Fun stuff: Short and simple note on Stars.

In the series: Note 3: Short and simple note on Stars.

Version 0.5, 5 May, 2020.
Status: Ready.
By: Albert van der Sel.

Here, I like to discuss some important properties of Stars.

Ofcourse, it won't be in minute detail. It's just a very short, and very simple overview
of some key elements. Although it will be very simple, it sure is fantastic stuff to study.
Yes, why actually are there some many differents stars, and variable stars. What is their evolution?
And can we say something about the physics involved?
But ofcourse, it's a very, very simple note.

It would help if you have a general idea about our own Galaxy (milky way), that is, that there
exists a "disk" with spiral arms, a nucleus, and a sort of spherical Halo around the disk.

You might take a look at note 1, section 5, which discusses some of the main features of our Milky way.

1. Populations, and Spectral classes:


In the first half of the former century, Baade and Oort found that we can at least discriminate
between two types of "populations" of stars.

Population I stars are the blue, white and yellow hot stars, but also the more moderate types
as our own Sun (a "middle of the road" yellow star).
They are certainly "luminous", and mainly live in the disk of our Galaxy, and especially in the Spiral Arms.
One other important characteristic, is that they contain significantly more heavier elements,
compared to older Population II stars.

Especially in the Halo of our Galaxy (and in the nucleus too), we can find the Population II stars,
which are older, and more reddish of colour.
They contain significantly less heavier elements compared to Population I type of stars.

This fits nicely in the Supernova model. Short-lived, large and very hot stars, have nuclear processes,
which transforms Hydrogen, and Helium, into ever more heavier elements. At some point (later more in this),
it causes a severe instability which results in a Nova or Supernova explosion. It's a mechanism
by which more heavier elements are blown into Space. New stars can be born from such compressed dust clouds,
containing Hydrogen, but a variety of heavier elements too.

The very old Population II stars, were already in existence before all that, and are very low
in containing heavier elements (astonomers say "low metallicity").

At some later point, the model was somewhat refined to:

-The earliest stars in the Universe: Population III (no metal content) and which are extinct,
-Old stars: Population II (low metallicity) and which are plenty around,
-Relatively Recent stars: Population I (high metallicity) and which are plenty around too.

By the way, Population is often abbreviated to "Pop", which makes it somewhat easier
to type your text.

Spectral classes and the Hertzprung-Russell diagram:

We should have first explored the meaning of analysing spectra. Why would astronomers do that?
I pospone that a bit.

Early in the 1900's, Hertzsprung and Russel, independent from each other, found a way
to characterize (or "categorize" might be a better term) the different types of stars.
Later on, it became know as the "Hertzsprung-Russel" diagram.

we can interpret it as a diagram, that "connects" the "spectral class" (or equivalently, the surface temperature),
to the "absolute magnitude" of a star.

-The absolute magnitude, is a measure of the intrinsic brightness of a star, as seen on a standardized distance.

Ofcourse, we must use a standard distance, since if we would observe a certain star from 500 ly away,
then it looks way dimmer, compared to as you would observe it from only 10 ly.
So, that explains why we need a standard distance. This was choosen to be 10 pc (about 32.6 ly).

The scale here, is a sort of an inverse logarithmic scale. If you know what a logarithmic function does,
then you would know that if you see it's graphic, it first rises steeply, and then slows down
more and more (but still rising all the time).

The exact math is not important here. For now, take for granted that the more lower the absolute magnitude is,
the more luminous it is compared to higher magnitudes. It seems the other way around from what you
might have expected. A larger negative number, means "much brighter" than a positive number.

The alinea's above, says something only about one axis of the diagram (namely the absolute magnitude).

-The spectral class is (more or less) equivalent to the surface temprature of the star.

Astronomers have found that bright blue, or white stars, are very hot.
On the other hand, red stars are usually much less hot.

We even see this in daily life. Slow burning coals (reddish), is not as hot as the white/blue flame
of a welding machine.

A way to categorize was choosen at some point, namely the classes: O B A F G K M.

Class O means a blue and very hot star. Class M means a reddish and much cooler star.
And the other classes sits in between.

(there are more classes, but later more on that).

It's not hard to remember those classifications, since you may identify it with:

-Oh B A Fine Girl Kiss Me.
Or using:
-Only Boys Accepting Feminism Get Kissed Meaningfully.
Or using:
-One Bug Ate Five Green Killer Moths.

(litterally dozens of such mnemonics have been thought of).

Well, it's important for now that from "O" to "M" means "Very hot and blue" to "Red en cooler".

Now, take a look at a nice "Hertzsprung-Russel" diagram, using the link below.

Please notice that:

- the "y axis" represents the absolute magnitude (or brightness, or luminosity).

- the "x axis" represents the class "O" all the way up to "M". Note that the surface temperature,
increases if you go "right to left" (from "M" to "O"). The reverse way, so to speak.

An example of a Hertzsprung-Russel diagram (Wikimedia commons).

There is much to discuss here.

You may notice several "area's" here.

=> First, we have the smaller band of "main sequence" (or "main stream") stars, which goes from upper left,
to down right corner. The graph shows exactly what we would expect:

Large blue/white stars have a high brightness, and smaller reddish stars, have a much lower brightness.

=> Then there is an area with Super giants, with an incredable high luminocity/brightness.
Later more on this.

=> Then there is a section describing the "white dwarf" stars.
Later more on this.

In the graph, there are also typical lifetimes included.

Do you see that large, blue/white hot stars have a relatively short lifetime?
Some do not get older than 10 million years or so.

Do also see that the small reddish stars may reach enormously high lifetimes?
Some are listed as in the order of 1011 years. That means: they may get that old,
but are not yet that old. The Universe itself is likely to be around 13.8 * 109 years of age.

Refinement of the O .. M classes:

You cannot stop astronomers. Impossible. If there is a clear sky, they run to their telescopes.
As time progressed, they found many more stars, which sits more or less between the "O" and "M".
So, a more finegrained scale was deviced, going from O0..O9, A0..A9, B0..B9 etc.. all the way
to M0...M9.

Note that the figure above, for it's y-axis, does not use the "absolute magnitude",
but uses a luminosity expressed in "n times Solar luminocity" (which amounts to the same thing).

2. A few words on Star Formation:

It seems we need to distinquish, at least, between two types of Star Formation.
However, it's likely that there exists multiple routes for star formation.

If we stick for two for now:... then why?

Pop III stars:

First, the Pop III stars, or the non-metallic stars (having no heavier elements) are believed
to be very old. In fact, they were formed not far from the time that the Universe was suffciently
cooled down.
The circumstances were different, if we for example compare it to "current" conditions in a Spiral arm,
with molecular clouds, dust, heavier elements etc..

Indeed, at those times, it all was quite a bit different.

There are quite a few ideas how they were formed, but it is also tied to the Cosmological model
one wants to use.
It's also likely that some Pop III stars, significantly contributed to the amount of heavier
elements in the early Universe. Most of them were indeed be supposed to be very massive.

Pop I and Pop II are still around, but to make sure we are on same frequency: Pop III is supposed
to be "extinct" by now.

There are indeed lots of articles in the "arxiv" libary, investigating all possible conditions
for them to form, and their evolution.
However, I must say that it all also depends a bit on which Cosmological model one would like to use.

You might Google on "Population III Star formation arxiv" and see for yourself that
there is no "full proof" theory yet.

Star formation of "recent" stars:

In many articles, folks often discuss the processes that leads to formation of stars, which would apply
for rather "recent" stars, or for (almost born) stars, as observed today, which are in the "protostar" phase.
In this case, folks often look at large molecular clouds with dust (as e.g. exists in typical Spiral arms),
which is the initial phase in the model to explain Star Formation.

As in the past many stars died, they returned further metal-enriched material to the InterStellar medium (ISM),
that is, in dust and molecular clouds, enriching them even further.
This is a positive factor for possible new stars to emerge.

Let's take a short look then, which processes may be at work for this type of Star Formation.

One important initiator is, local dense regions or lumps, which might then get triggered to contract
furher. There have been many suggestions put forward, as to what the possible mechanisms might be,
for local dense regions to form.

(1). Some studies even suggest that it's a consequence of Galactic activities. Processes in the Galaxy,
or nucleus, may periodically induce "star formation bursts". This then, would be a "non-monotonous"
sort of behaviour. This too, is under active study.
A recent idea is that activities of the massice central Black Hole (e.g. periodic jets) in the nucleus
of our Galaxy, might be related to "star formation bursts".

(2). Other studies (possibly related to (1)), indicate a "turbulence" factor, by which in larger
clouds, local densities can occur, which then forms the basis for Star formation.

(3). A classical mechanism, already suggested a long time ago, are Nova and SuperNova shock bubbles,
which may lead to ISM turbulences, and causing local densties, and consequently Star formations.

(4). The Jeans instability is also favoured by many, and it describes the gravitational "instability"
of a self-gravitating molecular cloud.
If an initial compression takes place, and we see the cloud as a fluid, then it will try to push back.
However, once a serious compression has occurred, gravity will play a larger role in the attraction.
If the "speed of sound" (variations in density which move in the cloud) is lower than a certain treshold,
then Gravity is "faster" than anything else which wants to push back. Namely, fluid furher away, does not know yet
about the compression, but Gravity already does ! So, it wins the competition.

This is often called the "Jeans instability" and might be a good explanation why collapsing of clouds
in lumps may occur, and consequently forms the basis of Star formation.

(5). Above we have seen the Jeans instability. There, we found that an initial compression might
make a cloud collapse, since gravity wins over pressure.

However, an important argument exists, using the socalled "Jeans mass". Simply put, if the mass of the cloud
is large enough, then a collapse will happen anyway. Gravity then wins over pressure.
Dependencies here, are the density and temperature of the cloud. But, for many clouds, it seems
reasonable that a "Jeans mass" exists, for which a collapse will occur,

But, is a some sort of trigger not needed in this case, like a Supernova shock bubble?

It seems to me, that many astronomer still see an initial trigger as essential, as a sort of needed
"push over the edge", to start the collapse.

Note that (1), or (2), or (3) (or possibly something else), may lead to (4) or (5).

Many current observations suggest, that star formation seems to happen in "star-nurseries",
where multiple proto stars are created. In such cases, enormous molecular clouds are neccessary.
Indeed, many "open clusters" of stars, are formed that way, in "star-nurseries", meaning that
many lumps (after the first collapse) went into further individual collapses, and finally
entered the star formation phases.

Flattening to disk-like shape:

As such lump further collapses, the net Angular momentum of the lump is translated to rotation,
in one direction, and the lump flattens to a disk-like shape.
It is assumed, that in that "era", still mass is continuing to spiral towards the core.

I must now admit, that the theoretical decription of the formation towards a "protostar" is quite
elaborate, and involves turbulences, magnetic fields, and conversion of potential energies into radiation.

The whole process of the collapse of the lump, towards the protostar, towards a near star object,
might take hunderds of thousends of years.

While matter influx continues, gravity increases, temperature rises, then at a certain point,
nuclear fusion processes start in the core. Again, at some point, there exists a balance between
the gravitational force to further collapse the star, and the pressure arising from nuclear fusion.
By the way, this sort of balance is also a normal feature of "mature" stars.

The last few decades, it became rather clear that Protostellar disks, may actually also be
Protoplanetary disks. Already today, the number of found exoplanets is astounding, while only
a smaller arc of the sky has been thoroughly investigated (among others by the Kepler telescope).

Fantastic images of star nurseries, as well disk structures near protostars have been made.
See the links below.
Especially the 5th link is spectacular, showing Proto stellar/Proto planetary disks.

Growth spurt of the HOPS 383 protostar (in Orion nebula).
Molecular clouds, dust, and star nurseries.
The Radcliff wave (later turned out to be connected nurseries).
Protostellar disk HL Tauri.
Protoplanetary disk systems. Young Solar Systems in the making !!!

3. Differences in Stars, and some Special Stars:

It is rather well-known that, generally speaking, the "red dwarf" star (like the M spectral class),
is the most abundant star type, as is observed up to now.

However, we have a dazzling collection of different type of Stars, in our local neighborhood (say within 100 ly from the Sun),
as well as in Large systems, like our Milky way.

3.1 Binary systems.

This is not so much about a type of star, but about a "configuration".
There are indeed systems of stars, of two (and sometimes more), which rotate on a common
center of gravity. Indeed, they are physically close, like a distance that often can be expressed
in lighthours, lightdays, lightweeks (but it can be shorter, or a bit larger).

In our Solar neighborhood, like, say in a sphere of about 40 ly around the Sun,
a typical distance between stars is about 5 ly or so.

So, indeed, true binaries are physically close, and affecting each others orbit.
They have a mutual point of gravity.

If you look at the partner stars of such binary system, both can vary substantially in Size
and Mass. For example, Sirius is large white star (spectral class A1), but it's companion is
a small white dwarf.

It's most likely, generally, that the partners of a binary system, were created (more or less)
together during the star formations phases. Only a smaller fraction of the systems, originated
by gravitational capture.

Binary system are very abundant. Now, let's go to the real types of Stars.

3.2 The Cepheid variable stars.

This is such a cool star, and has proven to be a great help for astronomers in distance determinations

During regular periods, they become dimmer and brighter again, in a repeating fashion.
This behaviour. resembles a sort of "harmonic" function not unlike a sine function.
Thus, this behaviour has a well-defined period.

Also, the luminocity (brightness) at the tops and crests, are well-defined.

There are multiple types, but the "classical Cepheid" is a larger Orange star, with a mass > 2 Solar mass.
As said, there are multiple types, for example the RRLyrae stars, which have a very short period (< 1 day).

In the early 1900's, the power of Cepheids was discovered by Henrietta Leavitt.
At that time, she studied a large number of periodic variable stars, in the Magellanic Clouds.

As she worked through all the data, she found a "period-luminosity relationship":
Cepheids with longer periods are intrinsically more luminous than those with shorter periods.

It turned out that: the Period-Luminosity relation, is a distance indicator.
It's not "perfect", but is is a fairly accurate distance indicator, especially throughout
almost all of the former century, a valuable tool.

You may wonder why distances can be obtained.

- You can easily observe the "Period".
- You can thus derive the "intrinsic luminocity" (due to the Period-Luminosity relation).
- You know that the "absolute magnitude", is standardized for a distance of 10 pc (32.6 ly).
- You can see "apparant magnitude" (this is what you see on Earth).

Thus: you can calculate the distance. For example, if know that if a star has "X" brightness at 32.6 ly
and then you see an exact duplicate of that star with an "0.1 * X" brightness, then you know
how far that second star must be.

The various types of Cepheids, help in determining distances, up to 20 Mly (Mega ly, a million ly).
With telescopes in space, this can be pushed up to about 55 Mly.

Why are these stars "variable" in brightness?

In the core of most stars, nuclear fusion works. In upper layers, a multitude of stuff is going on.
In the upper layer, the Cepheids have a surplus of He nuclei, which is very opaque for light.
Therefore, the temperature will rise, because energy cannot so easily radiate away.
The star becomes dimmer.

Shortly afterwards, an expansion takes place, which relatively will cool down that layer,
by which He gets lesser ionized, and becomes more transparant for light.
As an effect, the star becomes brighter again.
And this is repeated over and over again. Indeed, the variable stars are special in that behaviour.

3.3 The White dwarfs, and Neutron stars

We have not dealt with Stellar evolution yet (chapter 2), but beforehand we can say
a few nice things about "white dwarfs" and "Neutron stars".

It is so, that younger stars, initially (and then for a long time afterwards), "burn"
Hydrogen (H) into Helium (He). Ofcourse, it's not really "burning" as we know it from Earth,
but in reality, nuclear fusion processes are at work here.

For heavy stars:

This continues on for a very long time. But when the Hydrogen starts to run out, the original outward pressure
caused by fusion, starts to lower, and the gravitational pressure increases. So, at some point,
conditions are met to progressively fusion ever heavier elements, from the next element,
to the following element.

During that phase, the star may expand, en possibly get "redder".
However, it all depends on the initial mass of the Star, if it's really will become a Giant.

The fusion goes rather "well", until we reach Iron. There is a sort of turning point
with respect to Iron (Fe56), where fusion turns from "releasing" energy, to "needing" energy.
Well, the turning point is somewhere at the Iron/Nickel phase.
The point here is, that the "releasing" energy part of fusion thus slips away, and Gravity
finds no resistence anymore, and takes over.

The star, starts to collapse !

-For lighter stars (see below) It looses the outer shells, which may later form a nebula,
and the core starts to collapse further into a white dwarf.

-For really heavy stars, the collaps may end in a SuperNova explosion, and the core collapses
further into a Neutron star.

Now, Chandrasekhar determined, on the basis of the theory of Gravity, and Quantum Mechanics,
that there exists a limit of about 1.4 Solar Mass.
In chapter 2, we will see more of that. This "limit" says the following:

If the mass of the collapsing core < 1.4 Solar Mass, we probably end up with a white dwarf star.
If the mass > 1.4 Solar Mass, then there is a good chance for a route to become a Neutron star.

White dwarf:

For intermediate mass stars, the fusion chain will end when Carbon and Oxigen is reached.
The gravitational collapse will then proceed.

Here on Earth, in moderate circumstances, you know that an atom has a nucleus (protons and neutrons),
and around the nucleus, we have electrons in a sort of elctroncloud.

In a star, things are different, and stuff is in a plasma like state. However, for our
collapsing star, the pressure gets too enormous, and electrons are squeezed into a too thight state,
until Quantum Rules get dominant, most notably the Pauli excusion principle.

Electrons with the same quantum numbers, "must" be apart, and this leads to a sort of pressure,
the "Electron Degeneracy Pressure", counteracting the Gravity.

A white dwarf is born ! Also note that "free space" between the particles is really low, so a tea spoon of
white dwarf material, would weight many tons on Earth.

Neutron star scenario:

For high mass stars, the fusion chain continues, up to Iron.
Then, fusion effectively stops, and further gravitational collapse is unavoidable.

If the mass > 1.4 Solar Mass, then there is a good chance for a route to a Neutron star.
At some point, gravity is so absurdly intense, that protons combine with electrons, resulting in a core
of a pure neutron state.

The star is now so absurdly dense, that an estimate of the diameter is in the order of 20km,
while it has a mass > 1.4 Solar Mass.
One teaspoon of Neutron star matter, would on Earth weight about the same as a large mountain.

Here too, rules of Quantum Mechanics are dominant, most notably the Pauli excusion principle.

3.4 The Giants

Relative sizes of various Stars:

Although the smaller e.g. K- and M-types of stars (like red dwarfs) seem to be very abundant,
there exists a large "variety" of stars, in terms of Mass, Luminocity, Spectral Class, and size.

Sure, the extremely large stars, are in a strong minority compared to the main stream stars.
However, it's fun to see some comparisons in size, of the larger, to extremely large, stars.

If the diameter of our Sun is denoted by "Rsol", then a few of the largest stars
(in terms of size) observed so far, would be:

UY Scuti: about 1700 * Rsol, Rigel: about 80 * Rsol, VY Canis Majoris: about 1400 * Rsol
Betelgeuse: about 850 * Rsol, etc.. etc..

Although the sizes with comparision to the Sun, can be very large (like 1500 * Rsol), their Masses
usually have not such extremely values. For example, It's rather rare if a (normal) star would have
a mass more than 30 * the mass of the Sun (for good reasons from Physics).
Indeed, the "density" of such stars is much less compared to the more mundane main stream stars.
However, masses of the Largest ones, which are over 30 * Mass (Sun), actually do exist.

In extreme cases, some stars have been observed with masses of 100-150 * Mass (Sun).

It's generally assumed that large stars, with a mass near or over 8 * Mass (Sun), may end up
as a Neutron Star, after they end their "star-life" in a Supernova explosion.

According to the Chandrasekhar theory, we have:

If the mass of the collapsing core < 1.4 Solar Mass, we probably end up with a white dwarf star.
If the mass > 1.4 Solar Mass, then there is a good chance for a route to become a Neutron star.

Even more heavier stars, may end into a Black Hole. It must be said however, that such numbers seem not to have
full (?) consensus among astronomers and other scientists in related fields.
So, I like to be a bit carefull here.

See the links below for some nice illustrations, about extreme sizes of some famous stars.

Size of the Sun, compared to Arcturus and Antares
Comparison from ""
Comparison from ""

If you like some information on Black Holes, please see note 1.

That's it. Hope you enjoyed it.