What are double stars visually. double stars

A large number of stars visible in our galaxy and beyond belong to double and more multiple. That is, we can say with confidence that our single star the Sun belongs to the minority in the classification of stellar systems. Let's talk about what these systems are.

Some sources say that only 30% of the total number of stars are single, in others you can find the number 25. But with the improvement of methods for measuring and studying double and multiple stars, the percentage of single stars changes. This is primarily due to the difficulty of detecting small (in size, but not mass) stars. To date, astronomers have discovered many that, when first discovered, may fit the description of secondary stars in a system of two or more stars, only after a detailed study and many calculations, the option is excluded that this is a star, and the found object is classified as a planet (this is determined by mass, by gravitational attraction, by relative position behavior and many other factors).

double stars

Kappa Bootes

A system of two stars bound by gravity is called double star system or simply double star.

First of all, it should be emphasized that not all optically adjacent two stars are binary. It follows that stars that are visible in the sky close to each other for an observer from the Earth, but at the same time not connected by gravitational forces and not having a common center of mass are called optical double. A good example is α Capricornus - a pair of stars are at a great distance from each other (about 580 light years), but it seems to us that they are nearby.

Physical binary stars revolve around a common center of mass and are interconnected by gravitational forces. An example is η () of Cassiopeia. From the period of rotation and the mutual distance, one can determine the mass of each of the stars. The rotation period has an impressive range: from several minutes, when it comes to the rotation of dwarf stars around neutron stars, to several million years. The distances between the stars can approximately be from 10 10 to 10 16 m (about 1 light year).

Binary stars have a very broad classification. Here are just the main points:

Astrometric(you can see the movement of two objects at once);
Spectral(duality is determined by spectral lines);
eclipsing binaries(due to the different angle of inclination to the orbit, a dimming of one star by another is periodically observed);
Microlensed(when there is a space object with a strong gravitational field between the system and the observer. Low-mass brown dwarfs are found using this method);
Speckle interferometric(according to the diffraction limit of the resolution of stars, binary stars are found);
X-ray.

Multiple stars

As the name implies, if the number of interconnected stars exceeds two, then this multiple star systems or . They are also divided into optically and physically multiple stars. If the number of stars in the system can be seen with the naked eye, through binoculars or a telescope, then such stars are called visually multiple. If additional spectral measurements are required to determine the multiplicity of the system, then this spectral multiple system. And, if the multiplicity of the system is determined by the change in brightness, then this eclipsing multiple system. A simple example of a triple star is shown below - this is a star HD 188753 in the constellation Cygnus:

Triple star HD 188753

As you can see in the image above, in the triple system there are a pair of closely related stars and one distant one with a larger mass, around which the pair rotates. But more often, a distant star revolves around a pair of closely related stars that are a single whole. Such a pair is called main.

Of course, the multiplicity is not limited to three stars. There are systems of four, five and six stars. The higher the multiplicity, the fewer such systems. For example, the star ε Lyra is two pairs of interconnected, remote from each other at a great distance. Scientists have roughly calculated that the distance between pairs should be 5 or more times greater than the distance between stars within one pair.

The best example of a sixfold system of stars is Castor in the constellation. In it, three pairs of stars interact in an organized manner with each other. More than 6 stars in the system have not yet been discovered.

Multiple stars occupy astronomers-observers no less than deep sky objects. Star systems look especially beautiful when the components in them have a different color tint, for example, one of them is cold red, and the other is a hot, bright blue star. There are many reference books with detailed characteristics of the most famous and interesting binary and multiple stars for observation. I will introduce you to some of the systems in a separate article.

Stars on celestial body exist in the form of clusters, associations, and not as single bodies. Star clusters may or may not be very densely dotted with stars.
Closer connections may exist between the stars, we are talking about double stars, or binary systems, as astronomers call them. In a pair of stars, the evolution of one directly affects the other.

Opening

The discovery of binary stars, as they are currently called, was one of the first discoveries made with the help of astronomical binoculars. The first pair of this type of stars was Mizar from the constellations Ursa Major. The discovery was made by the Italian astronomer Riccioli. Given the huge number of stars in the universe, scientists came to the conclusion that Mizar was not the only binary system among them, and they turned out to be right, observations soon confirmed this hypothesis. In 1804, the famous astronomer William Herschel, who devoted 24 years of scientific observation, published a catalog containing descriptions of about 700 binary stars. At first, scientists did not know for sure whether the components of the binary system were physically related to each other.

Some bright minds believed that the stellar association as a whole acts on binary stars, especially since the brilliance of the components was not the same in a pair. In this regard, it seemed that they were not close. To clarify the true state of affairs, it was necessary to measure the parallactic displacements of the stars. This is what Herschel did. To the greatest surprise, the parallactic shift of one star relative to another during the measurement gave an unexpected result. Herschel noticed that instead of a symmetrical wobble with a period of 6 months, each star follows a complex ellipsoidal path. In accordance with the laws of celestial mechanics, two bodies connected by gravity move in an elliptical orbit. Herschel's observations confirmed the thesis that binary stars are physically connected, i.e. gravity forces.

Classification of double stars

There are three main classes of binary stars: visual binaries, photometric binaries, and spectroscopic binaries. This classification does not fully reflect the internal differences of the classes, but gives an idea of the stellar association.

The duality of visual double stars is clearly visible in the telescope as they move. Currently, about 70,000 visual binaries have been identified, but only 1% of them have had an accurate orbit.

This figure (1%) should not be surprising. The fact is that orbital periods can be several tens of years, if not whole centuries. And to build a path in orbit is a very painstaking work that requires numerous calculations and observations from different observatories. Very often, scientists have only fragments of the movement along the orbit, they restore the rest of the path by the deductive method, using the available data. It should be borne in mind that the orbital plane of the system may be tilted to the line of sight. In this case, the reconstructed orbit (visible) will differ significantly from the true one. Of course, if the calculations were carried out with great accuracy, it is possible to calculate the true orbit of a system of binary stars using the first two laws of Kepler.

If the true orbit is determined, the period of revolution and the angular distance between the two stars are known, it is possible, by applying Kepler's third law, to determine the sum of the masses of the components of the system. The distance of the double star to us must also be known.

Double photometric stars

The duality of this system of stars can only be judged from periodic brightness fluctuations. When moving, such stars alternately block (outshine) each other. They are also called "eclipsing binaries". For these stars, the planes of the orbits are close to the direction of the line of sight. How large area occupies an eclipse, the more pronounced the brilliance. If we analyze the light curve of binary photometric stars, we can determine the inclination of the orbital plane.

The light curve can also be used to determine the orbital period of the system. If, for example, two eclipses are fixed, the light curve will have two decreases (minimum). The time period during which three successive decreases along the light curve are recorded corresponds to the orbital period.

The periods of binary photometric stars are much shorter compared to the periods of visually binary stars and last for several hours or several days.

Spectral binary stars

With the help of spectroscopy, one can notice the splitting of spectral lines due to the Doppler effect. If one of the components is a faint star, then only periodic fluctuations in the positions of single lines are observed. This method is used when the components of a binary star are very close to each other and it is difficult to identify them with a telescope as visually binary stars. Binary stars, determined using a spectroscope and the Doppler effect, are called spectral-binary. Not all binary stars are spectral. The two components of binary stars can recede and approach in the radial direction.

Observations indicate that double stars are found mainly in our galaxy. It is difficult to determine the percentage of double and single stars. If we use the subtraction method and subtract the number of identified binary stars from the total stellar population, we can conclude that they are a minority. This conclusion may be wrong. In astronomy, there is the concept of “selection effect”. To determine the duality of stars, it is necessary to identify their main characteristics. This requires good equipment. Sometimes it is difficult to identify double stars. For example, visually binary stars cannot always be seen at a great distance from the observer. Sometimes the angular distance between the components is not fixed by the telescope. In order to detect photometric and spectroscopic binary stars, their brightness must be strong enough to collect the modulations of the light flux and carefully measure the wavelengths in the spectral lines.

The number of stars suitable in all respects for research is not so large.

According to theoretical developments, it can be assumed that binary stars make up from 30 to 70% of the stellar population.

Mass - one of the most important physical characteristics of stars - can only be determined by its effect on the motion of other bodies. Such other bodies are the satellites of some stars that revolve with them around a common center of mass.

If you look at the gamma of B. Ursa, the second star from the end of the "handle" of her "ladle", then with normal vision you will see a second faint star very close to it. She was noticed by the ancient Arabs and called Alcor (Horseman). They named the bright star Mizar. They can be called a double star. Mizar and Alcor are separated from each other by 11 ". You can find a lot of such stellar pairs with binoculars. So, Lyra's epsilon consists of two identical stars of the 4th magnitude with a distance of 5" between them.

Binary stars are called visual binaries if their duality can be seen with direct observations through a telescope (and in rare cases with the naked eye), Epsilon Lyrae is a visual quad star. Systems consisting of three or more stars are called multiples.

Many of the visual binaries turn out to be optical binaries, i.e., the proximity of such two stars is the result of their random projection onto the sky. In space, they are far from each other. Over many years of observations, one can be convinced that one of the stars passes by the other in a straight direction at a constant speed.

Sometimes it gradually turns out that a weaker companion star revolves around a brighter star. The distances between them and the direction of the line connecting them systematically change. Such stars are called physical binaries.

The shortest known orbital period for visual binary stars is 5 years. Pairs with circulation periods of tens of years have been studied, and pairs with periods of hundreds of years will be studied in the future. The closest star to us, a Centauri, is a double star. The circulation period of its constituents (components) is 70 years. Both stars in this pair are similar in mass and temperature to the Sun.

Double stars in a telescope are often a beautiful sight: the main star is yellow or orange, and the satellite is white or blue. Imagine a wealth of colors on a planet revolving around one of a pair of stars, where the red Sun shines in the sky, then the blue one, then both together.

If our line of sight lies almost in the plane of the orbit of a spectral binary, then the stars of such a pair will alternately block each other. During eclipses, the overall brilliance of a pair whose components we cannot see individually will weaken. For the rest of the time, in the intervals between eclipses, it will be constant and the longer, the shorter the duration of the eclipses and the greater the radius of the orbit. If the satellite is large and gives little light itself, when bright Star outshines it, the total brightness of the system will decrease slightly.

The brightness minima of eclipsing binary stars occur when their components move across the line of sight. Analysis of the light curve over time makes it possible to determine the size and brightness of the stars, the size of the orbit, its shape and inclination to the line of sight, and the masses of the stars. Thus, eclipsing binaries, also observed as spectroscopic binaries, are the best studied systems.

Eclipsing binary stars are also called Algols by the name of the blue typical representative of the betta Perseus. The ancient Arabs called it Algol (corrupted el gul, which means "devil"). It is possible that they noticed its strange behavior: for 2 days 11 hours the brightness of Algol is constant, then in 5 hours it weakens from 2.3 to 3.5 magnitudes, and then in 5 hours its brightness returns to its previous value.

The periods of known spectroscopic binary stars and Algols are mostly short, about a few days. In general, the duality of stars is a very common phenomenon. Up to 30% of the stars are probably binary.

Obtaining a variety of data on individual stars and. their systems from the analysis of spectroscopic binaries and eclipsing binaries can be called examples of "astronomy of the invisible".

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

visual binary stars

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

The ability to observe a star as a visual binary is determined by the resolution of the telescope, the distance to the stars and the distance between them. Thus, visual binary stars are mainly stars in the vicinity of the Sun with a very large period of revolution (a consequence of the large distance between the components). Due to the long period, the orbit of a binary can only be traced from numerous observations over decades. To date, there are over 78,000 and 110,000 objects in the WDS and CCDM catalogs, respectively, and only a few hundred of them can be orbited. For less than a hundred objects, the orbit is known with sufficient accuracy to give the mass of the components.

Speckle interferometric binary stars

Speckle interferometry is effective for binaries with a period of several tens of years.

Astrometric double stars

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 the duality can still be detected by a change in the position of the second in the sky. In this case, one speaks of astrometric binary stars.

If high-precision astrometric observations are available, then duality can be assumed by fixing the non-linearity of motion: the first derivative own movement and second [ clarify] . Astrometric binaries are used to measure the mass of brown dwarfs of different spectral types.

Spectral binary stars

spectral double called a star, the duality of which 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 with time, then this means that the speed of the source is changing. There can be many reasons for this: the variability of the star itself, the presence of a dense expanding shell in it, formed after a supernova explosion, etc.

If the spectrum of the second component is obtained, which shows similar shifts, but in antiphase, then we can say with confidence that we have a binary system. If the first star is approaching us and its lines are shifted to the violet side of the spectrum, then the second one 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 binary star is the periodicity of radial velocities and the large difference between the maximum and minimum speeds. But, strictly speaking, it is possible that an exoplanet has been discovered. 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 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 period of revolution 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 spoken of as calculated up to the angle of inclination.

As with any type of object studied by astronomers, there are catalogs of spectroscopic double stars. The most famous and most extensive of them is "SB9" (from the English Spectral Binaries). As of 2013, it has 2839 objects.

eclipsing binary 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, on an edge towards us. In such a system, the stars will periodically outshine each other, that is, the brightness of the pair will change. Binary stars in which such eclipses are observed 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 binaries

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, and in such a case one speaks of microlensing. If the engraving body is a binary star, the light curve obtained when passing it along the line of sight differs greatly from the case of a single star.

Microlensing searches for binary stars where both components are low-mass brown dwarfs.

Phenomena and phenomena associated with binary stars

Algol paradox

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

The explanation of this paradox is related to the phenomenon of mass flow in close binary systems and was first proposed by the American astrophysicist D. Crawford. If we assume that in the course of evolution one of the components has the possibility of transferring mass to a neighbor, then the paradox is removed.

Mass exchange between stars

Consider the approximation of a close binary system (named Roche approximations):

Stars are considered to be point masses and their own angular momentum can be neglected in comparison with the orbital one.
Components rotate synchronously.
Orbit is circular

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

Φ = − G M 1 r 1 − G M 2 r 2 − 1 2 ω 2 [ (x − μ a) 2 + y 2 ] (\displaystyle \Phi =-(\frac (GM_(1))(r_(1) ))-(\frac (GM_(2))(r_(2)))-(\frac (1)(2))\omega ^(2)\left[(x-\mu a)^(2) +y^(2)\right]),

where r1 = √ x2+y2+z2, r2 = √ (x-a)2+y2+z2, μ= M 2 /(M 1 +M 2) , and ω is the orbital frequency of the components. Using Kepler's third law, the Roche potential can be rewritten as follows:

Φ = − 1 2 ω 2 a 2 Ω R (\displaystyle \Phi =-(\frac (1)(2))\omega ^(2)a^(2)\Omega _(R)),

where is the dimensionless potential:

Ω R = 2 (1 + q) (r 1 / a) + 2 (1 + q) (r 2 / a) + (x − μ a) 2 + y 2 a 2 (\displaystyle \Omega _(R) =(\frac (2)((1+q)(r_(1)/a)))+(\frac (2)((1+q)(r_(2)/a)))+(\frac ((x-\mu a)^(2)+y^(2))(a^(2)))),

where q = M 2 /M 1

The equipotentials are found from the equation Φ(x,y,z)=const . Near the centers of stars, they differ little from spherical ones, but as the distance increases, the deviations from spherical symmetry become 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 inside the Roche lobe of the neighboring star, due to thermal chaotic motion.

New

X-ray doubles

Symbiotic stars

Interacting binary systems consisting of a red giant and white dwarf 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 outbursts, during during which their brightness increases by two or three magnitudes.

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

Bursters

Type Ia supernovae

Origin and evolution

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

Double frequency. On average, it is 50%, but it is different for stars of different spectral types. For O stars, this is about 70%, for stars like the Sun (spectral type G) it is close to 50%, and for spectral type M, about 30%.
Period distribution.
The eccentricity of binary 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 homogeneous and lies within 0.2

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

Theories with an intermediate core
Intermediate disc theories
Dynamic theories

Theories with an intermediate core

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

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

Another of the early theories assumed the multiplication of collapsing nuclei, due to deformation into various elliptical shapes.

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

Intermediate disc theories

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

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

Dynamic theories

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

As one of the mechanisms that work under these conditions, a combination of fragmentation with an intermediate core and a dynamic hypothesis is proposed. This makes it possible to reproduce the frequency of multiple stars in star clusters. However, the fragmentation mechanism has not yet been accurately described.

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

Exoplanets in binary systems

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

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

S-class exoplanets revolve around one of the components (for example, OGLE-2013-BLG-0341LB b). There are 57 of them.
The P-class includes those revolving around both components. They 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 conduct statistics, it turns out:

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

Important features of formation processes

Circumcision of the protoplanetary disk. While in single stars the protoplanetary disk can stretch up to the Kuiper belt (30-50 AU), in binary stars its size is cut off by the influence of the second component. Thus, the length of the protoplanetary disk is 2-5 times less than the distance between the components.

Curvature of the protoplanetary disk. The disk remaining after cutting continues to be influenced by the second component and begins to stretch, deform, intertwine and even break. Also, such a disk begins to precess.

Reducing the lifetime of the protoplanetary disk. For wide binaries, as well as for single ones, the lifetime of the protoplanetary disk is 1-10 million years, however, for systems with separation< 40 а. е. время жизни диска должно находиться в пределах 0,1-1 млн лет.

Planetesimal Formation Scenario

Inconsistent Education Scenarios

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

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

Astronomical data and their analysis

light curves

In the case when the binary star is eclipsing, it becomes possible to plot the dependence of the integral brightness on time. The brightness variability on this curve will depend on:

The eclipses themselves
ellipsoidal effects.
The effects of reflection, or rather the processing of the radiation of 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, reduces to solving the following system of equations:

1 − l 1 (Δ) = ∬ S (Δ) I a (ξ) I c (ρ) d σ (\displaystyle 1-l_(1)(\Delta)=\iint \limits _(S(\Delta) )I_(a)(\xi)I_(c)(\rho)d\sigma )

1 − l 2 (Δ) = ∬ S (Δ) I c (ξ) I a (ρ) d σ (\displaystyle 1-l_(2)(\Delta)=\iint \limits _(S(\Delta) )I_(c)(\xi)I_(a)(\rho)d\sigma )

∫ 0 r ξ c I c (ξ) 2 π ξ d ξ + ∫ 0 r ρ c I c (ρ) 2 π ρ d ρ = 1 (\displaystyle \int \limits _(0)^(r_(\xi c))I_(c)(\xi)2\pi \xi d\xi +\int \limits _(0)^(r_(\rho c))I_(c)(\rho)2\pi \rho d\rho=1)

where ξ, ρ are the polar distances on the disk of the first and second stars, 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 the areas dσ for different components, Δ is the overlap region, r ξc ,r ρc are the total radii of the first and the second star.

The solution of this system without a priori assumptions is impossible. Exactly like the analysis of more complex cases with ellipsoidal 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 by means of other kinds of observations.

Radial velocity curves

If a binary star is observed spectroscopically, that is, it is a spectroscopic binary star, then it is possible to plot the change in the radial velocities of the components with time. If we assume that the orbit is circular, then we can write the following:

V s = V 0 s i n (i) = 2 π P a s i n (i) (\displaystyle V_(s)=V_(0)sin(i)=(\frac (2\pi )(P))asin(i) ),

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, and a is the radius of the component's orbit. Now, if we substitute Kepler's third law into this formula, we have:

V s = 2 π P M s M s + M 2 s i n (i) (\displaystyle V_(s)=(\frac (2\pi )(P))(\frac (M_(s))(M_(s) +M_(2)))sin(i)),

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:

F (M 2) = P V s 1 2 π G (\displaystyle f(M_(2))=(\frac (PV_(s1))(2\pi G))),

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

F (M 2) ≡ (M 2 s i n (i)) 3 (M 1 + M 2) 2 (\displaystyle f(M_(2))\equiv (\frac ((M_(2)sin(i))^ (3))((M_(1)+M_(2))^(2)))).

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 (1 − e 2) 3 / 2 (\displaystyle (1-e^(2))^(3/2)).

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

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

Determining the Masses of the Components

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 (see the Taylor-Hulse pulsar) one has to use general relativity. By studying the observational manifestations of relativistic effects, one 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.

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

But binary stars would not be studied so seriously if all their significance was reduced to mass information. 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. Hubble in the ultraviolet. The photo shows an accretionary "tail" directed from the main component - the red giant to the companion - the white dwarf

Physically, binary stars can be divided into two classes:

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

If we separate binary systems according to the method of observation, then we can distinguish visual, spectral, eclipsing, astrometric double systems.

Visual double stars

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

When observing a visual binary 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 pole of the world 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 sum, these three factors give: 1) that visual binary 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 there are more than 78,000 and 110,000 objects in the WDS and CCDM catalogs, respectively, then only a few hundred can calculate the orbit, and for less than a hundred objects, the orbit is known with sufficient accuracy in order to obtain a mass of components.

Spectral binary stars

A conditional example of bifurcation and shift of lines in the spectra of spectroscopic binary stars.

spectral double called a system of binary stars, whose duality can be detected using spectral observations. To do this, a star is observed for several nights, and if it is found that the lines “walk” along the spectrum: on one night their measured wavelengths are one, on the other they are already different. This says that the speed of the source is changing. There can be a variety of reasons for this: the star itself is variable, maybe it has a dense expanding shell 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, 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 we have a double star - the periodicity of radial velocities and a large difference between the maximum and minimum speed. But, if you think hard, then citing the same arguments, it can be argued that an exoplanet has been discovered. To dispel all doubts, it is necessary to calculate the mass function. And from it one can already judge the minimum mass of the second component and, accordingly, whether an invisible object is a planet, a star, or even a black hole.

Also, according to spectroscopic data, in addition to the masses of the components, the distance between them, the period of revolution, the eccentricity of the orbit can be calculated, but the angle of inclination to the picture plane can no longer be observed. Therefore, the mass and the distance between the components can only be spoken of as calculated up 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 in it.

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, 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 double of this type is the star Algol (Devil's Eye) in the constellation Perseus.

Astrometric double stars

There are such close stellar 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 considered, but it is still possible to detect duality. 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 moves along a straight line. Such perturbations will be proportional to the mass of the satellite. Studies of one of the stars closest to us, known as Ross 614, showed that the amplitude of the deviation of the star from the expected direction reaches 0.36``. The period of revolution of the star relative to the center of mass is 16.5 years. Among the stars close to the Sun, about 20 astrometric binaries have been discovered.

Components of binary stars

There are different binary stars: there are two similar stars in a pair, but there are different ones. 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, 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. 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.

Belonging to a binary system greatly affects the life of a star, especially when partners are close to each other. The streams of matter rushing from one star to another lead to dramatic outbursts, such as explosions of new and supernovae.

Links

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

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