,00:30:17
you have obtained the masses by accurately measuring binary systems.00:30:20
Taking advantage of the fact that stars are objects of a00:30:24
fairly simple nature, you00:30:27
can do the following. A00:30:29
star is largely characterized by00:30:33
its spectrum00:30:34
and therefore you can do the following00:30:38
procedure. some single star is00:30:41
distant, but you measured it Spectrum,00:30:44
select Spectrum and select a similar one And00:30:47
when you found it, you can say that00:30:49
these are stars with the same masses, you00:30:50
select similar Spectrum among stars with00:30:52
measured masses,00:30:54
naturally the procedure does not look as00:30:56
naive as I described, but the essence is exactly00:30:58
this that is, often when they say that00:31:01
some star has a mass of 12.3 masses,00:31:04
as determined, most likely00:31:06
spectral data were used and all00:31:09
this was based on the fact that there are Well-00:31:11
studied stars with measured masses in00:31:14
binary systems,00:31:16
how stars are distributed by mass. This is00:31:20
where I want make an important lyrical00:31:22
digression00:31:25
with some exceptions. What do you think are the00:31:28
most cited articles in00:31:31
different sciences, as a rule,00:31:36
or an experimental technique or a00:31:39
theoretical model that everyone00:31:41
uses,00:31:42
or now a description of algorithms,00:31:47
maybe some kind of software, that is, it is essential00:31:51
that everyone needs it; the ideas are very00:31:53
simple in childhood, the cleverness00:31:56
was puzzled in a house of 164 floors on each00:32:00
floor the number of apartments depends on how I don’t00:32:03
know the third root of the00:32:06
floor number an infinitely complex problem in the house00:32:09
there are 15 elevators We choose the seventh00:32:12
elevator on the left Which button in the elevator00:32:15
is used most often00:32:17
yes the first floor because everyone needs it00:32:19
most often they use it Maybe00:32:21
Elton John lives there on some floor But his00:32:24
Button will be used less often more often they00:32:27
will still use the first floor00:32:28
and so one of the most cited articles00:32:31
in astrophysics is an ancient article, already 5500:32:34
years old, many have not put a link00:32:38
they write that this is Salfetorov’s00:32:40
distribution of mass. I think in my00:32:42
life, but maybe I quoted it once.00:32:46
But this is what everyone needed back in00:32:50
1955. Peter, who, generally speaking in theory,00:32:52
did some kind of exercise with00:32:56
observational data and he obtained a00:32:58
distribution of stars by mass in a rather00:33:02
narrow interval of horizontal force00:33:05
burns masses of00:33:06
solar units one mass of the Sun is00:33:10
about a third three ten and in such a00:33:14
narrow range he00:33:16
programmed00:33:18
power functions with an index of00:33:22
-1.3500:33:27
-2.3500:33:31
So this is the distribution by mass.00:33:35
It’s really good,00:33:38
it doesn’t stretch well into the region of the most the lowest00:33:41
masses the highest modifications, but nevertheless,00:33:46
training courses often directly use the00:33:49
Salfetorov mass function from beginning to00:33:51
end, everything is directly integrated in the mind,00:33:53
easily calculated and we see with you00:33:56
that the number of stars giving birth very00:34:00
much depends on the mass; the mass can00:34:02
change by three orders of magnitude, respectively00:34:05
the number of stars changes by00:34:08
seven orders of magnitude, that is, low-massive00:34:11
stars are born much more often than00:34:14
massive stars,00:34:15
and therefore00:34:17
the Galaxy in pieces consists mainly00:34:20
of red dwarfs from small00:34:22
massive stars, and therefore you00:34:25
can often see a discrepancy in the00:34:28
number of stars in the Galaxy, while being00:34:30
very precise the mass of the goal is known.00:34:33
This is quite funny, but the mass00:34:36
is practically measured now, the number of00:34:39
stars is still recalculated through00:34:41
some kind of mass distribution,00:34:44
the details are important, somewhere you can see 30000:34:46
billion, somewhere 400 even less than 30000:34:50
Well, there is such a simple distribution00:34:53
that we sometimes with we will use you, I will00:34:57
even write again00:35:02
exactly in the form in which it is usually00:35:05
used00:35:13
well, it means that massive stars are00:35:16
rare, but they have a high00:35:18
luminosity and therefore are easy to observe,00:35:22
so when we look at the sky, although00:35:27
we are surrounded by solid red dwarfs,00:35:30
we do not see them00:35:32
we see bright stars and the bright stars are00:35:36
either massive stars; they00:35:38
already have a high00:35:40
luminosity on the main sequence, or are they some kind of giants00:35:43
from supergiants stars in late00:35:45
evolutionary stages, that is, go out00:35:47
there in the winter and see the beautiful constellations00:35:50
of Orion There are two bright stars. It’s quite00:35:53
distant. Well, relatively distant stars00:35:55
Betelgeuse is a red giant and therefore00:35:57
bright in the sky and the rigel is a massive00:36:01
star and therefore00:36:04
how are our masses related? Their luminosity00:36:07
means look at what the00:36:09
point is here since mass is the main00:36:12
parameter, then first of all all00:36:14
other parameters of the star depend on00:36:16
it, especially if we are at the stage of the00:36:18
main sequence, that is, this is the00:36:20
picture that is drawn,00:36:22
drawn exclusively for the main00:36:24
sequence:00:36:25
giants, supergiants There is00:36:29
no need to add anything else here,00:36:31
and naturally, the greater the mass of the star,00:36:35
the greater the luminosity; this is easy to understand, which00:36:37
means look, the greater the mass, the00:36:40
greater the pressure created in the center of the00:36:43
the temperature in the center is greater, namely on00:36:46
the temperature, and the00:36:48
rate of nuclear reactions depends to a very high degree, so00:36:51
even if you take two stars on the00:36:54
main sequence, inside you00:36:56
hydrogen turns into helium just even00:36:59
in one cycle,00:37:01
but the stars have a mass of 10 from Tom the sun,00:37:04
then the second star has a higher00:37:08
temperature in the center there is a higher00:37:10
rate of reactions and, accordingly, there will be00:37:12
more luminous stars. Looking ahead,00:37:14
we can say that the lifetime will be shorter00:37:16
because the00:37:19
supply of hydrogen will be consumed very quickly,00:37:21
respectively, the00:37:23
dependence is not monotonic throughout the00:37:26
entire main sequence for low-00:37:29
mass stars while gas pressure dominates00:37:33
the coefficient of proportionality is somewhere00:37:35
between three 400:37:37
for massive stars When the00:37:40
radiation pressure becomes important, asymptotically00:37:43
this thing comes to a relationship00:37:45
proportional to the mass. That is, if we00:37:48
take there the sun and a star twice00:37:50
as massive as the sun, these are the types of questions there will be00:37:52
questions Two stars One has a mass one00:37:55
mass The sun is the other two masses of the sun,00:37:57
how many times does their lamp differ?00:37:59
Two main stars follow00:38:01
Well, accordingly, we raised two to the00:38:04
power of three and a half, for example,00:38:06
we got the answer.00:38:08
And for massive stars, if now00:38:10
the conditions of the problem one star has us00:38:13
Tom the sun the second 200 on the sun, then there00:38:16
will be a difference00:38:18
the picture is just drawn twice, this is the measured00:38:20
data00:38:21
and you can see a pretty good00:38:24
relationship here, the slope is 395, it00:38:28
becomes a little flatter for00:38:32
essentially red ones00:38:34
and there it is little by little approaching three,00:38:38
this relationship can be obtained from00:38:43
me in five minutes, here I have it00:38:45
since I’ll probably get the00:38:51
dependence of mass luminosity. So00:38:54
we have our favorite00:38:59
equation, they’re warming up. Let’s even write it like this.00:39:09
I’m not writing MRI here anymore because the00:39:13
whole star will be important to me. I’m00:39:17
interested in the average00:39:19
characteristics and the average pressure, I can00:39:22
roughly estimate it this way.00:39:25
Now I’ll explain00:39:28
why pressure from energy density00:39:32
thermal energy density00:39:34
thermal energy is of the order of potential00:39:37
but only the sign needs to be changed00:39:39
accordingly when we talk about00:39:41
pressure we get a coefficient of00:39:43
1/3 1/300:39:45
respectively this is the average pressure00:39:48
in the Star00:39:49
potential energy of course we00:39:51
can calculate the potential energies00:39:53
It’s simple00:39:57
Well again, without going into the details of00:40:01
the distribution for us, I can set00:40:03
proportionality everywhere. Although I’ll00:40:06
put it approximately so as not to confuse you,00:40:09
accordingly then I get that00:40:12
the average pressure is simply taken and00:40:14
substituted, I00:40:15
will have a00:40:19
GM square, I’ll also express the roll in terms of mass00:40:23
and I consider the radius that the density is always00:40:31
good means on the other hand from00:40:35
some 10th grade You know that P00:40:38
=00:40:40
N is that we have the average density divided00:40:44
by the mass of one particle00:40:47
I mean the average density is good in00:40:50
brackets00:40:52
something averaging is good So that00:40:56
means I’ll00:40:59
write down separately what is natural for me00:41:03
I believe that the radius is proportional to the mass to the00:41:06
degree of 1/3 because I think that the00:41:07
density is the same everywhere. So then the00:41:10
average density is equal to00:41:13
the average pressure. Sorry, the average00:41:16
density00:41:20
and accordingly I get from here that CT00:41:24
scans are what I have written00:41:29
GM on m average divide by how much00:41:34
so you can do the arithmetic here is00:41:37
quite simple okay I want to get00:41:40
to the luminosity I have a00:41:45
simple law working we believe that00:41:48
a star is a ball of gas emitting like a00:41:50
black body reconnaissance is really a00:41:51
first approximation00:41:54
so I can use this00:41:57
simple formula00:41:59
accordingly00:42:00
[applause]00:42:04
write down what not to write down Let's 4 PC00:42:08
Sigma, instead of the radius, I will substitute the radius00:42:12
expressed in terms of mass and density,00:42:16
mass divided by the average density, all00:42:20
these are powers of 2/300:42:24
and the average mass of a particle is n-concentration,00:42:28
respectively, the average density is divided by the00:42:31
average mass of one particle; in naivety,00:42:34
you can take hydrogen, well, you can average00:42:36
a little more and00:42:39
multiply it like this by multiply by we continue,00:42:43
I have 4 left temperature, expressing00:42:46
because of that expression00:42:49
three to I transfer here R to the power of 400:42:54
now Well, I just left all these00:42:57
expressions for them to look at, but now00:42:59
we will collect everything in a pile that we00:43:01
get from here I have mass to the00:43:04
power of two-thirds comes out from here, I have a00:43:07
mass of 4 coming out here But there is also a00:43:11
radius below. The radius is mass to the power of00:43:13
1/3, which means there is also mass to the power of minus 43,00:43:17
and accordingly, after we00:43:20
put it all together, we get that this is00:43:23
mass to the power of 3 1/300:43:27
that is, for gas pressure for a00:43:29
gas ball we got this00:43:30
correct dependence like00:43:39
this, well, the exercise is accessible, so I would00:43:44
tell every 10th grade student,00:43:46
but we got a qualitatively correct00:43:50
dependence taking into account radiation pressure,00:43:53
it will help to do all this more accurately Better00:43:57
there taking into account the structure of the star, of course, the00:44:00
density is not the average chemical00:44:02
composition, but the essence will remain, even you will00:44:04
get a degree between three and00:44:07
good.00:44:10
Well, okay, let's move on.00:44:15
The radius, the radius, also depends on the mass, but the00:44:19
dependence is weaker. But on this00:44:21
graph, the dependence is quite difficult to00:44:23
calculate because there are rather00:44:24
strange scales here made for convenience,00:44:27
but you can approximate this as a kind of00:44:31
dependence. That is, you can write an00:44:32
analytical function. But this is not a00:44:36
theoretical conclusion. But generally speaking, for00:44:40
stars like the sun and smaller, the figure is00:44:43
approximately 0.8; for large masses, approximately00:44:47
0.6 is not a minus, but a hyphen00:44:51
in principle This can also be deduced and00:44:54
I have a second, yes,00:44:58
let’s deduce it quickly.00:45:01
So, we believe that00:45:04
kinetic, that is, thermal energy is00:45:06
of the order of potential in absolute value,00:45:09
naturally,00:45:11
since my object is stable00:45:15
in this case, this is energy, which is three00:45:18
second to the number of particles everywhere,00:45:22
and accordingly this is proportional to the00:45:24
mass of the star per the mass of one particle, we00:45:27
CT00:45:31
potential energy00:45:35
potential energy, respectively,00:45:36
you need to take the double integral over all00:45:39
the pieces Yes,00:45:42
interacting with each other,00:45:45
but you know that we will come to00:45:49
this expression00:45:51
and then we just write down00:46:01
we have one step left, respectively,00:46:04
the radius will be simple is proportional to the mass00:46:06
divided by the temperature00:46:08
and it remains to find out how our temperature00:46:11
depends on the mass. It’s difficult to figure this out on your fingers,00:46:13
but00:46:15
if you do it in a complicated way, then we00:46:19
get that it’s one and a half to 10 to the seventh00:46:22
Kelvin, who cares about the mass in units of00:46:26
mass of the sun, power 1/3 then there is, in short,00:46:28
the temperature is proportional to the mass to the00:46:30
power of 1/3 and therefore the radius in this00:46:34
approach turns out to be proportional to00:46:36
approximately two-thirds. Which, again, well00:46:39
describes the general average behavior of stars and00:46:43
also successfully describes those in00:46:47
which gas pressure dominates in00:46:50
which radiation pressure dominates.00:46:53
Okay, let's do it00:47:00
continue00:47:06
well, I00:47:08
give the idea of making professor’s lollipops00:47:11
so that they dissolve in five minutes,00:47:12
I don’t have time,00:47:15
well, it means how luminosity depends on the00:47:19
mass on the main sequence, I’ll00:47:20
emphasize, we talked about how the radius00:47:22
was talked about. Let’s now see How00:47:25
the structure of a star changes, what it is,00:47:29
who is interested, this is very good00:47:31
online accessible such a textbook on the00:47:34
English language of the00:47:35
evolution of stars,00:47:37
it is not super new, but since then no00:47:40
such Mega miracles Mega revolutions in00:47:43
Stellar evolution have occurred. It00:47:44
tells the basics.00:47:48
So we have on this graph horizontally.00:47:51
Everything is simple horizontally, the logarithm mass is00:47:53
plotted00:47:55
vertically. such a00:47:59
specific Lagrangian coordinate is plotted vertically. That00:48:02
is, this is a fraction of the total mass of the star00:48:06
and, accordingly, for example, Let's00:48:10
look at 0 this is the sun00:48:15
here, but it00:48:18
turns out that the00:48:22
sketched area is the area where00:48:24
convection occurs. In the sun, a00:48:28
negligible fraction of the mass of the star is covered by convection.00:48:33
But since the density falls strongly00:48:35
outward then along the radius As you remember, the00:48:38
convective zone is 20-25 percent of the00:48:41
radius of the star from the mass, takes up just00:48:43
a little bit, we move to the left towards00:48:46
lighter stars towards red dwarfs00:48:49
and we see that the convective zone becomes deeper and00:48:52
deeper and that's when we00:48:54
got to a mass there of about 0.200:48:57
the mass of the Sun,00:48:59
then virtually the entire star00:49:01
turns out to be covered by convection and that00:49:04
’s why red dwarfs are so active,00:49:06
powerful flares occur there, which00:49:09
creates problems for life on00:49:13
planets in the habitable zone around this00:49:16
object, these lines correspond to00:49:18
radii like since these two lines00:49:22
correspond to the radii,00:49:24
respectively, half the radius of the00:49:27
star shows that the lines go down steeply,00:49:30
especially here00:49:32
because the density is highly00:49:35
concentrated in such stars.00:49:38
But here, on the contrary, such a flat00:49:41
piece is visible, respectively, the00:49:43
density does not change much for the star; the00:49:46
same line for 0.25 radius and two00:49:50
dotted lines for luminosity In the sense of00:49:53
generation, luminosity00:49:57
is generated due to thermonuclear00:49:59
reactions that occur only in the depths there,00:50:02
something can happen outside, something00:50:04
happens, but the bulk of the reaction occurs00:50:07
inside and So, accordingly, in a star00:50:11
like the sun, we see that a few00:50:13
percent masses00:50:16
determine half of the luminosity and,00:50:19
accordingly, how much is00:50:22
less than 30 In any case, less than 3000:50:26
percent of the mass This is the entire region00:50:27
of energy release For a star like the sun, but00:50:31
We remember that in terms of volume it is only00:50:33
one and a half percent, but the density00:50:35
increases greatly; the density in the center is about 10000:50:39
times greater than the average density Therefore,00:50:41
accordingly, this one and a half percent by00:50:43
volume turns into00:50:47
almost 30 percent by mass; well,00:50:51
with a mass slightly greater than the solar00:50:55
outer convective zone, the convective zone00:50:56
disappears altogether, that is, all sorts of00:50:59
delights associated with the usual mechanism for the00:51:02
occurrence of sunspots disappear and the00:51:04
structure of the star turns over00:51:07
in more massive stars convective00:51:10
core This is quite important because00:51:13
look, we will meet this on one of the00:51:16
slides, if the core is convective, then00:51:20
this mixing in the core all the time00:51:22
equalizes its chemical composition, a00:51:25
light star where the radiant core burns00:51:31
from the inside out. That is, there are still00:51:33
areas of energy release, but00:51:36
inside the core, hydrogen runs out00:51:39
faster this whole structure is the00:51:41
main sequence stage of00:51:42
hydrogen combustion hydrogen ends00:51:45
faster and00:51:47
accordingly a00:51:49
gel core slowly grows inside you the sun for a star with a00:51:53
mass of 08 the gel core grows inside00:51:57
due to the reaction And if the core00:51:59
is mixed all the time your gel core does not00:52:02
grow you just in everything in the core the00:52:04
proportion of hydrogen gradually decreases and00:52:07
eventually it will reach a00:52:09
critical value almost to zero and00:52:13
your reactions will stop at once, they00:52:16
will simply turn off in the entire core at once this is00:52:18
very important for Evolution and the outer00:52:20
shells are radiant and, accordingly,00:52:23
for such stability of the star This is00:52:25
very important it is the pressure radiation that00:52:28
the luminosity is higher and there are large radiant00:52:33
zones just outside.00:52:38
Now we will look in more detail at the evolution00:52:40
on the Russell diagram for different types of00:52:43
stars00:52:45
and on the right is shown the Evolution for a star00:52:47
like the sun, but now one more curl has been added. This is what we00:52:55
still need to get to the main sequence, the00:52:57
star must arise and we00:53:00
see objects at the stage of prota star00:53:03
proto star in a certain sense somewhat00:53:06
similar to red giants but only00:53:08
here the objects move Up and here00:53:11
they move down the red giant00:53:13
is expanding but the star is simply contracting00:53:16
its source of energy is00:53:19
gravitational energy simply high00:53:22
light is achieved due to fast00:53:26
rapid compression This is several million years00:53:28
For example,00:53:30
accordingly, we have stages of00:53:33
this rapid compression, which we00:53:35
will talk in more detail in the future here00:53:37
high luminosity low temperature00:53:40
and then the star itself was practically formed, but the00:53:45
reaction of hydrogen combustion in the core has not yet begun and00:53:49
the star is slowly warming up and00:53:52
moving to the left00:53:55
Russell diagram without00:53:57
increasing the temperature, if it00:54:00
warms up00:54:01
but the luminosity does not change, what is changing is00:54:09
the temperature increases until the luminosity does00:54:12
not change, which means that the00:54:14
area radius is still changing correctly,00:54:16
respectively, the star is compressed, that is,00:54:20
here the compression still continues00:54:23
Well, in such a00:54:26
specific regime when the luminosity is00:54:28
almost fixed at last we came00:54:31
to the main sequence and then00:54:32
everything is clear, here evolutionary00:54:36
tracks are shown for stars of different masses from one00:54:38
mass of the sun to 15 and these are already calculations, that00:54:42
is, here in a beautiful color picture00:54:44
it’s like a picture drawn from the00:54:47
results of similar calculations, but not exactly,00:54:52
and accordingly, here you can see a lot of00:54:55
such pictures here, I00:54:56
want to make one more comment: sometimes the00:55:01
evolutionary tracks in such pictures are00:55:04
not fully counted,00:55:06
and what’s more, the special meanness is00:55:10
that for different stars they count to00:55:12
different stages,00:55:13
so00:55:15
looking at such pictures you understand that you00:55:18
will have to climb for all the details article00:55:21
and see how it was carefully considered00:55:24
here, the stages are indicated by letters and,00:55:26
accordingly, it is clear that different ones are00:55:29
reached, here we have00:55:32
the sun00:55:43
in the infrared range in the millimeter wave breaking off.00:55:46
This can all be perfectly observed there00:55:48
transparently. Thanks for the question,00:55:50
evolution of the sun.00:55:52
So the left picture shows the track on00:55:56
the diagram where the groove is already quite00:55:58
detailed, well, that is, always when there is00:56:01
some kind of ugly picture, it means that they00:56:04
most likely actually calculated it,00:56:06
but Let’s pay attention to this,00:56:09
it’s quite significant,00:56:13
now our luminosity of the sun is growing, we00:56:17
talked about this a little, but I00:56:19
want to see the luminosity00:56:21
the temperature of the sun increases, the temperature of the surface practically does not change00:56:23
and the increase in luminosity is associated with an00:56:28
increase in radius.00:56:30
There is a general rule that if a star’s00:56:34
core contracts, its shell expands. It’s00:56:39
quite difficult to calculate this from first principles, by the way, and just recently00:56:41
there was another article00:56:43
in which the author is trying to00:56:45
create such an00:56:47
understandable toy model of how00:56:50
red giants arise, this is actually a very00:56:52
difficult task,00:56:53
this is a toy model, it takes up a00:56:55
page of 30 formulas, almost covered with formulas, but00:56:59
be that as it may. If the core shrinks, the00:57:01
shell expands, and the fact that00:57:04
now the luminosity of the sun is increasing due00:57:06
to an increase in radius suggests we know00:57:09
that the core is compressed and the core is compressed for a00:57:12
very simple reason, we have hydrogen00:57:15
turning into helium00:57:17
and this means that we have a change in00:57:19
the number of00:57:22
NKT particles and you reduce N,00:57:25
you combine four Protons into one00:57:30
particle and to compensate for this you00:57:33
need to increase the temperature00:57:37
At the same time, if you want increase00:57:40
the temperature you need to tighten up and as a result00:57:43
the core of the sun tightens up The temperature there00:57:46
begins to rise, the00:57:47
center of myberring reactions increases, the00:57:49
luminosity increases That is, everything is fine,00:57:52
the energy we understand where it comes from,00:57:54
why the luminosity increases From an energy point of view,00:57:56
but due to the fact that the core00:57:58
is compressed, your radius increases,00:58:01
so the temperature the surface00:58:02
practically does not change, but the radius00:58:04
grows a little, this happens on a00:58:06
scale of billions of years, as you can see,00:58:08
the effect is small global, don’t00:58:10
tell Trump at all, but00:58:12
this doesn’t explain Global Warming00:58:14
for 10,20,100,200 years, nothing00:58:18
significant happens here,00:58:20
but on a scale of a billion years, this is a00:58:23
serious effect and let me remind you that the sun00:58:26
will come out of the sun the sun will take the earth out of the00:58:29
habitable zone in about a billion00:58:31
years in about a billion years the00:58:34
luminosity of the sun will increase by 1000:58:35
percent and this will be enough for00:58:38
the Earth to be outside the habitable zone00:58:41
there is another funny problem if we00:58:44
turn this back into the past then when the sun00:58:47
appeared on the main sequence,00:58:48
this piece was when she was relaxing there,00:58:51
here the sun was actually born00:58:54
as a full-fledged real star, the00:58:57
luminosity was approximately 70 percent of the00:59:00
modern one, and this leads to an interesting00:59:03
paradox that00:59:05
the seventies realized and This is the paradox of the00:59:08
young sun,00:59:11
geologists00:59:14
confidently tell us that it is very the young00:59:17
earth already had liquid water, but if we00:59:21
naively calculate, it turns out that with00:59:24
the sun's luminosity 70 percent of00:59:26
today, there will be no liquid water on the00:59:28
surface of the Earth, but it was. So00:59:30
somehow it is necessary to explain00:59:33
and this can be explained due to greenhouse00:59:36
effects and for00:59:39
decades00:59:41
people were actively discussing this topic, in00:59:45
particular, Carl Sagan was00:59:47
also very actively involved in this00:59:50
relatively recently. A work appeared in00:59:52
which Yes, the actual question is What. It is clear00:59:56
that this is a greenhouse effect, it is not clear What00:59:57
gases were responsible for it,00:59:59
I want to solve the problem exactly, but01:00:02
apparently it was carbon dioxide gas was01:00:04
once there the main candidate was not01:00:07
there once else what And now it is believed01:00:09
that this is carbon dioxide, respectively01:00:12
Changes in the composition of the atmosphere can01:00:14
lead to a different temperature01:00:16
regime on the planet with, for01:00:18
example, the same luminosity of a star01:00:21
or vice versa Let's have identical thermal01:00:23
regimes at different luminosities from star A, the01:00:26
right picture shows the evolution of01:00:30
the Sun's luminosity over time.01:00:32
Pay attention to the gaps in the scales01:00:34
because, recalling the later stages,01:00:36
they pass very quickly and therefore on one01:00:40
non-linear Nile graphic scale you will not01:00:43
show all the details of the evolution, here is01:00:46
the stage of the main sequence at01:00:47
which the Sun's luminosity increases then there is,01:00:51
after all, a star on the main sequence, the consequences are01:00:53
not sitting at the point, but the sun is moving a little,01:00:55
basically moving upwards,01:00:59
the luminosity is increasing,01:01:01
so the Sun leaves the main01:01:04
sequence and begins to move01:01:06
towards the giant branch, it has reached the01:01:08
giant branch, it has climbed up the giant branch,01:01:11
respectively, the sun01:01:14
will sit on the main sequence about 1101:01:16
billion years ago,01:01:18
the sun climbed up onto the red01:01:22
giant branch, helium flared up in the core,01:01:26
we fell to the stage of burning Helium,01:01:29
then we went a second time to the giant branch,01:01:31
here time is already ticking faster. You see, the01:01:33
fourth decimal place is needed.01:01:35
That is, the pace of evolution The pace of these flares is01:01:39
already characteristic times less than millions of01:01:41
years and after a series of flares the sun01:01:44
will lose its shell and eventually turn01:01:47
white01:01:48
so for the sun it takes quite01:01:51
a lot of time01:01:54
and what about us with stars of other masses I01:01:57
won’t even write on the board ideas01:01:59
terribly simple life time Now you are01:02:01
not temperature but time maybe it01:02:03
was necessary to write T small it01:02:05
was clearer the lifetime of a star in a01:02:08
first approximation, we can estimate how the01:02:10
mass is divided by the luminosity Why is this01:02:13
because01:02:15
90 percent of the time Approximately this is sitting01:02:17
on the main sequence a01:02:19
seat on the main sequence01:02:21
is a01:02:22
seat with almost constant luminosity01:02:25
What happens on the main01:02:27
sequence hydrogen is consumed,01:02:29
not all of it is consumed. But the amount of01:02:33
hydrogen consumed is comparable in order01:02:35
of magnitude to the mass of the star. We are01:02:37
interested in proportionality. Therefore, in01:02:39
principle, it is clear that if we take two01:02:42
stars with one solar mass and hundreds of01:02:45
solar masses, then the second one will burn a hundred times01:02:48
more hydrogen with fairly good01:02:51
accuracy, therefore lifetime is simply01:02:54
mass divided by luminosity illuminated01:02:57
As you remember, for massive stars it is01:02:59
proportional to the mass, and for low-01:03:02
massive stars it is proportional to the mass to about the01:03:05
third power, maybe a third with a01:03:07
tail, and in the end we get that for01:03:10
low-massive stars the lifetime is01:03:11
proportional to mass to the power of minus 201:03:13
in general speaking through01:03:16
2 and 3 2 and 5, maybe for simple01:03:19
estimates a square will do, but for01:03:22
massive stars it just comes out to01:03:23
constants, this graph is drawn based on01:03:26
real calculated data using simple01:03:29
proxies. But that’s exactly how it works, for01:03:32
massive stars we come out to approximately01:03:34
a constant and this is about 2-3 million01:03:36
years, the lifespan of a massive star is only01:03:39
2-3 million years, this is generally01:03:41
nonsense. You remember planetary systems take01:03:43
longer to form. Well, low-mass01:03:46
stars take longer to form; they are01:03:48
active. The stellar phase here is very01:03:50
short. And when we move towards01:03:53
smaller ones mass, then the lifetime increases and01:03:57
at the limit becomes gigantic. This is01:04:00
the age of the Universe.01:04:01
Accordingly, if we draw01:04:03
the boundary like this, then look what a wonderful01:04:05
thing we get: that all stars with a mass of01:04:09
approximately 0.89 solar masses have a01:04:13
lifespan greater than the01:04:14
current age of the Universe, if01:04:16
ever among population 3 stars,01:04:19
a star with a mass of 0.8 solar masses was born,01:04:22
it should survive to this day. Well, 0701:04:25
060501:04:27
0403.01008 all this should survive to01:04:31
our time, on the contrary, if that means you01:04:34
[music]01:04:36
are looking for extraterrestrial life and reasonably01:04:39
assume that for the development of01:04:42
intelligent life we need there are some01:04:45
billions of years there, maybe not four and a01:04:47
half billion years How we are a01:04:48
little faster Well, 3 billion years01:04:51
is what it turns out one two three01:04:56
it’s useless to look for life in stars intelligent01:05:00
life in stars with a mass of already one and a half times the mass of the01:05:03
Sun we’ve done a little bit a star more01:05:07
massive than the sun01:05:08
and its life expectancy01:05:11
has dropped so sharply that no several01:05:13
billion years for a gradual, imposing01:05:16
evolutionary development leading to01:05:20
what we call intelligent life is01:05:21
impossible01:05:25
well01:05:27
Once again, let's look at the01:05:30
child's Russell diagram from such a new01:05:33
article,01:05:34
here the01:05:36
data is drawn for the small Magellanic01:05:39
only for massive stars, here are the boundaries01:05:42
by mass 5,01:05:46
here the luminosity is shown, but we really01:05:48
know well the distance to the Magellanic01:05:50
cloud. But it was possible01:05:51
to draw the visible magnitude; it would be no worse with01:05:54
luminosity; it’s just clearer how to01:05:56
operate with all this; by the way, it’s01:05:59
very revealing that the01:06:02
stars are clearly here a lot, that is,01:06:05
massive Pravda stars are01:06:07
rare and can be clearly seen, they are easy to01:06:09
identify. But they are still very01:06:11
rare and therefore there are always few of them on real01:06:15
diagrams.01:06:17
If we draw a diagram for the upper01:06:19
gorosua according to Gaia data, then of course the01:06:23
upper part of the main sequence01:06:24
will not be populated at all. But01:06:27
In general, a red giant can be seen quite a lot; it’s01:06:29
still not a very short stage of life01:06:31
because stars like the sun end up there. The01:06:33
sun’s total lifespan is01:06:35
more than 10 billion years. Well, the01:06:38
red giant stage ultimately lasts hundreds of01:06:40
millions of years. It’s quite a long time to01:06:42
find a star there01:06:44
I like this diagram because01:06:47
here01:06:49
real astrophysicists drew what they01:06:52
call blue supergiants what they01:06:55
call Yellow supergiants Red01:06:57
supergiants01:06:59
red giants themselves sit01:07:02
what else is interesting here black01:07:05
these are the tracks These are standard01:07:07
standard standard evolutionary01:07:09
tracks01:07:11
you can add something non-standard you01:07:14
can add rapid rotation01:07:16
will affect the redistribution of01:07:19
matter in the interior in particular, and then the01:07:21
tracks will differ; with rapid01:07:23
rotation, the tracks begin to go away for01:07:25
massive stars, here to the left the stars01:07:29
begin to lose their01:07:30
outer parts, which are very powerful. Stellar01:07:33
winds lead to the fact that as the01:07:35
star evolves, it goes in the wrong direction01:07:37
Inflating the red stars with the shell, you01:07:40
see the surface of this shell The01:07:41
swamp01:07:43
shell is lost and you begin to see the01:07:46
hot interior, the luminosity01:07:48
practically does not change because the01:07:49
machine in the center is the same all the time,01:07:53
but in this case you see the inner01:07:56
part And in this case you see the outer part01:07:59
and therefore here the temperature is low here it is01:08:01
high And here01:08:03
the stars are actually observed, these are all the points this is all the01:08:07
observed object01:08:10
Here in this gray area I hope you can01:08:12
see a little contrast in this gray01:08:15
area01:08:16
the stars turn into standard models01:08:19
into red giants or supergiants and01:08:22
flare up like ordinary supernovae01:08:26
core collapse We will talk in detail about the types of supernovae01:08:29
in one of the next lectures.01:08:31
Okay, now there will be01:08:34
many many pictures with evolution on01:08:37
the diagram, the01:08:39
pictures will be of two types, firstly, there is01:08:42
such a good program with the simple01:08:45
name sse, this is singles Stella01:08:48
Revolution, it has a bse version biner01:08:52
stel Revolution but we are interested in01:08:54
the evolution of single stars about double stars we will01:08:56
talk later01:08:58
this is a01:09:00
simple program so easy to download and01:09:03
install and therefore it is convenient to count the01:09:05
tracks yourself and draw so as not to look for01:09:08
what is there01:09:09
accordingly here the01:09:12
tracks for three masses are shown on such a large scale01:09:15
one mass of the Sun stream sun 8 in01:09:18
the sun,01:09:21
they all turn into white dwarfs, they all01:09:24
fall into this region, in the01:09:26
end they all pass through01:09:29
more or less pronounced two stages of01:09:31
giants, through the usual stage of giants and01:09:35
through the asymptotic branch. Well, the same01:09:38
thing here, here is the first stage of giants,01:09:39
the second is01:09:41
here Everywhere there is a shedding of the01:09:44
shell, the01:09:47
second group of tracks here they are in an01:09:51
unsightly form further more carefully01:09:53
drawn based on the results of very detailed01:09:55
calculations01:09:57
taken from the work of Bressan with the authors01:10:03
and these calculations were carried out for a very01:10:06
wide range of oils, essentially01:10:08
minimum to maximum In the sense of01:10:10
galactic masses, here I’ll probably01:10:13
pay attention to that01:10:16
for low-mass stars,01:10:19
only the exit to the main01:10:21
sequence is shown here. Here is the first track01:10:23
from here to here to here. This is the Birth of a01:10:25
star here and then the main01:10:28
sequence of the court and the main01:10:29
sequence. And here the star only01:10:32
reaches the main sequence and01:10:33
then sits there because often01:10:36
calculations of such are quite a labor-intensive task01:10:39
is being done for comparison with observation, a01:10:42
star sits on the main01:10:44
sequence for 1000 billion years.01:10:46
Why should we count further nothing01:10:49
happens there was such a project in its time01:10:51
Twitter of a stone there was a message every day01:10:53
today nothing happened01:10:56
and therefore it is important to calculate the exit to the01:10:59
main sequence So they01:11:00
counted it and hello And as you remember,01:11:03
only in the vicinity of one mass of the sun01:11:05
during the life of the Universe the star manages to01:11:08
significantly revolutionize Well,01:11:11
now let’s look at the Podoland tracks in01:11:13
finer details, now the different01:11:16
stages are numbered, that is, each01:11:18
circle is first second third fourth01:11:20
so on for this track up to 1501:11:24
and here Let's look So the first thing is01:11:27
just somewhere you had to start counting01:11:29
this is a star that is still being born about that star01:11:32
and now it is compressing01:11:35
Here it is compressing to the main01:11:37
sequence it will only reach the01:11:39
fourth point one two three 4 here,01:11:43
in fact, a star is born and now it01:11:46
evolves on the main01:11:47
sequence,01:11:48
accordingly, at the beginning, basically upwards,01:11:51
the sun increases luminosity does not change01:11:54
the temperature practically01:11:56
then it will change a little and01:11:58
the temperature will01:11:59
end reactions in the core,01:12:02
here is the sixth, this is the end of the reaction in the core,01:12:06
here they are over01:12:10
and, accordingly,01:12:13
the star begins to shrink and moves to the01:12:16
base of the giant branch of these tracks the01:12:19
evolution of a star like the sun is counted until the01:12:23
gel flare until the end of the01:12:26
red giant stage, then the star falls01:12:28
down01:12:29
I can’t draw it because I haven’t01:12:31
counted three on the sun, the beginning is similar,01:12:35
but only all the parameters are shifted to the01:12:37
region of higher luminosity and01:12:39
temperatures, here a little more01:12:42
bizarre evolution is like this with a squiggle01:12:44
they'll talk about the01:12:46
first branch of the giants later, we'll discuss01:12:50
here you can guess that such a thick01:12:53
line It came from the addition of two even01:12:55
three movement up movement down a loop01:12:58
and again an upward movement already on the01:13:01
syntactic giants and here everything01:13:04
is counted until the moment when it begins to01:13:06
reset when thermal events occur01:13:13
Well let's zoom in on individual01:13:16
pieces of these graphs, here01:13:22
the group of points01:13:24
here, 45, has finally broken up, now they are still visible as01:13:27
slightly different,01:13:28
and for the three masses of the sun, this loop also became visible01:13:34
after the end of the branch, the red giant01:13:37
here is where helium is burning at this stage in the01:13:39
core the gel is burning01:13:41
about access to the main sequence,01:13:43
we will talk separately later I won’t01:13:45
linger here I will draw your attention01:13:47
Only to the time scale time is delayed01:13:49
in seconds logarithm of time in seconds01:13:52
14.5 is 10 million years this is calculated01:13:56
for a star with the mass of the sun I think01:14:02
accordingly from the beginning of compression01:14:06
before the formation of a star takes place01:14:09
there, it turns out tens of millions of years, that is,01:14:14
this is a process in general, quite a01:14:15
long01:14:17
time for the formation of a star depends on its01:14:19
mass. Therefore, if you begin01:14:22
to form a large cluster of stars,01:14:24
different masses of the cluster are formed01:14:26
slightly at different times.01:14:29
Well, we’ll talk about this later why it01:14:32
grows luminosity on the main01:14:33
sequence we talked01:14:35
because hydrogen turns into helium in our country. And01:14:37
now we will see this on the graphs01:14:42
and that we have one two three 4 5 here,01:14:47
respectively, here the01:14:50
combustion of hydrogen began and the main01:14:53
sequence here is from five to01:14:54
six and here it is clear that the luminosity01:15:01
the temperature increases noticeably and decreases quite a bit; the core shrinks; the01:15:03
shell swells, so the temperature01:15:05
drops a little; this is an01:15:07
interesting hook; we’ll also talk about it01:15:10
later, but here, since the01:15:13
star is more massive, the01:15:15
loops are better visible after the01:15:18
first stage of the giant; the01:15:20
high-mass star01:15:23
at the Helium burning stage goes to the side01:15:26
higher temperatures and, as you might01:15:28
guess, at a higher temperature01:15:30
the star will burn through helium faster, which01:15:36
again shows us that the greater01:15:39
the mass of the star, the faster it01:15:41
evolves at any stage; comparison01:15:43
with a smaller mass;01:15:47
even smaller details; tracks;01:15:54
Let's talk about the hook directly; I'll talk about the wire01:15:58
this hook that is, look here is the beginning the01:16:00
main end here the hydrogen is finished the01:16:04
core is all gone at once there is a01:16:08
big difference this hook appears01:16:10
for stars with a mass greater than 12501:16:13
solar masses which do not01:16:15
[applause]01:16:17
which have a convective core which do01:16:20
not have a pure core respectively these01:16:22
stars, hydrogen immediately runs out01:16:25
in the entire core and the core sharply contracts, it01:16:30
contracts very sharply and01:16:32
contracts here, in response to the compression of the core, it01:16:36
contracts and the whole star,01:16:38
that is, an additional source of energy, here01:16:41
it is for the first time called its source,01:16:44
such a layered source, it did not turn on and01:16:47
therefore the star simply collapses at01:16:49
it just ran out of all the energy, it’s01:16:51
just compressed and therefore it goes01:16:53
into this area when compressed, your01:16:55
temperature and luminosity naturally increase,01:16:57
the energy you take from the01:17:00
gravitational potential energy01:17:03
is good. Another feature is what it01:17:07
means, look, there is a main01:17:09
sequence, there are giants,01:17:11
stars with the main sequence01:17:13
fall in appearance they cannot jump into giants; they01:17:15
cannot teleport to01:17:18
this giant where they must01:17:19
go. But if stars like the sun have01:17:23
this isthmus of transition, it is visible01:17:25
quite well;01:17:27
more massive stars, there are01:17:30
very few objects; such a gap arises,01:17:33
which is called a failure.01:17:35
Why is this so? Well, the natural explanation01:17:38
is The fact is that stars01:17:41
go through this interval very quickly in the course of their evolution,01:17:43
they evolve very01:17:46
quickly, this needs to be explained and this is the explanation.01:17:54
We have a gel core. Now01:17:57
let's say what a source is.01:18:06
So we have a gel core and outside01:18:09
we are in shock it stretches somewhere01:18:11
far to the surface01:18:15
inside the core, the temperature has not yet reached the01:18:18
required values for01:18:21
thermonuclear burning to begin, the helium-01:18:24
carbon reactions are not yet taking place, but on the surface of01:18:27
the core we have hydrogen located at a01:18:29
very high temperature because01:18:31
the core is hot and here we can a01:18:34
layer source will arise, this is where the01:18:36
reactions of converting hydrogen01:18:39
into a gel will occur; they will not go higher because01:18:41
the temperature is low, right here, right at01:18:43
the boundary of the core, the temperature is high, and01:18:45
this01:18:48
part of the star is called a layer01:18:50
source,01:18:52
and accordingly, it is important for us that the Star01:18:57
gets to the giants01:19:00
quickly01:19:02
to expand,01:19:05
we need to achieve01:19:11
degeneracy in the core,01:19:13
respectively, low-mass stars01:19:17
have a way to01:19:20
increase the mass of the core, at the beginning the mass of the01:19:23
gel cores is below critical, you01:19:26
slowly increase it01:19:28
by burning hydrogen in the layer source. That01:19:30
is, your core continues to grow01:19:33
from the outside01:19:34
and01:19:36
continues until the01:19:40
critical mass is reached01:19:42
Schonberg Chandro Sikar limit at01:19:45
which01:19:46
the core will still shrink and the01:19:49
red giant stage will begin so that the shell swells01:19:51
greatly, you need the core to01:19:53
shrink strongly, it cannot yet do this01:19:55
until it reaches a critical mass, and in01:19:57
massive stars the core immediately has01:20:00
sufficient mass01:20:02
and therefore the01:20:04
transition from the main sequence01:20:07
when the gel core has formed, the01:20:09
combustion of hydrogen to the giant branch has ended01:20:12
very quickly, the star01:20:15
still goes through all these investments, but01:20:18
they pass quickly, so the probability of01:20:20
catching a star at this stage is small,01:20:21
respectively, in some large01:20:24
statistical data we see a01:20:25
failure here, what else do we have? It’s interesting01:20:29
we have an01:20:32
instability strip on the diagram.01:20:36
It is located in the region of giants. That is,01:20:38
this works for evolved01:20:40
stars01:20:41
and, accordingly, if the stars fall into01:20:44
this region, then pulsations are observed in them. The01:20:46
most famous type of01:20:48
cruising stars are cifeids. The01:20:51
pulsation period is about the physics of pulsations. We01:20:55
will not talk about it01:20:58
in The details are quite complex01:21:02
and the pulsation period is quite easy to calculate.01:21:04
I don’t even know if we need to write01:21:06
wisdom or the01:21:10
speed of sound. This01:21:18
is,01:21:20
accordingly, in a first approximation, the01:21:22
speed of sound. This is simply the01:21:26
root of pressure on density.01:21:29
Pressure. As you remember, we can01:21:32
estimate the01:21:36
density of internal energy and the01:21:39
internal energy is of the order of potential01:21:40
Therefore, we simply divide the GM square by R and divide it01:21:43
by R, and we obtain the pressure with the accuracy of01:21:47
some coefficients that we are01:21:48
not interested in now; we consider the density to be a01:21:53
constant; we01:21:55
neglect the compressibility and that’s all, and then01:21:58
we obviously, in general, have01:22:01
studied this; we could immediately expect01:22:03
that the speed of sound will, of course, be just01:22:06
about01:22:12
circular velocity If the system is already01:22:15
implemented, then naturally you have01:22:17
thermal thermal motion of particles will01:22:21
have a characteristic speed the same as01:22:25
test particles would have in such a gravitational potential. Well, well, the01:22:29
characteristic pulsation time01:22:34
will be simply proportional to R01:22:37
divided by the speed of sound since01:22:40
This is obvious and then we we get that this01:22:45
time, to a01:22:46
first approximation, is proportional to01:22:48
unity divided by the root of the zhanaroo,01:22:52
it turns out very simply01:22:54
time, the pulsation period is inversely01:22:57
proportional to the root of the density, such a01:23:00
simple formula and our density,01:23:03
accordingly, depends on us and the radius,01:23:05
the radius, depends on the mass, I repeat, these are not01:23:08
main sequence stars here01:23:10
we cannot assume that the radius there is01:23:13
proportional to the mass to the power of 08.01:23:16
But nevertheless, the radius at this stage01:23:20
will depend on the mass and the01:23:22
following chain of reasoning turns out: you have determined the01:23:25
pulsation period,01:23:27
which means, in principle, from here you have determined01:23:30
the density. If you have determined the density,01:23:33
you have determined the mass,01:23:35
and if you you have determined the mass, you have determined01:23:38
the luminosity,01:23:40
so we can expect that the01:23:45
pulsation period will be related to the01:23:49
luminosity for some stars that are naturally of the same type,01:23:55
well, there are such stars of the same type,01:23:59
for example, the most famous. These are Cepheids01:24:01
because the first star of this type is01:24:04
variable; it is clearly visible to the eye; it01:24:06
is in the constellation Cepheus and according to them the01:24:09
whole class was called cichlids, there are01:24:12
other types, there are01:24:15
variable stars. Types01:24:18
they all fall here and, accordingly,01:24:20
for all these types there will be their own01:24:22
dependence of the01:24:23
pulsation period with luminosity, this is01:24:26
very cool remember luminosity, I really01:24:28
want to determine it. Because if you01:24:30
compare the apparent magnitude with the01:24:33
absolute magnitude you have calculated01:24:35
the dedication, you determine the distance01:24:40
to it01:24:42
and for the most part this is impossible for01:24:44
ciphit it is possible plus There is a huge01:24:48
advantage of Cepheids these are massive01:24:50
provoking stars they have01:24:52
colossal luminosity they can be seen from01:24:54
great distances and therefore you can01:24:56
not just Determine the distance to the01:24:58
Cepheid let’s say in what - in a01:25:00
cluster of stars you determined the distance01:25:03
immediately to the cluster or you found a Cepheid01:25:06
in the Andromeda nebula, you immediately determined the01:25:10
distance to the Andromeda nebula and01:25:13
because of all this sophiids, first of all,01:25:16
there are subclasses. This is a very01:25:19
important object because01:25:21
they are an important important step in the01:25:25
so-called distance ladder that is,01:25:27
at close range we measure the distance with01:25:29
parallaxes, but it’s important to use prolaxes.01:25:33
Reach the cephi, learn to really01:25:35
accurately determine the distance to the cephid, and01:25:39
then the pucypheids you can jump01:25:41
straight to other galaxies, but after01:25:45
that you have your own distance indicators,01:25:47
you can move further than a type 1A supernova.01:25:50
For the first time, the luminosity period dependence01:25:53
was discovered by this one. lady henriet and Levite01:25:58
Accordingly, what she did was she took01:26:02
Cepheids in the large Magellanic Where01:26:06
in any such case we can assume01:26:09
that all the stars are at the01:26:10
same distance and therefore their difference in01:26:13
visible magnitude corresponds to01:26:15
their difference in absolute01:26:16
magnitude if two stars are different by01:26:19
one magnitude Apparently you can01:26:21
say that the luminosity of these stars01:26:24
turns on 251201:26:26
And then you can plot the01:26:29
dependence of the pulsation period zifit on the01:26:31
absolute magnitude henriet01:26:34
Levit The first thing was done and since then they01:26:37
continue to do this continuously01:26:39
because it needs to be endlessly refined01:26:42
in order accurately determine the01:26:44
distance already on cosmological01:26:46
scales,01:26:47
several different classes of Cepheids have been identified,01:26:50
plus there is a dependence on the chemical01:26:54
composition which, let me remind you,01:26:56
is called metallicity, that is, these are the01:27:01
shares of heavy elements in the Star, but in01:27:04
general, the longer the pulsation period, the01:27:06
greater the luminosity as you see, this01:27:09
fits perfectly into this logic01:27:11
because that look,01:27:13
the greater the mass, the greater the luminosity.01:27:17
And the greater the mass, the lower the density,01:27:21
respectively, because with a large mass you have a01:27:24
very swollen star and you01:27:26
get a lower average01:27:29
density; a low average density gives a01:27:30
longer pulsation period and in the end01:27:33
we get the following dependencies:01:27:36
which people continue to01:27:38
clarify which are actively used01:27:41
well, I01:27:48
will repeat that the stages of the01:27:52
entire evolutionary stage of more01:27:54
massive stars are01:27:56
shorter than those of stars with less mass and01:28:01
all stages of subsequent combustion Well, there are01:28:04
exceptions, all stages of01:28:06
subsequent combustion pass faster01:28:09
because to trigger the next reactions01:28:12
you still need to raise the temperature and as01:28:16
the temperature rises, your temperature increases,01:28:18
so01:28:20
hydrogen helium can survive for billions of01:28:23
years, helium carbon for hundreds of millions of years01:28:27
for a star like the sun, but if01:28:31
subsequent reactions take place that the Sun does not01:28:34
take place,01:28:35
they pass very quickly and in the end01:28:39
for a star there, let’s say, well, let’s01:28:43
compare the01:28:44
three masses accordingly the time before the sun is01:28:48
not the time of combustion, but at what01:28:50
age does this or that event occur?01:28:53
hydrogen is exhausted in 400 million01:28:57
years and after 80 million years,01:29:02
helium is exhausted01:29:05
20 in the sun01:29:07
80 86 million years and here you just need to01:29:12
add a little bit already, how much01:29:15
is 700 thousand years Yes, in 700 thousand01:29:19
years the entire evolution of the gel nuclei goes through01:29:21
to the end, such a star explodes like a01:29:23
supernova and finally a star of 12001:29:27
solar masses there, as you remember, everything comes out01:29:28
approximately constant, the lifetime of all01:29:32
massive millions of years can be01:29:35
broken down into stages, the main01:29:37
sequence is the path to01:29:40
giant subtigant stage duration of the01:29:46
red giant stage And again, this is01:29:51
calculated for stars of different masses and we01:29:54
see that the time decreases very strongly01:29:57
everywhere in each column, that is, the greater01:30:01
the mass, the faster the star, the evolutioners01:30:03
can see01:30:05
all this in detail here in this book, available online01:30:08
you see all the01:30:11
important evolutionary stages are numbered01:30:13
in the table, you can see the01:30:15
characteristic time01:30:17
that a star of a given mass spends at the01:30:20
corresponding stage01:30:24
Kolya a star evolves, its01:30:26
internal structure changes and it is convenient01:30:28
to show this on such diagrams. We01:30:30
have already seen more or less such a diagram,01:30:33
but now on the horizontal axis before01:30:35
was the mass of the star, we looked at the structure01:30:38
on the main sequence for stars of01:30:40
different masses. And now we have01:30:42
time on the horizontal axis, we look at the01:30:44
evolution of a star with a mass of 5 solar masses,01:30:47
this is not too much, but not01:30:50
too little, it has quite an interesting01:30:52
evolution, so the first stage can be discussed01:30:54
in detail look So here is a star on the01:30:57
main sequence,01:30:59
the core in which reactions take place, the transformation of01:31:01
hydrogen into gels in the mass is not a very01:31:04
large fraction, but it is important that the core01:31:06
is convective, that is, it will01:31:08
mix and fresh hydrogen will be01:31:10
brought into this area. Look here01:31:13
hydrogen. Only the innermost01:31:16
part of it burns can be brought from this01:31:19
part01:31:21
means the convective zone and the radiant zone01:31:25
outside01:31:27
here is a breaker we01:31:30
have formed a gel core here01:31:32
the hydrogen is over at this stage this is the01:31:35
moment with01:31:36
here we are here01:31:40
Okay let's continue after the break01:31:43
10 minutes ago01:31:46
[music]Description:
На этой лекции уважаемый Сергей Борисович расскажет про ЭВОЛЮЦИЮ ЗВЁЗД и познакомит зрителей с ДИАГРАММОЙ ГЕРЦШПРУНГА - РАССЕЛА! Слушатели узнают о различных соотношениях МАССА - СВЕТИМОСТЬ и МАССА - РАДИУС, ВНУТРЕННЕЙ структуре звёзд, времени жизни ЗВЁЗД. Какие ПОПУЛЯЦИИ ЗВЁЗД существуют? Как ЗВЁЗДЫ распределяются по МАССАМ? Почему СВЕТИМОСТЬ растёт на ГЛАВНОЙ ПОСЛЕДОВАТЕЛЬНОСТИ ДИАГРАММЫ ГЕРЦШПРУНГА - РАССЕЛА? Как связаны ПЕРИОД ПУЛЬСАЦИИ и СВЕТИМОСТЬ? Вы сможете ответить на эти вопросы, прослушав эту лекцию! Таймкоды: 00:00:00 Интро 00:00:41 Организационные вопросы по поводу контрольной работы 5 ноября. 00:04:37 Начало. 00:04:45 Повторение солнечных параметров. 00:05:07 Повторение строения Солнца. 00:06:14 Повторения параллакса. 00:06:29 Устойчивость звезды. 00:07:41 Отрицательная теплоёмкость. 00:08:30 Диаграмма Герцшпрунга - Рассела. 00:19:54 Эволюция звёзд. 00:22:46 Эволюция одиночной звезды. 00:26:51 Масса - главный параметр. 00:31:16 Распределение звёзд по массам. 00:36:03 Соотношение масса - светимость. 00:38:38 Получаем зависимость масса - светимость. 00:44:14 Соотношение масса - радиус. 00:44:49 Получаем зависимость масса - радиус. 00:46:53 Перерыв. 00:47:00 Шутка Сергея Борисовича про профессорские леденцы :) 00:47:15 Внутренняя структура звёзд. (учебник по эволюции звёзд на английском языке: https://users-phys.au.dk//jcd/) 00:52:35 Эволюция на диаграмме Герцшпрунга - Рассела. 00:55:49 Эволюция Солнца. 00:58:41 Парадокс тусклого Солнца. 01:01:48 Время жизни звезды. 01:05:25 Диаграмма Герцшпрунга - Рассела новой статьи для массивных звёзд Малого Магеланового облака. 01:08:32 От Главной последовательности до белых карликов. 01:09:45 До и после Герцшпрунга - Рассела. 01:13:40 Выход на Главную последовательность. 01:14:31 Почему растёт светимость на Главной последовательности? 01:14:42 В деталях и малых деталях... 01:15:54 Что за "крюк"? 01:17:03 Провал Герцшпрунга и субгиганты. 01:20:26 Область неустойчивости. 01:21:02 Считаем период пульсации. 01:25:50 Зависимость период - светимость. 01:27:47 Характерные времена. 01:30:02 Эволюционные стадии звезды в таблицах. 01:30:24 Эволюция структуры звезды. 01:31:40 Конец. Наши соцсети: паблик ВК: https://vk.com/public212939391 Инстаграм канала "МГУ 112" (признана запрещённой социальной сетью на территории РФ): https://www.facebook.com/unsupportedbrowser YouTube канал Сергея Борисовича: https://www.youtube.com/channel/UCGk5wyYgpGKuu5Wkjg0WIzQ ВК Сергея Борисовича: https://vk.com/id6382040 Социальные сети оператора (Всеволод Наумов): ВК: https://vk.com/piiv0_seva_tri_k0mpa Инстаграм (признана запрещённой социальной сетью на территории РФ): https://www.facebook.com/unsupportedbrowser
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