Binary and multiple star systems.

Double stars (physical doubles)

- two stars united by gravitational forces and revolving in elliptical (in a particular case, circular) orbits around a common center of mass. There are also multiples of physical. stars - triple, quadruple, etc., but their number is significantly less than physical ones. D. z. If the components are physical D. z. can be seen directly through a telescope or in photographs (obtained for this purpose using long-focus astrographs), then it is called. visually a double star. Close dynamic stars, the duality of which cannot be detected even in the largest telescopes, may turn out to be spectroscopic doubles or eclipsing doubles (otherwise - eclipsing variables, see). The first show their duality periodically. fluctuations or splits in the spectrum. lines, the second - periodic. changes in the total brightness of stars. In some cases, it is possible to establish duality using methods, or by high-speed recording of lunar occultations of stars (the photometric curves of changes in the brightness of a single and double star turn out to be different). To D. z. also include: astrometric stars with dark satellites (about 20 astrometric stars have been discovered among stars close to the Sun); stars with complex spectra (combinations of two different spectra); wide pairs are stars with a large common property. movement (i.e. with a large angular movement of the star across the celestial sphere, expressed in seconds of arc per year). In space, the components can be separated by tens of thousands of AU, and the orbital periods can reach several. million years. Photometric D. z. sometimes called also double (multiple) systems, the multiplicity of which is revealed by methods of multicolor photometry of stars based on its comparison on two-color (multicolor) diagrams (see).

Relates. the number of known double (and multiple) stars is steadily increasing; it is currently believed that most (perhaps more than 70%) of stars are united in systems of greater or lesser multiplicity; from among the known D. z. about 1/3 turn out to be triple stars or stars of higher multiplicity. Six- and seven-fold stars are known.

Of great interest are D. z., which includes physical. variable stars (e.g.), and, possibly, because in this case, it is possible to estimate the masses of these objects.

The number of discovered visual double stars (including wide pairs) exceeds 60 thousand. Of these, only 10 thousand have been measured more or less regularly. In more than 500 of them, a curvature of the path has already been detected, sufficient to try to determine the shape of the relative. orbits. For approximately 150 D. z. orbits are determined, i.e. Based on the apparent trajectory of the satellite around the main star, the elements of the true orbit were calculated, indicating the shape and dimensions of the orbit and its spaces. orientation. From these data, it is possible to pre-calculate the position of the satellite in orbit (Fig. 2). Only orbits 80 DW. can be considered determined reliably enough to use them to try to determine the masses of stars that are components of binaries. Application of Kepler's third law to motion of motion. with known distances to them makes it possible (almost the only one) to determine the masses of stars (see).

Changes in spectrum shifts or splits. lines of spectroscopic double stars make it possible to determine , which is the projection of the orbital velocity onto the line of sight (Fig. 3). Radial velocity curves (Fig. 4) - of one component or both, if the satellite does not differ too much in brightness from the main star and the lines of both components are visible and can be measured in the spectrum - make it possible to calculate the elements of the true orbit (the bright component around the common center of mass , either a fainter component around the bright one, placed at the focus of the relative orbit, or, finally, each component relative to the center of mass of the system, Fig. 5). Certain periods of spectroscopic double stars range from 0.1084 days (Ursa Minor) to 59.8 years (visually the D. of Ursa Major). The vast majority of spectroscopic binary stars have periods of the order of several. days In total, more than 3000 spectroscopic double stars have been discovered, and orbital elements have been calculated for approximately 1000 of them.

Light curve of the eclipsing star. shows periodic decrease in brightness - one or two per period and a constant brightness between minima (for stars of the Algol type) or a continuous change (for stars of the Lyra or W Ursa Major type, in the latter case the minima are almost the same depth, see). Number of open eclipsing stars. exceeds 5 thousand

Rice. 4. Influence of the shape and orientation of the orbit on the shape
radial velocity curve: 1 - circular orbit;
2 - orbital eccentricity e=- 0.5, periastron longitude;
3 - orbital eccentricity e=0,5, ;
a, b, c, d - positions of the satellite star and
their corresponding radial velocity values.

Analysis of the curves makes it possible to determine not only the elements of the orbit of the eclipsing star, but also certain characteristics of the components themselves (shape, dimensions, expressed either in fractions of the semi-major axis of the orbit, or in kilometers, if additional radial velocity measurements are available). High precision modern photovoltaic Light measurements in some cases make it possible to identify and take into account the influence on the light curve of the so-called. subtle effects, e.g. darkening towards the edge of the star's disk, and also quantify the degree of deviation of the shape of the components from the spherical one for very close binaries (types Lyra and W Ursa Major). With a noticeable eccentricity of the orbit, it is possible to detect the effect of rotation of the line of apses (i.e., the line connecting periastron and apoaster, see), which may be associated with the existence of a third, not yet discovered component of the system, or with a noticeable difference in the shape of stars from spherical due to tidal influence deformations of nearby components. If one of the components of the eclipsing D. z. - a hot star, and the other is a supergiant with an extended atmosphere, then it is possible to study in great detail the structure and composition of the supergiant’s atmosphere by changes in the eclipse spectrum, when a hot star shines through the supergiant’s atmosphere during an eclipse. The absorption lines will change as the hot star “sinks” into denser layers of the supergiant’s extended atmosphere. Examples of such pairs are: Auriga (period 27 years, of which the eclipse lasts about 2 years!) and Auriga (period 972 days, the eclipse lasts about 40 days).

With the help of double stars, it is possible to find out the masses of stars and construct various dependencies. And without knowing the relationship between mass - radius, mass - luminosity and mass - spectral class, it is practically impossible to say anything about the internal structure of stars or their evolution.

But double stars would not be studied so seriously if all their significance was reduced to information about mass. Despite repeated attempts to search for single black holes, all black hole candidates are found in binary systems. Wolf-Rayet stars were studied precisely thanks to double stars.

Gravitational interaction between components

Types of double stars and their detection

An example of a close binary system. The picture shows an image of the Variable star Mira (omicron Ceti), taken by the space telescope named after. Hubble in the ultraviolet. The photograph shows an accretion “tail” directed from the main component, a red giant, to its companion, a white dwarf.

Physically, double stars can be divided into two classes:

the stars between which there is, will be, or was an exchange of masses - close binary systems,
stars between which mass exchange is impossible in principle - wide double systems.

If we divide binary systems according to the method of observation, we can distinguish visual, spectral, eclipsing, astrometric dual systems.

Visual double stars

Double stars that can be seen separately (or, as they say, that can be allowed), are called visible double, or visually double.

When observing a visual double star, the distance between the components and the position angle of the line of centers are measured, in other words, the angle between the direction to the north celestial pole and the direction of the line connecting the main star with its satellite. The determining factors here are the resolution of the telescope, the distance to the stars and the distance between the stars. In total, these three factors give: 1) that visual double stars are stars in the vicinity of the Sun, 2) the distance between the components is significant and, according to Kepler’s laws, the period of this system is quite large. The last fact is the saddest, since it is impossible to trace the orbit of a binary without conducting numerous multi-decade observations. And if today the WDS and CCDM catalogs contain over 78,000 and 110,000 objects, respectively, then the orbit of only a few hundred can be calculated, and for less than a hundred objects the orbit is known with sufficient accuracy to obtain the mass of components.

Spectral binary stars

A conditional example of bifurcation and displacement of lines in the spectra of spectroscopic double stars.

Spectral double called a system of double stars, whose duality can be detected using spectral observations. To do this, they observe the star over several nights, and if it is discovered that the lines “walk” along the spectrum: on one night their measured wavelengths are the same, on the next they are different. This says that the speed of the source is changing. There may be many different reasons for this: the star itself is variable, it may have a dense expanding envelope formed after a supernova explosion, etc., etc. If we see the spectrum of the second star, and the behavior of its radial velocity is similar to the behavior of the radial velocity first, then we can say with confidence that we have a dual system. At the same time, we must not forget that if the first star approaches us and its lines are shifted to the violet part of the spectrum, then the second one then moves away, and its lines are shifted to the red part of the spectrum, and vice versa.

But if the second star is much inferior in brightness to the first, then we have a chance not to see it, and then all possible scenarios must be considered. The main arguments for the fact that this is a double star are the periodicity of radial velocities and the large difference between the maximum and minimum velocities. But, if you think hard, then using the same arguments, you can say that an exoplanet has been discovered. To dispel all doubts, we need to calculate the mass function. And from it one can already judge the minimum mass of the second component and, accordingly, whether the invisible object is a planet, a star, or even a black hole.

Also, from spectroscopic data, in addition to the masses of the components, it is possible to calculate the distance between them, the orbital period, and the eccentricity of the orbit, but the angle of inclination to the picture plane can no longer be observed. Therefore, the mass and distance between the components can only be said to be calculated accurate to the angle of inclination.

Like any type of object studied by astronomers, there are catalogs of spectroscopic double stars. The most famous and most extensive is “SB9” (from the English Spectral Binaries). At the moment there are 2839 objects.

Eclipsing binary stars

It happens that the orbital plane passes or almost passes through the eye of the observer. The orbits of the stars of such a system are located, as it were, edge-on to us. Here the stars will periodically eclipse each other, the brightness of the entire pair will change with the same period. This type of binary is called an eclipsing binary. 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 (Eye of the Devil) in the constellation Perseus.

Astrometric double stars

There are such close star pairs when one of the stars is either very small in size or has a low luminosity. In this case, such a star cannot be seen, but duality can still be detected. The bright component will periodically deviate from a rectilinear trajectory, first in one direction, then in the other, as if the center of mass of the system was moving in a straight line. Such disturbances will be proportional to the mass of the satellite. Studies of one of the stars closest to us, known as Ross 614, have shown that the amplitude of the star’s deviation from the expected direction reaches 0.36``. The star's orbital period relative to the center of mass is 16.5 years. Among the stars close to the Sun, about 20 astrometric binary stars have been discovered.

Components of binary stars

There are different double stars: there are two similar stars in a pair, and there are different ones. But, regardless of their type, these stars are the most amenable to study: for them, unlike ordinary stars, by analyzing their interaction, you can find out almost all the parameters, including mass, shape of orbits, and even roughly determine the characteristics of stars located close to them. As a rule, these stars have a somewhat elongated shape due to mutual attraction. About half of all the stars in our Galaxy belong to binary systems, so binary stars orbiting one another are a very common phenomenon.

Belonging to a binary system greatly influences the entire life of a star, especially when partners are close to each other. Streams of matter rushing from one star to another lead to dramatic explosions such as novae and supernovae.

Links

Star systems
Bound by gravitation	Galaxy · Dwarf galaxy · Globular star cluster · Open star cluster · Physically double star· Physically multiple star
Unrelated	Stellar Stream · Stellar Association · Moving Group of Stars · Runner Star · Supervelocity Star
Connected only visually	Optical double star· Optical multiple star · Constellation · Asterism · Star cloud

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See what “Double stars” are in other dictionaries:

Two stars revolving in elliptical orbits around a common center of mass under the influence of gravity. According to observation methods, visually double stars are distinguished, the duality of which can be seen through a telescope, spectrally double stars, ... ... Big Encyclopedic Dictionary

Stars that are visible to the naked eye as one star and only in a telescope are separated into two stars. D. Z. are: a) optical, if the proximity is only perspective (in reality, one star is much further than the other, and only by chance it ... ... Marine Dictionary

Two stars revolving in elliptical orbits around a common center of mass under the influence of gravitational forces... Astronomical Dictionary

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Double stars- Double stars DOUBLE STARS, two stars united by gravitational forces and revolving around a common center of mass; the most common type of multiple stars (systems combining two, three, four, etc. stars). Double stars, components... ... Illustrated Encyclopedic Dictionary

An artist's impression of a binary system of O-stars

A double star, or binary system, is a system of two gravitationally bound stars revolving in closed orbits around a common center of mass. Double stars are very common objects. About half of all stars belong to binary systems.

By measuring the orbital period and distance between stars, it is sometimes possible to determine the masses of the system's components. This method practically does not require additional model assumptions, and therefore is one of the main methods for determining masses in astrophysics. For this reason, binary systems whose components are or are of great interest for astrophysics.

Classification

Physically, double stars can be divided into two classes:

stars between which mass exchange is impossible in principle - separated binary systems.
the stars between which there is, will be, or was an exchange of masses - close binary systems. They in turn can be divided into:
- Semi-detached, where only one star fills its Roche lobe.
- Contact stars, where both stars fill their Roche lobes.

Binary systems are also classified according to the method of observation, we can distinguish visual, spectral, eclipsing, astrometric dual systems.

Visual double stars

Double stars that can be seen separately (or, as they say, that can be allowed), are called visible double, or visually double.

The ability to observe a star as a visual double is determined by the resolution of the telescope, the distance to the stars and the distance between them. Thus, visual binary stars are mainly neighborhood stars with very long orbital periods (a consequence of the large distance between the components). Due to the long period, the binary's orbit can only be traced through numerous observations over decades. To date, the WDS and CCDM catalogs contain over 78,000 and 110,000 objects, respectively, and only a few hundred of them can have their orbits calculated. For fewer than a hundred objects, the orbit is known with sufficient accuracy to obtain the mass of the components.

Speckle interferometric binary stars

Speckle interferometry, along with adaptive optics, makes it possible to reach the diffraction limit of stellar resolution, which in turn makes it possible to detect double stars. That is, in essence, speckle-interferometric binaries are the same visual binaries. But if in the classical visual-dual method it is necessary to obtain two separate images, then in this case it is necessary to analyze speckle interferograms.

Speckle interferometry is effective for binaries with periods of several decades.

Astrometric double stars

Behavior of an astrometric binary in the sky.

In the case of visual double stars, we see two objects moving across the sky at once. However, if we imagine that one of the two components is not visible to us for one reason or another, then duality can still be detected by a change in the position of the second in the sky. In this case, they speak of astrometric double stars.

If high-precision astrometric observations are available, then duality can be assumed by recording the nonlinearity of the motion: the first derivative of the proper motion and the second. Astrometric binary stars are used to measure the mass of different spectral classes.

Spectral binary stars

A conditional example of bifurcation and displacement of lines in the spectra of spectroscopic double stars.

Spectral double called a star whose duality is detected using spectral observations. To do this, she is observed for several nights. If it turns out that the lines of its spectrum periodically shift over time, then this means that the speed of the source is changing. There may be many reasons for this: the variability of the star itself, the presence of a dense expanding shell formed after an outburst, etc.

If a spectrum of the second component is obtained, which shows similar displacements, but in antiphase, then we can say with confidence that we have a double system. If the first star is approaching us and its lines are shifted to the violet side of the spectrum, then the second is moving away, and its lines are shifted to the red side, and vice versa.

But if the second star is much inferior in brightness to the first, then we have a chance not to see it, and then we need to consider other possible options. The main feature of a double star is the periodicity of changes in radial velocities and the large difference between the maximum and minimum velocities. But, strictly speaking, it is possible that . To find out, we need to calculate the mass function, which can be used to judge the minimum mass of the invisible second component and, accordingly, what it is - a star or even a black hole.

Also, from spectroscopic data, in addition to the masses of the components, it is possible to calculate the distance between them, the orbital period and the eccentricity of the orbit. It is impossible to determine the angle of inclination of the orbit to the line of sight from these data. Therefore, the mass and distance between the components can only be said to be calculated to an accuracy of the angle of inclination.

As with any type of object studied by astronomers, there are catalogs of spectroscopic binary stars. The best known and most extensive of them is “SB9” (from the English Spectral Binaries). At the moment there are 2839 objects in it.

Eclipsing double stars

It happens that the orbital plane is inclined to the line of sight at a very small angle: the orbits of the stars of such a system are located, as it were, edge-on to us. In such a system, the stars will periodically eclipse each other, that is, the brightness of the pair will change. Binary stars that experience such eclipses are called eclipsing binaries or eclipsing variables. The most famous and first discovered star of this type is Algol (Devil's Eye) in the constellation Perseus.

Microlensed Dual

If there is a body with a strong gravitational field on the line of sight between the star and the observer, then the object will be lensed. If the field were strong, then several images of the star would be observed, but in the case of galactic objects, their field is not so strong that the observer could distinguish several images, in which case they talk about microlensing. If the engraving body is a double star, then the light curve obtained when it passes along the line of sight is very different from the case of a single star.

Using microlensing, we look for binary stars where both components are low-mass brown dwarfs.

Phenomena and phenomena associated with double stars

Algol's paradox

This paradox was formulated in the mid-20th century by Soviet astronomers A.G. Masevich and P.P. Parenago, who drew attention to the discrepancy between the masses of Algol’s 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 a star with a mass comparable to or slightly more than the Sun. It is obvious that the components of the binary star formed at the same time, therefore, the massive component should evolve earlier than the low-mass one. However, in the Algol system the more massive component was younger.

The explanation of this paradox is associated with the phenomenon of mass flow in close binary systems and was first proposed by the American astrophysicist D. Crawford. If we assume that during evolution one of the components has the opportunity to transfer mass to its neighbor, then the paradox is removed.

Mass exchange between stars

Section of surfaces of equal potential in the Roche model in the orbital plane of a binary system

Let us consider the approach of a close binary system (called Roche approximations):

Stars are considered point masses and their own moment of axial rotation can be neglected compared to the orbital one
The components rotate synchronously.
Circular orbit

Then, for the components M 1 and M 2, with the sum of the semimajor axes a=a 1 +a 2, we introduce a coordinate system synchronous with the orbital rotation of the RDS. The reference center is at the center of the star M 1, and the X axis is directed from M 1 to M 2 and the Z axis is directed along the rotation vector. Then we write down the potential associated with the gravitational fields of the components and centrifugal force:

Where r 1 = √ x 2 +y 2 +z 2 , r 2 = √ (x-a) 2 +y 2 +z 2, μ= M 2 /(M 1 +M 2) , and ω is the rotation frequency along the orbit of the components. Using Kepler's third law, the Roche potential can be rewritten as follows:

where is the dimensionless potential:

where q = M 2 /M 1

Equipotentials are found from the equation Φ(x,y,z)=const. Near the centers of stars they differ little from spherical ones, but as they move away, the deviation from spherical symmetry becomes stronger. As a result, both surfaces meet at the Lagrange point L 1. This means that the potential barrier at this point is equal to 0, and particles from the surface of the star located near this point are able to move into the Roche lobe of a neighboring star due to thermal chaotic motion.

Symbiotic stars

Interacting binary systems consisting of and surrounded by a common nebula. They are characterized by complex spectra, where, along with absorption bands (for example, TiO), there are emission lines characteristic of nebulae (OIII, NeIII, etc. Symbiotic stars are variable with periods of several hundred days, they are characterized by nova-like flares, during during which their brightness increases by two to three magnitudes.

Symbiotic stars represent a relatively short-term, but extremely important and rich in astrophysical manifestations stage in the evolution of binary stellar systems of moderate masses with initial orbital periods of 1-100 years.

Origin and evolution

The mechanism of formation of a single star has been studied quite well - it is compression due to gravitational instability. It was also possible to establish the distribution function of the initial masses. Obviously, the scenario for the formation of a double star should be the same, but with additional modifications. It should also explain the following known facts:

Double frequency. On average it is 50%, but is different for stars of different spectral classes. For O-stars this is about 70%, for stars like the Sun (spectral class G) it is close to 50%, and for spectral class M about 30%.
Period distribution.
The eccentricity of double stars can take any value 0
Mass ratio The distribution of the mass ratio q = M 1 / M 2 is the most difficult to measure, since the influence of selection effects is large, but at the moment it is believed that the distribution is uniform and lies within 0.2

At the moment, there is no final understanding of exactly what modifications need to be made, and what factors and mechanisms play a decisive role here. All currently proposed theories can be divided according to what formation mechanism they use:

Theories with an intermediate core
Theories with intermediate disk
Dynamic theories

Theories with an intermediate core

The most numerous class of theories. In them, the formation occurs due to the rapid or early division of the protocloud.

The earliest of them believes that during collapse, due to various kinds of instabilities, the cloud breaks up into local Jeans masses, growing until the smallest of them ceases to be optically transparent and can no longer cool effectively. However, the calculated stellar mass function does not coincide with the observed one.

Another early theory suggested the multiplication of collapsing nuclei due to deformation into various elliptical shapes.

Modern theories of the type under consideration believe that the main reason for fragmentation is the increase in internal energy and rotational energy as the cloud contracts.

Theories with intermediate disk

In theories with a dynamic disk, formation occurs during the fragmentation of the protostellar disk, that is, much later than in theories with an intermediate core. This requires a fairly massive disk that is susceptible to gravitational instabilities and whose gas is effectively cooled. Then several companions may arise, lying in the same plane, which accrete gas from the parent disk.

Recently, the number of computer calculations of such theories has increased greatly. Within the framework of this approach, the origin of close binary systems, as well as hierarchical systems of various multiplicities, is well explained.

Dynamic theories

The latter mechanism suggests that binary stars formed through dynamic processes driven by competitive accretion. In this scenario, it is assumed that the molecular cloud, due to various types of turbulence inside it, forms clumps of approximately Jeans mass. These clumps, interacting with each other, compete for the substance of the original cloud. In such conditions, both the already mentioned model with an intermediate disk and other mechanisms, which will be discussed below, work well. In addition, dynamic friction with the surrounding gas brings the components closer together.

A combination of fragmentation with an intermediate core and the dynamic hypothesis is proposed as one of the mechanisms that works under these conditions. This allows you to reproduce the frequency of multiple stars in . However, at the moment the mechanism of fragmentation is not precisely described.

Another mechanism involves an increase in the gravitational interaction cross section near the disk until a nearby star is captured. Although this mechanism is quite suitable for massive stars, it is completely unsuitable for low-mass ones and is unlikely to be dominant in the formation of double stars.

Exoplanets in binary systems

An exoplanet located in the binary system Kepler-47 through the eyes of an artist.

Of the more than 800 currently known exoplanets, the number orbiting single stars significantly exceeds the number of planets found in star systems of different magnitudes. According to the latest data, there are 64 of the latter.

Exoplanets in binary systems are usually divided according to the configurations of their orbits:

S-class exoplanets orbit one of the components (for example, OGLE-2013-BLG-0341LB b). There are 57 of them.
The P-class includes those orbiting both components. These were found in NN Ser, DP Leo, HU Aqr, UZ For, Kepler-16 (AB)b, Kepler-34 (AB)b and Kepler-35 (AB)b.

If you try to carry out statistics, you will find out:

A significant part of the planets live in systems where the components are separated in the range from 35 to 100., concentrating around a value of 20. e.
Planets in wide systems (>100 AU) have masses ranging from 0.01 to 10 MJ (almost the same as for single stars), while the masses of planets for systems with less separation range from 0.1 to 10 MJ
Planets in wide systems are always single
The distribution of orbital eccentricities differs from single ones, reaching values of e = 0.925 and e = 0.935.

Important features of formation processes

Trimming of a protoplanetary disk. While in single stars it can extend up to (30-50 AU), in double stars its size is cut off by the influence of the second component. Thus, the extent of the protoplanetary disk is 2-5 times less than the distance between the components.

Curvature of the protoplanetary disk. The disk remaining after circumcision continues to experience the influence of the second component and begins to stretch, deform, intertwine and even rupture. Also, such a disk begins to precess.

Reducing the lifetime of a protoplanetary disk For wide binaries, as for single ones, the lifetime of the protoplanetary disk is 1-10 million years. One for split systems< 40 а. е. Время жизни диска должно составлять в пределах 0,1-1 млн лет.

Planetosimal formation scenario

Incompatible education scenarios

There are scenarios in which the initial, immediately after formation, configuration of the planetary system differs from the current one and was achieved during further evolution.

One such scenario is the capture of a planet from another star. Since a double star has a much larger interaction cross section, the probability of a collision and capture of a planet from another star is significantly higher.
The second scenario assumes that during the evolution of one of the components, already at stages after the main sequence, instabilities arise in the original planetary system. As a result, the planet leaves its original orbit and becomes common to both components.

Astronomical data and their analysis

Light curves

The eclipses themselves

Effects of ellipsoidality.

The effects of reflection, or rather processing of radiation from one star in the atmosphere of another.

However, the analysis of only the eclipses themselves, when the components are spherically symmetric and there are no reflection effects, comes down to solving the following system of equations:

where ξ, ρ are the polar distances on the disk of the first and second star, I a is the function of absorption of radiation from one star by the atmosphere of another, I c is the function of the brightness of areas dσ for various components, Δ is the overlap area, r ξc ,r ρc are the total radii of the first and the second star.

Solving this system without a priori assumptions is impossible. Just like the analysis of more complex cases with the ellipsoidal shape of the components and reflection effects, which are significant in various variants of close binary systems. Therefore, all modern methods of analyzing light curves in one way or another introduce model assumptions, the parameters of which are found through other types of observations.

Radial velocity curves

If a double star is observed spectroscopically, then it is a spectroscopic double star. Then we can plot the dependence of the change in the radial velocities of the components on time. If we assume that the orbit is circular, then we can write the following:

where V s is the radial velocity of the component, i is the inclination of the orbit to the line of sight, P is the period, a is the radius of the orbit of the component. Now, if we substitute Kepler’s third law into this formula, we have:

where M s is the mass of the component under study, M 2 is the mass of the second component. Thus, by observing both components, one can determine the ratio of the masses of the stars that make up the binary. If we reuse Kepler's third law, then the latter is reduced to the following:

where G is the gravitational constant, and f(M 2) is a function of the mass of the star and, by definition, is equal to:

If the orbit is not circular, but has an eccentricity, then it can be shown that for the mass function the orbital period P must be multiplied by the factor .

If the second component is not observed, then the function f(M 2) serves as a lower limit on its mass.

It is worth noting that by studying only the radial velocity curves it is impossible to determine all the parameters of the binary system; there will always be uncertainty in the form of an unknown orbital inclination angle.

Determination of component masses

Almost always, the gravitational interaction between two stars is described with sufficient accuracy by Newton's laws and Kepler's laws, which are a consequence of Newton's laws. But to describe double pulsars we have to use general relativity. By studying the observational manifestations of relativistic effects, we can once again check the accuracy of the theory of relativity.

Kepler's third law relates the period of revolution to the distance between the components and the mass of the system:

where is the period of revolution, is the semimajor axis of the system, and is the mass of the components, and is the gravitational constant. For a visual binary, it is possible to determine the orbits of both components, calculate the period and semi-axis, and the mass ratio. But often the duality of a system can be judged only from spectral data (spectral binaries). From the movement of spectral lines, one can determine the radial velocities of one component, and in rare cases, two components at once. If the radial velocity of only one component is known, then complete information about the masses cannot be obtained, but it is possible to construct a mass function and determine the upper limit on the mass of the second component, and therefore say whether it can be a black hole or a neutron star.

History of discovery and study

Reverend John Michell was the first to put forward the idea of the existence of double stars. In a speech to the Royal Society in 1767, he suggested that many stars seen as binaries might actually be physically related. Observational evidence for this hypothesis was published by Sir William Herschel in 1802.

Binary stars are those stars that, upon thorough examination using one of the methods described below, turn out to consist of two stars located spatially close to each other and therefore physically interacting. In this case, each of the stars is considered as a component (component) of a physical pair of stars or, in the general case, a multiple star (triple, quadruple, etc.). Binary stars are not uncommon; on the contrary, one might think that single stars that are not part of binary or multiple systems are the exception rather than the rule (see below).

VISUAL DOUBLE STARS

Two stars located close in space, but far from the earthly observer, merge into one for the naked eye, but in a telescope with sufficient magnification (KPA 18, 26) they are visible separately. This is exactly how they were discovered in the 17th century. the first double stars. In accordance with the method by which they were discovered, they are called visual double stars. It may turn out that two stars located almost in the same direction are spatially very distant from each other (for example, one is three times further away than the other). Such stars form an optical pair and are not considered binaries.

Whether this pair is physical or optical is determined from many years of telescopic observations. In a physical pair, there must be movement of each component around a common center of mass along a conical section - most often along an ellipse. Therefore, one component will describe an ellipse relative to the other. Even if the orbital period is several hundred years (which often happens), the curvature of the path nevertheless becomes noticeable over several decades, when observations are quite accurate. However, there are many double stars whose orbital period is tens of years or several years, and then the fact of orbital motion becomes visible from shorter observations. The observations themselves consist of measuring with a micrometer (thread or other) the angular distance between the components and the angle between the direction to the north celestial pole and the line connecting the components (Fig. 74).

This angle is called the position angle and is always measured counterclockwise (east). The distance p is usually expressed in seconds of arc. If , then photographic observations with long-focus astrographs should be preferred to visual ones. At shorter distances, visual observations are more accurate. At the limit of the resolving power of the telescope, it is better to use an ocular-type interferometer. Below the resolution limit, a stellar interferometer (KPA 458) is used. However, interferometers work well only when the brightness of both components is approximately the same.

The angular distance d" between the components corresponds to the linear distance, expressed in astronomical units,

provided that the segment d is perpendicular to the line of sight. If the star pair is very distant, then its parallax is very small and therefore even large distances d will be visible at a very small angle. It is clear that visual double stars are observed mainly among stars close to us.

Rice. 74. Measuring the relative position of components A and B in a binary system. Supposed. that A is the main (brighter) component. E - indicates the direction east of it

Wider physical pairs, in which the components are separated from each other at distances of thousands and tens of thousands of astronomical units, will also be relatively widely spaced in the sky even at a very great distance, but, as shown further [see. formula (12.2)], in such systems the orbital motion proceeds very (!) slowly and it is possible to identify such a pair either by the commonality of physical characteristics or by the commonality of the spatial motion of the components.

Rice. 75. Multiple star system “Trapezium of Orion”, or O, Orion. Consists of six evezdas physically connected to each other: . The sizes of the circles representing stars have nothing to do with their true sizes, but only approximately express their brilliance. On the scale adopted in the drawing for the mutual distances of the stars, their diameters would be expressed in fractions of a micrometer

An example of the first kind is a multiple star in the center of the Orion Nebula, Orion or the “Trapezium of Orion” (Fig. 75), consisting of four bright components of spectral classes O-B and two weaker ones, also class B. If we construct a spectrum diagram for them - apparent magnitude (Sp, m), then they will be well located along one line, which can be taken as the upper left end of the main sequence of the G - P diagram, when all visible magnitudes are given the same value, converting to M.

This means that all the stars of the Trapezium have the same distance from the Earth. They are physically connected to the Orion Nebula, but are quite far apart from each other: with a value of 21.5", the angular distance between A and D corresponds to a linear distance of at least 11,000 AU.

An example of the second kind is the discovery of a star of the lowest luminosity, a satellite of the star. This latter has long been known to have a fairly significant proper motion in the direction. Van Biesbrouck, who began in 1940 to search for faint satellites of stars with large , found at a distance of 74" from a star having its own motion in the direction. The similarity is so great that it is necessary to consider both stars moving in space along almost parallel paths, i.e. i.e. a physical pair. Since the parallax of this star is , the absolute magnitude of the satellite is equal (spectrum with emission lines H and K and hydrogen), and the linear distance between the components is a. It is curious that the star closest to Earth has a Centauri For the same sign, a faint satellite was found at a distance of 2.2°, which corresponds to a linear distance of about 10,600 AU. This star is slightly closer to Centauri itself, which is why it received the name Proxima (proxima - closest) Centauri.

Centauri itself is a typical binary, in which the components revolve around a common center of mass in elliptical orbits (Fig. 76). The simplest are relative observations, in which the coordinates of satellite B are measured with a micrometer relative to the main star A. If we determine the position of A and B relative to stars that are random for a given pair, but are immediately in the field of view of the telescope, then the proper motion of the pair in the celestial direction will be revealed. sphere (uniform motion along the arc of a great circle will have their common center of mass G) and elliptical motion of components A and B, which occurs in such a way that three points A, G and B always lie on the same straight line. In this case there should be

where are the masses of the components. The determination of AG/GB is best made from large-scale photographs of the binary star taken over a number of years.

Binary stars attract attention when they occur among bright stars, especially when both components are close to each other not only in position but also in brightness. Indeed, with the numerous stars in the firmament, there will always be some faint star in close proximity to a given bright star; in the same way, among very faint stars there are always - in a small field of view - two or more stars close to each other.

But all of these will, of course, be random, optical combinations of stars, not really connected by anything.

Rice. 76. Movement in the a Centauri system. The relative orbit of satellite B is shown, i.e. its movement relative to the main star A (for the years 1830-1940). In fact, the movements of A and B occur near a common center of mass, but these movements can be identified separately only by measuring the position of A and B relative to the surrounding field stars, which have no relation to the system

The greatest expert on double stars in our century, Aitken, when compiling his catalog of double stars, included only those pairs that satisfy the condition

where is the total brightness of the system. But this is a deliberately liberal estimate, with the goal of not missing a single physical pair among the observed double stars. And, of course, we must take into account the fact that there are very wide pairs identified when analyzing our own. movements such as those described above will not satisfy condition (11.3), as well as some close physical pairs separated by the keen naked eye, for example Mizar and Alcor in Ursa Major Taurus or Lyra.

> Double stars

– features of observation: what it is with photos and videos, detection, classification, multiples and variables, how and where to look in Ursa Major.

Stars in the sky often form clusters, which can be dense or, on the contrary, scattered. But sometimes stronger connections arise between stars. And then it is customary to talk about double systems or double stars. They are also called multiples. In such systems, stars directly influence each other and always evolve together. Examples of such stars (even with the presence of variables) can be found literally in the most famous constellations, for example, Ursa Major.

Discovery of double stars

The discovery of double stars was one of the first advances made using astronomical binoculars. The first system of this type was the Mizar pair in the constellation Ursa Major, which was discovered by the Italian astronomer Riccoli. Since there are an incredible number of stars in the Universe, scientists decided that Mizar could not be the only binary system. And their assumption turned out to be completely justified by future observations.

In 1804, William Herschel, a famous astronomer who had been making scientific observations for 24 years, published a catalog detailing 700 double stars. But even then there was no information about whether there was a physical connection between the stars in such a system.

A small component "sucks" gas from a large star

Some scientists have taken the view that double stars depend on a common stellar association. Their argument was the heterogeneous shine of the components of the pair. Therefore, it seemed that they were separated by a significant distance. To confirm or refute this hypothesis, measurements of the parallactic displacement of stars were required. Herschel took on this mission and, to his surprise, found out the following: the trajectory of each star has a complex ellipsoidal shape, and not the appearance of symmetrical oscillations with a period of six months. In the video you can observe the evolution of double stars.

This video shows the evolution of a close binary pair of stars:

You can change the subtitles by clicking on the "cc" button.

According to the physical laws of celestial mechanics, two bodies connected by gravity move in an elliptical orbit. The results of Herschel's research became proof of the assumption that there is a gravitational force connection in binary systems.

Classification of double stars

Binary stars are usually grouped into the following types: spectral binaries, photometric binaries, and visual binaries. This classification gives an idea of the stellar classification, but does not reflect the internal structure.

Using a telescope, you can easily determine the duality of visual double stars. Today there is evidence of 70,000 visual binary stars. Moreover, only 1% of them definitely have their own orbit. One orbital period can last from several decades to several centuries. In turn, building an orbital path requires considerable effort, patience, precise calculations and long-term observations in an observatory.

Often, the scientific community has information about only some fragments of orbital movement, and they reconstruct the missing sections of the path using a deductive method. Do not forget that the orbital plane may be inclined relative to the line of sight. In this case, the apparent orbit is seriously different from the real one. Of course, with high accuracy of calculations, it is possible to calculate the true orbit of binary systems. To do this, Kepler's first and second laws are applied.

Mizar and Alcor. Mizar is a double star. On the right is the Alcor satellite. There's only one light year between them

Once the true orbit is determined, scientists can calculate the angular distance between the binary stars, their mass, and their rotation period. Often, Kepler's third law is used for this, which helps to find the sum of the masses of the components of the pair. But to do this you need to know the distance between the Earth and the double star.

Double photometric stars

The dual nature of such stars can be learned only from periodic fluctuations in brightness. As they move, stars of this type take turns blocking each other, which is why they are often called eclipsing binaries. The orbital planes of these stars are close to the direction of the line of sight. The smaller the area of the eclipse, the lower the brightness of the star. By studying the light curve, the researcher can calculate the inclination angle of the orbital plane. When two eclipses are recorded, there will be two minima (decreases) in the light curve. The period when 3 successive minima are observed in the light curve is called the orbital period.

The period of double stars lasts from a couple of hours to several days, which makes it shorter in relation to the period of visual double stars (optical double stars).

Spectral dual stars

Through the method of spectroscopy, researchers record the process of splitting spectral lines, which occurs as a result of the Doppler effect. If one component is a weak star, then only periodic fluctuations in the positions of single lines can be observed in the sky. This method is used only when the components of the binary system are at a minimum distance and their identification using a telescope is complicated.

Binary stars that can be studied through the Doppler effect and a spectroscope are called spectrally dual. However, not every double star has a spectral character. Both components of the system can approach and move away from each other in the radial direction.

According to the results of astronomical research, most of the double stars are located in the Milky Way galaxy. The percentage ratio of single and double stars is extremely difficult to calculate. Working through subtraction, one can subtract the number of known double stars from the total stellar population. In this case, it becomes clear that binary stars are in the minority. However, this method cannot be called very accurate. Astronomers are familiar with the term “selection effect.” To fix the binarity of stars, their main characteristics must be determined. Special equipment will be useful for this. In some cases, it is extremely difficult to detect double stars. Thus, visually, double stars are often not visualized at a significant distance from the astronomer. Sometimes it is impossible to determine the angular distance between stars in a pair. To detect spectroscopic binaries or photometric stars, it is necessary to carefully measure wavelengths in spectral lines and collect modulations of light fluxes. In this case, the brilliance of the stars should be quite strong.

All this sharply reduces the number of stars suitable for study.

According to theoretical developments, the proportion of double stars in the stellar population varies from 30% to 70%.