## Fun stuff: Some astronomical maps and tables of nearby stars and exoplanets. And Galaxies too... And more !

In the series: Note 1: Some maps, tables of nearby stars, and stuff about Galaxies etc...

Version 0.8, 21 April, 2020.
By Albert van der Sel.

- I hope that especially young folks like this sort of stuff...

## 1. Some Maps of (nearby) stars:

For a few interactive links, you need to have Java, or have "Adobe Flash" enabled in your browser.

(Static) Map of nearby stars (< 14 ly)
(Interactive) Map of nearby stars
(Static) Map of nearby stars (< 10 parsec, or 32.6 ly)
(Static) atlasoftheuniverse.com: Map of Nearby stars (< 12.5 ly)
(Static) atlasoftheuniverse.com: Map of Nearby stars (< 50 ly)
(Static) atlasoftheuniverse.com: Map of Nearby stars (< 250 ly)
(Static) Knotted Map of nearby stars (< 14 ly)
(Interactive) Nearby stars - Interactive 3D Rotatable map (You need Java, and activate it)
(Interactive) Nearby stars - Interactive 3D map (up, down, left, right)
(Interactive) Great map of constellations, stars, objects

-Question:
Suppose we represent the Sun as a ball of 10 cm (= 0.1 m = 0.0001 km).
Then how far is the nearest star, "Proxima Centauri" from the Sun, using the above scale?

The distance of Proxima Centauri to the Sun, is about 4.2 lightyears.
This is about 4.2 * 9.4 * 1012 km = 39.5 * 1012 km.

The real diameter of the Sun is about 1392700 km.
Transforming the diameter of Sun, to the scale of 0.1 m (0.0001 km), we have then as the rescaled distance
of Proxima Centauri to the Sun, as: (0.0001/1392700) * 39.5 * 1012 = (about) 2800 km.
(Note: in the calculation above, all values are in km, It's just a rough calculation,
to show the order of magnitude we are dealing with. So, the number is somewhere around 2500km or something like that).

So, if the Sun would be rescaled to a ball somewhat larger than a tennisball, then
proxima centauri would be about 2800 km (or about 1750 miles) away.
Now, this is only about the nearest star. Yes, the nearest star (except for the Sun, ofcourse).

## 2. Some Tables of (nearby) stars and exoplanets:

List of Exoplanets (rather complete)
List of Exoplanets
List of Exoplanets
List of Exoplanets
List of Exoplanets
List of Exoplanets
Nearby stars
List of important stars

List of Exoplanets per period of discovery
Potentially habital exoplanets

## 3. Looking into the Sky, is looking in the Past:

In Astronomy, the unit to express distances, often is the "lightyear", abbreviated to "ly",
which is the distance that light has travelled in one year of time.

Since light travels with about 300000 km/s in vacuum, the ly is an enormous distance
on a Human scale.

It also means that if you watch the night sky, and you watch for example the star called "Sirius",
which is (only) about 8.6 ly away from us, then you see the light that was send out
8.6 years ago.

In a way, you are looking "in the past", if you watch objects in the nightsky.

Take look at the link below. It's a picture of the "Andromeda" spiral galaxy (also denoted by "M31").
It's about 2.5 million ly away from us.

From Wikipedia: The "Andromeda" spiral galaxy.

So, actually, we are looking at M31 "as it was" 2.5 million years ago.

Suppose "now", somewhere in M31, a heavy star explodes into a Supernova. Suppose that happens
somewhere at the rim of that Galaxy. Then we have to wait for 2.5 million years to observe
a rather bright spot at that location at the rim of M31.

Notes:

Note 1: the distance of M31 to us, varies slightly in scientific articles. Usually it is listed
as in between 2.2 to 2.56 million ly. Don't worry too much about that.

Note 2: The "disk" of M31 is usually estimated to be about 250000 ly across. This "star island"
is often estimated to contain 300 to 400 * 109 stars.
But, the "halo" (a sort of sphere around it) contains many stars and objects as well.

Astronomers also often use the "parsec" (pc) to express distances in the Universe.
1 parsec is about 3.26 ly.
So, if an astronomer would tell you that an object is about 100 Mpc away (100 Mega parsec),
then it would be about 100 * 1000000 * 3.26 = (about) 326000000 ly = 3.26 * 108 ly distance.

It's not really neccessary (for the scope of this note) to explore the origin of the "parsec",
but maybe you like to Google on it.

## 4. 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
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.
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.
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.

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 (with respect to the collapsing core).

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.

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 "schoolsobservatory.org"
Comparison from "jpl.nasa.gov"

## 5. Some Maps of our Milkyway (our own Spiral Galaxy, we live in):

There are 3 main types of Galaxies (or 4, if you would subdivide the Spiral Galaxies
into Spirals- and Barred-Spirals).

The main types are: Elliptical (shaped), Spiral (shaped), and Irregular (no obvious structure).

I must immediately say that there are certainly more ways to characterize Galaxies.
Like for example some folks characterize a certain system as a "lenticular" system.
And indeed, some other types exists too.

However, the three main types listed above, are the most prominent ones.

Our own Milky way is a Spiral Galaxy, with a rather dense "core", and spiralling "arms",
which contain stars, gas, and dust clouds.

Here are some nice "maps" illustrating the structure of our own Milky way.

(Static) Map 1
(Static) Map 2
(Interactive) Map 3
(Static) Map 4
(Static) Map 5 Illustration of Globular clusters around the Milky way.

And next we have a striking picture, which zooms in to the position of the Sun
in the local Spiral arms (the yellow circle represents the Sun):

(Static) Zoomed in position of the Sun.

- Our Milky way, has the appearance of a disk, having spiral arms around a dense, and luminous center of stars.
Spherically around the disk, there is a Halo with older stars, and somewhere in the order of
150-200 or so, Globular clusters.

The disk is about 105 ly across, and it is estimated that our Milky way contains
close to 200 * 109 stars (spiral arms plus center plus halo).

-Especially in the spiral arms, we find gas and dust clouds, and a large variety of young
and older stars. It has been found that new stars are mainly born in those spiral arms.
But between those arms, there are many stars as well, but the most of the youngest and brightest ones,
are in the arms.

-It seems rather typical, that spiral galaxies, have a number of smaller, compact, "globular clusters"
distributed around them. Compared to a Galaxy, they are rather small, containing
several tens of thousands-, to several hundreds of thousends-, or sometimes close to a million stars.
So they are really not that small, but compared to the Galaxy as a whole, where they are near,
they seem relatively small.

They live in the Halo, and in the disk, of our Milky way. They have certain orbits around the Galaxy.
Typically, they contain mostly "low metallic" stars, which strongly suggest that they are
extremely old.

Tip: why don't you Google on "types of galaxies", and see the most remarkable
and beautiful galaxies yourself ?

## 6. Some Images of Superclusters of Galaxies ("Milky ways"):

The Individual Galaxies, most often are part of a "Cluster" of galaxies, which themselves form Superclusters.
The Observable Universe resembles a sort of "soap bubbles" type of large scale structure, with large
empty voids, and strings and/or walls of Superclusters (consisting of member Galaxies).

Some of the images below, try to illustrate this "large scale structure".

The nearest Superclusters (1) (atlas of the Universe)
The nearest Superclusters (2) (atlas of the Universe)
The 2MASS redshift survey

Our local patch in the cluster (about 10 million ly accross), is the "The Local Group",of which
the Galaxies M33, M31 (Andromeda) and our own Milky way are the most prominent members.
However, a large number of smaller dwarf- and elliptical systems, are distributed among this region.
The figure in the link below, nicely illustrates the Local Group.

Our local patch: The Local Group of Galaxies.

Tip: For very large structures: You might like to Google on "The Sloan great wall" and the "BOSS great wall"
as observed superstructures (of clusters) in the Universe. Great stuff to read.

## 7. A few words on modern Black Hole theories:

The next phrase is not entirely correct, but if you would approach a black hole (ofcourse still being
at a large distance), it would resemble a pitch black "spherical" object.
It's indeed often said, that at the "event horizon" (or "Schwarzschild radius"), gravity is so high
that even light cannot escape anymore.

Some folks argue (or have good reasons) to rephrase that to: SpaceTime near the Horizon is so streched,
so that light is so extremely far redshifted, that it becomes "invisible".
Then it only "looks like" as if Gravity is so strong that even light cannot escape anymore.

Indeed, talking about Black Holes can be confusing at certain moments. However, it remains true
that from the "outside", near the Horizon, gravitational effects, like strong Spacetime curvature, time dillatation,
and other effects we expect to happen according General Relativity, seems all to be true.

Many different theoretical studies have been done, and still are intensively active, on the "nature"
of a Black hole. Classically, one important tool has always been Einstein's General Theory of Relativity (GTR).
But, many modern insights and theories have emerged the last decades.

### 1. An example of a modern approach:

One important other approach, using elements from Thermodynamics, surely produced
additional insights. For example, take a look at the Bekenstein-Hawking relation below:

 S = kB * A ------- 4 * Lp

The most important elements here, are "S" (entropy) and "A" (surface area of the Black Hole).
We can ignore the other parameters (kB and Lp), for now.

The notion of "Entropy" (S) is often interpreted as a measure of the number of microstates that "sits"
behind a particular macrostate.

Many folks also interpret this as a measure of "information". The remarkable thing about the
upper formula is, that this Black Hole entropy seems to be proportional to the Surface Area "A"
of the Black Hole (at the horizon).

Note the remarkable fact, that this view is unrelated to the interior of the Black Hole.
It's just the area defined by the horizon, which plays a role.

It's indeed very remarkable ! Contrary: If a Black Hole would be a "singularity", then many folks often
argued that when matter is sucked in into the Black Hole, information would be lost forever.
Indeed, for many physicists a true infinitely small "singularity" was never much appealing.
However, the Bekenstein-Hawking relation might suggest that information (in whatever form)
might get "stored" (?) at (or near) the Horizon (the surface "A").
This model is actually rather close to the socalled "Firewall model" of Black Holes.

In a way, the more microstates a system has (larger Entropy), the more information it caries.
You might wonder why this is so. An analogy from ordinary datatransmission (networking) might help.
A monotone signal has no intrinsic information. But if you "modulate" it, by varying the frequency
or amplitude, then it can carry information. As it were, the number of "states" have increased.

You might thus go as far, as saying that when a Black Hole aggresively sucks up matter,
then "A" would increase, and so does it's entropy, and so does the "information".

All in all, I have not mentioned a lot here, but I tell you that it is quite a different approach
compared to the idea of an infinite small singularity, with a "Schwarzschild radius" (or event horizon)
which "surrounds" it.

### 2. The semi-classical approach, using Relativity Theory:

It's also important to take a look at the (semi-) Classical approach using General Relativity.
It's still very important, since many physicist uses GTR, or derived theories (like EiBI gravity),
which still up to this day, produces stunning results.

In a nutshell, the semi-classical approach goes a bit like this:

SpaceTime is a 4D continuum, and Einstein uses a lot of differential Geometry (a sort of Math),
to search for his answers. One main result is, that SpaceTime "warps" or "is curved" when Mass-Energy
is near. Curved SpaceTime can be associated with Gravity.
When there is no Mass-Energy, or we are very far from it, SpaceTime is "flat" (and no Gravity).

This is all reflected in his General "Field Equations".

Einstein's field equations provide for a framework, but not a specific solution like a "metric",
for example, to calculate a distance in a certain SpaceTime.

Schwarzschild found a solution, that is a "way" to calculate distances, and a general description of SpaceTime,
which conforms to Einstein's equations.

But there are also very interesting collaries to his findings. It became clear (in this semi-classical theory),
that any mass has a "critical radius", meaning that if you would extremely compress that mass
under that treshold, it would fully collapse into a Black Hole. Intially, the interpretation
was such, that at that "critical radius", gravitation would be so strong that even light could
not escape anymore.

In somewhat "better" words, the "mass-density" would be so high, that the surrounding SpaceTime would be so
streched, that even light would so redshifted, that it does not show anymore.

For that critical radius, called Rs, Schwarzschild found that the relation
to any Mass "M" is:

### Rs = 2 G M / c2

Where "G" is the gravitational constant, "c" is the speed of light, and "M" is the mass inside

For any mass "M", a corresponding critical Schwartzschild Radius rs (or "R") can be calculated,
which defines the Horizon, and effectively says when then mass becomes a "black hole".
For example, if the Sun's Total mass were to be compressed within (about) 2 miles (the Rs for that Mass)
then it would become a black hole. For Earth, we need to compress our planet within 1 cm.

All in all, also the semi-classical theories provided the framework to describe Black Holes.

I must be extremely carefull in not suggesting of the existence of any "structure" inside the Black Hole.
It's simply not known.

-The classical model seems to point at an infinitely small "singularity" within the critical radius (Horizon).
-The conjectures of Bekenstein/Hawking seem to suggest a sort of storage of information at or near the Horizon.

At least, a singularity seems to be in conflict with Quantum Theories.

There is a tiny problem perhaps in using phrases as "length stretches", or "SpaceTime stretches"
and that sort of statements.
We know from Special Relativity, that the SpaceTime distance between "events" must be constant.
That requirement has not dropped.
The only thing we can rightfully say is that SpaceTime gets very curved as you approach the critical radius,
And it will even be asymptotic at, or very near, the critical radius.
This means, according to most physicists, SpaceTime is so streched, that light will be infinitely redshifted.
Indeed, also according to GTR, the clock will go slower and slower, nearer and nearer to the Horizon.

In many discussions, it is often said that a remote observer may see a spacecraft to get "spagettified",
as it would get nearer and nearer to the critical radius. The observation however, is indeed correct.
It's correct for a remote observer, since light and time seems to "freeze" for that observer,
when the object get's very near the Horizon.
For that spacecraft itself, it's probably true that other events will take place.

Lastly, I must say that many treatments of Black Holes, consider Mass, Charge, and Angular momentum
at the initial state, and then looks (theoretically) what happens when a Black Hole forms,
when for example a massive star collapses at the end of her life.
Different models go around, like e.g. the Kerr Black Hole, and others.

Even rather exotic models were published. It never found much support in the community (as it seems
to me), but maybe you like to Google on the "Fuzzball" black hole theory.
It's a valid model, or maybe I should say, a valid attempt to explore Black Holes.

### 3. Now, what has been observed in reality, so far? Here are just a few examples.

-Cygnus X-1:

Also from my youth, I remember that it was strongly suspected that Cygnus X-1 was likely
to be a black hole. It's a black hole near a (normal) large blue star, and the black hole is
rather brutally sucking material away from it, leading to intense X-ray radiation.
The intense radiation, is produced due to the large acceleration of the material towards
the black hole, in a rotating disk, spiraling towards the black hole.
The radiation was detected during the '60's/'70's of the former century.
Today, almost nobody doubts that we actually have a black hole in this system.

It then would be the first one, that was ever discovered.

It's about 6000 ly away, and the black hole itself is likely to have a mass of (only) 0.8 Solar Mass.

-Massive Black Hole in the Center of our Milky way.

Gradually, it became clearer and clearer, that a very massive Black Hole, sits in the center
of our own spiral galaxy (the Milkyway). It's located at Sagittarius A, the center of the Milky way.

Even stronger: Today, It is generally assumed that having a massive Black Hole at it's center, is a
rather common feature of Spiral Galaxies in general !

For the Milky way: many clues were acumulated. For example, the socalled "S" stars have very close
orbits near that massive black hole, and have enormous speeds in higly rosettic orbits (elliptic with precession).
Using that data, it can be inferred that this Black Hole has a mass of around 4 million Solar Masses.
If you see the data on the orbit of star "S2" around the Black Hole, you can hardly believe it.

It is indeed fenomenal, that the orbit is exactly for what General Relativity predicts.

-Massive (and not so massive) Primordial Black Holes.

Interestingly, rather recently, more and more articles appear from astronomers who make a case for abundant
massive "primordial" black holes.
For example, in the "arxiv" library, many recent articles can be found.
However, the theory is not new, but it seems that it received a renewed interest from the community.

It's indeed highly remarkble. In essence, the abundant number of massive "primordial" black holes
came into existence, relatively short after the Big Bang. A number of astronomers believe
that they were actually a motor around Galaxy formation.

Note: For about Galaxy formation after the Big Bang: it was often assumed that small fluctuations during
the Inflationary period, were actually the source for later Galaxy formations.
But, it seems now, that an alternative is considered.

-Detected Gravitational waves due to Black Hole collisions.

Already predicted by Einstein's GTR, finaly, in september 2015, the first "direct" observation
of gravitational waves was performed by the the LIGO and Virgo Scientific Collaboration.
Only after extremely careful examinations, the result was announced to the public, in februari 2016.

Since Relativity Theory plays in a Continuum "background", all relative motions (especially accelerations)
of Mass-Energies must produce distortions in SpaceTime which propagate, not unlike
the usual ElectroMagnetic radiation (like radio waves). However, those are generally extremely weak
and connot currently be detected.

However, when Massive Black Holes gets nearer and nearer, they have an "interaction" (acceleration)
resulting in evenly proportional distortions (waves) in SpaceTime, which might be
detected, here on Earth.

And that's exactly what happened in 2016!

The label of the event: GW150914
The source: 2 black holes of approximately 30 and 35 Solar Masses, spiraled to each other
ever faster and faster, resulting in an incredible sort of "merger" of those two entities.
Distance: About 1.4 * 109 ly away from our Sun.
Peak signal: due to the merger, resulting in 3 Solar Masses energy conversion into Gravitational waves.

Note: ofcourse, since the event was calculated to be as far as 1.4 * 109 lightyears away from us,
we must understand that it actually happened about 1.4 * 109 years ago (indeed: that far in the past).

Tip: Why don't you Google on the LIGO detection equipment, and it's ability to measure extremely
small distortions in SpaceTime. I am quite sure you will knocked out of your socks!

-April 2019: The very first photo of the Massive black hole in M87.

In April 2019, the "Event Horizon Telescope" organization, published the first image
of a very massive black hole in the galaxy M87.

M87 is a galaxy, at a distance of about 55 * 106 ly.

Using a worldwide array of radiotelescopes, with telescopic devices distributed across the Globe,
it has proven to be possible to capture images of the Black Hole in the core of M87.

In that period, typically about 350 Terrabytes per telescope, per day, were processed by Supercomputers,
using smart algolrithms, ultimately resulting in very clear pictures.

The pictures essentially show extremely hot matter and gas, under the enormous gravitational pull
of that super massive black hole. On the pictures, the "shadow" of the Event Horizon is visible.
Also the twists of the matter and gas near the Horizon, due to extreme gravity, is shown.

The true Event Horizon is about 2.5 smaller than the Shadow it casts on the clouds.
It has been calculated to be around 7 * 109 km, which makes it quite comparable
to the size of our own Solar system. How about that !
The mass of this Black Hole is about 6.5 * 109 Solar masses.

Event Horizon Telescope
Picture and explanation M87 and it's supermassive Black Hole
Picture and explanation M87 and it's supermassive Black Hole
Nice article of National Geographic

## 8. Hubble redshifts and interpretations:

### 1. Origin and basic idea:

You may generally say, that well before the year 1920, the observed Nebula (even those with a spiral structure),
were not generally understood to be real Galaxies (independent "star islands", like our own Milky way).

Well, that is, by the main stream astronomers. Already in the early 1800's, some folks really
already suspected, that some nebula were "star islands", just like our own Spiral Galaxy is.

Then, in the early 1920's, it became more and more accepted that many Nebula were indeed
independent "star islands", that is, Galaxies.

It's all very facinating history ofcourse. But one feature stood out: The more distant a Galaxy
seemed to be from us, the more "redshift" was noticable in it's spectrum.

That was quite weird in a Universe which most folks, at that time, characterized as "Stable" and "Steady".

But it seemed that those remote Galaxies, recede from us, and "the further they are, the faster they go".

It's a bit similar as the "doppler effect" with sound waves.
If a car with a sirene races towards you, the pitch is higer. When it has passed, and drives
away from you, the pitch gets lower.

However, consensus exists that this is not a "doppler effect", although the effect looks pretty similar.
In socalled "comoving" coordinates, galaxies do not move, but Space is expanding. This is what we think is going on.
Space is expanding, giving rise to a "redshift" in the wavelenght of light.
The furher away, the more Space was expanded, the more redshift of light is observed.

As historians have made clear, it was Lemaitre who came in 1927 with the idea that such an expanding universe
can be "calculated back" in time, to some "sort" of origin.

However, it remains rather peculiar that galaxies flee away faster and faster, depending
on the distance to us. Even today, this is not fully solved, but complex ideas exists
like "some Dark Energy" which is responsible for the effect, but other theories exists too.

It's important to understand (as consensus exists among astronomers), that those galaxies do not fly
through space (except their smaller random/peculiar motion), but space itself expands.

One nice analogy is a balloon. If you blow a small bit of air in it, you can draw some small galaxies
on the surface. Now, you inflate the balloon more and more. As you will notice, for every galaxy,
it seems that all others flee away. No galaxy is "special", and for every galaxy, it seems that all
others go further and further away. In this example, the balloon surface streches more and more,
explaining the observed effect.

But what about the real Universe? Does SpaceTime "strech out" as time goes by, or what?

Let's first get back to Hubble, or I should say "Hubble-Lemaitre", since both independently had the same
sort of ideas (actually, so it seems, Lemaitre a little bit before Hubble).

The mathematical relation Hubble and Lemaitre found, describing the receding speed "v" and distance "d",
looks remarkable "simple". It's just a linear relation:

### v = H0 * d

Where H0 is a constant (Hubble's constant).

So, it relates the speed of a fleeing Galaxy, with respect to it's distance to us.

It must be said, that the relation does not work well, with objects which are "relatively" close,
that is, within 300 million ly (or thereabout). Do not take that lower limit "too strict".
However, for relatively remote objects, the "law" works "rather" well, but has limitations.

For one thing, it turned out that's not so easy to determine the Hubble constant H0,
and different considerations produced different values over time.
One recent study (2017) produced a generally accepted value of approximately "70 kilometres per second per megaparsec".

The theory presented sofar, is an oversimplification ofcourse. But, it's a note by Albert,
so we already knew that fact.

However, we are not done yet with Hubble's constant. The modern (socalled) Planck CMB data,
have introduced a rather remarkable "tension", between established methods to determine Hubble's constant,
and what we can derive from Planck CMB data.
It might well be that the Hubble constant is dependent on the densities of normal matter, dark matter, and

### 2. Accelerated expansion?:

That the Universe expands, might not sound too strange, if one accepts the Big Bang model
of the Universe.
For many Physicsts, Astronomers and other scientists, the socalled "Inflationary epoch" seems
to be good refinement of the Big Bang Theory.

A Universe which expands is one thing, but there seems to exist strong indications that we might
have an accelerated expansion, and this, possibly, is somewhat harder to understand.

One experimental study (1998) was with observations on Supenova Type 1a, which are supposed to behave
as "standard candles" and provide a well-defined luminocity (they all have the same brightness).
This standard brightness can be used to calculate the distance. At the same time, the researchers
can use the redshift to determine the distance and relative speed.

The study turned out to deliver somewhat slightly unexpected results.
The Supernova were "fainter" (less bright) as what was expected from redshift/distance calculations.

Or, they seem farther away, then was expected. Below you can see how the experimental data looks like.

The "Supernova Cosmology Project" data.

Although the data does not seem to deviate a lot, by the "eye", it's still scientifically significant.
All in all, the data seems to point to an acceleration of remote objects.

The "acceleration" should be perhaps be interpreted as follows (it's not an explnation):

The way SpaceTime determines the "metric", or how to "calculate" a distance, is changing.
In such an opinion, it's not really so that Space is added, or Space gets streched,
but an intrinsic property of SpaceTime, still unknown to us, rescales the distance between objects.
This sounds somewhat mysterious, and most people simply say that Space streches more and more.

Anyway, whether the above is true, or something else is going on, for remote objects,
it "looks like" if they are moving through Space, but it is actually Space
itself, which "streches" (or perhaps in better words, rescales itself continuously).

For ease of argument, I will often say that SpaceTime will strech over time, but that
might be an incomplete statement.

Next should follow an explanation of this effect. I think it's fair to say that it is still
a subject that's debated, and investigated, intensively.

Indeed: one fundamental question thus seems to be: What is it exactly, that expands, in an expanding Universe??

One line of reasoning, is the proposition that the Vacuum has an intrinsic energy which is the
driving force behind the streching, or rescaling, of SpaceTime. However, nobody knows for sure right now.

Anyway, the objective of this section, namely a few words on the Hubble Redshift,
is hopefully achieved.

## 9. The "Age" and "size" of the Universe:

In this section we like to see, if the are any answers about the "age" and "size" of the Universe.
For about the "size", we will see that there are some extra considerations we must keep in mind.

But, there are reasonable answers to these questions.

### What about the age of the Universe?

Astronomers have a rather large tookit, to determine to age of the Universe.

1. Using Hubble's law in a backwards calculation:

Hubble's Law tells us that the universe is expanding, and we already have seen in the section above,
that "v=H0 * d". If needed, please see section 8 again.

Using solely that relation, and assuming a constant expansion (which procedure in this case
is not fully correct), you can calculate backwards, to the "point" where it all started.
I must explicitly state, that this calculation is extremely rough, and can do no better
than to point us to the order of magnitude of the age of the Universe.

-> What's more, how do we know for sure that Hubble's constant does not depend on time?
For example, was it the same value, 3 billion years ago?
For now, as many astronomers do, Hubble's constant is taken as constant with respect to time.

-> Also, let's assume a constant expansion (which is probably incorrect too).

Not withstanding all counter arguments, I am not "a piece of cotton wool", so let's simply
try our shaky calculation:

Note: you do not need to follow this calculation.

v=H0 * d and we have d = v * t (constant expansion) => t = d/v thus:

t=d/v = d/(H0 * d) thus:

t=1/H0

A good (*) value for H0 seems to be H0=72 km/s*Mpc, where 1 Mpc=(about) 3 * 1019km

Now, we have a time unit (s) in the relation above, so we can rework H0 to:

1/t = 72/(3*1019) = 24/10-19 => 1/t = 2.4 * 10-18

=> t = 1/2.4 * 10-18 = 4.2 * 1017 seconds.

Now, let's rework the number in seconds, to years:

=> t = 13.3 * 109 year.

So, this very rough calculation (which is quite shaky indeed), gives us 13.3 billion years,
or 13.3 * 109 years, for the age of the Universe.

Amazingly, this comes quite close to the value which astronomers believe to be the
correct (or reasonable) value of 13.8 * 109 year.

(*): Since the WMAP and Planck CMB data, there exists a "tension" between different
methodologies to determine H0. Below we find some more information on this.

2. Investigating old stars, and Globular Clusters:

Astronomers say that especially Globular Clusters are very, very old.
If one would study articles about Globular Clusters, then a typical age is somewhere
around 11 to 12 * 109 years. Actually, they must have been formed
rather shortly after the birth of the Universe.

Serious thoughts are, that for example for the Globular Clusters around our Milky way,
that they might be older than the Milky way itself.

In a way, these Clusters place a lower limit to the minimum age, because obviously,
the Universe must have been created, before Globular Clusters could have formed.

So, from the study of some established older objects, like Globular Clusters, we can say
that the age of the Universe must be larger than 12 * 109 years.

3. CMB data:

The "start" of the Universe, is widely believed to be described by the Big Bang Theory.

In 1980, a possible refinent was proposed (or added), called the "Inflationary epoch",
or "Inflationary Cosmology" (by Guth). Since then, many revisions to the theory happened, leading to a large
amount of great articles and opinions.
However, in the scientific community, as (almost) always, we have scientist who are "pro",
but also quite a few of other scientists which don't like it much.

But, Inflation certainly has an answer to some former "tough problems" like the "horizon-" and "flatness" problems.

And, the recent Planck CMD data (see below), makes it really hard to dispute the Inflationary scenario.

The Inflationary theory says, that at an (almost) absurdly small time scale from the very start of the Universe,
from say, 10-37 to 10-31 seconds, a period of exponential (extremely rapid) expansion
of SpaceTime took place.
At slightly later phases, after inflation, several rather complicated events happened.
(For this note, the details are not important).

Let's say that, as of 10-6 seconds (or so), more "mundane" (or familiar) physics took over.

After the "Inflationary epoch", Universe expanded further (non-inflationary), and also cooled down.
A while later on, was a rather lengthy period where particles like protons, electrons, and
intense radiation was present, as a "plasma", or soup of loose particles, where photons constantly interacted
with those particles.
So, for this radiation, the Universe was opaque, and "free paths" were impossible.

Then, approximately 380000 years after the Big Bang, the Universe was sufficienly cooled down
for particles to finally form atoms (primarily Hydrogen). For radiation, it meant a "free path",
and the Universe became transparant for radiation. Finally set free !

This first free radiation of the early Universe, is the source of the "Cosmic Microwave Background" radiation,
or CMB, as we observe it today.

At that time, at the moment the Universe became transparant, the temperature was about 3000K.
From then, up to now, the Universe has steadily expanded, cooled down, and the present "afterglow"
is about 2.72K. As the Universe expanded over time, so did this radiation, until it reached
microwave length, as it is today.
It's really a background radiaton, corresponding to about 2.72K, observable at all places,
where ever you would measure it.

There exists very slight variations in the radiation. After carfefull examination, they seem
to match extremely early quantum flucuations, which were preserved during the Inflationary period.
This is reflected in very small Temperature variations in CMB maps.

Although the very firs ideas of CMB, already slumbered around in 1948, it was actually
only discovered in 1964, by Penzias and Wilson.

However, in the last couple of decades, better and highly detailed maps were devised.
For example, using the COBE satellite (1989), and quite some time later, by using the WMAP
satellite (2001). Lastly, the Planck Surveyor mission (launched in 2009), provided the best details
in the map of the CMB. Indeed, COBE and WMAP did not have the enormous precision of the Planck data.

All in all, the details of the Planck data, really seems to hint to "dark energy" for example,
and other facinating features, like a rather strange "colder spot".
Putting this even stronger: there is a lot of new physics to be discovered.

Some nice links on Planck CMB data:

Planck CMB map (1)
Planck CMB map (2), and a facinating explanation.

The age of the Universe, as established by the Planck Collaboration team, is 13.8 * 109 years.

This was done on the basis of the Planck CMB data. Amazingly, the Hubble constant they derived
is quite a bit lower than the values derived from study of ordinary objects.

For about the age of the Universe, a (rather spicy) derivation can be found in:

Flat Space, Dark Energy, and the Cosmic Microwave Background (arxiv)

At page 14, you can see a mathematical integral, showing the calculated age of the Universe.

Such scientific articles are indeed a bit hard to read.
I primarily placed the link here, to show you (or prove to you), that the Planck CMB data, actually
gives rise to a number of renewed astronomical parameters, among which is the age of the Universe.

In the article, and other articles on CMB data, folks very cleverly expressed the Hubble constant
in density rates (density of all matter/energy, depending on time from t="0" to t="now", and integrating
the whole lot, and amazingly producing the number of 13.8 * 109 years. Simply stunning.

### What about the "size" of the Universe? (see next note).

This is a bit of a spicy question.

In the past, I always believed that SpaceTime over a Global Scale, had curvature, maybe positive,
or perhaps negative (hyperbolic, ever expanding), also depending on the density of mass-energy.

However, for example by the "Inflationary Theory", or the latest data, e.g. from the Planck CMB data,
and even lots of more clues, it'really seems that SpaceTime is flat (except for local curvature near Masses).

Or is it not flat, but (positively?) curved? Is the data really convincing to say the one
or the other? Well, according to the standardized model called ΛCDM, and the latest data, it seems flat.

Many pointers say that SpaceTime is flat. Do not laugh, but I personally, am still not convinced...
Some scientist indeed still have doubts, if you scan modern articles.

To say something usefull, it's unavoidable to talk about a Primary Cosmological model of today,
which is the ΛCDM model of the Universe, but some other ideas are important too.
All in all, it's quite a bit of material to discuss.

I will try that in the next note.

## Appendices:

### Appendix 1. Optional section. Fun stuff: Parallel Universes?

Parallel Universes? No..., I am not really a "believer".
There exists no real clues that it's actually true, or neccessary.

However..., some theories are pretty strong. And it's fun to see a serious collection
of such theories. But, I like to emphasize on the "fun" part of it.

Still, it may help to give an additional perspective on our Universe. Who knows?

If you like to see it, use the following link:

A simple overview of some "Parallel Universe" theories.

Last update: 21 April, 2020.