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The brightness of some stars is not constant and changes over certain periods of time - from hours to weeks or even a year. The brightness of a variable star can be determined by comparison with surrounding stars that are of constant brightness. The main reason for the variable brightness is the change in the size of the star due to its instability. The best known are the pulsating stars of the Cepheid class, named after their prototype, the star Delta Cephei. These are yellow supergiants that pulsate every few days or weeks, changing their brightness as a result.
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The importance of such stars for astronomers is that their period of pulsation is directly related to brightness: the brightest Cepheids have the longest period of pulsation. Therefore, by observing the period of pulsation of Cepheids, one can accurately determine their brightness. By comparing the calculated brightness with the star's brightness as seen from Earth, we can determine how far it is from us. Cepheids are relatively rare. The most numerous type of variable stars are red giants and supergiants; they are all variable to some extent, but they do not have such a clear periodicity as the Cepheids. The best-known example of a volatile red giant is the Ceti omicron, known as Mira. Changes in some red variable stars, such as the supergiant Betelgeuse, have no regularity.
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The eclipsing binary stars belong to a completely different type of variable stars. They consist of two stars with interconnected orbits; one of them periodically closes the other from us. Every time one star outshines another, the light we see from the system of stars is weakened. The most famous of these is the star Algol, also called Beta Perseus.
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The greatest impression is produced by variable stars, the brightness of which changes suddenly and often very strongly. They are called novae and supernovae. It is believed that the new one is two closely spaced stars, one of which is a white dwarf. The gas from another star is pulled away by the white dwarf, explodes, and the star's light increases thousands of times for a while. When a new star explodes, it does not collapse. Explosions of some new ones were observed more than once, and it is possible that new ones appear again after some time. Novae are often the first to be noticed by amateur astronomers. Even more spectacular are supernovae - celestial cataclysms that mean the death of a star. When a supernova explodes, it breaks into pieces and ends its existence, flashing for a while millions of times stronger than ordinary stars. Where a supernova explodes, debris from the star is left flying in outer space, as, for example, in the Crab Nebula in the constellation Taurus and in the Veil Nebula in the constellation Cygnus.
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Supernovae are of two types. One of them is the explosion of a white dwarf in a binary star. Another type is when a star many times larger than the Sun becomes unstable and explodes. The last supernova in our galaxy was observed in 1604, another supernova erupted and was visible to the naked eye in the Large Magellanic Cloud in 1987.
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Binary Stars The Sun is a single star. But sometimes two or more stars are located close to each other and revolve one around the other. They are called double or multiple stars. There are a lot of them in the Galaxy. So, the star Mizar in the constellation Ursa Major has a satellite - Alcor. Depending on the distance between them, binary stars revolve around each other quickly or slowly, and the period of revolution can range from several days to many thousands of years. Some binary stars are turned to the Earth by the edge of the plane of their orbit, then one star regularly outshines the other. At the same time, the overall brightness of the stars weakens. We perceive this as a change in the brightness of the star. For example, the "devil star" Algol in the constellation Perseus has been known since ancient times as a variable star. Every 69 hours - such is the period of revolution of stars in this binary system - there is an eclipse of a brighter star by its cold and less bright neighbor. From the Earth, this is perceived as a decrease in its brilliance. Ten hours later, the stars diverge, and the brightness of the system again becomes maximum.
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Binary stars are two (sometimes three or more) stars revolving around a common center of gravity. There are different binary stars: there are two similar stars in a pair, but there are different ones (as a rule, these are a red giant and a white dwarf). But, regardless of their type, these stars lend themselves most well to study: for them, unlike ordinary stars, by analyzing their interaction, you can find out almost all parameters, including mass, the shape of orbits, and even approximately find out the characteristics of stars close to them. As a rule, these stars have a somewhat elongated shape due to mutual attraction. Many such stars were discovered and studied at the beginning of our century by the Russian astronomer S. N. Blazhko. Approximately half of all the stars in our Galaxy belong to binary systems, so that binary stars orbiting one around the other are a very common phenomenon.
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Binary stars are held together by mutual gravity. Both stars of the binary system rotate in elliptical orbits around a certain point lying between them and called the center of gravity of these stars. One can think of these as fulcrums if one imagines the stars sitting on a children's swing, each at its own end of a board placed on a log. The farther the stars are from each other, the longer their paths in orbits last. Most double stars are too close together to be seen individually even with the most powerful telescopes. If the distance between the partners is large enough, the orbital period can be measured in years, and sometimes a whole century or even more. Binary stars that can be seen separately are called visible binaries.
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A spectroscopic binary is a pair of stars that are too close together to be visible through a telescope; the existence of a second star is revealed by analyzing the light with a spectroscope.
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The movement of the stars. In the sky, longitude and latitude are analogous to right ascension and declination. Right Ascension begins at the point where the Sun crosses the celestial equator in a northerly direction each year. This point, called the vernal equinox, is the celestial counterpart of the Greenwich meridian on Earth. Right ascension is measured eastward from the vernal equinox in hours, from 0 to 24. Each hour of right ascension is divided into 60 minutes, and each minute is divided into 60 seconds. Declination is defined in degrees north and south of the celestial equator, from 0 at the equator to +90° at the north celestial pole and down to -90° at the south celestial pole. The celestial poles are directly above the Earth's poles, and the celestial equator runs directly overhead as viewed from the Earth's equator. Thus, the position of a star or other object can be accurately determined by right ascension and declination, as well as by the coordinates of a point on the surface of the Earth. Grids in hours of right ascension and degrees of declination are plotted on the star maps of this book.
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However, space cartographers face two problems that land cartographers do not. First, each star moves slowly relative to the surrounding stars (the star's proper motion). With a few exceptions, such as Barnard's Star, this movement is so slow that it can only be determined using special measurements. However, after many thousands of years, this movement will lead to a complete change in the real shape of the constellations, some of the stars will move to neighboring constellations. Someday, astronomers will have to revise the modern nomenclature of stars and constellations. The second problem is that the overall grid shifts due to the Earth's wobble in space, which is called precession. This leads to the fact that the zero point of right ascension makes a complete revolution in the sky in 26,000 years. The coordinates of all points in the sky are gradually changing, so usually the coordinates of celestial objects are given for a certain date.
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Binary Stars The Sun is a single star. But sometimes two or more stars are located close to each other and revolve one around the other. They are called double or multiple stars. There are a lot of them in the Galaxy. So, the star Mizar in the constellation Ursa Major has a satellite - Alcor. Depending on the distance between them, binary stars revolve around each other quickly or slowly, and the period of revolution can range from several days to many thousands of years. Some binary stars are turned to the Earth by the edge of the plane of their orbit, then one star regularly outshines the other. At the same time, the overall brightness of the stars weakens. We perceive this as a change in the brightness of the star. For example, the "devil star" Algol in the constellation Perseus has been known since ancient times as a variable star. Every 69 hours - such is the period of revolution of stars in this binary system - there is an eclipse of a brighter star by its cold and less bright neighbor. From the Earth, this is perceived as a decrease in its brilliance. Ten hours later, the stars diverge, and the brightness of the system again becomes maximum.
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Double starDouble star, or double system - system
from two gravitationally bound stars,
revolving in closed orbits around
common center of mass. Double stars - very
common objects. Approximately half
of all the stars in our galaxy belongs to
double systems.
circulation and distance
between the stars, sometimes
masses can be determined
system components. This
method is practically
requires additional
model
assumptions, and therefore
is one of the main
mass determination methods
in astrophysics. By this
reason dual systems,
whose components
are black
holes or neutron
stars, represent
big interest
for astrophysics.
visual binary stars
The ability to observe a star as a visual binarydetermined by the resolution of the telescope,
the distance to the stars and the distance between them. So
Thus, visual double stars are mainly
stars in the vicinity of the Sun with a very large
period of revolution (a consequence of the large distance
between components).
When observing a visual binary star, measure
distance between components and position angle
center lines, in other words, the angle between
direction to the north celestial pole and direction
line connecting the main star with its satellite.
Speckle interferometric binary stars
Speckle interferometry, along withwith adaptive optics allows you to achieve
diffraction limit of stellar resolution,
which in turn makes it possible to discover
double stars. That is, in essence, speckle interferometric binaries are the same
the most visually double. But if in
classical visual double method
need to get two separate
images, in this case it is necessary
analyze speckle interferograms.
Speckle interferometry is effective for
binaries with a period of several decades
Astrometric double stars
In the case of visual binary stars, we seemoving two objects across the sky at once. However,
if we imagine that one of the two
components are not visible to us for one reason or another
reasons, then duality is still possible
detect by changing position in the sky
second. In this case, one speaks of
astrometric binary stars.
eclipsing binary stars
It happens that the orbital planetilted to the line of sight under very
small angle: orbits of stars
such a system is located as if
edge towards us. In such a system
stars will periodically
outshine each other, that is, brilliance
couples will change. Double
stars that are observed
such eclipses are called
eclipsing binary or eclipsing variable. most famous and
the first discovered star of such
type is Algol (Eye
Devil) in the constellation Perseus. If there are high-precision
astrometric observations, then
duality can be assumed
fixing the non-linearity of motion:
first derivative of own
motion and the second astrometric
double stars are used for
measurements of the mass of brown dwarfs
different spectral types
Algol paradox
This paradox was formulated in the middle of the 20th century by Sovietastronomers A. G. Masevich and P. P. Parenago, who turned
attention to the discrepancy between the masses of Algol components and their
evolutionary stage. According to the theory of stellar evolution,
the rate of evolution of a massive star is much greater than that of
stars with a mass comparable to the sun, or a little more.
Obviously, the components of a binary star formed in
the same time, hence the massive component
must evolve earlier than the low-mass one.
However, in the Algol system, the more massive component was
younger.
The explanation for this paradox is related to the phenomenon of overflow
masses in close binary systems and was first proposed
American astrophysicist D. Crawford. If a
assume that in the course of evolution one of the components
there is a possibility of transferring mass to a neighbor, then
the paradox is removed
mass of stars
The mass of all stars, without exception, is quite high.This explains the ability to hold the planets and
other celestial bodies, because the greater the mass of the body, the
its gravity is stronger.
Mass affects not only the gravitational force of a star, but also
its other characteristics. For example, mass straight
proportional to pressure and temperature at the center of the star,
and these two parameters are decisive
star characteristics.
The direct mass of a star can only be determined by
the basis of the law of universal gravitation. However, this
only possible for stars in binary systems. So
A pair of stars revolving around a common center is called. AT
in other cases, the masses of stars are calculated by analyzing
various characteristics indirectly related to mass.
This is usually done using the luminosity of stars,
proportional to mass.
The mass of the lightest stars is about 10 times less
solar, and the heaviest about 10 more than
Sun.
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DOUBLE STARS
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Types of double stars
First, let's find out which stars are called that. Let's immediately discard the type of binaries that is called "optical binaries". These are pairs of stars that happened to be side by side in the sky, that is, in the same direction, but in space, in fact, they are separated by large distances. We will not consider this type of doubles. We will be interested in the class of physically binary, that is, stars really connected by gravitational interaction.
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Center of mass position
Physically, binary stars rotate in ellipses around a common center of mass. However, if we count the coordinates of one star relative to another, it turns out that the stars move relative to each other also in ellipses. In this figure, we have taken a more massive blue star as the origin. In such a system, the center of mass (green dot) describes an ellipse around the blue star. I would like to warn the reader against a common misconception that it is often assumed that a more massive star attracts a star with a low mass more strongly than vice versa. Any two objects attract each other equally. But an object with a large mass is more difficult to budge. And although a stone falling on the Earth attracts the Earth with the same force as its Earth, it is impossible to disturb our planet with this force, and we see how the stone moves.
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Often, however, there are so-called multiple systems, with three or more components. However, the motion of three or more interacting bodies is unstable. In a system of, say, three stars, it is always possible to single out a binary subsystem and a third star rotating around this pair. In a system of four stars, there may be two binary subsystems rotating around a common center of mass. In other words, in nature, stable multiple systems always reduce to two-term systems. The notorious Alpha Centauri, considered by many to be the closest star to us, belongs to the three-star system, but in fact, the third faint component of this system - Proxima Centauri, a red dwarf, is closer. All three stars of the system are visible separately due to their proximity. Indeed, sometimes the fact that the star is double is visible through a telescope. Such binaries are called visual binaries (not to be confused with optical binaries!). As a rule, these are not close pairs; the distances between the stars in them are large, much larger than their own sizes.
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Shine of double stars
Often, stars in pairs differ greatly in brilliance, a dull star is overshadowed by a bright one. Sometimes in such cases, astronomers learn about the duality of a star by deviations in the motion of a bright star under the influence of an invisible companion from the trajectory calculated for a single star in space. Such pairs are called astrometric binaries. In particular, Sirius for a long time belonged to this type of double, until the power of the telescopes made it possible to see the hitherto invisible satellite - Sirius B. This pair became visually double. It happens that the plane of revolution of stars around their common center of mass passes or almost passes through the eye of the observer. The orbits of the stars of such a system are, as it were, edged towards us. Here the stars will periodically outshine each other, the brightness of the entire pair will change with the same period. This type of binaries is called eclipsing binaries. If we talk about the variability of a star, then such a star is called an eclipsing variable, which also indicates its duality. The very first discovered and most famous binary of this type is the star Algol (Devil's Eye) in the constellation Perseus.
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Spectral binary stars
The last type of binaries are spectroscopic binaries. Their duality is determined by studying the spectrum of the star, in which periodic shifts of absorption lines are noticed or it is seen that the lines are double, on which the conclusion about the duality of the star is based.
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Why are double stars interesting?
First, they make it possible to find out the masses of stars, since it is most easily and most reliably calculated from the apparent interaction of two bodies. Direct observations allow us to find out the total "weight" of the system, and if we add to them the known relationships between the masses of stars and their luminosities, which were discussed above in the story about the fate of stars, then we can find out the masses of the components, test the theory. Single stars do not provide us with such an opportunity. In addition, as was also mentioned earlier, the fate of stars in such systems can be strikingly different from the fate of the same single stars. Celestial pairs, the distances between which are large compared to the size of the stars themselves, at all stages of their lives live according to the same laws as single stars, without interfering with each other. In this sense, their duality does not appear in any way.
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Close couples: the first exchange of masses
Binary stars are born together from the same gas and dust nebula, they have the same age, but often different masses. We already know that more massive stars live "faster", therefore, a more massive star in the process of evolution will overtake its peer. It will expand, turning into a giant. In this case, the size of the star can become such that the matter from one star (swollen) will begin to flow to another. As a consequence, the mass of the initially lighter star may become larger than the initially heavy one! In addition, we will get two stars of the same age, and the more massive star is still on the main sequence, that is, helium fusion from hydrogen continues in its center, and the lighter star has already used up its hydrogen, a helium core has formed in it. Recall that in a world of single stars this cannot happen. For the discrepancy between the age of the star and its mass, this phenomenon is called the Algol paradox, in honor of the same eclipsing binary. The Beta Lyra star is another pair that is undergoing a mass exchange right now.
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The matter from the swollen star, flowing onto the less massive component, does not fall on it immediately (this is hindered by the mutual rotation of the stars), but first forms a rotating disk of matter around the smaller star. Friction forces in this disk will reduce the speed of matter particles, and it will settle on the surface of the star. Such a process is called accretion, and the resulting disk is called accretion. As a result, an initially more massive star has an unusual chemical composition: all the hydrogen in its outer layers flows to another star, and only a helium core with impurities of heavier elements remains. Such a star, called a helium star, rapidly evolves to form a white dwarf or relativistic star, depending on its mass. At the same time, an important change took place in the binary system as a whole: the initially more massive star gave way to this leadership.
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Second mass exchange
In binary systems, there are also X-ray pulsars emitting in a higher energy wavelength range. This radiation is associated with the accretion of matter near the magnetic poles of a relativistic star. The source of accretion is the particles of the stellar wind emitted by the second star (the nature of the solar wind is the same). If the star is large, the stellar wind reaches a significant density, the radiation energy of an X-ray pulsar can reach hundreds and thousands of solar luminosities. An X-ray pulsar is the only way to indirectly detect a black hole, which, as we remember, cannot be seen. Yes, and a neutron star is the rarest object for visual observation. This is far from everything. The second star will also swell sooner or later, and the matter will begin to flow to the neighbor. And this is already the second exchange of matter in the binary system. Having reached a large size, the second star begins to "return" what was taken during the first exchange.
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If a white dwarf appears in the place of the first star, then as a result of the second exchange, flares can occur on its surface, which we observe as new stars. At one point, when there is too much material that has fallen onto the surface of a very hot white dwarf, the temperature of the gas near the surface rises sharply. This provokes an explosive burst of nuclear reactions. The luminosity of the star increases significantly. Such outbreaks can be repeated, and they are already called repeated new ones. Repeated outbursts are weaker than the first ones, as a result of which the star can increase its brightness by dozens of times, which we observe from the Earth as the appearance of a "new" star.
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Another outcome in a white dwarf system is a supernova explosion. As a result of the flow of matter from the second star, the white dwarf may reach a limiting mass of 1.4 solar masses. If this is already an iron white dwarf, then it will not be able to keep the gravitational contraction and will explode. Supernova explosions in binary systems are very similar in brightness and development to each other, since stars of the same mass always explode - 1.4 solar. Recall that in single stars this critical mass is reached by the central iron core, while the outer layers can have different masses. In binary systems, as is clear from our narrative, these layers are almost absent. That is why such flashes have the same luminosity. By noticing them in distant galaxies, we can calculate distances far greater than can be determined using stellar parallax or Cepheids. The loss of a significant part of the mass of the entire system as a result of a supernova explosion can lead to the disintegration of a binary. The force of gravitational attraction between the components is greatly reduced, and they can scatter due to the inertia of their movement.
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Astronomically double stars
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The concept of "double stars"
Binary stars are two or more stars revolving in elliptical orbits around a common center of mass under the influence of gravitational forces. Approximately half of all "stars" are actually binary or multiple systems, although many of them are located so close that the components cannot be observed separately.
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Opening
As a rule, double stars in the sky are detected visually by a change in apparent brightness (can be confused with Cepheids) and close proximity to each other. Sometimes it happens that two stars are accidentally seen side by side, but in fact they are at a considerable distance and do not have a common center of gravity (i.e. optical binary stars), however, this is quite rare.
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Kinds
These stars have a somewhat elongated shape due to mutual attraction. Many such stars were discovered and studied at the beginning of our century by the Russian astronomer S. N. Blazhko. About half of all the stars in our Galaxy belong to binary systems, so that binary stars orbiting one around the other are a very common phenomenon.
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Normally, physical binary stars are bound by gravitational forces. The components of a binary star form close pairs. The periods of revolution of the components of a binary star do not exceed hundreds of years, sometimes they are much shorter.
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optical binary stars
An example of an optical binary star, but they are not physically related to each other. According to Mizar and Alcor, the ancient Greeks tested the vigilance of the eye. The angular distance between Mizar and Alcor is 12 minutes, and the linear distance between these stars is about 17000 AU,
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Often the duality of stars can be detected by the periodic change in their brightness. The first eclipsing variable star, Algol (β Perseus), was discovered in 1669 by the Italian astronomer Montanari. Algol's light curve repeats every 2 days, 20 hours and 49 minutes. In 1784, Goodryk discovered the second eclipsing star, β Lyrae. Its period is 12 days 21 hours and 56 minutes, and, unlike Algol, the brightness changes smoothly. Eclipsing binary stars Algoli
Slide 8
Warm binary stars
In a system of closely spaced binary stars, mutual gravitational forces tend to stretch each of them, to give it the shape of a pear. Around these two stars there is a certain area in the form of a three-dimensional figure-eight, the surface of which is a critical boundary. These two pear-shaped figures, each around its own star, are called Roche lobes. If one of the stars grows so much that it fills its Roche lobe, then the matter from it rushes to the other star at the point where the cavities touch. Often, stellar material does not fall directly onto the star, but is first swirled in a vortex, forming what is known as an accretion disk.
Slide 9
x-ray stars
At least 100 powerful X-ray sources have been found in the Galaxy. According to astronomers, the X-ray emission could be caused by matter falling on the surface of a small neutron star. In binary systems with small masses, a gaseous disk is formed around the neutron star. In the case of systems with large masses, the material rushes directly to the neutron star - its magnetic field sucks it in like a funnel. It is these systems that often turn out to be X-ray pulsars.
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Measurement of parameters of binary stars
If we assume that the law of universal gravitation is constant in any part of our galaxy, then it is possible to measure the mass of binary stars based on Kepler's laws. According to Kepler's III law: where m1 and m2 are the masses of the stars P is their period of revolution T is one year A is the semi-major axis of the satellite's orbit relative to the main star a is the distance from the Earth to the Sun. From this equation, you can find the sum of the masses of the binary star, that is, the mass of the system. Let M of the sun = 1, taking into account that M⊙>> M⊕, T = 1 year, and – 1 AU. Then Considering that, we get
