Abstract: Evolution and structure of the galaxy. Presentation on the topic "physical nature of stars" Presentation on the topic physical nature of stars

13.01.2022

The nature of stars. While observing the starry sky, you may notice that the colors of the stars are different. The color of the hot metal can be used to judge the temperature of its photosphere. The sun is a yellow star. Stars with a temperature of 3500-4000K are reddish in color. The spectra of most stars are absorption spectra: dark lines are visible against the background of a continuous spectrum. The sequence of spectral types reflects differences in the color and temperature of stars. The diversity of stellar spectra is explained by the fact that stars have different temperatures. In addition to temperature, the type of spectrum of a star is determined by the pressure and density of the gas of its photosphere, the presence magnetic field, features of the chemical composition.

Slide 5 from the presentation "Astronomy as a Science". The size of the archive with the presentation is 391 KB.

Astronomy 11th grade

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The luminosity of stars is calculated from their absolute magnitude M, which is related to the apparent magnitude m by the relations

M = m + 5 + 51gπ (116)

M = m + 5 - 51gr, (117)

where π is the annual parallax of the star, expressed in arcseconds (") and r is the distance of the star in parsecs (ps). The absolute magnitude M, found using formulas (116) and (117), belongs to the same type as the apparent magnitude m, i.e. it can be visual Mv, photographic Mpg, photoelectric (Mv, Mv or Mv), etc. In particular, the absolute bolometric magnitude, which characterizes the total radiation,

M b = M v + b (118)

and can also be calculated from the apparent bolometric magnitude

m b = m v + b, (119)

where b is the bolometric correction, depending on the spectral type and luminosity class of the star.

The luminosity of L stars is expressed in the luminosity of the Sun, taken as unity (L = 1), and then

log L = 0.4(M - M), (120)

where M is the absolute magnitude of the Sun: visual M v = +4 m .79; photographic M pg - = +5m,36; photoelectric yellow Μ ν = +4 m 77; photovoltaic blue M B = 5 m ,40; bolometric M b = +4 m .73. These magnitudes must be used when solving problems in this section.

The luminosity of a star calculated using formula (120) corresponds to the type of absolute magnitudes of the star and the Sun.

Stefan-Boltzmann law

applicable to determine the effective temperature T e only of those stars whose angular diameters are known. If E is the amount of energy falling from a star or the Sun along the normal onto an area of 1 cm 2 of the boundary of the earth's atmosphere in 1 s, then with an angular diameter Δ, expressed in arcseconds ("), the temperature

(121)

where σ = 1.354 10 -12 cal/(cm 2 s deg 4) = 5.70 10 -5 erg/(cm2 s deg 4) and is selected depending on the units of measurement of the amount of energy E that is located from formula (111) by the difference in bolometric magnitudes of the star and the Sun by comparison with the solar constant E ~ 2 cal/(cm2 min).

The color temperature of the Sun and stars, in the spectra of which the energy distribution is known, can be found using Wien's law

Τ = K/λ m , (122)

where λ m is the wavelength corresponding to the maximum energy, and K is a constant depending on the units of measurement of λ. When measuring λ in cm, K=0.2898 cm·deg, and when measuring λ in angstroms (Å) K=2898· 10 4 Å·deg.

With a sufficient degree of accuracy, the color temperature of stars is calculated from their color indices C and (B-V)

(123)

(124)

The masses of M stars are usually expressed in solar masses (M = 1) and are reliably determined only for physical binary stars (with a known parallax π) according to Kepler's third generalized law: the sum of the masses of the components of a binary star

M 1 + M 2 = a 3 / P 2, (125)

where Ρ is the period of revolution of the companion star around the main star (or both stars around a common center of mass), expressed in years, and a is the semimajor axis of the orbit of the companion star in astronomical units (AU).

The value of a in a. e. is calculated from the angular value of the semi-major axis a" and the parallax π obtained from observations in arcseconds:

a = a"/π (126)

If the ratio of the distances a 1 and a 2 of the components of a double star from their common center of mass is known, then the equality

M 1 / M 2 = a 2 / a 1 (127)

allows you to calculate the mass of each component separately.

The linear radii R of stars are always expressed in solar radii (R = 1) and for stars with known angular diameters Δ (in arcseconds)

(128)

logΔ = 5.444 - 0.2 m b -2 log T (129)

The linear radii of stars are also calculated using the formulas

logR = 8.473-0.20M b -2 logT (130)

logR = 0.82C-0.20M v + 0.51 (131)

And logR = 0.72(B-V) - 0.20 Mv + 0.51, (132)

in which T is the temperature of the star (strictly speaking, effective, but if it is not known, then color).

Since the volumes of stars are always expressed in volumes of the Sun, they are proportional to R 3, and therefore the average density of stellar matter (average stellar density)

(133)

where ρ is the average density of solar matter.

For ρ = 1, the average density of the star is obtained in solar matter densities; if you need to calculate ρ in g/cm3, you should take ρ = 1.41 g/cm3.

Radiation power of a star or Sun

(134)

and the every second loss of mass through radiation is determined by Einstein’s formula

(135)

where c = 3 10 10 cm/s is the speed of light, ΔΜ is expressed in grams per second and ε 0 - in ergs per second.

Example 1. Determine the effective temperature and radius of the star Vega (a Lyrae), if its angular diameter is 0",0035, annual parallax is 0",123 and bolometric brightness is 0 m .54. The bolometric magnitude of the Sun is -26 m.84, and the solar constant is close to 2 cal/(cm 2 min).

Data: Vega, Δ=3",5·10 -3, π = 0",123, m b = -0 m,54;

Sun, m b = - 26m.84, E = 2 cal/(cm 2 min) = 1/30 cal/(cm 2 s); constant σ= 1.354 x 10 -12 cal/(cm 2 s deg 4).

Solution. The radiation from a star falling normally per unit area of the earth's surface, which is similar to the solar constant, is calculated using formula (111):

log E/E=0.4 (m b - m b) = 0.4 (-26 m .84 + 0 m .54) = -10.520 = -11 + 0.480,

whence E/E = 3.02 10 -11,

or Ε = 3.02 10 -11 1/30 = 1.007 10 -12 cal/(cm2 s).

According to (121), the effective temperature of the star

According to formula (128), the radius of Vega

Example 2. Find the physical characteristics of the star Sirius (and Canis Majoris) and its satellite according to the following observational data: the apparent yellow magnitude of Sirius is -1 m .46, its main color index is 0 m .00, and that of the satellite star is, respectively, +8 m .50 and +0 m ,15; the parallax of the star is 0",375; the satellite revolves around Sirius with a period of 50 years in an orbit with an angular value of the semi-major axis of 7",60, and the ratio of the distances of both stars to the common center of mass is 2.3:1. The absolute magnitude of the Sun in yellow rays is taken to be +4 m .77.

Data: Sirius, V 1 = - 1 m .46, (B-V) 1 = 0 m .00;

satellite, V 2 = +8 m ,50, (B-V) 2 = +0 m ,15, P = 50 years, a"=7",60; a 2 /a 1 = 2.3:1; n=0",375.

Sun, M v = +4 m .77.

Solution. According to formulas (116) and (120), the absolute magnitude of Sirius

M v1 = V 1 + 5 + 5 logп = -1 m .46 + 5 + 5 log 0.375 = +1 m .41, and the logarithm of its luminosity

hence the luminosity L 1 = 22.

According to formula (124), the temperature of Sirius

according to formula (132)

and then the radius of Sirius is R 1 = 1.7, and its volume is R 1 3 = 1.7 3 = 4.91 (the volume of the Sun).

The same formulas are given for the satellite of Sirius: M v2 = +11 m,37; L 2 = 2.3·10 -3; T 2 = 9100°; R2 = 0.022; R 2 3 = 10.6·10 -6.

According to formula (126), the semimajor axis of the satellite’s orbit

according to (125) the sum of the masses of both stars

and, according to (127), the mass ratio

from where, when solving equations (125) and (127) together, we find the mass of Sirius M 1 = 2.3 and the mass of its satellite M 2 = 1.0

The average density of stars is calculated using formula (133): for Sirius

and his companion

Based on the characteristics found - radius, luminosity and density - it is clear that Sirius belongs to the main sequence stars, and its satellite is a white dwarf.

Problem 284. Calculate the visual luminosity of stars whose visual brightness and annual parallax are indicated in parentheses: α Eagle (0m,89 and 0",198), α Ursa Minor (2m, 14 and 0",005) and ε Indian (4m,73 and 0 ",285).

Problem 285. Find the photographic luminosity of stars for which the visual brightness, the usual color index and the distance from the Sun are indicated in brackets: β Gemini (lm,21, +1m,25 and 10.75 ps); η Leo (3m,58, +0m,00 and 500 ps); Kapteyn's star (8m.85, + 1m.30 and 3.98 ps). The magnitude of the Sun is indicated in problem 275.

Problem 286. How many times does the visual luminosity of the stars in the previous problem exceed their photographic luminosity?

Problem 287. The visual brilliance of Capella (and Auriga) is 0m.21, and that of its satellite is 10m.0. The color indices of these stars are +0m.82 and +1m.63, respectively. Determine how many times the visual and photographic luminosity of Capella is greater than the corresponding luminosity of its satellite.

Problem 288. The absolute visual magnitude of the star β Canis Majoris is -2m.28. Find the visual and photographic luminosity of two stars, one of which (with a color index of +0m.29) is 120 times absolutely brighter, and the other (with a color index of +0m.90) is 120 times absolutely fainter than the star β Canis Majoris.

Problem 289. If the Sun, Rigel (β Orionis), Toliman (a Centauri) and its satellite Proxima (Nearest) were at the same distance from the Earth, then how much light would it receive from these stars compared to the sun? The visual magnitude of Rigel is 0m.34, its parallax is 0.003, the same values for Toliman are 0m.12 and 0.751, and for Proxima 10m.68 and 0.762. The magnitude of the Sun is indicated in problem 275.

Problem 290. Find the distances from the Sun and the parallaxes of the three stars of Ursa Major by their brightness in yellow rays and absolute magnitude in blue rays:

1) a, V = 1m.79, (B-V) = + lm.07 and Mв = +0m.32;

2) δ, V = 3m.31, (Β-V) = +0m.08 and Mв = + 1m.97;

3) η, V = 1m.86, (B-V) = -0m.19 and Mv = - 5m.32.

Problem 291. At what distance from the Sun is the star Spica (a Virgo) and what is its parallax, if its luminosity in yellow rays is 720, the main color index is -0m.23, and its brightness in blue rays is 0m.74?

Problem 292. The absolute blue (in B-rays) magnitude of the star Capella (a Auriga) is +0m.20, and the star Procyon (a Canis Minor) is + 3m.09. How many times are these stars in blue rays absolutely brighter or weaker than the star Regulus (a Leo), whose absolute yellow (in V rays) magnitude is -0m.69, and the main color index is -0m.11?

Problem 293. What does the Sun look like from the distance of the star Toliman (a Centauri), whose parallax is 0.751?

Problem 294. What is the visual and photographic brilliance of the Sun from the distances of the stars Regulus (a Leo), Antares (a Scorpius) and Betelgeuse (a Orion), whose parallaxes are respectively 0.039, 0.019 and 0.005?

Problem 295. How much do bolometric corrections differ from the basic color indicators when the bolometric luminosity of a star is 20, 10, and 2 times greater than its yellow luminosity, which, in turn, is 5, 2, and 0.8 times greater than the blue luminosity of the star, respectively?

Problem 296. The maximum energy in the spectrum of Spica (a Virgo) falls on an electromagnetic wave with a length of 1450 Å, in the spectrum of Capella (a Auriga) at 4830 Å and in the spectrum of Pollux (β Gemini) at 6580 Å. Determine the color temperature of these stars.

Problem 297. The solar constant periodically fluctuates from 1.93 to 2.00 cal/(cm 2 min) How much does the effective temperature of the Sun, whose apparent diameter is close to 32", change in this case? Stefan's constant σ = 1.354 10 -12 cal/( cm 2 s deg 4).

Problem 298. Using the result of the previous problem, find the approximate value of the wavelength corresponding to the maximum energy in the solar spectrum.

Problem 299. Determine the effective temperature of the stars from their measured angular diameters and the radiation reaching the Earth from them, indicated in brackets:

α Leo (0",0014 and 3.23·10 -11 cal/(cm 2 min));

α Eagle (0",0030 and 2.13·10 -11 cal/(cm 2 min));

α Orion (0",046 and 7.70·10 -11 cal/(cm 2 min)).

Problem 300. The apparent bolometric magnitude of the star α Eridani is -1m.00 and the angular diameter is 0",0019, the star α Crane has similar parameters +1m.00 and 0",0010, and the star α Tauri +0m.06 and 0",0180 Calculate the temperature of these stars, taking the apparent bolometric magnitude of the Sun equal to -26m.84 and the solar constant close to 2 cal/(cm2 min).

Problem 301. Determine the temperature of the stars whose visual and photographic brightness is indicated in brackets: γ Orionis (1m.70 and 1m.41); ε Hercules (3m.92 and 3m.92); α Perseus (1m.90 and 2m.46); β Andromeda (2m.37 and 3m.94).

Problem 302. Calculate the temperature of the stars from the photoelectric yellow and blue magnitudes indicated in brackets: ε Canis Majoris (1m.50 and 1m.29); β Orionis (0m,13 and 0m,10); α Carinae (-0m.75 and - 0m.60); α Aquarius (2m.87 and 3m.71); α Bootes (-0m.05 and 1m.18); α Kita (2m.53 and 4m.17).

Problem 303. Using the results of the two previous problems, find the wavelength corresponding to the maximum energy in the spectra of the same stars.

Problem 304. The star Bega (a Lyrae) has a parallax of 0",123 and an angular diameter of 0",0035, Altair (a Orel) has similar parameters of 0",198 and 0",0030, and Rigel (β Orion) - 0",003 and 0",0027 and for Aldebaran (and Taurus) - 0",048 and 0",0200. Find the radii and volumes of these stars.

Problem 305. The brightness of Deneb (and Cygnus) in blue rays is 1m.34, its main color index is +0m.09 and parallax is 0",004; the same parameters for the star ε Gemini are 4m.38, +1m.40 and 0",009, and the star γ Eridani has 4m.54, + 1m.60 and 0",003. Find the radii and volumes of these stars.

Problem 306. Compare the diameters of the star δ Ophiuchi and Barnard’s star, whose temperatures are the same, if the first star has an apparent bolometric magnitude of 1m.03 and parallax 0.029, and the second has the same parameters 8m.1 and 0.545.

Problem 307. Calculate the linear radii of stars whose temperature and absolute bolometric magnitude are known: for α Ceti 3200° and -6m.75, for β Leo 9100° and +1m.18, and for ε Indian 4000° and +6m.42.

Problem 308. What are the angular and linear diameters of the stars, the apparent bolometric magnitude, temperature and parallax of which are indicated in parentheses: η Ursa Major (-0m.41, 15500° and 0.004), ε Ursa Major (+ lm.09, 10,000 ° and 0",008) and β Draco (+ 2m,36, 5200° and 0",009)?

Problem 309. If two stars of approximately the same temperature have radii that differ by factors of 20, 100, and 500, then how many times do their bolometric luminosities differ?

Problem 310. How many times does the radius of the star α Aquarius (spectral subclass G2Ib) exceed the radius of the Sun (spectral subclass G2V), if its apparent visual magnitude is 3m.19, bolometric correction -0m.42 and parallax 0",003, the temperature of both stars is approximately the same, and the absolute bolometric magnitude of the Sun is +4m.73?

Problem 311. Calculate the bolometric correction for stars of the spectral subclass G2V, to which the Sun belongs, if the angular diameter of the Sun is 32", its apparent visual magnitude is -26m.78 and its effective temperature is 5800°.

Problem 312. Find the approximate value of the bolometric correction for stars of the spectral subclass B0Ia, to which the star ε Orionis belongs, if its angular diameter is 0",0007, the visible visual magnitude is 1m.75 and the maximum energy in its spectrum occurs at a wavelength of 1094 Å.

Problem 313. Calculate the radius and average density of the stars indicated in problem 285 if the mass of the star β Gemini is approximately 3.7, the mass of η Leo is close to 4.0, and the mass of the Kapteyn star is 0.5.

Problem 314. The visual brightness of the Polaris is 2m.14, its usual color index is +0m.57, parallax is 0",005 and the mass is 10. The same parameters for the star Fomalhaut (and Southern Pisces) are 1m.29, +0m.11, 0", 144 and 2.5, and for the van Maanen star 12m.3, + 0m.50, 0",236 and 1.1. Determine the luminosity, radius and average density of each star and indicate its position on the Hertzsprung - Russell diagram.

Problem 315. Find the sum of the masses of the components of the binary star ε Hydra, whose parallax is 0",010, the satellite's orbital period is 15 years, and the angular dimensions of the semi-major axis of its orbit are 0",21.

Problem 316. Find the sum of the masses of the components of the binary star α Ursa Major, whose parallax is 0",031, the satellite's orbital period is 44.7 years and the angular dimensions of the semi-major axis of its orbit are 0",63.

Problem 317. Calculate the masses of the components of double stars using the following data:

Problem 318. For the main stars of the previous problem, calculate the radius, volume and average density. The apparent yellow magnitude and the main color index of these stars are: α Aurigae 0m.08 and +0m.80, α Gemini 2m.00 and +0m.04 and ξ Ursa Major 3m.79 and +0m.59.

Problem 319. For the Sun and stars indicated in problem 299, find the radiation power and mass loss per second, day and year. The parallaxes of these stars are as follows: α Leo 0",039, α Aquila 0",198 and α Orion 0",005.

Problem 320. Based on the results of the previous problem, calculate the duration of the observed intensity of radiation from the Sun and the same stars, assuming it is possible until the loss of half of its modern mass, which (in solar masses) for α Leo is 5.0, for α Eagle 2.0 and for α Orion 15 Take the mass of the Sun to be 2·10 33 g.

Problem 321. Determine the physical characteristics of the components of the binary star Procyon (a Canis Minor) and indicate their position on the Hertzsprung-Russell diagram, if the following are known from observations: visual brightness of Procyon 0m.48, its usual color index +0m.40, apparent bolometric magnitude 0m.43 , angular diameter 0",0057 and parallax 0",288; the visual brightness of the Procyon satellite is 10m.81, its usual color index is +0m.26, the period of revolution around the main star is 40.6 years in an orbit with a visible semi-major axis of 4.55; the ratio of the distances of both stars from their common center of mass is 19: 7.

Problem 322. Solve the previous problem for the double star α Centauri. The main star has a photoelectric yellow magnitude of 0m.33, a primary color index of +0m.63, and an apparent bolometric magnitude of 0m.28; for the satellite, similar values are 1m.70, + 1m.00 and 1m.12, the orbital period is 80.1 years at an apparent average distance of 17",6; the parallax of the star is 0",751 and the ratio of the distances of the components from their common center of mass is 10 :9.

Answers - Physical nature of the Sun and stars

Multiple and variable stars

The brightness Ε of a multiple star is equal to the sum of the brightness Ε i of all its components

E = E 1 + E 2 + E 3 + ... = ΣE ί , (136)

and therefore its apparent m and absolute magnitude M are always less than the corresponding magnitude m i and M i of any component. Putting in Pogson’s formula (111)

log (E/E 0) = 0.4 (m 0 -m)

E 0 = 1 and m 0 = 0, we get:

log E = - 0.4 m. (137)

Having determined the brightness E i of each component using formula (137), find the total brightness E of the multiple star using formula (136) and again using formula (137) calculate m = -2.5 log E.

If the gloss ratios of the components are given

E 1 /E 2 = k,

E 3 /E 1 = n

etc., then the brightness of all components is expressed through the brightness of one of them, for example E 2 = E 1 /k, Ε 3 = n Ε 1, etc., and then E is found using formula (136).

The average orbital velocity ν of the components of an eclipsing variable star can be found from the periodic greatest displacement Δλ of lines (with wavelength λ) from their average position in its spectrum, since in this case it can be assumed

v = v r = c (Δλ/λ) (138)

where v r is the radial velocity and c = 3·10 5 km/s is the speed of light.

Using the found values of v components and the period of variability P of the star, the semimajor axes a 1 and a 2 of their absolute orbits are calculated:

a 1 = (v 1 /2p) P And a 2 = (v 2 /2p) P (139)

then - the semimajor axis of the relative orbit

a = a 1 + a 2 (140)

and, finally, according to formulas (125) and (127) - the mass of the components.

Formula (138) also allows us to calculate the expansion rate of gas shells ejected by novae and supernovae.

Example 1. Calculate the apparent visual magnitude of the components of a triple star if its visual magnitude is 3m.70, the second component is 2.8 times brighter than the third, and the first is 3m.32 brighter than the third.

Data: m = 3 m ,70; E 2 /E 3 = 2.8; m 1 = m 3 -3 m ,32.

Solution. Using formula (137) we find

logE = - 0.4m = - 0.4 3 m .70 = - 1.480 = 2.520

To use formula (136), it is necessary to find the ratio E 1 /E 3 ; by (111),

log (E 1 / E 3) = 0.4 (m 3 -m 1) = 0.4 3 m, 32 = 1.328

where E 1 = 21.3 E 3

According to (136),

E = E 1 + E 2 + E h = 21.3 E 3 + 2.8 E 3 + E 3 = 25.1 E 3

E 3 = E / 25.1 = 0.03311 / 25.1 = 0.001319 = 0.00132

E 2 = 2.8 E 3 = 2.8 0.001319 = 0.003693 = 0.00369

And E 1 = 21.3 E 3 = 21.3 0.001319 = 0.028094 = 0.02809.

According to formula (137)

m 1 = - 2.5 lg E 1 = - 2.5 lg 0.02809 = - 2.5 2.449 = 3 m .88,

m 2 = - 2.5 lg E 2 = - 2.5 lg 0.00369 = - 2.5 3.567 = 6 m .08,

m 3 = -2.5 lg E 3 = - 2.5 lg 0.00132 = - 2.5 3.121 = 7 m .20.

Example 2. In the spectrum of an eclipsing variable star, the brightness of which changes over 3.953 days, the lines relative to their average position periodically shift in opposite directions to values of 1.9·10 -4 and 2.9·10 -4 from the normal wavelength. Calculate the masses of the components of this star.

Data: (Δλ/λ) 1 = 1.9·10 -4 ; (Δλ/λ) 2 = 2.9·10 -4 ; Ρ = 3 d.953.

Solution. According to formula (138), the average orbital velocity of the first component

v 1 = v r1 = c (Δλ/λ) 1 = 3·10 5 ·1.9·10 -4 ; v 1 = 57 km/s,

Orbital velocity of the second component

v 2 = v r2 = c (Δλ/λ) 2 = 3·10 5 ·2.9·10 -4 ;

v 2 = 87 km/s.

To calculate the values of the semimajor axes of the orbits of the components, it is necessary to express the period of revolution P, equal to the period of variability, in seconds. Since 1 d = 86400 s, then P = 3.953·86400 s. Then, according to (139), the first component has the semimajor axis of the orbit

a 1 = 3.10 10 6 km,

and the second one a 2 = (v 2 /2p) P = (v 2 /v 1) a 1, = (87/57) 3.10 10 6;

a 2 =4.73·10 6 km,

and, according to (140), the semimajor axis of the relative orbit

a = a 1 + a 2 = 7.83 10 6; a = 7.83·10 6 km.

To calculate the sum of the masses of the components using formula (125), one should express a in a. e. (1 au = 149.6·10 6 km) and P - in years (1 year = 365 d.3).

or M 1 + M 2 = 1.22 ~ 1.2.

The mass ratio, according to formula (127),

and then M 1 ~ 0.7 and M 2 ~ 0.5 (in solar masses).

Problem 323. Determine the visual brightness of the double star α Pisces, whose components are bright 4m,3 and 5m,2.

Problem 324. Calculate the brightness of the quadruple star ε Lyrae from the brightness of its components, equal to 5m.12; 6m,03; 5m,11 and 5m,38.

Problem 325. The visual magnitude of the binary star γ Aries is 4m.02, and the difference in magnitude of its components is 0m.08. Find the apparent magnitude of each component of this star.

Problem 326. What is the brilliance of a triple star if its first component is 3.6 times brighter than the second, the third is 4.2 times fainter than the second and has a magnitude of 4m.36?

Problem 327. Find the apparent magnitude of a double star if one of the components has a magnitude of 3m.46, and the second is 1m.68 brighter than the first component.

Problem 328. Calculate the magnitude of the components of the triple star β Monoceros with a visual magnitude of 4m.07, if the second component is fainter than the first by 1.64 times and brighter than the third by 1m.57.

Problem 329. Find the visual luminosity of the components and the total luminosity of the double star α Gemini, if its components have a visual magnitude of 1m.99 and 2m.85, and the parallax is 0",072.

Problem 330. Calculate the visual luminosity of the second component of the binary star γ Virgo, if the visual magnitude of this star is 2m.91, the magnitude of the first component is 3m.62, and the parallax is 0.101.

Problem 331. Determine the visual luminosity of the components of the double star Mizar (ζ Ursa Major), if its magnitude is 2m.17, parallax 0.037, and the first component is 4.37 times brighter than the second.

Problem 332. Find the photographic luminosity of the binary star η Cassiopeia, the visual magnitude of whose components is 3m.50 and 7m.19, their usual color indices are +0m.571 and +0m.63, and the distance is 5.49 ps.

Problem 333. Calculate the masses of the components of eclipsing variable stars using the following data:

Star	Radial velocity of components	Period of variability
β Perseus U Ophiuchus WW Auriga U Cepheus	44 km/s and 220 km/s 180 km/s and 205 km/s 117 km/s and 122 km/s 120 km/s and 200 km/s	2 d.867 1 d.677 2 d.525 2 d.493

Problem 334. How many times does the visual brightness of the variable stars β Perseus and χ Cygnus change if for the first star it ranges from 2m.2 to 3m.5, and for the second from 3m.3 to 14m.2?

Problem 335. How many times does the visual and bolometric luminosity of the variable stars α Orionis and α Scorpius change if the visual brightness of the first star varies from 0m.4 to 1m.3 and the corresponding bolometric correction from -3m.1 to -3m.4, and for the second stars - brightness from 0m.9 to 1m.8 and bolometric correction from -2m.8 to -3m.0?

Problem 336. To what extent and how many times do the linear radii of the variable stars α Orionis and α Scorpius change if the first star has a parallax of 0",005 and the angular radius changes from 0",034 (at maximum brightness) to 0",047 (at minimum brightness), and the second has a parallax of 0",019 and a angular radius from 0",028 to 0",040?

Problem 337. Using the data from problems 335 and 336, calculate the temperature of Betelgeuse and Antares at their maximum brightness, if at their minimum the temperature of the first star is 3200K, and the second is 3300K.

Problem 338. How many times and with what daily gradient does the luminosity change in the yellow and blue rays of the Cepheid variable stars α Ursa Minor, ζ Gemini, η Aquila, ΤΥ Scuti and UZ Scuti, information about the variability of which is as follows:

Problem 339. Using the data from the previous task, find the amplitudes of brightness changes (in yellow and blue rays) and the main indicators of the color of stars, construct graphs of the dependence of the amplitudes on the period of variability, and formulate a conclusion about the pattern discovered from the graphs.

Problem 340. At minimum brightness, the visual magnitude of the star δ Cephei is 4m.3, and the star R Trianguli is 12m.6. What is the brightness of these stars at maximum luminosity if their luminosity increases by 2.1 and 760 times, respectively?

Problem 341. The magnitude of New Eagle in 1918 changed in 2.5 days from 10m.5 to 1m.1. How many times did it increase and how did it change on average over half a day?

Problem 342. The brightness of Nova Cygnus, discovered on August 29, 1975, was close to 21m before the outburst, and at maximum it increased to 1m.9. If we assume that on average the absolute magnitude of new stars at maximum brightness is about -8m, then what luminosity did this star have before the outburst and at maximum brightness, and at what approximate distance from the Sun is the star located?

Problem 343. The hydrogen emission lines H5 (4861 A) and H1 (4340 A) in the spectrum of Novaya Orla 1918 were shifted to the violet end by 39.8 Å and 35.6 Å, respectively, and in the spectrum of Novaya Cygnus 1975 - by 40 .5 Å and 36.2 Å. At what speed did the shells of gas ejected by these stars expand?

Problem 344. The angular dimensions of the M81 galaxy in the constellation Ursa Major are 35"X14", and the M51 galaxy in the constellation Canes Venatici-14"X10". The greatest brilliance of supernovae that erupted at different times in these galaxies was 12m.5 and 15m.1, respectively. , Taking on average the absolute magnitude of supernovae at maximum brightness close to -15m.0, calculate the distances to these galaxies and their linear sizes.

Answers - Multiple and Variable Stars

Federal State Budgetary Educational Institution
higher professional education
"South Ural State University"

Faculty of Economics and Management
Department of World Economy and Economic Theory

Nature and composition of stars

Essay

In the discipline "Concepts of modern natural science"

Associate Professor, Department of Physical Chemistry

Teplyakov Yuri Nikolaevich

student group 236

Glushko Olga

annotation

The purpose of the essay is to study the nature and composition of stars. In accordance with the chosen topic, the following tasks are set:

Consideration of the concept, parameters and classifications of stars.

Description of the evolution of stars.

Study of star clusters and associations

Study of the composition of stars.

Introduction…………………………………………………………………………………4

The concept of stars, their parameters and classification…………………………….5

Evolution of stars……………………………………………………………. .9

Star clusters and associations………………….……………...……… …..13

Chemical composition of stars…………………………………………………….18

Conclusion…………………………………………………………….….....21
Applications…………………………………………………………….………22
Bibliography……………………………………………………... 24

Introduction

The science of stars - astronomy - is one of the most ancient, because these mysterious celestial bodies have always interested people. Like all bodies in nature, stars do not remain unchanged, they are born, evolve, and finally “die”. To trace the life path of stars and understand how they age and what they are, you need to know how they arise and what they are.
The relevance of the study of stars is increasing every day, which is associated with the expansion of the horizon of human knowledge about space and extraterrestrial life forms. The Universe consists of 98% stars. They are also the main element of the galaxy.

1. Concept and classification of stars

Stars are masses of luminous gas, more or less evenly scattered across the sky (although sometimes they form groups), which we can see as small dots in the night sky. Stars are the main bodies of the Universe; more than 90% of the observable matter is concentrated in them.

The main parameters of stars are:

luminosity (the total amount of energy emitted by a star per unit time L),

surface temperature.

Mass of stars
The mass of a star became more important when sources of stellar energy were discovered. The mass of the Sun is M c = 2 10 30 kg, and the masses of almost all stars lie in the range of 0.1 - 50 solar masses. Practically, the most reliable way to determine the mass of a star is to study the motions of double stars. It turned out that the position of a star on the Main Sequence is determined by its mass

Luminosity
The luminosity of a star L is often expressed in solar luminosity units, which is 3.86 10 26Tue Stars vary greatly in their luminosity. There are white and blue supergiant stars (though there are relatively few of them), the luminosity of which exceeds the luminosity of the Sun by tens and even hundreds of thousands of times. But the majority of stars are “dwarfs”, whose luminosity is much less than the Sun, often thousands of times. The luminosity characteristic is the so-called “absolute magnitude” of the star. Absolute magnitude ( M) for stars is defined as the apparent magnitude of an object if it were located at a distance of 10 parsecs from the observer. The apparent magnitude of a star depends, on the one hand, on its luminosity and color, on the other, on the distance to it. The absolute magnitude of the Sun over the entire radiation range is M = 4.72. Stars with high luminosity have negative absolute values, for example -4, -6. Low luminosity stars are characterized by large positive values, for example +8, +10.

Radius
Using the most modern technology of astronomical observations, it has now been possible to directly measure the angular diameters (and from them, knowing the distance, and linear dimensions) of only a few stars. Basically, astronomers determine the radii of stars by other methods. One of them is given by the formula.
Having determined the radii of many stars, astronomers became convinced that there are stars whose sizes differ sharply from the size of the Sun. Supergiants have the largest sizes. Their radii are hundreds of times greater than the radius of the Sun. For example, the radius of a star A Scorpio (Antares) is no less than 750 times larger than the Sun. Stars whose radii are tens of times greater than the radius of the Sun are called giants. Stars that are close in size to the Sun or smaller than the Sun are classified as dwarfs.
The radius of stars is not a constant value. It can change, for example, like Betelgeuse, whose radius has decreased by 15% over the past 15 years.
Temperature
Temperature determines the color of a star and its spectrum. So, for example, if the surface temperature of the layers of stars is 3-4 thousand. K., then its color is reddish, 6-7 thousand K. is yellowish. Very hot stars with temperatures above 10-12 thousand K. have a white or bluish color. Cool red stars have spectra characterized by absorption lines of neutral metal atoms and bands of some simple compounds. As the surface temperature increases, molecular bands disappear in the spectra of stars, many lines of neutral atoms, as well as lines of neutral helium, weaken. The appearance of the spectrum itself is changing radically. For example, in hot stars with surface temperatures exceeding 20 thousand K, predominantly lines of neutral and ionized helium are observed, and the continuous spectrum is very intense in the ultraviolet part. Stars with a surface temperature of about 10 thousand K have the most intense lines of hydrogen, while stars with a temperature of about 6 thousand K have lines of ionized calcium, located on the border of the visible and ultraviolet parts of the spectrum. Note that the spectrum of our Sun has this type I.

Classification of stars
Classifications in any field of science can be either artificial (based on some individual characteristics that are easily determined) or natural, i.e. reflecting the essence of the object, its complex characteristics, origin, etc., although belonging to a particular class in this case is not always easily determined. Objects can be combined both into real existing groups (based on qualitative characteristics) and into conditional groups that differ only quantitatively. Modern stellar astronomy shows us all these cases.
Classifications of stars began to be built immediately after their spectra began to be obtained. To a first approximation, the spectrum of a star can be described as the spectrum of a black body, but with absorption or emission lines superimposed on it. Based on the composition and strength of these lines, the star was assigned one or another specific class. This is still done now, however, the current division of stars is much more complex: in addition, it includes the absolute magnitude, the presence or absence of variability in brightness and size, and the main spectral classes are divided into subclasses.
The most famous and common classification is based on the color, size and temperature of the star.. Astronomers classify stars into different spectral classes. Spectral classification, the development of which began in the 19th century, was originally based on the intensity of hydrogen absorption lines. The classes that best describe the temperature of stars are still used today. Typical spectra for the seven main spectral classes – OBAFGKM. It turns out that blue stars of spectral type O are the largest stars. They exceed the Sun by more than forty times in mass, twenty times in size and a million times brighter than the Sun. Next on the stellar mass scale are white stars of spectral classes B and A. Next come yellow-white class F stars and yellow class G stars, similar to our Sun. Stars with lower mass are fainter and smaller in size. The masses and sizes of orange stars belonging to class K are about three to quarters the mass of the Sun. M stars are the coolest and have a deep orange-red color. Typical representatives of this class are approximately five times smaller than the Sun in mass and radius and two times lower in surface temperature, which is about 3000 K. About a hundred such stars will have the same luminosity as our Sun. Class M ends the Harvard classification of stars.
At the very beginning of the twentieth century, the Danish astronomer Hertzsprung and the American astrophysicist Russell discovered the existence of a relationship between the temperature of the surface of a star and its luminosity. This dependence is illustrated by a diagram, on one axis of which the spectral type is plotted, and on the other, the absolute magnitude. Instead of absolute magnitude, luminosity can be plotted on a logarithmic scale, and instead of spectral classes, surface temperature can be plotted directly. Such a diagram is called a spectrum-luminosity diagram or a Hertzsprung–Russell diagram. In this case, the temperature is plotted in the direction from right to left in order to preserve the old form of the diagram, which arose even before the dependence of the color of a star on the temperature of its surface was studied.
If there were no relationship between luminosities and their temperatures, then all the stars would be distributed evenly on such a diagram. But the diagram reveals several patterns, which are called sequences. The position of each star at one point or another on the diagram is determined by its physical nature and age (stage of evolution). A star does not remain in place throughout its entire life, but moves along the H-R diagram. Therefore, the G-R diagram seems to capture the entire history of the set of stars under consideration. Analysis of this diagram allows us to identify different groups of stars united by common physical properties. The most star-rich diagonal, 90% of all stars, going from the upper left to the lower right, is called the main sequence. It is along it that the stars we talked about above are located. It has now become clear that main sequence stars are normal stars, similar to the Sun, in which hydrogen combustion occurs in thermonuclear reactions. The main sequence is a sequence of stars of different masses. The largest stars by mass are located at the top of the main sequence and are blue giants. The smallest stars by mass are dwarfs. They are located at the bottom of the main sequence. (see Fig. No. 1)
Stars that exist in nature have wider ranges of parameters than main sequence stars. We observe such stars on the H-R diagram outside the main diagonal zone. They also form sequences, i.e. in these groups there are also certain relationships between luminosities and temperatures, different for each group. These groups are called luminosity classes. There are only seven of them. Namely: I-supergiants (a star on the eve of a supernova explosion), II-bright giants (stars lying between giants and supergiants), III-giants, IV - subgiants (a former main sequence star, similar to the Sun or slightly more massive than the Sun, in the core of which the hydrogen fuel has dried up.), V - main sequence stars, VI - subdwarfs (these are stars dimmer than main sequence stars same spectral class. ), VII - white dwarfs (stars smaller than the Sun).
(see Fig. No. 2; Table No. 1)
2. Evolution of stars

The evolution of stars is the change over time in the physical characteristics, internal structure and chemical composition of stars. The modern theory of stellar evolution is able to explain the general course of stellar development in satisfactory agreement with observational data.
The course of a star's evolution depends on its mass and initial chemical composition, which, in turn, depends on the time when the star was formed and on its position in the Galaxy at the time of formation.
The early stage of the star's evolution is very small and the star at this time is immersed in a nebula, so the protostar is very difficult to detect.
Stars are formed as a result of gravitational condensation of matter in the interstellar medium. Young stars are those that are still in the stage of initial gravitational compression. The temperature in the center of such stars is insufficient for nuclear reactions to occur, and the glow occurs only due to the conversion of gravitational energy into heat.
Gravitational compression is the first stage in the evolution of stars. It leads to heating of the central zone of the star to the “switching on” temperature of the thermonuclear reaction (approximately 10-15 million K) - the transformation of hydrogen into helium (hydrogen nuclei, i.e. protons, form helium nuclei). This transformation is accompanied by a large release of energy. Since the amount of hydrogen is limited, sooner or later it burns out. The release of energy in the center of the star stops, and the core of the star begins to shrink and the shell begins to swell. The more massive the star, the greater the supply of hydrogen fuel it has, but to counteract the forces of gravitational collapse it must burn hydrogen at an intensity that exceeds the growth rate of hydrogen reserves as the mass of the star increases. Thus, the more massive the star, the shorter its lifetime, determined by the depletion of hydrogen reserves, and the largest stars literally burn out in tens of millions of years. The smallest stars, on the other hand, live comfortably for hundreds of billions of years. Sooner or later, however, any star will use up all the hydrogen suitable for combustion in its thermonuclear furnace.
Sooner or later, however, any star will use up all the hydrogen suitable for combustion in its thermonuclear furnace. What happens next depends on the mass of the star. The sun (and all stars not exceeding its mass by more than eight times) end my life in a very banal way. As the reserves of hydrogen in the bowels of the star are depleted, the forces of gravitational compression, which have been patiently waiting for this hour since the very moment of the birth of the star, begin to gain the upper hand - and under their influence the star begins to shrink and become denser. This process has a twofold effect: The temperature in the layers immediately around the star's core rises to a level at which the hydrogen contained there finally undergoes thermonuclear fusion to form helium. At the same time, the temperature in the core itself, now consisting almost entirely of helium, rises so much that the helium itself - a kind of “ash” of the fading primary nucleosynthesis reaction - enters into a new thermonuclear fusion reaction: from three helium nuclei one carbon nucleus is formed. This process of secondary thermonuclear fusion reaction, for which the products of the primary reaction serve as fuel, is one of the key moments in the life cycle of stars.
During the secondary combustion of helium in the core of the star, so much energy is released that the star literally begins to inflate. In particular, the shell of the Sun at this stage of life will expand beyond the orbit of Venus. In this case, the total energy of the star's radiation remains approximately at the same level as during the main phase of its life, but since this energy is now emitted through a larger surface area, the outer layer of the star cools down to the red part of the spectrum. The star turns into a red giant.
Further, if the star is less than 1.2 solar masses, it sheds its outer layer (formation of a planetary nebula). After the envelope separates from the star, its inner, very hot layers are exposed, and meanwhile the envelope moves further and further away. After several tens of thousands of years, the shell will disintegrate and only a very hot and dense star will remain, which gradually cools. The temperature inside the core is no longer able to rise to the level necessary to initiate the next level of thermonuclear reaction. The star turns into a white dwarf. Gradually cooling down they turn invisible black dwarfs . Black dwarfs are very dense and cool stars, slightly larger than the Earth, but with a mass comparable to the mass of the sun. The cooling process of white dwarfs lasts several hundred million years.
Stars more massive than the Sun (1.2 to 2.5 solar masses) face a much more spectacular end. After the combustion of helium, their mass during compression turns out to be sufficient to heat the core and shell to the temperatures necessary to launch the following nucleosynthesis reactions - carbon, then silicon, magnesium - and so on, as the nuclear masses grow. Moreover, with the start of each new reaction in the core of the star, the previous one continues in its shell. In fact, all the chemical elements, including iron, that make up the Universe, were formed precisely as a result of nucleosynthesis in the depths of dying stars of this type. But iron is the limit; it cannot serve as fuel for nuclear fusion or decay reactions at any temperature or pressure, since both its decay and the addition of additional nucleons to it require an influx of external energy. As a result, a massive star gradually accumulates an iron core inside itself, which cannot serve as fuel for any further nuclear reactions.
Once the temperature and pressure inside the nucleus reach a certain level, electrons begin to interact with the protons of the iron nuclei, resulting in the formation of neutrons. And in a very short period of time - some theorists believe that this takes a matter of seconds - the electrons free throughout the previous evolution of the star literally dissolve in the protons of the iron nuclei, the entire substance of the star’s core turns into a solid bunch of neutrons and begins to rapidly compress in gravitational collapse , since the counteracting pressure of the degenerate electron gas drops to zero. The outer shell of the star, from under which all support appears to be knocked out, collapses towards the center. The energy of the collision of the collapsed outer shell with the neutron core is so high that it bounces off at tremendous speed and scatters in all directions from the core - and the star literally explodes in a blinding supernova flash. In a matter of seconds, a supernova explosion can release more energy into space than all the stars in the galaxy put together during the same time.
There are several hypotheses about the cause of star explosions (supernovae), but there is no generally accepted theory yet. There is an assumption that this is due to the too rapid decline of the inner layers of the star towards the center. The star quickly contracts to a catastrophically small size of the order of 10 km, and its density in this state is 10 17 kg/m 3, which is close to the density of the atomic nucleus. This star consists of neutrons (at the same time, electrons are pressed into protons), which is why it is called « neutron » . Its initial temperature is about a billion Kelvin, but in the future it will quickly cool down.
This star, due to its small size and rapid cooling, was long considered impossible to observe. But after some time, pulsars were discovered. These pulsars turned out to be neutron stars. They are named so because of the short-term emission of radio pulses. Those. the star seems to “blink.” This discovery was made completely by accident and not so long ago, namely in 1967. These periodic impulses are due to the fact that during very rapid rotation, the cone of the magnetic axis constantly flashes past our gaze, which forms an angle with the axis of rotation.
A pulsar can only be detected for us in conditions of orientation of the magnetic axis, and this is approximately 5% of their total number. Some pulsars are not located in radio nebulae, since nebulae dissipate relatively quickly. After a hundred thousand years, these nebulae cease to be visible, and the age of pulsars is tens of millions of years.
Stars with a high mass of 8-10 solar masses evolve in the same way as with an average one until the formation of a carbon-oxygen core. This core collapses and becomes degenerate before the carbon ignites, forcing an explosion known as carbon detonation - the equivalent of a helium flash. Although in principle carbon detonation could cause a star to explode as a supernova, some stars can survive this stage without exploding. As the temperature in the core increases, the degeneracy of the gas can be lifted, after which the star continues to evolve as a very massive star.
Very massive stars, with masses greater than 10 solar masses, are so hot that helium in the core ignites before the star reaches the red giant branch. Burning occurs even when these stars are blue supergiants and the star continues to monotonously evolve towards redness; While helium burns in the convective core, hydrogen burns in the layer source, providing most of the star's luminosity. After helium is exhausted in the core, the temperature there is so high that carbon ignites before the gas becomes degenerate and carbon combustion begins gradually without explosive processes. Burning occurs before the star reaches the asymptotic giant branch. During the entire combustion of carbon in the core, energy flows out of the core due to neutrino cooling, and the main source of surface luminosity is the combustion of hydrogen and helium in layer sources. These stars continue to produce heavier and heavier elements up to iron, after which the core collapses to form a neutron star or black hole (depending on the mass of the core) and the outer layers fly apart in what appears to be a Type II supernova explosion.
From all of the above, it is clear that the final stage of the evolution of a star depends on its mass, but it is also necessary to take into account the inevitable loss of this very mass and rotation
(see Fig. No. 3)

3. Star clusters and associations

A star cluster is a group of stars located in space close to each other, connected by a common origin and mutual gravity.
According to modern data, at least 70% of the stars in the Galaxy are part of binary and multiple systems, and single stars (such as our Sun) are rather an exception to the rule. But often stars gather into more numerous “collectives” - star clusters.All stars included in the cluster are at the same distance from us (up to the size of the cluster) and have approximately the same age and chemical composition. But at the same time, they are at different stages of evolution (determined by the initial mass of each star), which makes them a convenient object for testing theories of the origin and evolution of stars. There are two types of star clusters: globular and open. Initially, this division was accepted based on appearance, but with further study it became clear that globular and open clusters are not similar in literally everything - in age, stellar composition, nature of motion, etc.

Globular star clusters contain from tens of thousands to millions of stars. This type of cluster is characterized by a regular spherical or somewhat oblate shape (which, apparently, is a sign of axial rotation of the cluster). But star-poor clusters are also known, indistinguishable in appearance from scattered ones (for example, NGC 5053), and classified as globular based on the characteristic features of the “spectrum-luminosity” diagram. The two brightest globular clusters are designated Omega Centauri and 47 Tucanae as ordinary stars because, due to their significant apparent brightness, they are clearly visible to the naked eye, but only in southern countries. And in the middle latitudes of the northern hemisphere, only two are accessible to the naked eye, albeit with difficulty - in the constellations Sagittarius and Hercules. (see Fig. No. 4)
There are currently about 150 known globular clusters in the Galaxy, but it is obvious that this is only a small part of those that actually exist (their total number is estimated at about 400-600). Their distribution across the celestial sphere is uneven - they are strongly concentrated towards the galactic center, forming an extended halo around it. About half of them are located no further than 30 degrees from the visible center of the Galaxy (in Sagittarius), i.e. in an area whose area is only 6% of the entire area of the celestial sphere. This distribution is a consequence of the peculiarities of the rotation of globular clusters around the center of the Galaxy, characteristic of objects of the spherical subsystem - in highly elongated orbits. Once per period (10 8 -10 9 years), a globular cluster passes through the dense central regions of the Galaxy and its disk, which contributes to the “sweeping out” of interstellar gas from the cluster (observations confirm that there is very little gas in these clusters). Some globular clusters are so far from the center of the Galaxy that they can be classified as intergalactic.
The spectrum-luminosity diagram for globular clusters has a characteristic shape due to the absence of massive stars on the main sequence branch. This indicates a significant age of globular clusters (10-12 billion years, i.e. they were formed simultaneously with the formation of the Galaxy itself) - during this time, the reserves of hydrogen are exhausted in stars with a mass close to the Sun, and they leave the main sequence ( and the greater the initial mass of the star, the faster), forming a branch of subgiants and giants. Therefore, in globular clusters, the brightest stars are red giants. In addition, variable stars are observed in them (especially often of the RR Lyrae type), as well as the end products of the evolution of massive stars, manifesting themselves in the form of X-ray sources of various types. But in general, double stars are rare in globular clusters. It should be noted that in other galaxies (for example, in the Magellanic Clouds) globular clusters that are typical in appearance have been found, but with a stellar composition of small age, and therefore such objects are considered young globular clusters. Another feature of globular clusters is the reduced content of heavy (heavier than helium) elements in the atmospheres of their constituent stars. Compared to their content in the Sun, the stars of globular clusters are depleted in these elements by 5-10 times, and in some clusters - up to 200 times. This feature is characteristic of objects in the spherical component of the Galaxy and is also associated with the great age of the clusters - their stars were formed from primordial gas, while the Sun was formed much later and contains heavy elements formed by previously evolved stars.

Open star clusters contain relatively few stars - from several tens to several thousand, and, as a rule, there is no question of any regular shape here. The most famous open cluster is the Pleiades, visible in the constellation Taurus. In the same constellation is another cluster - the Hyades - a group of faint stars around bright Aldebaran.
There are about 1,200 known open star clusters, but it is believed that there are many more of them in the Galaxy (about 20 thousand). They are also distributed unevenly across the celestial sphere, but, unlike globular clusters, they are strongly concentrated towards the plane of the Galaxy, therefore almost all clusters of this type are visible near the Milky Way, and are generally no more than 2 kpc from the Sun (see Fig. No. 5 ). This fact explains why such a small proportion of the total number of clusters is observed - many of them are too distant and are lost against the background of the high stellar density of the Milky Way, or are hidden by light-absorbing gas and dust clouds, also concentrated in the galactic plane. Like other objects in the galactic disk, open clusters orbit the galactic center in nearly circular orbits. The diameters of open clusters range from 1.5 pc to 15-20 pc, and the concentration of stars ranges from 1 to 80 per 1 pc 3. As a rule, clusters consist of a relatively dense core and a more sparse crown. Among open clusters, double and multiple ones are known, i.e. groups characterized by their spatial proximity and similar proper motions and radial velocities.
The main difference between open clusters and globular clusters is the large variety of spectrum-luminosity diagrams in the former, caused by differences in their ages. The youngest clusters are about 1 million years old, the oldest are 5-10 billion years old. Therefore, the stellar composition of open clusters is diverse - they contain blue and red supergiants, giants, variables of various types - flares, Cepheids, etc. The chemical composition of the stars included in open clusters is quite homogeneous, and on average the content of heavy elements is close to that of the Sun, which is typical for objects in the galactic disk.
Another feature of open clusters is that they are often visible together with a gas-dust nebula - a remnant of the cloud from which the stars of this cluster once formed. Stars can heat up or illuminate “their” nebula, making it visible. The well-known Pleiades (see photo) are also immersed in a blue, cold nebula. In a galaxy, open clusters can only exist where there are many gas clouds. In spiral galaxies such as ours, such places are found in abundance in the flat component of the galaxy, and young clusters serve as good indicators of spiral structure, since in the time that has passed since their formation, they do not have time to move away from the spiral arms in which this formation occurs .
etc.................

Description of the presentation by individual slides:

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White dwarf, the hottest known, and the planetary nebula NGC 2440, 05/07/2006 Physical nature of stars

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Spectrum λ = 380 ∻ 470 nm – violet, blue; λ = 470 ∻ 500 nm – blue-green; λ = 500 ∻ 560 nm – green; λ = 560 ∻ 590 nm – yellow-orange λ = 590 ∻ 760 nm – red. Distribution of colors in the spectrum = K O F Z G S F Remember, for example: How Once Jacques the City Beller Broke the Lantern. In 1859, G.R. Kirchhoff (1824-1887, Germany) and R.W. Bunsen (1811-1899, Germany) discovered spectral analysis: gases absorb the same wavelengths that they emit when heated. Stars have dark (Fraunhofer) lines against the background of continuous spectra - these are absorption spectra. In 1665, Isaac Newton (1643-1727) obtained spectra of solar radiation and explained their nature, showing that color is an intrinsic property of light. In 1814, Joseph von Fraunhofer (1787-1826, Germany) discovered, identified and by 1817 described in detail 754 lines in the solar spectrum (named after him), creating in 1814 an instrument for observing spectra - a spectroscope. Kirchhoff-Bunsen spectroscope

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Spectra of stars Spectra of stars are their passport with a description of all stellar patterns. From the spectrum of a star, you can find out its luminosity, distance to the star, temperature. The study of stellar spectra is the foundation of modern astrophysics. Spectrogram of the Hyades open cluster. William HEGGINS (1824-1910, England), an astronomer who was the first to use a spectrograph, began the spectroscopy of stars. In 1863 he showed that the spectra of the Sun and stars have much in common and that their observed radiation is emitted by hot matter and passes through overlying layers of cooler absorbing gases. Combined emission spectrum of a star. Above is “natural” (visible in a spectroscope), below is the dependence of intensity on wavelength. size, chemical composition of its atmosphere, speed of rotation around its axis, features of movement around the common center of gravity.

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Chemical composition The chemical composition is determined by the spectrum (intensity of Fraunhofer lines), which also depends on temperature, pressure and density of the photosphere, and the presence of a magnetic field. Stars are composed of the same chemical elements known on Earth, but mainly hydrogen and helium (95-98% of mass) and other ionized atoms, while cool stars have neutral atoms and even molecules in their atmosphere. As the temperature increases, the composition of particles capable of existing in the stellar atmosphere becomes simpler. Spectral analysis of stars of classes O, B, A (T from 50,000 to 10,0000C) shows in their atmospheres lines of ionized hydrogen, helium and metal ions, in class K (50000C) radicals are already detected, and in class M (38000C) molecules oxides The chemical composition of a star reflects the influence of factors: the nature of the interstellar medium and those nuclear reactions that develop in the star during its life. The initial composition of the star is close to the composition of the interstellar matter from which the star arose. Supernova remnant NGC 6995 is hot, glowing gas formed after the star exploded 20-30 thousand years ago. Such explosions actively enriched space with heavy elements from which planets and stars of the next generation were subsequently formed.

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Color of stars In 1903-1907. Einar Hertzsprung (1873-1967, Denmark) was the first to determine the colors of hundreds of bright stars. Stars come in a variety of colors. Arcturus has a yellow-orange tint, Rigel is white-blue, Antares is bright red. The dominant color in a star's spectrum depends on its surface temperature. The gas shell of a star behaves almost like an ideal emitter (absolutely black body) and is completely subject to the classical laws of radiation by M. Planck (1858–1947), J. Stefan (1835–1893) and V. Wien (1864–1928), relating body temperature and the nature of its radiation. Planck's law describes the distribution of energy in the spectrum of a body and indicates that with increasing temperature, the total flux of radiation increases, and the maximum in the spectrum shifts towards shorter waves. During observations of the starry sky, one might notice that the color (the property of light to cause a certain visual sensation) of stars is different. The color and spectrum of stars is related to their temperature. Light of different wavelengths excites different color sensations. The eye is sensitive to the wavelength that carries the maximum energy λmax = b/T (Wien's law, 1896). Like precious stones, the stars of the open cluster NGC 290 shimmer in different colors. Photo by CT named after. Hubble, April 2006

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Temperature of stars The temperature of stars is directly related to color and spectrum. The first measurement of the temperature of stars was made in 1909 by the German astronomer Julius Scheiner (1858-1913), having carried out absolute photometry of 109 stars. The temperature is determined from the spectra using Wien's law λmax.T=b, where b=0.289782.107Å.K is Wien's constant. Betelgeuse (Hubble Telescope image). In such cool stars with T=3000K, radiation in the red region of the spectrum predominates. The spectra of such stars contain many lines of metals and molecules. Most stars have temperatures of 2500K<Т< 50000К Звезда HD 93129A (созв. Корма) самая горячая – Т= 220000 К! Самые холодные - Гранатовая звезда (m Цефея), Мира (o Кита) – Т= 2300К e Возничего А - 1600 К.

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Spectral classification In 1866, Angelo Secchi (1818-1878, Italy) gave the first spectral classification of stars by color: White, Yellowish, Red. The Harvard spectral classification was first presented in the Catalog of Stellar Spectra of Henry Draper (1837-1882, USA), prepared under the direction of E. Pickering (1846-1919) by 1884. All spectra were arranged according to line intensities (later in temperature sequence) and designated by letters in alphabetical order from hot to cold stars: O B A F G K M. By 1924, it was finally established by Anna Cannon (1863-1941, USA) and published in a catalog of 9 volumes on 225330 stars - HD catalogue.

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Modern spectral classification The most accurate spectral classification is represented by the MK system, created by W. Morgan and F. Keenan at the Yerkes Observatory in 1943, where the spectra are arranged both by temperature and luminosity of stars. Luminosity classes were additionally introduced, marked with Roman numerals: Ia, Ib, II, III, IV, V and VI, respectively indicating the size of the stars. Additional classes R, N and S denote spectra similar to K and M, but with a different chemical composition. Between each two classes, subclasses are introduced, designated by numbers from 0 to 9. For example, the spectrum of type A5 is halfway between A0 and F0. Additional letters sometimes mark the features of stars: “d” – dwarf, “D” – white dwarf, “p” – peculiar (unusual) spectrum. Our Sun belongs to the spectral class G2 V

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Luminosity of stars In 1856, Norman Pogson (1829-1891, England) established a formula for luminosities in terms of absolute M magnitudes (i.e. from a distance of 10 pc). L1/L2=2.512 M2-M1. The Pleiades open cluster contains many hot and bright stars that were formed at the same time from a cloud of gas and dust. The blue haze accompanying the Pleiades is scattered dust reflecting the light of the stars. Some stars shine brighter, others weaker. Luminosity is the radiation power of a star - the total energy emitted by a star in 1 second. [J/s=W] Stars emit energy over the entire range of wavelengths L = 3.846.1026 W/s Comparing the star with the Sun, we get L/L=2.512 M-M, or logL=0.4 (M -M ) Star luminosity: 1.3.10-5L

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The sizes of stars are determined: 1) Direct measurement of the angular diameter of the star (for bright ≥2.5m, close stars, >50 measured) using a Michelson interferometer. For the first time on December 3, 1920, the angular diameter of the star Betelgeuse (α Orionis) was measured = A. Michelson (1852-1931, USA) and F. Pease (1881-1938, USA). 2) Through the luminosity of the star L=4πR2σT4 in comparison with the Sun. Stars, with rare exceptions, are observed as point sources of light. Even the largest telescopes cannot see their disks. According to their sizes, stars have been divided since 1953 into: Supergiants (I) Bright giants (II) Giants (III) Subgiants (IV) Main sequence dwarfs (V) Subdwarfs (VI) White dwarfs (VII) The names dwarfs, giants and supergiants were introduced Henry Russell in 1913, and they were discovered in 1905 by Einar Hertzsprung, introducing the name “white dwarf”. Sizes of stars 10 km

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Mass of stars One of the most important characteristics of stars, indicating its evolution, is the determination of the star’s life path. Determination methods: 1. Mass-luminosity relationship L≈m3.9 2. Kepler’s 3rd refined law in physically binary systems Theoretically, the mass of stars is 0.005M

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Abstract: Evolution and structure of the galaxy. Presentation on the topic "physical nature of stars" Presentation on the topic physical nature of stars

Astronomy 11th grade

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