To the eye of the starry sky, unbroken by the telescope, a rose of flecks that shine., to wash the difference. The brightness of the star., or rather, that illumination, Yaku create viprominyuvannya zirka on the surface of the primach (for example, on the city of Oka, on a sensitive sphere of a photographic plate. P. ) , astronomers estimate by a real numerical parameter, the name of the visible star value m. The scale of visible dawn values ​​is based on the experimental law of Weber-Fechner: if E is the illumination of any maidan, dE is the change in the illumination of that maidan, and dP is the change in light visibility, then the following is true:

d P~d E/E (1)

tobto. The change of the zorovogo vіdchuttya lie down not just in the form of a change in the lightness, but in the case of the change of the lightness to the lightness. The Weber-Fechner law can be formulated as follows:

If teasing grows in a geometric progression, then it seems to change in an arithmetic progression.

3 (1) vyplivaє:

P ~ lgE. (2)

Spivvіdnoshennia (2) underlie the connection with the photometric physical scale for grading clarification, brightness and intensity.

Brightness (“bliss”) of astronomical objects (both extended and point) are scaled in the scale of “eye magnitudes”. The term “star size” is a given irradiation, tobto. the more you see the (point) object, the more you see posters behind the wines. Strictly seeming, "irradiation" - the appearance of visible expansions of the light, which is guarded for the borders of the decimal (hood) expansion.

The dawn value m is visible - a numerical proof of the dawn sighting for an hour of warning of viprominuyuchih astronomical objects. The same applies to the Weber-Fechner law (1):

Dm ~ dE/E, m ~ lgE. (3)

The practice of astronomical warnings has shown that mіzh m і lgE is linear, tobto.

m = a + b × lgE. (four)

The eye is a viable primach of viprominuvannya, tobto. Vіn zdatny otsіnyuvati fotometrіchnі characteristics of dzherel only against other dzherel vipromіnyuvannya. Todі with caution two stars may be:

m 1 \u003d a + b × lgE 1,

m 2 \u003d a + b × lgE 2,

or

M 1 - m 2 \u003d b × (lgE 1 - lgE 2) \u003d b × lg (E 1 / E 2). (5)

In the nineteenth century after having reached the possible value of the coefficient "b" Pogson, having proponuvati b = -2.512. Viraz (5) can be rewritten in the look:

m 1 - m 2 \u003d - 2.512 × log (E 1 / E 2), (6)

or

lg (E 1 / E 2) \u003d 0.4 × (m 2 - m 1). (7)

Formula (7) is Pogson's formula.

It is taken as a unit of illumination E illumination in the light, the visible light value is m = 0 m. Todі z (6) we take the links between E and m:

m = -2.512 × lgE. (eight)

Visible star valuem is the tenth logarithm of the illumination E, created by the light at the point of caution on the normal straight line of the plane, multiplied by -2.512.

If E = 1, then from (4): a = m, then. a - the visible dawn value of a unit of illumination.

So, as if it were shining, which is to be guarded, I create on the basis of the improvement of the illumination E \u003d, then a \u003d -14 m 18 (without improving the atmosphere) or a = -13 m 89 (with the improvement of the atmosphere, that is "foreatmospheric" value of the unit of illumination).

The scale of visible dawn values ​​is calibrated as follows, sho , like a glint of two stars (illumination, svoryuvanі tsimi mi on priymachі vipromіnuvannya) are divided into 2. 512 times, then their visible star values ​​differ by one, moreover, less meaning m maє yaskravisha. Visible star values ​​m can be negative and positive, integers or fractions. Nayaskravishi objects of the sky may have a negative visible star magnitude: for example , for Soncia m ⊙ = -26m.5. Weakest objects, how can you look after the help of the largest telescopes, possessed of sensitive primacies mayut m =+25 m÷+30m. Pogson's speech is blaring, that the brightness of the Sun is visible approximately 10 22 times exceeding the brightness of the stars available between the largest telescopes.

The scale of visible dawn values ​​was introduced by Hipparchus ( II in. BC). The visible star value m is in no way related to the visible, nі z diysnym rozmіrom (diameter) zirka. More than that, comparing the visible magnitudes of two stars, we can’t say anything about visibility in today’s world. Zirki vіdrіznyayutsya one kind of one for the diameter i, later , beyond the surface, for surface temperature nareshti, can be on different occasions in the form of posterigach. A cold dwarf from a meager sweating, but the one who is close to Sontsya, maybe the mother is so visible yaskravіst, yak i hot giant, in the distance from us to the great distance. Sounds are screaming, what do you know come up to the dawn on the principle of importance for the assessment of the actual physical parameters of the spectrum, later , for understanding physical processes, stars.

(illumination is too small), and most of all, historically it turned out so that the glare of the stars began to fade back before the introduction of physicists to understand the illumination, the vicorist pozasistemnuyu singleness of the world - star value m* .

table. Physical characteristics of Sontsya

cm/sec2

4m.8

12.2. The dawn of magnitude

Zoryan values ​​were introduced by Hipparchus in the II century BC. Vіn divided by the visible invisible eye of the star behind the equal їхної brightness into six classes - dawning sizes. The weakest stars were up to the first class - they were smaller than the first star value, and the weakest ones were up to the sixth class and were smaller than the sixth star value

(The designation is 1m and 6m). In this manner, it is important to remember which is the greater star value, the weaker star.

The link between illumination and star values ​​was introduced in the 19th century by Pogson, and it indicates the difference in illumination, created by two stars, through the difference of their star values:

Like a cob in view of the dawning magnitudes of the bula, the star Vega (Lyr) was selected. Were washed away

On the other side, ninth victorious are fractional values ​​of dawn magnitudes, and the brightest stars, lower Vega, may be negative magnitudes of dawn. For example, Sirius (CMa) may be close m=-1m.58.

It is quite obvious that the size of the dawn is practically nothing to tell us about the correct light of the star. Yaskrava star of the first star size can be a close star-dwarf of low lightness, and a weak star of six star size can appear even more distant supergiant majestic lightness. Therefore, to characterize the lightness of stars, a scale was introduced absolute staring values ​​M. The absolute star value is the star value, but the star value is small, changing with the winder 10 pc. It is easy to know the link between the visible and the absolute star value, victorious Pogson's law and hanging up to the star in parsecs:

Remaining taken:

The luminosity of the stars in the lamps of the Sontsya can be manually rotated through the absolute dawn value of the Suntsya:

12.3. Spectra zirok. Doppler effect

Crimea looked more than integrated (behind all the winds) lightness E,

connected as a lot of energy, which should be seen from the sky on a perpendicular single maidanchik for one hour in a single interval dozhin hvil (= erg / (cm)

At different times, on different days, the wind falls, the difference is the amount of energy, so they look at the distribution of energy according to the days of the wind and call it yoga spectral distribution of energy chi is just a spectrum of stars. Fallow in the temperature of the sky, the maximum at the spectral rozpodіlі posіdaє raznі dovzhini hvil. Chim the star is hotter, the time is less long, the wind falls to the maximum of the spectral distribution of energy. That is why hot stars behind the color are black and white, and cold - yellow and red.

In the spectra of zіrok and natomіst of the uninterrupted spectrum, there are dark numerical dark lines along the narrow lines of clay. The stench settles down during transitions between the energy levels of various atoms and ions at the surface of the star's spheres. The leather transition is characterized by a singing wind. However,

watch out for the spectra of signs of longevity and their transitions do not avoid laboratory

Earth. In the wake of the collapse of the stars, all the rest of the sickness, which are afraid, are afraid of their laboratory values, the Doppler effect. As the star approaches us, the lines in the її spectrum shift into the blue region of the spectrum, and as it moves away from us, then the red. The value of usunennya z to lie in

Here, c = 300,000 km/s is the speed of light in the vacuum.

In this way, based on the lines of the spectra of stars and other celestial bodies according to their laboratory conditions, we can take away a lot of information about the change in the speed of stars, about the speed of expansion of the shells of stars (the dawn wind, the vibes of New and Supernew stars),

12.4. Galaxies. Hubble law

At the beginning of the 20th century, it was left enough to know that we will surround our star system, the Galaxy (Chumatsky Way), where the Sun can enter, and it’s still close to a hundred billion stars, and explore more mirror systems- galaxies, hundreds and thousands away from us

megaparsec (1 Mpc = 106 pc) and this is how tens and hundreds of billions of stars are added up.

In 1929, Edwin Hubble showed that in the spectra of galaxies a marvelous regularity is observed: the farther the galaxy is ripped out of us, the more it is shifted into the red line in the її spectrum. Tse means that the galaxy is far away from us, the galaxy is farther away from us. This law took the name of Hubble's law:

The value of 50-100 km/(sec Mpc) is called the post-Hubble. We can, knowing the value of the red shift z, signify a distance to galaxies

IPC.

Hubble's law means that our Universe (or Metagalaxy) is expanding and mutually expanding between galaxies without interruption. Decide what the law is

Hubble is not absolutely accurate and zastosovuєtsya less with the lack of distance or otherwise. At 0.1, it is necessary to correct relativistic corrections.

67. Calculate the luminosity of the star Altair (Aql), so that you can reach it d = 5 pc, and the visible value of the star is m = 0m.

Solution: First of all, you need to know the absolute star value of Altair: M = m +5-5 lg 5 = 2m. Sweat, equaling її with the absolute star value of the Sun

, to know the luminosity of Altair, which is reflected in the luminosity of the Son:

Abo, stars

68. Nova Zirka, born in 1901, which blew off Perseus at Suzir, increased its glare from 12m to 2m in two dobies. How many times did the brightness increase (illumination was illuminated by it)?

Solution: Accelerated by Pogson's law lg (E 1 /E 2 ) = -0.4 (m 1 -m 2) = -0.4 (2-12) = 4. Also, clarity increased in 104 times.

69. Calculate the radius of the star, so that the temperature T eff = 13000 K, and the luminosity ?

Solution: Speed ​​up by formula (43) and we can see from it that

Substituting the given value and remembering that sho = 6000 K, it is calculable that .

70 (786)

the values ​​of the її components equal 2m .28 and 5m .08?

Solution: When arranging such tasks, it is necessary to remember that it is possible to sum up the illumination, created by different stars, but with their sizes.

We know beforehand the ratio of lightness, created by the components of the light lg E2/E1=-0.4(5.08-2.28)=-1.12 or E2/E1=0.076. The total dawn value of the components also depends on Pogson's law m -m 1 \u003d -2.5 lg ((E 1 + E 2) / E 1) \u003d -2.5 lg (1 + 0.076) or m \u003d m 1 -

0.08 = 2m.20.

71. (760) In the spectrum of the star, the calcium line h = 4227 was shifted to blue

end spectrum by 0.7. Significantly, with some kind of swiftness, the star is collapsing for the change of dawn, are you seeing it, are you approaching?

Solution: Oskilka line is shifted to the blue end of the spectrum, then, the star is approaching us, and from the formula (49) it is obvious that

49.7 km/s

72. (756) 6th magnitude can such a gleam itself, like one star of 1st magnitude?

73. (755) Let the day of the star periodically pulse for a constant surface temperature. How many star values ​​change at the same glare, so the minimum radius of the star is 2 times greater than the maximum?

74. (1014) Warehouse to Sirius 2.7 ps, but through the mutual movement of the Sontsya and Sirius, it changes from the speed of 8 km / s. Through skіlki rokіv iskravіst sirіus zroste vdvіchі?

75. (759) Star of the 6th magnitude in the beer sky 2000. How many times did they create lightness greater than the lightness that is created by Sirius m =-1m .6?

76. (764) At Spectra Novoї 1934 at Hercules, the dark lines were shifted from a normal station to a blue color. Line(=4341) appeared shifted on

10.1. What is the speed of expansion of the shell of the zirka?

77. (1093) Podvina zіrka Hydri May period obіgu 15.3 roku, parallax 0.02 and the top of the Great Orb 0.23. Calculate the linear differences of the great number and the sum of the mass components.

78. (788) The star of the Centauri is underwine, moreover, the total star value is 0m.06.

Zoryan's value of the brightest component is 0m .33. What is the value of the smaller yaskravogo component?

79. (1002) How bright is the star of Proxima Centauri, for which, less light of the Sun.

80. (1000) Calculate the absolute dawn magnitude of Sirius, knowing that its parallax is 0". 371, and the visible magnitude m=-1m.58.

The Zoryan value is a numerical characteristic of an object in the sky, most of which is a star, which shows how little light is to go to the point where the sign is located.

Visible (visual)

The current understanding of the visible dawn magnitude is broken down so that it was similar to the magnitudes attributed to the stars by the ancient Greek astronomer Hipparchus in the II century BC. e. Hipparchus divided the mustache into six sizes. Nayaskravishi wines were called stars of the first magnitude, naytmyanishi - stars of the sixth magnitude. The intermediate values ​​of the wines were divided equally between the stars, which were lost.

The dawn value is visible only in view of how much light the object is, and in addition, in a certain country, there are signs of guilt. Visible dawn value is respected by the unity of the world Bliska stars, moreover, the glare is greater, while the value is smaller, and navpaki.

In 1856 M. Pogson propagated the formalization of the scale of dawn values. Visible dawn value is assigned to the formula:

De I- Light flow from the object, C- Stay.

If the scale is visible, then the zero-point (0 m ) is designated as the brightness of such a star, in which the light flux reaches 10 quants / (cm² s Å) in the green light (UBV scale) or 10 6 quants / (cm² s ·Å) in the entire visible range of light. Zirka 0 m posture of the earth's atmosphere creates illumination of 2.54 10 −6 lux.

The scale of dawn values ​​is logarithmic, the scales of change of brightness in the same number of times are accepted as the same (Weber-Fechner law). In addition, hipparch's oskilki virishiv, that the magnitude of those less lower star I'm better, then the formula є has a minus sign.

The advancing two powers help to coristuvati with visible dawning magnitudes in a practical way:

1. An increase in the light flux at 100 times shows a change in the visible dawn value by exactly 5 units.
2. A change in the dawn value by one unit means an increase in the light flux by 10 1/2.5 = 2.512 times.

In our days, the dawn value is visible not only for stars, but also for other objects, for example, for the Moon and the Sun and the planets. Shards of stink can be bright for the best star, then they can have a negative visible star value.

Visible zoryan value to fall in the spectral sensitivity of the reception of viprominuvannya (glasses, photoelectric detector, photographic plate thinly)

• visual star value ( V or m v ) is determined by the spectrum of sensitivity of the human eye (we see light), which has a maximum of sensitivity at a maximum of 555 nm. or photographically with an orange filter.

• Photographic abo "blue" dawn value ( B or m p ) photometering of the image of the star on a photographic plate, sensitive to blue and ultraviolet changes, or for the help of an antimony-cesium photomultiplier with a blue filter.

• ultraviolet star value ( U) may have a maximum in ultraviolet at a long time of whilal close to 350 nm.

Differential values ​​of one object in different ranges U−Bі B−Vє іntegralnym pokazniki koloru object, scho more, even more so chervonim є ob'єkt.

• Bolometric zoryan value shows the total tightness of the viability of the eye, so that the tightness, implied by the entire spectrum of the viprominuvannya. For її vimiryuvannya zastosovuєtsya special attachment - a bolometer.

absolute

Absolute dawn value (M ) appears as a visible dawn value of the object, yakbi vіn buv raztoshovaniya on vіdstanі 10 parsecs vіd posterigach. The absolute bolometric value of Sontsya is +4.7. As soon as the dawn value is visible, and when you reach the object, you can calculate the absolute dawn value using the formula:

de d 0 \u003d 10 pc ≈ 32.616 light years.

Clearly, even as you can see that absolute dawn value, you can calculate the difference using the formula

The absolute dawn value is connected with the light of the upcoming spivvіdnoshennia: de і - svіtnіst і is the absolute dawn value of Sontsya.

Dawns of the magnitude of deyakyh objects

Sunshine from spring days

Navit distant astronomy people to know that the stars make a different glint. The greatest bright stars are easily seen in the illuminated Moscow sky, and the dark ice is remembered for the ideal minds of guarding.

To characterize the bliss of the stars and other celestial bodies (for example, planets, meteors, the Sun and the Moon), they vibrated the scale of dawn magnitudes.

Visible star value(m; often її they call it simply "the dawn value") showing the future of the development near the posterigach, so that the brightness of the heavenly dzherel is guarded, as to lay not only in the real tightness of the development of the object, but in the distance before the new one.

This is an astronomical value that is unfathomable, which characterizes the illumination that is created by a celestial object near the posterigach.

Illumination- Svіtlova value, which is better than the light stream, which falls on a small plot on the surface, up to one area.
Lux (1 lux = 1 lumen per square meter) is the unit of illumination in the International System of Units (SI), in CGS (centimeter-gram-second) - phot (one phot equals 10,000 lux).

Illumination is directly proportional to the strength of the light of the light. When in the distance the dzherela is visible on the surface, which is illuminated, the illumination changes back in proportion to the square of the distance (the law of return squares).

A subjectively visible dawn value is perceived as a glint (for point-shaped dzherels) or brightness (for lingering ones).

At the same time, the glint of one dzherel is indicated by a way of matching yoga with the glimmer of another, taken as a standard. Such standards should serve as specially selected unchanging stars.

The Zoryan size was introduced as an indicator of the visible glare of the stars in the optical range, and later they expanded the range of vibrance: infrared, ultraviolet.

In this way, the magnitude of m is visible, but it is blissful of the world's lightness E, which is created as a dzherel on a perpendicular to one change on the surface in the space of caution.

Historically, everything began over 2000 years ago, since the ancient Greek astronomer and mathematician Hipparchus(II century BC) sublime the visible eye of the star by 6 magnitudes.

To the most beautiful stars, Hipparchus, adding the first star size, and to the naytmyanishim, ice with a visible eye, - to the distance, evenly rozpodіl according to the intermediate values. Moreover, Hipparchus added to the stars of magnitude Gipparch so that the stars of the 1st magnitude were given the floorings as bright as the stars of the 2nd magnitude, and the scales of those are made as bright as the stars of the 3rd magnitude and so on. one and the same value.

As far as it was known, the link of such a scale with real physical values ​​is logarithmic, the scales of the change of lightness in the same number of times are accepted by the eye as a change by the same value. empirical psychophysiological law of Weber - Fechner, zgіdno z yakim the intensity is apparently directly proportional to the logarithm of the intensity of the podraznik.

It is due to the peculiarities of the human spirit, for example, as in the chandelier 1, 2, 4, 8, 16 of the same light bulbs are sequentially lit, then we are given that the illumination in the room is constantly increasing by one and the same value. That is why the number of light bulbs is guilty of zbіshuvatisya in the same number of times (at the butt of vdvіchі), so that we were given that the increase in brightness is constant.

The logarithmic occurrence of the apparent strength E of the physical intensity of the sub-item P is expressed by the formula:

E = up to log P + a, (1)

de k and a - deacons imminent, mindfulness with the sensory system.

In the middle of the 19th century The English astronomer Norman Pogson zdijsniv formalization of the scale of dawn values, as a way to protect the psychophysiological law of the dawn.

primed on real results watch out, postulate that

THE ZIRKA OF THE FIRST SIZE OF THE RIVNE IS 100 TIMES JARRIER THAN THE ZIRKA OF THE SHOSTA SIZE.

When it is visible up to the virase (1), the Zoryan value is visible and equal:

m = -2.5 lg E + a, (2)

2.5 - Pogson's coefficient, minus sign - Danina historical tradition (short stars can be smaller, including negative, dawning value);
a - zero-point of the scale of dawning values, which is established by international favor, tied to the choice of the base point of the vimiruval scale.

If E 1 and E 2 correspond to the dawning values ​​m 1 and m 2 then z (2) follows that:

E 2 /E 1 \u003d 10 0.4 (m 1 - m 2) (3)

A change in the dawn value by one m1 - m2 \u003d 1 leads to an increase in lightness E approximately 2.512 times. At m 1 - m 2 = 5, which changes the range from 1-ї to 6-ї mirror value, the change in lightness will be E 2 / E 1 = 100.

Pogson's formula in a classic way set the link between the visible star values:

m 2 - m 1 \u003d -2.5 (lgE 2 - lgE 1) (4)

This formula allows you to determine the difference between the dawn values, but also the values ​​themselves.

In order to help induce the absolute scale, it is necessary to set zero point- Blisk, for which the zero dawn value (0 m) is confirmed. Spontaneous yak 0 m buv blisk Vega. Let's use the zero-point of the remapping letters, but for the visual guards Vega dosi can be a standard of zero visible dawn magnitude (for current system, in smooth V of the UBV system, її glare is more expensive +0.03 m (which does not look like zero on the eye).

Sound the zero-point of the scale of the dawning values ​​to take it mentally for the order of the stars, the photometry of such vikonan is measured by different methods.

Also, for 0 m, the entire lighting was taken, which is a healthy energy value E = 2.48 * 10 -8 W / m². Vlasne, the very illumination and signify with the caution of astronomers, and then we will specially translate at the star's magnitude.

To shy away the stink is not only for the one who is “so loud”, but also for the one whose zirkova value seemed to be more understandable.

the zіrkov value appeared even more clearly understood

It is very cumbersome to reduce the illumination at Wat per square meter: for the Sun, the value is great, and for weak telescopic stars - even small. At the same time, it is easier to operate with star values, because the logarithmic scale is vinyatkovo convenient for displaying large ranges of values.

Pogson's formalization of the distance has become the standard way of assessing the size of the sun.

True, the current scale is not between six star values ​​and less visible light. Even yaskra ob'єkti may have a negative dawn value. For example, Sirius, nayaskravisha zirka the celestial sphere, which I can see the value of minus 1.47 m. The current scale also allows you to take the values ​​for Month and Sun: the last month may have a value of -12.6 m, and the Sun -26.8 m. The Hubble Orbital Telescope can detect objects whose glare is up to about 31.5 m.

Scale of specter magnitudes
(the scale is reversed: smaller values ​​are given as the best objects)

We see the stellar magnitudes of some celestial bodies

Sun: -26.73
Month (last month): -12.74
Venus (at maximum closeness): -4.67
Jupiter (at maximum closeness): -2.91
Sirius: -1.44
Vega: 0.03
Weakest stars, visible with an unbroken eye: close to 6.0
Sun from the sky 100 bright rocks: 7.30
Proxima Centauri: 11.05
Biggest quasar: 12.9
Weakest objects, images of those captured by the Hubble telescope: 31.5