STAR VALUE (apparent stellar magnitude), a measure of the illumination created by a celestial body (star, planet, etc.) on a plane perpendicular to the incident rays; a measure of the brilliance of a heavenly body. If the measurements are taken from the Earth, then the magnitudes are usually corrected to take into account the attenuation of light in the Earth's atmosphere, and such magnitudes are extra-atmospheric. The concept of "magnitude" was introduced in the 2nd century BC by Hipparchus, who divided all the stars visible to the naked eye into 6 groups (magnitudes): he attributed the brightest stars to the 1st magnitude, the weakest to the 6th . The magnitude m is related to the illumination E by the dependence m = klgE + С 0 . The coefficient k, at the suggestion of the English astronomer N. Pogson (mid-19th century), was taken equal to -2.5; it sets the magnitude scale step, and the constant C 0 is its zero point, which is determined by the results of measurements of a certain set of stars chosen as standard. A change in magnitude by 5 units corresponds to a change in illumination by 100 times. Thus, the magnitude scale is logarithmic with base (100) 1/5 = 10 0.4 ≈ 2.512. The brighter the luminary, the smaller its magnitude; for particularly bright luminaries, it is negative.
These angles are only slightly below 90°. This star produced a wonderful motorcycle and therefore should have been much closer to other stars that showed zero or just tangible shifts. If Cygnus 61 was close, compared to the distant background stars, its parallax could be measured.
A few months later, Scottish astronomer Thomas Henderson of the Cape Town Observatory measured the parallax of the star Alpha in the constellation Centaur, which turned out to be 0.75 arcseconds. Thus, this star was much closer to 61 Cygnus, and in fact it is only 4 years and 4 months of light from us. Subsequently, the faint star associated with Alpha Centauri was still slightly closer.
There are visual magnitudes (determined by the eye with the help of a visual photometer), photographic (from photographs on a photographic emulsion), photoelectric (using a photoelectric photometer) and bolometric (using bolometers). Star magnitudes obtained by photographing the luminaries on a photographic plate with an orthochromatic or panchromatic emulsion through a yellow light filter are called photovisual (they are close to visual). The use of various radiation receivers and light filters makes it possible to measure the brightness of luminaries in different parts of the spectrum and thereby determine stellar magnitudes in different photometric systems (see Astrophotometry). The most commonly used system is UBV, in which stellar magnitudes are given in the ultraviolet U, blue B, and yellow V parts of the spectrum. The B values are close to photographic ones, and the V values coincide with the photovisual ones. In addition to the UBV system, stellar magnitudes are used in the red and IR regions of the spectrum: R, I, J, H, K, etc. The differences in stellar magnitudes, called color indices (for example, B-V, U-B, etc.) , characterize the distribution of energy in the spectra of stars.
By the end of the century, the distances of many stars were measured by the parallax method; however, beyond certain limits, with this method you could not go. The smallest parallax estimated today using the best available instruments is hundredths of a second, so we cannot estimate distances beyond 300 light years. But beyond that limit, there are billions of other stars, how do you rate that?
A very rough system might be to estimate the distance according to their brightness, assuming that all stars have more or less the same intrinsic brightness. It is known that the brightness of a light source decreases with the square of the distance, according to a known physical law. Therefore, a light source that will appear, for example, nine times less bright than another suppository with the same intrinsic brightness will be three times as bright.
A star magnitude is a dimensionless quantity. To indicate it, they usually use the letter m (from the Latin magnitude - magnitude) in the form of the right superscript of a number, for example 6 m. If a range of the spectrum is specified (for example, V or m V), then the index m is usually not indicated. The accuracy of photographic and visual measurements of the brightness of stars is about 0.05 m, photoelectric - about 0.01 m. The brightest star in the night sky Sirius has magnitude m V = -1.46, the faintest stars measured are 28 m . The star magnitude of the Sun is m V = -26.8, the full Moon is m V = -12.7.
In fact, stars are not all equally bright, so the method applied to specific cases turned out to be very inaccurate. Indeed, if you look in the sky at night, you will see a large white band crossing it, and what the ancients called the Milky Way, as they imagined it to be the milk that came out of Juno's breast when she laid Ercole. The light bar is nothing more than a collection of stars that we cannot distinguish individually with the naked eye, since we cannot distinguish the individual leaves of a forest species from a plane.
Therefore, we seem to be surrounded by this band of stars, and then we find ourselves in the center of it. The set of these stars is now called the Galaxy. Herschel, taking samples of stars at different points in the sky, counted the number of stars present in everything milky way. This number was estimated at about one hundred million. In fact, the stars in the galaxy are at least a thousand times larger.
In addition to the apparent stellar magnitude, astronomy uses the concept of absolute stellar magnitude - the stellar magnitude that a celestial body would have, being at a standard distance of 10 pc from the Earth. Absolute stellar magnitudes (as opposed to visible ones) characterize the physical properties of the luminaries themselves, their luminosity. The absolute stellar magnitude M is related to the apparent stellar magnitude m by the dependence: M = m + 5 - 5 lgr, where r is the distance to the star, expressed in parsecs.
Based on the brightness of the stars, Herschel was also able to estimate the size of the entire complex, which was, however, much smaller than the real one. However, although imperfect, the framework of our Galaxy provided by Herschel in its main lines will prove to be credible.
The next step towards measuring stellar distances was the discovery by American astronomer Henrietta Leavitt of Cepheid variables in the Magellanic Small Cloud. Cepheid reversals are stars whose brightness changes with time, reaching a maximum and then returning to the initial brightness: they are called "Cepheids" because the first one was observed in the constellation Cepheo. The time between maximum brightness and the next is called the period and can vary from less than two months. It should also be noted that the brightness reached before the maximum glow can be more or less intense and not related to the period of pulsation in the sense that there are Cepheids with a long period of time and low final brightness and Cepheids with a short period and intense final brightness, or conversely, Cepheids with a long and intense final luminosity and Cepheids with a short time period and low final luminosity.
Lit .: Mironov A. V. Precision photometry. M., 2007.
El sueño de la razón produce monstruos
In astronomy, when talking about celestial bodies, specific terms are sometimes used to characterize their color and brightness, for example, magnitude or color index.
magnitude- an indicator characterizing the brightness of a star or some other astronomical object.
Since the time of Hipparchus in Nicaea, stars have been classified according to their luminosity, on a scale of 1 to the least luminous stars ranked sixth, and the brightest ranked first magnitude. Subsequently, this classification was given a more rigorous scientific discipline, and at first the star was defined as exactly 100 times brighter than one sixth. As a result of this specification, wanting to go from one size to another, you need to multiply the brightness of the least bright star by the fifth root of 100, that is, by 2.
With the improvement of the magnitude scale, some very bright stars turned out to be in brightness higher than those that needed to be ranked first. Currently, for example, Betelgeuse is assigned a magnitude of 0.80, Vega is assigned a magnitude of 0.04, and Syrio, which is the brightest star of all, is assigned a magnitude of -1.
There are two types of stellar magnitudes - apparent and absolute.
Apparent magnitude characterizes the brightness that we see or can see. That is, it determines the conditions for observing an object from the Earth.
This value dates back to the II century BC, when Hipparchus proposed dividing all stars by brightness into six magnitudes - he called the brightest and best visible stars of the first magnitude, and the dimmest - the sixth.
Of course, such a subjective approach is not applicable for modern purposes, moreover, most of the astronomical objects are not visible to the naked eye. At the same time, the characteristic of apparent brightness is a very useful thing. Therefore, in our time, Hipparchus' classification has been modernized and has become measurable and objective - and, despite the modernization, Hipparchus' classes have been preserved.
The classification of apparent brightness is based on two principles.
First, the brightness is determined by the number of radiation quanta of the object received by the eye or photodetector per unit time. This allows you to evaluate the brightness objectively.
Secondly, it takes into account the peculiarity of human vision. The fact is that a person evaluates brightness not linearly, but logarithmically - the Weber-Fechner psychophysiological law states that for a person, the sensation caused by a certain stimulus changes in proportion to the logarithm of the intensity of the stimulus, that is, in relation to light, the brightness of light is perceived by us in proportion to the logarithm of light flow.
In this regard, the apparent magnitude m is determined by the formula:
m \u003d - 2.5 lgI + C,
where I is the luminous flux, and C is a certain constant
The constant C is chosen so that the magnitude scale is as close as possible to the hipparchus, that is, for a very bright star apparent magnitude m was zero. Strictly speaking, C is chosen so that in the above formula m is equal to zero for an object that creates (without taking into account the influence of the earth's atmosphere) an illumination of 2.54 10^-6 lux.
Then a star of the first magnitude creates illumination, approximately 2.512 times lower than indicated, the second magnitude - 6.31 times lower, and so on. That is, an increase (decrease) in magnitude by one means a decrease (increase) in the intensity of light from the source by about 2.512 times, and by five units - exactly one hundred times. Objects of magnitude greater than six are almost invisible to the naked eye.
The light from a star that reaches Earth can now be estimated with great precision using very sophisticated photometers. The magnitudes determined by the measurement of the light emanating from the stars are called "apparent magnitudes", since the radiation that we perceive depends, in addition to the actual brightness of the beam, also on the distance at which it is located. To estimate the actual brightness of a star, we need to know its distance.
Astronomers determine the "absolute magnitude" of a star, its apparent brightness at a distance of 10 parsecs. To measure the true magnificence of a star, scientists agreed to imagine all stars at the same distance and consider the apparent brightness at that distance as an expression of their intrinsic luminosity. This standard distance, as we have said, has been fixed at 10 parsecs, which is 32.6 light years.
However, it is still not so simple. A star or other object emits (or reflects) light of different wavelengths - and a person perceives them differently. At the same intensity, green light is perceived brighter, red light is dimmer, and infrared, of course, is not perceived at all. But the photographic plate perceives light in its own way. And some other photodetector - somehow. Therefore, there are several visible stellar magnitudes.
Visual magnitude V is determined by the number of quanta emitted by the object and perceived through a "physiological" green light filter, the maximum of which is equal to the maximum sensitivity of the eyes of an average person (555 nanometers).
Photographic magnitude B is determined by the number of quanta emitted by the object and perceived through a standard blue light filter, the maximum of which is 445 nanometers. A blue filter is usually used when photographing astronomical objects in optics.
Ultraviolet magnitude U determined using an ultraviolet light filter with a maximum of 350 nanometers.
As a result, if all three values are determined, the real observed color of the object can be characterized. Namely, for this, the differences in the measured magnitudes of U and B (U-B), as well as B and V (B-V), called integrated color indicators. The larger they are, the more red the object is.
Of course, these are not all visible stellar magnitudes. In addition to the above-mentioned light filters, others are also used, and the corresponding stellar magnitudes have the following designations:
R (red light filter) - 658 nanometers.
I - 806 nanometers.
Z - 900 nanometers.
Y - 1020 nanometers.
J - 1220 nanometers.
H - 1630 nanometers.
K - 2190 nanometers.
L - 3450 nanometers.
M - 4750 nanometers.
N - 10500 nanometers.
It is easy to see that magnitudes from I to N already belong to the infrared region - from near to far.
But that's not all. Astronomical objects radiate in the entire spectrum of electromagnetic radiation, and many - predominantly, not at all in the visible range (for example, very hot stars mainly emit ultraviolet radiation, and very cold stars - infrared radiation). Therefore, there is another indicator of their brightness - bolometric magnitude, characterizing the power of their radiation observed from the Earth in the entire range of electromagnetic waves simultaneously.
Using this formula, one can determine the value of the absolute magnitude of a star if one knows the apparent and its distance, or, as we will see below, estimate the distance of a star, knowing its absolute and apparent brightness. Then, at a distance of 10 parsecs, Siri's brightness decreases by almost three points, ranging from magnitude -1.46 to magnitude 1.
Now if we take Polaris for example, it looks less bright than Syrio just because it is much farther away. If Polaris were placed at the same distance as Sirius, it would appear much brighter: this depends on the fact that the intrinsic brightness of Polaris is much greater than that of Sirio, and if the two stars were placed 10 parsecs apart it would immediately visible. On the other hand, our bright, bright sun, which in its presence the whole sky, at a distance of 10 parsecs, will only be magnitude 4.8, so the small star will be visible to the naked eye.
To illustrate, here are a few examples of apparent stellar magnitudes:
Sun -26.7 (note the minus!);
The full moon is -12.74 (four hundred thousand times weaker);
Venus at its maximum -4.67;
Jupiter at maximum -2.94;
Mars at maximum -2.91;
Sirius A -1.47;
Vega +0.03;
Rigel +0.12;
Large Magellanic Cloud +0.9;
Andromeda Galaxy +3.44;
Let us return now to the Cepheids and to the discovery of Henrietta Leavitt. This star system contained many Cepheids that had a pulsation period, longer, when they looked bright until the luminosity maximum. As you remember, this regularity was not found in Cepheids that could be observed in other regions of the sky. How could this happen specifically for the Small Magellanic Cloud? Leavitt understood that this must depend on the fact that the Cepheids in the Magellanum Cloud were more or less located at the same distance from us, so their apparent magnitude was practically an absolute magnitude, with the difference that it was mentioned at a distance to the Small Cloud Magellan instead of 10 parsecs.
Brightest quasar +12.6;
Farthest known galaxy +30.1;
The faintest object photographed by Hubble, +31.5.
And examples of color indicators:
Blue supergiant Rigel: B-V = -0.03, U-B = -0.66;
Blue hypergiant eta Carina: B-V = -0.45, U-B = 0.61;
Blue Hypergiant Pistol: B-V = -0.93, U-B = -0.13;
White Sirius A: B-V = 0.01, U-B = -0.05;
Yellow Sun: B-V = 0.64, U-B = 0.18;
However, this distance was unknown, but if he could measure it, the star's absolute magnitude could be established during its pulsation period, which, as we have already said, the longer the intensity is brighter before the maximum brightness. By carefully examining photographs of the Magellanic Small Cloud taken later, Leavitt was able to write relationships that related the absolute magnitude of the Cepheids to the length of the pulsation period. From this period-luminosity relation, it was possible to determine which period should have a Cepheid having a certain absolute value, and vice versa, to which absolute value a Cepheid having a certain period of pulsation should correspond.
Red Betelgeuse: B-V = 1.86, U-B = 2.06.
But this is not all.
Of course, the apparent stellar magnitude cannot objectively characterize the true brightness of an object - it determines only the brightness of this object that we observe and depends on the distance to it.
Therefore, for an objective characteristic, one more parameter is adopted - absolute magnitude M(visual, photographic, ultraviolet, bolometric), defined as the apparent magnitude of that object if it were 10 parsecs (approximately 32.616 light years) away.
And here our Sun is already becoming inconspicuous ... Its absolute magnitude is only +4.7. But Sirius has +1.42. Rigel has -7 (! from a distance of 32 light years it would be hundreds of times brighter than Sirius!) Eta Carina has -12 (!! even a hundred times brighter !!). The largest star has R136a1 -12.5. And the brightest known star, LBV 1806-20, has an absolute magnitude of -14.2 and, from a distance of 10 parsecs, would shine in the sky almost five times brighter than our Moon on a full moon.
At this point, there was nothing to determine the absolute magnitude of one Cepheid, to know that of all the others. But to find out the absolute magnitude of a Cepheid, it was necessary to determine its distance. The fact is that Cepheids, unfortunately, are all very distant stars, so the parallax method cannot be used to measure the distance.
Thus, an attempt was made to arrive at a determination of their distance using statistical methods based on the determination of their own motion. We have already mentioned that the nearest stars have more obvious movement than the farthest, and therefore, the more you see a star moving in the sky over time, the closer it must be. In fact, the method is not very accurate, but in the absence of a better one, reliable enough that it can obtain the parallax values of a dozen Cepheids.
The explosion of the brightest supernova -20.4 (from a distance of 32.6 light years, it would shine three hundred times weaker than the Sun. Or was more than a thousand times brighter than the Moon) ...
Nebula Andromeda -21. If you collect the entire giant galaxy into a point, it would shine a little stronger than this supernova.
The most powerful gamma-ray burst is -36.4 ... Minus thirty-six with a little ... from a distance of ten parsecs it would be brighter than the Sun we see in our sky by almost ten thousand times, burning the surface of the Earth ...
These measures were considered acceptable. The first to use this method was the Danish astronomer Einar Hertzsprung, who analyzed the motion of groups of stars containing also Cepheids, and finally stated that a Cepheid with a period of 6.6 days should have an absolute magnitude, shadow at most, of -2. A few years later, the American Harlow Shapley, one of the astronomers of the last century, repeated the procedure and concluded that a Cepheid with an absolute magnitude of -2.3 must have had a pulsation period of 5.96 days: a result very close to that found by the Danish astronomer.
To summarize:
The magnitude - the smaller it is, the brighter the visible object. At a magnitude greater than six, the object is no longer visible to most people with the naked eye. More than thirty - the object is not visible in the most powerful modern telescope. A decrease by one value means a decrease in brightness by a factor of 2.5, by five values - by a hundred. Magnitude zero corresponds to a very bright star (Vega).
Absolute magnitude is the brightness of an object that would be 32.616 light years away.
And the color of the object. A color index of zero is white. Less than zero is blue, and the lower the value, the more blue it is. More than zero - yellow. Much more than zero (close to one) - orange. Significantly more than one - red.
Thus, the relationship between the absolute magnitude of a given Cepheid and its period of pulsation has been established, using the pronounced period relationship discovered by Leavitt can determine the absolute magnitude of any Cepheid. These measurements led, among other things, to the discovery that Cepheids are very large stars that are likely to pulsate due to subsequent expansions and contractions caused by strong and rhythmic explosions that occur in their core: the stronger the explosion, the larger the star expands, the brighter it becomes at the maximum expansion and hence the longer the time taken to shrink.
