Does the apparent brightness of a star reflect its luminosity. Star luminosity

22.09.2019

If you look at the starry sky, you immediately notice that the stars differ sharply in their brightness - some shine very brightly, they are easily noticeable, others are difficult to distinguish with the naked eye.

Even the ancient astronomer Hipparchus proposed distinguishing the brightness of stars. The stars were divided into six groups: the first includes the brightest - these are stars of the first magnitude (abbreviated - 1m, from the Latin magnitudo - magnitude), weaker stars - the second magnitude (2m) and so on until the sixth group - barely visible to the naked eye stars. Stellar magnitude characterizes the brilliance of a star, that is, the illumination that the star creates on earth. The brilliance of a 1m star is 100 times greater than the brilliance of a 6m star.

Initially, the brightness of stars was determined inaccurately, by eye; later, with the advent of new optical instruments, luminosity began to be determined more accurately and became less known bright stars with a magnitude greater than 6. (The most powerful Russian telescope - a 6-meter reflector - allows you to observe stars up to 24th magnitude.)

With increasing accuracy of measurements and the advent of photoelectric photometers, the accuracy of measuring the brightness of stars increased. Stellar magnitudes began to be denoted by fractional numbers. The brightest stars, as well as planets, have zero or even negative magnitude. For example, the Moon at full moon has a magnitude of -12.5, and the Sun has a magnitude of -26.7.

In 1850, the English astronomer N. Posson derived the formula:

E1/E2=(5v100)m3-m1?2.512m2-m1

where E1 and E2 are the illuminances created by stars on Earth, and m1 and m2 are their magnitudes. In other words, a star, for example, of the first magnitude is 2.5 times brighter than a star of the second magnitude and 2.52 = 6.25 times brighter than a star of the third magnitude.

However, the magnitude value is not enough to characterize the luminosity of an object; for this it is necessary to know the distance to the star.

The distance to an object can be determined without physically reaching it. You need to measure the direction towards this object from both ends of a known segment (basis), and then calculate the dimensions of the triangle formed by the ends of the segment and the distant object. This method is called triangulation.

The larger the basis, the more precisely the result measurements. The distances to the stars are so great that the length of the basis must exceed the dimensions globe, otherwise the measurement error will be large. Fortunately, the observer travels around the Sun with the planet for a year, and if he makes two observations of the same star with an interval of several months, it turns out that he is viewing it from different points of the earth’s orbit - and this is already a decent basis . The direction towards the star will change: it will shift slightly against the background of more distant stars. This displacement is called parallax, and the angle by which the star has shifted on the celestial sphere is called parallax. The annual parallax of a star is the angle at which the average radius of the Earth's orbit was visible from it, perpendicular to the direction of the star.

The concept of parallax is associated with the name of one of the basic units of distance in astronomy - parsec. This is the distance to an imaginary star whose annual parallax would be exactly 1". The annual parallax of any star is related to the distance to it by a simple formula:

where r is the distance in parsecs, P is the annual parallax in seconds.

Now the distances to many thousands of stars have been determined using the parallax method.

Now, knowing the distance to the star, you can determine its luminosity - the amount of energy actually emitted by it. It is characterized by its absolute magnitude.

Absolute magnitude (M) is the magnitude that a star would have at a distance of 10 parsecs (32.6 light years) from an observer. Knowing the apparent magnitude and distance to the star, you can find its absolute magnitude:

M=m + 5 - 5 * lg(r)

The closest star to the Sun, Proxima Centauri, a tiny dim red dwarf, has an apparent magnitude of m=-11.3 and an absolute magnitude of M=+15.7. Despite its proximity to Earth, such a star can only be seen with a powerful telescope. Even fainter star No. 359 according to the Wolf catalog: m=13.5; M=16.6. Our Sun shines 50,000 times brighter than Wolf 359. The star doradus (in the southern hemisphere) has only the 8th apparent magnitude and is not visible to the naked eye, but its absolute magnitude is M = -10.6; she's a million times brighter than the sun. If it were at the same distance from us as Proxima Centauri, it would shine brighter than the Moon at full moon.

For the Sun M=4.9. At a distance of 10 parsecs, the sun will be visible as a faint star, barely visible to the naked eye.

Luminosity

For a long time, astronomers believed that the difference in the apparent brightness of stars was associated only with the distance to them: the further away the star, the less bright it should appear. But when the distances to the stars became known, astronomers discovered that sometimes more distant stars have greater apparent brightness. This means that the apparent brightness of stars depends not only on their distance, but also on the actual strength of their light, that is, on their luminosity. The luminosity of a star depends on the size of the surface of the stars and its temperature. A star's luminosity expresses its true luminous intensity compared to the luminous intensity of the Sun. For example, when they say that the luminosity of Sirius is 17, this means that the true intensity of its light is 17 times greater than the intensity of the Sun.

By determining the luminosity of stars, astronomers have found that many stars are thousands of times brighter than the Sun, for example, the luminosity of Deneb (alpha Cygnus) is 9400. Among the stars there are those that emit hundreds of thousands of times more light than the Sun. An example is the star symbolized by the letter S in the constellation Dorado. It shines 1,000,000 times brighter than the Sun. Other stars have the same or almost the same luminosity as our Sun, for example, Altair (Alpha Aquila) -8. There are stars whose luminosity is expressed in thousandths, that is, their luminous intensity is hundreds of times less than that of the Sun.

Colour, temperature and composition of stars

Stars have different colors. For example, Vega and Deneb are white, Capella is yellowish, and Betelgeuse is reddish. The lower the temperature of a star, the redder it is. The temperature of white stars reaches 30,000 and even 100,000 degrees; temperature yellow stars is about 6000 degrees, and the temperature of red stars is 3000 degrees and below.

Stars consist of hot gaseous substances: hydrogen, helium, iron, sodium, carbon, oxygen and others.

Cluster of stars

Stars in the vast space of the Galaxy are distributed quite evenly. But some of them still accumulate in certain places. Of course, even there the distances between the stars are still very large. But due to the enormous distances, such closely located stars look like a star cluster. That's why they are called that. The most famous of the star clusters is the Pleiades in the constellation Taurus. With the naked eye, 6-7 stars can be distinguished in the Pleiades, located very close to each other. Through a telescope, more than a hundred of them are visible in a small area. This is one of the clusters in which the stars form a more or less isolated system, connected by a common movement in space. The diameter of this star cluster is about 50 light years. But even with the apparent closeness of the stars in this cluster, they are actually quite far from each other. In the same constellation, surrounding its main - the brightest - reddish star Al-debaran, there is another, more scattered star cluster - the Hyades.

Some star clusters appear as hazy, blurry specks in weak telescopes. In more powerful telescopes, these spots, especially towards the edges, break up into individual stars. Large telescopes make it possible to establish that these are particularly close star clusters, having a spherical shape. Therefore, such clusters are called globular. More than a hundred globular star clusters are now known. All of them are very far from us. Each of them consists of hundreds of thousands of stars.

The question of what the world of stars is is apparently one of the first questions that humanity has faced since the dawn of civilization. Any person contemplating the starry sky involuntarily connects the brightest stars with each other into the simplest shapes - squares, triangles, crosses, becoming the involuntary creator of his own map of the starry sky. Our ancestors followed the same path, dividing the starry sky into clearly distinguishable combinations of stars called constellations. In ancient cultures we find references to the first constellations, identified with the symbols of the gods or myths, which have come down to us in the form of poetic names - the constellation of Orion, the constellation of Canes Venatici, the constellation of Andromeda, etc. These names seemed to symbolize the ideas of our ancestors about the eternity and immutability of the universe, the constancy and immutability of the harmony of the cosmos.

The characteristics of celestial bodies can be very confusing. Only stars have apparent, absolute magnitude, luminosity and other parameters. We will try to figure it out with the latter. What is the luminosity of stars? Does it have anything to do with their visibility in the night sky? What is the luminosity of the Sun?

Nature of stars

Stars are very massive cosmic bodies that emit light. They are formed from gases and dust as a result of gravitational compression. Inside stars there is a dense core in which nuclear reactions occur. They contribute to the glow of stars. The main characteristics of luminaries are spectrum, size, brilliance, luminosity, and internal structure. All these parameters depend on the mass of a particular star and its chemical composition.

The main “designers” of these celestial bodies are helium and hydrogen. In smaller quantities relative to them, they may contain carbon, oxygen and metals (manganese, silicon, iron). Largest quantity hydrogen and helium in young stars, over time their proportions decrease, giving way to other elements.

In the inner regions of the star, the situation is very “hot”. The temperature in them reaches several million Kelvin. Here there are continuous reactions in which hydrogen is converted into helium. On the surface the temperature is much lower and reaches only a few thousand Kelvin.

What is the luminosity of stars?

Thermonuclear reactions inside stars are accompanied by energy releases. Luminosity is called physical quantity, which reflects exactly how much energy it produces celestial body for a certain time.

It is often confused with other parameters, such as the brightness of stars in the night sky. However, brightness or visible value is an approximate characteristic that is not measured in any way. It is largely related to the distance of the star from the Earth and describes only how well the star is visible in the sky. The smaller the number of this value, the greater its apparent brightness.

In contrast, the luminosity of stars is an objective parameter. It does not depend on where the observer is. This is a characteristic of a star that determines its energetic power. It may change according to different periods evolution of a celestial body.

Approximate to luminosity, but not identical, is absolute. It denotes the brightness of a star visible to an observer at a distance of 10 parsecs or 32.62 light years. It is commonly used to calculate the luminosity of stars.

Determination of luminosity

The amount of energy a celestial body emits is measured in watts (W), joules per second (J/s), or ergs per second (erg/s). There are several ways to find the required parameter.

It can be easily calculated using the formula L = 0.4(Ma -M), if you know the absolute magnitude of the desired star. Thus, the Latin letter L denotes luminosity, the letter M is the absolute magnitude, and Ma is the absolute magnitude of the Sun (4.83 Ma).

Another way involves great knowledge about the luminary. If we know the radius (R) and temperature (T ef) of its surface, then the luminosity can be determined by the formula L=4pR 2 sT 4 ef. Latin s in this case means a stable physical quantity - the Stefan-Boltzmann constant.

The luminosity of our Sun is 3.839 x 10 26 Watts. For simplicity and clarity, scientists usually compare the luminosity of a cosmic body with this value. Thus, there are objects thousands or millions of times weaker or more powerful than the Sun.

Star luminosity classes

To compare stars with each other, astrophysicists use various classifications. They are divided by spectra, sizes, temperatures, etc. But more often than not, for more full picture use several characteristics at once.

There is a central Harvard classification based on the spectra that the luminaries emit. It uses latin letters, each of which corresponds to a specific color of radiation (O-blue, B - white-blue, A - white, etc.).

Stars of the same spectrum can have different luminosities. Therefore, scientists have developed the Yerke classification, which takes this parameter into account. It separates them by luminosity based on absolute magnitude. Moreover, each type of star is assigned not only the letters of the spectrum, but also numbers responsible for luminosity. So, they distinguish:

hypergiants (0);
brightest supergiants (Ia+);
bright supergiants (Ia);
normal supergiants (Ib);
bright giants (II);
normal giants (III);
subgiants (IV);
main sequence dwarfs (V);
subdwarfs (VI);
white dwarfs (VII);

The greater the luminosity, the less value absolute value. For giants and supergiants it is indicated with a minus sign.

Communication between absolute value, temperature, spectrum, luminosity of stars is shown by the Hertzsprung-Russell diagram. It was adopted back in 1910. The diagram combines the Harvard and Yerke classifications and allows us to view and classify the luminaries more holistically.

Luminosity difference

The parameters of stars are strongly interrelated with each other. The luminosity is influenced by the temperature of the star and its mass. And they largely depend on the chemical composition of the star. The mass of a star becomes greater, the less heavy elements it contains (heavier than hydrogen and helium).

Hypergiants and various supergiants have the largest mass. They are the most powerful and brightest stars in the Universe, but at the same time, they are also the rarest. Dwarfs, on the contrary, have low mass and luminosity, but make up about 90% of all stars.

The most massive star currently known is the blue hypergiant R136a1. Its luminosity exceeds that of the sun by 8.7 million times. The variable star in the constellation Cygnus (P Cygnus) exceeds the luminosity of the Sun by 630,000 times, and S Doradus exceeds this parameter by 500,000 times. One of the smallest famous stars 2MASS J0523-1403 has a luminosity of 0.00126 solar.

Stars are thrown into open space a huge number, almost completely represented different types rays. The total radiation energy of a star emitted over a period of time is the luminosity of the star. The luminosity index is very important for the study of luminaries, since it depends on all the characteristics of the star.

The first thing worth noting when talking about the luminosity of a star is that it can easily be confused with other parameters of the star. But in practice everything is very simple - you just need to know what each characteristic is responsible for.

A star's luminosity (L) primarily reflects the amount of energy emitted by the star - and is therefore measured in watts, like any other quantitative characteristic energy. This is an objective quantity: it does not change when the observer moves. This parameter is 3.82 × 10 26 W. The brightness indicator of our star is often used to measure the luminosity of other stars, which is much more convenient for comparison - then it is marked as L ☉, (☉ is the graphic symbol of the Sun.)

Obviously, the most informative and universal characteristic among the above is luminosity. Since this parameter displays the intensity of the star's radiation in the most detail, it can be used to find out many characteristics of the star - from size and mass to intensity.

Luminosity from A to Z

It doesn’t take long to search for the source of radiation in a star. All the energy that can leave the star is created in the process of thermonuclear fusion reactions in. Hydrogen atoms, merging under gravitational pressure into helium, release enormous amounts of energy. And in more massive stars, not only hydrogen, but also helium “burns” - sometimes even more massive elements, even iron. The energy then turns out to be many times greater.

The amount of energy released during nuclear reaction, directly depends on - the larger it is, the more gravity compresses the core of the star, and the more hydrogen is simultaneously converted into helium. But it is not nuclear energy alone that determines the luminosity of a star - after all, it must also be emitted outward.

This is where the radiation area comes into play. Its influence in the process of energy transfer is very great, which is easily verified even in everyday life. An incandescent lamp, the filament of which heats up to 2800 °C, will not significantly change the temperature in the room after 8 hours of operation, but a regular battery with a temperature of 50–80 °C will be able to warm the room to a noticeable stuffiness. Differences in efficiency are caused by differences in the amount of surface area emitting energy.

The ratio between the area of a star's core and its surface is often commensurate with the proportions of a light bulb filament and a battery - the diameter of the core can be only one ten-thousandth of the total diameter of the star. Thus, the luminosity of a star is seriously affected by the area of its emitting surface - that is, the surface of the star itself. The temperature here turns out to be not so significant. The incandescence of the star's surface is 40% less than the temperature of the Sun's photosphere - but due to its large size, its luminosity exceeds the Sun's luminosity by 150 times.

It turns out that in calculating the luminosity of a star, the role of size is more important than the energy of the nucleus? Not really. Blue giants with high luminosity and temperature have similar luminosities to red supergiants, which are much larger larger in size. In addition, the most massive and one of the hottest stars has the highest brightness of all known stars. Until the discovery of a new record holder, this puts an end to the debate about the most important parameter for luminosity.

Use of luminosity in astronomy

Thus, luminosity fairly accurately reflects both a star's energy and its surface area - which is why it is included in many classification charts used by astronomers to compare stars. Among them, it is worth highlighting the diagram

Luminosity stars, the luminous intensity of a star, i.e. the magnitude of the luminous flux emitted by a star, contained in a unit solid angle. The term "star luminosity" does not correspond to the term "luminosity" of general photometry. The solar radiation of a star can refer either to any region of the star’s spectrum (visual solar radiation of a star, photographic solar radiation of a star, etc.) or to its total radiation (bolometric solar radiation of a star). The luminosity of a star is usually expressed in units of solar luminosity, equal to 3·1027 international candles, or 3.8·1033 erg/sec. The luminosities of individual stars differ greatly from each other: there are stars whose bolometric luminosity reaches half a million in solar luminosity units (supergiant stars of spectral class O), as well as stars with a bolometric luminosity hundreds of thousands of times less than the Sun. It is believed that there are stars with even lower luminosity. Along with the masses, radii and surface temperatures of stars, luminosities are the most important characteristics stars The connection between these stellar characteristics is considered in theoretical astrophysics. The star's position L is related to the absolute magnitude M addiction:

M = - 2.5 log L + 4.77.

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