Hubble constant. Expansion of the universe

Consider two galaxies located at a distance L from each other and moving away from each other at speed V. What is the value of the redshift in the spectrum of the first galaxy, measured by an observer located on the second?

It would seem that the answer is obvious. Redshift value z is equal to:

However, this magnitude of redshift would be expected in a stationary Universe. But our Universe is expanding! Can the very fact of the expansion of the Universe affect the value of the redshift?

Let's change the problem condition. Now let's assume that the galaxies are at a fixed distance L from each other (for example, they rotate slowly around a common center of mass). Will an observer located in one galaxy detect a redshift in the spectrum of another due to the fact that the Universe is expanding?

When the Universe expands, it overcomes the gravitational attraction between its parts. Therefore, as the Universe expands, its expansion rate decreases. A photon, moving from one galaxy to another, just like any object inside the Universe, gravitationally interacts with expanding matter and, thereby, “slows down” the expansion of the Universe. Therefore, the energy of a photon moving in an expanding Universe must decrease. Let's make quantitative estimates.

When the photon left one galaxy, the gravitational potential inside the Universe, created by all the matter in the Universe, was equal to F 1. When the photon arrived at the second galaxy, the gravitational potential inside the Universe increased due to the expansion of the Universe and became equal to Ф 2 > Ф 1 (at the same time | Ф 2 |< | Ф 1 |, так как гравитационный потенциал меньше нуля). То есть фотон, вылетев из области с более низким гравитационным потенциалом, прилетел в область с более высоким гравитационным потенциалом. В результате этого энергия фотона уменьшилась.

Thus, the redshift value in the emission spectrum of a galaxy that is moving away from us will consist of two parts. The first part, caused directly by the speed at which galaxies are moving away, is the so-called Doppler effect. Its value is:

The second part is caused by the fact that the Universe is expanding, and therefore the gravitational potential inside it increases. This is the so-called gravitational red shift. Its value is:

(8.9)

Here F 1 is the gravitational potential of the Universe at the place of the photon’s departure, at the moment of its departure; Ф 2 – gravitational potential of the Universe at the place of photon registration, at the moment of its registration.

As a result, the redshift value in the emission spectrum of the galaxy moving away from us will be equal to:

(8.10)

And we come to a very important conclusion. Only part of the cosmological redshift observed in the emission spectra of distant galaxies is caused directly by the distance of these galaxies from us. The other part of the red shift is caused by an increase in the gravitational potential of the Universe. Therefore, the speed at which galaxies are moving away from us is less, than is assumed in modern cosmology, and the age of the Universe, accordingly, more.

Calculations performed in show that if the density of the Universe is close to critical (this conclusion is made based on studying the large-scale distribution of galaxies), then:

That is, only 2/3 of the cosmological redshift value z 0 in the spectra of distant galaxies (8.10) is caused by the speed at which the galaxies are moving away. Accordingly, the Hubble constant is 1.5 times less than assumed in modern cosmology, and the age of the Universe, on the contrary, is 1.5 times greater.

How is the question of the origin of the cosmological red shift resolved in the general theory of relativity? Let us consider two galaxies that participate in the cosmological expansion of the Universe and whose peculiar velocities are so small that they can be neglected. Let the distance between the galaxies at the moment the photon leaves the first galaxy be equal to L. When the photon arrives at the second galaxy, the distance between the galaxies will increase and be equal to L + L D. In the general theory of relativity, gravitational interaction is completely reduced to geometry. According to this theory, the most important quantity characterizing the expanding Universe is the so-called scale factor. If the peculiar velocities of two galaxies distant from each other can be neglected, then the scale factor will change in proportion to the change in the distance between these galaxies.

According to the general theory of relativity, the wavelength l of a photon moving in the expanding Universe changes proportionally to the change in the scale factor, and the red shift, accordingly, is equal to:

(8.12)

If V– speed of galaxies moving away from each other, t is the flight time of the photon, then:

As a result we get:

Thus, according to the general theory of relativity, the cosmological red shift does not depend either on the density of the Universe or on the speed with which the gravitational potential of the Universe changes, but depends only on the relative speed of recession of galaxies. And if, for example, our Universe was expanding at the same speed as it is now, but at the same time had several times less density, then, according to the general theory of relativity, the value of the cosmological red shift in the emission spectra of galaxies would be the same. It turns out that the existence of huge masses inside the Universe, restraining the expansion of the Universe, does not in any way affect the energy of moving photons! This seems unlikely.

Perhaps this is why serious problems arose when trying to explain, within the framework of the general theory of relativity, the dependence of red shifts in the spectra of very distant supernovae on the distance to them. And in order to “save” the general theory of relativity, at the end of the twentieth century, cosmologists put forward the assumption that our Universe is expanding not with deceleration, but, on the contrary, with acceleration, contrary to the law of universal gravitation (this topic is discussed in).

Here we will not discuss the hypothesis of the accelerated expansion of the Universe (although, in my deep conviction, not only the general theory of relativity, but no other theory is worth saving with the help of such hypotheses), but instead we will try to transfer this problem from the field theoretical physics into the field of experiment. Indeed, why conduct theoretical debates about the origin of the cosmological redshift if you can get the answer to this question in a physical laboratory?

Let us formulate this important question once again. Is there a cosmological redshift caused not by the Doppler effect of galaxies moving away, but by the fact that as a photon moves, the gravitational potential of the Universe increases?

To answer this question, it is enough to carry out the following experiment (see Fig. 33).

The laser beam is split into two beams so that one beam immediately hits the detector, and the second beam first moves for some time between two parallel mirrors and only then hits the detector. Thus, the second beam hits the detector with a time delay t (several minutes). And the detector compares the wavelengths of two rays emitted at moments in time t-ti t. A change in the wavelength of the second beam relative to the first should be expected due to the increase in the gravitational potential of the Universe caused by its expansion.

This experiment is discussed in detail in, so now we will consider only the main conclusions that can be drawn after it is carried out.

Rice. 33. Schematic diagram of an experiment to measure the cosmological redshift caused not by the Doppler effect, but change in gravitational potential inside the Universe.

The laser beam is directed onto a translucent mirror. In this case, one part of the beam passes through the mirror and hits the detector along the shortest path. And the second part of the beam, reflected from the mirror and passing through the system of mirrors 1, 2, 3, hits the detector with a certain time delay. As a result, the detector compares the wavelengths of two beams emitted at different times.

Firstly, we will be able to find out whether or not there is a cosmological red shift caused not by the speed of removal of the source, but by the very fact of the expansion of the Universe, that is, the increase in gravitational potential within the Universe.

Secondly, if such a shift is detected (and there is every reason for this), then, thereby, We, through a laboratory experiment, will prove the very fact of the expansion of the Universe. Moreover, we will be able to measure the rate at which the gravitational potential created by all matter in the Universe increases.

Thirdly, by subtracting from the value of the red shift in the spectra of distant galaxies that part that is caused not by the speed of their removal, but by a change in the gravitational potential, we find out true the rate at which galaxies are moving away, and thus be able to correct the current estimate of the age of the Universe.

There are a lot of amazing things in Nature, and trying to single out the most, most thankless task. Someone believes that Life is the most amazing thing in Nature. Someone - that Mind. If we turn to inanimate nature, some will talk about the amazing laws of the microworld, others about the processes of self-organization and chaos. But, probably, if you make a list, the expansion of the Universe will always be in the top ten most amazing phenomena.

We will not discuss here the validity of conclusions about the expansion of the Universe based on cosmological observations. Equally, we will not discuss the foundations of the special and general theories of relativity (STR and GTR). Leaving aside the question of “the very beginning,” which will not concern us significantly here (we will consider “beginning” to be a sufficiently distant moment in time - say, before the primary nucleosynthesis - so as not to go into speculation about the very early Universe, if you like, then we can assume that the “beginning” is the moment of the end of the inflationary stage, if there was one), then there is no doubt about the data on the expansion of the Universe, just as there are no big doubts about the applicability of General Relativity in this case (all possible effects of quantum gravity, etc. are not important here) . We will discuss the standard picture, following mainly the recent article by Tamara M. Davis and Charles H. Lineweaver, "Expanding confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe" and the book by Edward Garrison ( Edward Harrison) "Cosmology: the science of the universe". It is also worth mentioning the works of Kiang - T. Kiang - "Time, Distance, Velocity, Redshift: a personal guided tour", "Can We Observe Galaxies that Recede Faster than Light? - A More Clear-Cut Answer". In addition, the issues discussed are discussed in many textbooks and monographs on cosmology.

Fine details

"We undoubtedly do not know much..."
(A. Gunitsky)

The expansion of the Universe (we will write the Universe with a capital letter, although we are talking specifically about the observable world, which is sometimes written with a small letter) is a very strange process, the comprehension of which, firstly, causes a certain intellectual discomfort, and secondly, leads to some confusion. Of course, confusion in the heads does not apply to professional cosmologists and those who have seriously dealt with these issues (in standard cosmology textbooks everything is usually neatly outlined). However, inaccuracies abound in popular literature. Davis and Lineweaver, without in any way claiming to have discovered a new phenomenon, tried to discuss the main inaccuracies associated with the popular (and not only) presentation of some details related to the expansion of the Universe, and in our opinion they succeeded. So their work is more of an educational and pedagogical nature. In the appendix to their article they provide quotes from famous books by famous people, where these details are described inaccurately to one degree or another (without considering ourselves among the greats, it should be noted that we, too, at one time contributed to the dissemination of confused knowledge about which we are very sorry about). Looking ahead, we will say that the main source of confusion is the use of the formula for the relativistic Doppler effect where it cannot be applied.

Let's discuss two details: superluminal expansion (when the speed of a galaxy's retreat exceeds light speed) and horizons. The drawings from the article by Davis and Lineweaver will help us with this.

Theoretical introduction

"Caution Concept 14, Caution Concept 14"

First, a little clarification.

We will use the Robertson-Walker metric in a simplified version:

ds 2 =-c 2 dt 2 +R(t) 2 dχ 2

Here χ is the accompanying coordinate. For two galaxies (neglecting peculiar velocities) this value does not change. For a propagating photon, it, of course, changes (the peculiar speed of the photon is equal to the speed of light). But for a photon ds=0, and therefore we can write cdt=R(t)dχ for it. R(t) is the scale factor. In an expanding universe, it increases over time, reflecting the expansion process. For example, R(t 0)/R(t)=3 shows that from moment t to moment t 0 all proper distances between objects with zero peculiar velocities (χ=const) increased threefold. The product of the scale factor and the accompanying coordinate is called proper distance; we will denote it D, D=R(t) χ. It is this distance that is “our usual” concept. In addition, you can enter the so-called conformal time, τ:

Along with ordinary time, these quantities are used to construct the figures below. The vertical axis represents time, and the horizontal axis represents distance. The world lines of the “galaxies” are marked with a dotted line. They are numbered by the redshift at the current moment in time (in cosmology, the redshift is not directly related to speed, it is determined by the formula: 1+z=R(t 0)/R(t), note that the redshift of a given object changes with time, in In different models it can either increase or decrease). “Us” corresponds to the line χ=0 (and, of course, D=0). As can be seen in the second (1b) and third (1c) figures, when using the accompanying distance, the world lines of all “galaxies” are straight lines. The first figure (1a) shows the expansion of the Universe: the world lines of the “galaxies” are moving away from us - their own distance is increasing.

Recall that the Hubble constant is a quantity that changes over time. It is equal to the ratio of the derivative of the scale factor with respect to time to the scale factor itself: H=(dR/dt)/R. The escape velocity is defined as the derivative of the proper distance:

V rec =dD/dt=H(t)D(t)=(dR(t)/dt)χ(z).

Here we also described how the escape velocity is expressed in terms of different quantities. Among the written expressions there is also V rec =H(t)D(t). Hubble's law. Note that this expression follows from the cosmological principle (the Universe is homogeneous, isotropic and looks the same to any observer at a given moment in time). If Hubble had been able in due time to measure redshifts and determine distances to z>1, then a deviation from the simple law would have been discovered, because Hubble's approach used Doppler's law to determine velocity from redshift. If Hubble could reach high redshifts and would use the relativistic Doppler law to determine the velocity, then the beautiful straight line of the Hubble relationship would begin to bend. Meanwhile, if you use general relativity, then everything will be in order: the expression V rec =H(t)D(t) remains valid for any redshift.

In cosmology it can be dangerous to use SRT (and intuition based on it), because this can lead to erroneous conclusions (Kiang calls this “shadows of SRT”). The fact is that the escape speed is significantly different from the familiar concept of speed. For her, SRT is not applicable “head-on”. The escape velocity is not a property of the source, but a property of a point in space. Therefore, one should not expect a direct applicability of the concepts intuitively developed in SRT to cosmology.

Obviously, there is a distance - the Hubble sphere, D H - at which the escape velocity is equal to the speed of light. Moreover, as will be shown below, we can see these objects (of course, we must take into account that light needs time - and quite a lot - to get to us from these objects). This amazing fact does not contradict anything (including SRT, which simply cannot be applied here).

Ordinary intuition is applicable at short distances. Up to approximately z=0.1, the results from the above formulas and from the Doppler effect will be close to each other. Also, for such close sources, distances can be estimated by multiplying the speed of light by ((age of the Universe now) - (age of the Universe at the moment of radiation)).

Horizons

"When the blue January evening raises a flag over the horizon..."
(A. Gunitsky)

There is no great confusion in the literature regarding horizons. It's just useful to figure it out. Let's consider two important horizons: the particle horizon and the event horizon.

The particle horizon is the distance to the most distant source, in principle observable at a given moment in time (just in case, let us clarify that we are talking about the distance to the object at the moment of receiving the photon, and not at the moment of emission). Sometimes this radius is defined differently: the distance that a photon can travel from t=0 to a given moment (i.e., this is the distance over which information can be transmitted in a time equal to the age of the Universe). From Fig. 1c clearly shows that both definitions are equivalent. In a non-expanding Universe of finite age (i.e., with a “beginning”), this radius would grow linearly with time. In a Universe expanding at a slower rate, the radius would always grow, but more slowly. In an accelerating Universe, the radius tends to a finite value (in accompanying coordinates) as time tends to infinity (that is, there are objects that we will never see, no matter how long we wait). This horizon cannot be defined as the speed of light multiplied by the time after the expansion began. The accompanying coordinate of an object on the particle horizon at moment t is defined as the speed of light multiplied by the integral from 0 to a given time t; under the integral is dt"/R(t") - conformal time. Accordingly, to determine your own distance, you must then multiply the result by the scale factor at the given moment. Please note that the redshift of sources on the particle horizon is infinite.

In the figures, the particle horizon is illustrated by a light cone from the point t=0, χ=0 into the future. However, this cone itself is not a particle horizon! At each given moment t i the horizon is a section of this cone by the plane t=t i . Those. it is the three-dimensional sphere around us that changes over time. But the drawn cone allows you to see how the horizon of particles changes over time (in particular, how “galaxies” enter it, i.e. become visible to us).

The event horizon is a rather tricky concept (and it does not exist in every cosmological model). Let's look at Fig. again. 1st century In addition to our light cone (for the present moment in time), we see a light cone for a moment in the infinite future - this is the event horizon. It divides the plane (space-time) into two parts. Events inside the cone (recall that a point on this plane is precisely an event in space AND time) are divided into two groups. Those that are inside the cone have either been available to us for observation in the past, or will be available in the future. Events outside the cone are fundamentally inaccessible to us for observation.

Note that in the 30/70 model, an infinite future corresponds to a finite conformal time.

Let's try to give some addition/clarification about the event horizon. The distance to the event horizon at the moment is the distance to the particle that our light signal sent at the moment can reach. In Fig. 1c it is clear that if we continue our light cone into the future, it will hit the upper horizontal at a point that is at the same accompanying distance at which the cone from the infinite future intersects our horizontal ("now"). Or we can say this: the light cone of a particle on the event horizon will cross our world line in the infinite future.

Figure 2b shows that for the accompanying distance the event horizon shrinks. And this is understandable. In a Universe that is expanding at an accelerated rate, over time it becomes more and more difficult for a signal to reach distant galaxies - they are moving away too quickly (and will be even faster). The accompanying distance to a particle on this horizon is defined as the product of the speed of light and the integral from a given moment of time to the “end” (to infinity), under the integral, as above, dt"/R(t").

Conclusion

"This is the oratorio, brother..."
(A. Gunitsky)

Above we tried to clarify some subtle points related to the expansion of the Universe. We can observe (and are observing) sources that, both at the moment of emission and now, have an escape velocity exceeding the speed of light. Distances to distant objects exceed the product of the speed of light and the age of the Universe. The distance at which the escape velocity is compared to the speed of light is not the horizon (i.e., the boundary of the visible part of the Universe), and is not a physically distinguished distance at all (objects directly in front of this boundary and directly behind it are not fundamentally different, just as conditions of their observations). The horizon of the observable Universe is the horizon of particles, on which sources have infinite redshifts.

I express my deep gratitude to S. Blinnikov, P. Ivanov, M. Prokhorov for a number of valuable comments.

Currently, according to astronomical observations, it has been established that The universe is homogeneous on a large scale, i.e. all its regions from 300 million light years in size and more look the same. On a smaller scale, there are regions in the Universe where clusters of galaxies are found and, conversely, voids where there are few of them.

A galaxy is a system of stars that have a common origin and are connected by gravitational forces. The galaxy in which our Sun is located is the Milky Way

Distances to celestial bodies in astronomy are determined differently depending on whether these objects are close or far from our planet. In outer space, the following units are commonly used to measure distances:

1 a.u.( astronomical unit) = (149597870 2) km;

1 pc ( parsec) = 206265 a.u. = 3.086·10 m;

1st year ( light year) = 0.307 pc = 9.5·10 m. A light year is the path that light travels in a year.

This paper proposes a method for determining distances to distant galaxies using “redshift”, i.e. by increasing the wavelengths in the spectrum of the observed distant source of radiation in comparison with the corresponding wavelengths of the lines in the standard spectra.

The light source refers to the radiation from distant galaxies (the brightest stars or gas and dust nebulae in them). Under " redshift" - a shift of spectral lines in the spectra of the chemical elements that make up these objects to the long-wavelength (red) side, compared to the wavelengths in the spectra of standard elements on Earth. The "red shift" is caused by the Doppler effect.

Doppler effect is that radiation sent by a source moving away from a stationary receiver will be received by it as longer wavelength, compared to radiation from the same stationary source. If the source approaches the receiver, then the wavelength of the recorded signal, on the contrary, will decrease.

In 1924, Soviet physicist Alexander Friedman predicted that the Universe is expanding. Currently available data show that the evolution of the Universe began from the moment Big Bang. About 15 billion years ago, the Universe was a point (it is called singularity point), to which, due to the strong gravity in it, very high temperature and density, the known laws of physics do not apply. In accordance with the currently accepted model, the Universe began to inflate from the point of singularity with increasing acceleration.

In 1926, experimental evidence of the expansion of the Universe was obtained. American astronomer E. Hubble, while studying the spectra of distant galaxies using a telescope, discovered the red shift of spectral lines. This meant that the galaxies were moving away from each other, and at a speed that increased with distance. Hubble constructed a linear relationship between distance and speed associated with the Doppler effect ( Hubble's law):

(1) , Where

r– distance between galaxies;

v – speed of removal of galaxies;

N– Hubble constant. Meaning N depends on the time elapsed from the beginning of the expansion of the Universe to the present moment, and varies in the range from 50 to 100 km/s·Mpc. In astrophysics, as a rule, H = 75 km/s·Mpc is used. The accuracy of determining the Hubble constant is

0.5 km/s Mpc;

With– speed of light in vacuum;

Z– red shift of wavelength, so-called. cosmological factor.

(2) , Where

– wavelength of radiation received by the receiver;

– wavelength of radiation emitted by the object.

Thus, by measuring the displacement of lines, for example, ionized hydrogen (H+) in the visible part of the spectrum, it is possible for a galaxy observed from Earth to determine its red shift using formula (2) Z and, using Hubble’s law (1), calculate the distance to it or the speed of its removal:

Work order

1. Call the program “Determination of distances to galaxies” on the computer desktop. An area of ​​the Universe with nine different galaxies observed from the surface of the Earth will appear on the monitor screen. A visible light spectrum and a wavelength marker for ionized hydrogen H+ appear at the top of the screen.

2. Place the cursor on the galaxy indicated by the teacher and click the key.

3. Record the wavelength and λ emitted by this galaxy as it moves away.

In the relative proximity of our Milky Way galaxy, astronomers have discovered several small galaxies that have made them wonder about the laws of gravity they know. These galaxies form an entire ring with a diameter of 10 million light years and are flying away from us at such a high speed that scientists cannot find a clear explanation for such a rapid expansion.

Finding analogies between the discovered structure and the Big Bang, scientists are confident that it was formed and gained speed due to the convergence of the Milky Way and the Andromeda galaxy in the distant past.

The problem is one: scientists cannot understand why, with such an expansion, these small galaxies acquired such a high speed.

“If Einstein's theory of gravity is correct, our galaxy could never come so close to Andromeda that it would eject something at such a speed,” explained Zhao Hongsheng of the University of St. Andrews (Scotland), author of the study published in the journal MNRAS .

Zhao and his colleagues are studying the movements of this ring of small galaxies, which, together with the Milky Way and the Andromeda Galaxy, are part of the so-called Local Group, which includes at least 54 galaxies. Our spiral galaxy, the Milky Way, and the neighboring Andromeda galaxy are separated by 2.5 million light years, but unlike most known galaxies, our neighbor is not moving away from us, but is flying towards us at a speed of more than 400 km/s.

Using the Standard Cosmological Model (the so-called ΛCDM model) in their calculations, scientists suggest that in 3.75 billion years the two galaxies should collide, and after another several billion years this collision will lead to the severe destruction of both galaxies and the formation of a new one. But if these galaxies are approaching each other now, could they have approached each other in the past?

In 2013, Zhao's team suggested, that 7-11 billion years ago the Milky Way and Andromeda were already flying past each other at a very close distance.

This generated “tsunami-like” waves in them, thanks to which smaller galaxies were thrown out, which are observed today flying away from us.

Similar convergences of two galaxies are known to astronomers (in the illustration to the note - the convergence of the galaxies NGC 5426 and NGC 5427). However, they fly away too quickly. “The high Galactocentric radial velocities of some Local Group galaxies were caused by forces acting on them that our model does not take into account,” they concluded in the paper. Moreover, there is no doubt about the common past of the Milky Way, Andromeda and these scattering galaxies, if only because they are located approximately in the same plane, scientists argue.

“The ring-shaped distribution is very specific. These small galaxies look like raindrops scattering from a rotating umbrella, explained study co-author Indranil Banik.

“According to my estimates, the chance that randomly distributed galaxies will line up in this way is 1/640.

I traced their origin to a dynamic event that occurred when the Universe was half its age."

The ΛCDM model is a model that takes into account the presence in the Universe of ordinary (baryonic matter, dark energy, described in Einstein’s equations as a constant Λ) and cold dark matter.

The problem with the described scenario of the expansion of small galaxies is not only the hypothetical violation of the ΛCDM model. Calculations show that such a close approach of the Milky Way and Andromeda in the past should have led to their merger, which, as is known, did not happen.

“Such a high speed (of galaxy expansion) requires 60 times more stellar mass than we see today in the Milky Way and Andromeda. However, the friction that would arise between the massive dark matter halo at the center of the galaxies and these stars would lead to their merger, rather than the 2.5 million light-year separation that occurred,” Banik explained.

“Science evolves through challenges,” says Marcel Pawlowski, an astrophysicist at the University of California, Irvine. “This giant ring poses a serious challenge to the standard paradigm.”

The next stage in the organization of matter in the Universe is galaxies. A typical example is our galaxy, the Milky Way. It contains about 10 11 stars and is shaped like a thin disk with a thickening in the center.
In Fig. Figure 39 schematically shows the structure of our Milky Way galaxy and indicates the position of the Sun in one of the spiral arms of the galaxy.

Rice. 39. Structure of the Milky Way galaxy.

In Fig. Figure 40 shows the projection onto the plane of the 16 nearest neighbors of our galaxy.

Rice. 40. 16 nearest neighbors of our Galaxy, projected onto a plane. LMC and MMC − Large and Small Magellanic Clouds

Stars in galaxies are unevenly distributed.
The sizes of galaxies vary from 15 to 800 thousand light years. The mass of galaxies varies from 10 7 to 10 12 solar masses. The majority of stars and cold gas are concentrated in galaxies. Stars in galaxies are held together by the combined gravitational field of the galaxy and dark matter.
Our Milky Way galaxy is a typical spiral system. Stars in a galaxy, along with the general rotation of galaxies, also have their own velocities relative to the galaxy. The orbital speed of the Sun in our galaxy is 230 km/s. The Sun's own speed relative to the galaxy is
20 km/s.

The discovery of the world of galaxies belongs to E. Hubble. In 1923–1924, observing changes in the luminosity of Cepheids located in individual nebulae, he showed that the nebulae he discovered were galaxies located outside our galaxy, the Milky Way. In particular, he discovered that the Andromeda Nebula is another star system - a galaxy that is not part of our Milky Way galaxy. The Andromeda Nebula is a spiral galaxy located at a distance of 520 kpc. The transverse size of the Andromeda nebula is 50 kpc.
By studying the radial velocities of individual galaxies, Hubble made a remarkable discovery:

H = 73.8 ± 2.4 km sec -1 megaparsec -1 – Hubble parameter.

Rice. 41. Original Hubble graph from 1929 work.

Rice. 42. The speed of removal of galaxies depending on the distance to the Earth.

In Fig. 42 at the origin of coordinates the square shows the region of galaxy velocities and distances to them, on the basis of which E. Hubble derived relation (9).
Hubble's discovery had a backstory. In 1914, astronomer V. Slipher showed that the Andromeda nebula and several other nebulae move relative to the solar system at speeds of about 1000 km/h. E. Hubble, working on the world's largest telescope with a main mirror with a diameter of 2.5 m at the Mount Wilson Observatory in California (USA), managed for the first time to resolve individual stars in the Andromeda nebula. Among these stars were Cepheid stars, for which the relationship between the period of change in luminosity and luminosity is known.
Knowing the luminosity of the star and the speed of the star, E. Hubble obtained the dependence of the speed of removal of stars from the Solar System depending on the distance. In Fig. 41 shows a graph from the original work of E. Hubble.

Rice. 43. Hubble Space Telescope

The radial velocity of movement of celestial objects - stars, galaxies - is determined by measuring the change in the frequency of spectral lines. As the radiation source moves away from the observer, the wavelengths shift toward longer wavelengths (red shift). As the radiation source approaches the observer, the wavelengths shift toward shorter wavelengths (blue shift). By increasing the width of the spectral line distribution, the temperature of the emitting object can be determined.
Hubble divided galaxies according to their appearance into three large classes:

elliptical (E),

spiral (S),

irregular (Ir).

Rice. 44. Types of galaxies (spiral, elliptical, irregular).

A characteristic feature of spiral galaxies are spiral arms extending from the center throughout the stellar disk.
Elliptical galaxies are structureless systems of elliptical shape.
Irregular galaxies have an outwardly chaotic, clumpy structure and do not have any specific shape.
This classification of galaxies reflects not only their external shapes, but also the properties of the stars within them.
Elliptical galaxies are composed primarily of old stars. In irregular galaxies, the main contribution to radiation comes from stars younger than the Sun. Stars of all ages are found in spiral galaxies. Thus, the difference in the appearance of galaxies is determined by the nature of their evolution. In elliptical galaxies, star formation virtually ceased billions of years ago. In spiral galaxies, star formation continues. In irregular galaxies, star formation occurs as intensely as it did billions of years ago. Almost all stars are concentrated in a wide disk, the bulk of which is interstellar gas.
Table 19 shows a relative comparison of these three types of galaxies and a comparison of their properties based on E. Hubble's analysis.

Table 19