In 1835, Auguste Comte wrote in the Course of Positive Philosophy that stars will always remain for us as mechanical objects. We will be able to determine their position in the sky, measure the distances to them, we will be able to find out the laws of their movement, but this is what the luminous point is, what it is made of and what temperature it has – we will never know. But it was at this time that spectral analysis was born, which allows determining the composition and temperature of celestial bodies at a distance. Thanks to this method, we now know a lot about the evolution of stars. Astrophysics as a science has grown on observational data, not models.
When did you start studying the spectra of stars?
One of the first researchers of the spectral lines was Josef Fraunhofer. Studying the spectrum of the Sun, he created the first system for naming spectral lines, denoting them with the letters of the Latin alphabet. Now we know that these lines correspond to different chemical elements, which causes some confusion. For example, the Fraunhofer lines K and H do not belong to potassium and hydrogen, as one might think, but to ionized calcium, and line C belongs to hydrogen, not carbon.
At the beginning of the second half of the 19th century, astronomers’ attention shifted from solar to stellar spectra. It turned out that the spectra of different stars can be quite different. The first attempts at spectral classification of stars were based solely on the presence or absence of certain spectral lines in the spectrum. Then it turned out that it is possible to build spectral classes in a more logical sequence in temperature. The hottest stars belong to spectral classes O and Bed. They have maximum energy in the blue and ultraviolet regions of the spectrum. The coldest is K and M, and their maximum energy is in the red region of the spectrum. This means that just by looking at a star, you can estimate the color of how hot it is: the surface temperatures of the blue stars are high, and the red temperatures are much lower. The sequence of spectral classes of stars is made up of a sequence of letters O, B, A, F, G, K, M, for which they invented many mnemonic methods of memorization: “One shaved Englishman chewed like a carrot.” Or in English, for example, “Oh, Be A Fine Girl, Kiss Me”.
What do we know about the evolution of stars?
By the beginning of the twentieth century, physicists had learned how to determine the temperature of a star by the emission spectrum. The star radiates almost as an absolutely black body, and, therefore, its surface temperature can be determined using the Planck formula. We cannot measure the internal temperature of a star in a similar way, but there is a simple way to estimate it. If we assume that the star is in hydrostatic equilibrium, and this is a very logical assumption, its internal structure will be described by rather simple formulas that allow us to calculate the central temperature. In this case, you do not need to know anything about thermonuclear reactions, nor about any other features of the star. We simply consider it to be a gas ball of known mass and radius, which is in hydrostatic equilibrium — that’s all, that’s enough to calculate the temperature at its center.
The second important parameter of the star, which can be determined from observations, is the luminosity, that is, the total amount of energy emitted by the star per unit time. To estimate the luminosity, you need to know the distance to the star or compare it with some standard, for example, with a star of the same spectral class, the distance to which is known.
The most direct method for determining distances is the trigonometric parallax method, using the orbital motion of the Earth around the Sun. From this method, a measure of one parsec appeared – this is the distance at which an object shifts within six months by one arc-second. It works in the immediate vicinity of the solar system, but, fortunately, there are many stars in our galactic neighborhood, to which the distance can be measured directly. Then we can broadcast this knowledge to distant objects. How? With the help of so-called standard candles objects whose true luminosity is known to us. Such, for example, are variable stars of a special type – Cepheids (these include, in particular, the Polar Star), whose luminosity is related by a simple ratio to the periods of their pulsations, or type Ia supernovae presumably at the maximum brightness with the same luminosity. Having determined the distances to some “standard candles” by the method of trigonometric parallaxes, we can then determine the distance to other objects of the same type simply by the apparent brilliance, according to how brightly they shine for the earth observer. Remembering that the photon flux falls as the square of the distance, we can estimate the distance to these stars.
The radii of the largest stars can be measured directly. In other cases, you have to use a formula that directly links the luminosity, temperature, and radius of a star:
L = 4πR 2 σT 4 ,
Where σT 4 is the flux per unit area, and 4πR 2 is the surface area of the star. Those few stars for which we can measure the radius directly confirm that our calculations are generally correct.
The most important star parameter is the mass of the star. Having learned the mass of a star, you have learned about it all that you can learn about it – if it is a single star. In astronomy, there is the Russell-Vogt theorem, which states that the evolution of stars is completely determined by their initial mass and chemical composition. The chemical composition is about the same everywhere, it does not show any such great diversity: hydrogen, helium and a bit of everything else. The mass varies in a very wide range: from eighty Jupiters, that is, 8% of the mass of the Sun, and in our Galaxy to 150 solar masses.
How to determine the mass of a star? This is possible if the star is a member of a binary system wide enough that its components do not interact with each other. Observing the motion of stars in such pairs, it is possible, by applying the laws of Kepler, to determine the masses of the components. If we have additional information about the angle of inclination, we get the mass of each star. This is the only way to directly measure mass, there is no other. Everything else goes through the theory of the evolution of stars. Fortunately, the main parameters of the star are interconnected by simple relations, and the most famous of them is the relationship between temperature and luminosity — the Hertzsprung-Russell diagram.
Hertzsprung – Russell Chart
The most famous astrophysical diagram is called the Hertzsprung-Russell diagram. On its abscissa, its temperature increases to the left and not to the right, that is, it goes from 50,000 to 3,000 Kelvin – the surface temperature is meant: we see nothing else, so when we talk about the temperature of a star, we always mean the surface temperature.
The ordinate in the Hertzsprung-Russell diagram is the luminosity, that is, the radiation power. It is often measured in solar luminosities, from the order of a million suns up to one ten thousand down. The luminosity of the Sun is 4 * 10 26 watts. In 1912–1913, Einar Hertzsprung and Henry Russell independently discovered that if you draw such a diagram, the stars do not fill it randomly: most are on the large diagonal going from the upper left to the lower right.
This diagonal is called the main sequence. Almost all the stars are located on it, and beyond it are white dwarfs, red giants, red supergiants and giants of the asymptotic branch. In 1912, when this diagram appeared, the gravitational pattern of star formation prevailed: it was believed that the star glows due to the matter falling on it. At first, the star is cold, but matter falls and falls on it, and the star warms up gradually, coming to the top of the main sequence. When the fall of the substance ends, then the star only cools. This is how the term itself – sequence. Now we know that there is no sequence in this line, and the stars during life pass along the Hertzsprung-Russell diagram of other, rather complex trajectories.
How is the life and evolution of small stars?
A star, a substellar object, or even a planet can exist for a very long time. But this is possible only if they are in a quasi-equilibrium state. This state is called hydrostatic equilibrium, and it is made up of internal outward pressure and gravity inward. The pressure is created by the heat generated by thermonuclear reactions, and when the reactions subside, it drops.
Gravitational compression of the gas leads to two results. First, the gas is heated. Secondly, with a very large pressure, it degenerates, that is, it comes to such a quantum mechanical state, it becomes so dense that the Pauli principle begins to affect it: two electrons cannot occupy the same cell. So it turns out the electron degenerate gas. In the cores of massive stars, the neutron gas degenerates. This appears as a result of the indentation of electrons into protons and their transformation into neutrons. Gas degeneration is very important for understanding the evolution of stars.
What is the typical biography of the smallest star, that is, the object in which thermonuclear reactions take place? In order for thermonuclear reactions to begin, the temperature must rise to several million degrees. At this temperature, deuterium begins to burn, of which there are very few in star, thousandths of a percent. At first, it burns and, therefore, can provide short-term maintenance of pressure due to temperature. Then the deuterium burns out, compression begins. Further developments depend on what comes first: the firing of thermonuclear reactions with hydrogen or the degeneration of gas.
For objects whose mass does not exceed eighty Jupiter, degeneration occurs earlier. Because of the small mass, the temperature does not have time to rise to such a state that thermonuclear reactions ignite, and the gas is already degenerate. Degenerate gas does not need to be hot to maintain hydrostatic equilibrium. The result is an object that quietly exists for thousands of billions of years without thermonuclear reactions. It cools slowly, keeping from the compression by the pressure of a degenerate gas. Thus brown dwarfs turn out.
The smallest objects that are already called stars have a mass of more than eighty Jupiter, or 0.08 Sun mass, – red dwarfs. The temperature in their cores is sufficient for hydrogen to catch fire. During the life of a star, when in its interior hydrogen gradually turns into helium, the star is on the main sequence. Helium, in order to enter the next stage of thermonuclear burning, needs a temperature of about one hundred million kelvins. Small stars cannot warm up to such a temperature: helium simply does not ignite in them, and a helium core forms inside the star, which cools and degenerates and formed helium white dwarf. This is a hypothetical picture because no red dwarf in our universe has yet completed its evolution. Even astrophysicists are not very interested in modeling this process, because it will be impossible to compare the predictions of the model with the observations of a few more trillions of years.
How is the life and evolution of big stars?
The next mass threshold is stars like ours, which start from 0.6–0.8 solar masses. They pass through a helium flash in their lives. At first, everything is as usual: hydrogen in the core burns out and turns into helium. The core begins to cool and shrink. Along with it is compressed and the outer layers of hydrogen. Compressing, they heat up to such a temperature that they also begin a thermonuclear reaction. The so-called layer source starts to burn. It is very narrow, and it releases a lot of energy and the temperature rises sharply. And next to it is a relatively cold helium core. Steep temperature gradient causes convective instability. The outer layers of the star expand, and it becomes a red giant.
The star does not fly apart, but expands greatly and becomes very bright since the brightness is proportional to the radius in the square. If the radius grows a hundred times, the brightness increases by four orders of magnitude, and the surface temperature drops. In five billion years, when the Sun passes through this stage, its radius will grow to the orbit of Venus, and from Earth, if its orbit does not change by that time, it will blow away the atmosphere.
While the star is turning into a red giant, the layered source continues to heat the degenerate helium core. When a certain temperature is exceeded, the degeneracy is lifted, and suddenly in the center of the star, there is an overheated helium nucleus under very high pressure. There is almost an explosion – helium flash. True, its traces do not go outside: the star is large, and even if it had a huge explosion inside, nothing is visible outside.
After the explosion, the next stage begins – the burning of helium in the core. The star is again slowly moving towards the main sequence, again becoming almost normal in the sense that it has a thermonuclear reaction in its center. The radius decreases, the surface temperature increases. And this goes on until the moment when helium, which all this time turns into carbon and oxygen, ends. It turns out carbon-oxygen white dwarf – the final stage of the life of a solar-type star.
If the mass of the star is more than two or three times the mass of the Sun, helium does not have time to degenerate but just ignites. Otherwise, everything goes exactly the same way: helium core, a layered source that heats it. When the temperature in the core reaches one hundred million degrees, the triple-alpha process begins, and helium is converted into carbon and oxygen. After the helium in the core burns out, a layer source reappears, only now helium is already burning in it. And above it is another layer in which hydrogen burns. The star begins to swell again and falls on the asymptotic branch of the giants of the Hertzshprung-Russell diagram. After this comes the finish line: a white dwarf and a planetary nebula. Such a fate awaits Sirius and Vega – from well visible stars.
This all concerns stars with a mass of less than ten solar masses. Prior to this threshold, the stars turn into a white dwarf – helium, carbon-oxygen, oxygen-neon-magnesium, but definitely a white dwarf with a mass on the order of the mass of the Sun and a nucleus on the size of the Earth. Beyond the limit of ten solar masses, everything happens quite differently. There passes the full cycle of thermonuclear fusion, up to iron. To put it very simply, in the final stages of the life of such large stars, an “onion structure” is formed. Different thermonuclear reactions take place in different layers, in which, as it moves toward the center, more and heavier elements are formed.
In the final in the center of the star, an iron core is formed. There are no thermonuclear reactions in it. Accordingly, it is not able to withstand the gravitational compression until the degeneration of the neutron gas, and not of the electron gas. This is how a neutron star with a mass of the order of one or two solar masses with a size of 10–20 kilometers in diameter is obtained. If the core of such a star is twice the mass of the Sun or more, a black hole is formed.
How to develop more complex objects?
Even in a single star, a simple onion structure will be obtained only if it has spherical symmetry, and this is not necessarily the case. The stars spin fast. Massive stars rotate very fast. This means that, in addition to convection, meridional currents can occur.
When modeling such stars, it is no longer possible to confine ourselves to thermal pressure. The radiation pressure plays an important role in them. The radiation flux coming from the depths is so powerful that it transmits a significant part of its impulse to matter through which it spreads. This pressure is capable of disrupting a part of its substance from a star. As a result, such unusual objects as Wolf-Rayet stars may appear. Initially, these stars were allocated to a separate class, because their spectra show no signs of hydrogen. It is assumed that these are stars with broken hydrogen shells: looking at them, we see the bare inner part of the star, in which the hydrogen has already been processed. There are works in which the observed masses of Wolf-Rayet stars were estimated at several solar masses. That is, the loss of substance can be very large even in a single system.
Even more difficult is the evolution of binary systems with massive stars. One massive star is already the most complex object, and here there are two more. And they somehow interact with each other, not only gravitationally. Here is just one example. There is such a thing as a Roche cavity – this is a kind of border around a star, in which its own reign reigns. If a star’s substance extends beyond its Roche lobe, it falls into the range of the companion. In close binary systems, it happens. One star swells turn into a red giant, its substance goes beyond the limits of the Roche lobe and begins to flow towards the companion. As a result, two stars change roles: the big one becomes small, and the small one becomes big.
In massive stars, the interaction of matter can occur, even if they have not yet expanded. The stellar wind, a powerful stream of matter flowing from them, flows down from two massive stars. Two stellar winds collide with each other and begin to interact. Sometimes very powerful flashes occur on these stars, the nature of which is completely unclear at all. These are the so-called luminous blue variables – bright blue variables. The most famous of them is this Carina. Now it is completely dim, and in the 19th century, it was for some time one of the brightest stars in the sky. In dual systems, everything is very difficult, and we still have a lot to understand about them.