Algol is the second brightest star in the constellation of Perseus and is one of the eclipsing stars best known to astronomers , and one of the first to be cataloged for its variability in brightness.
Summary
[ hide ]
- 1 Features
- 2 Algol brightness curve
- 3 Radial velocity curve
- 4 Algol Paradox
- 5 Source
Characteristics
Algol magnitude regularly oscillates between 2.3 and 3.5 with a period of 2 days, 20 h and 49 min. The variability of Algol, already known to the Arabs, was discovered in 1669 by the Bolognese astronomer Geminiano Montanari, although it had been known since ancient times. Algol means “the head of the devil” or “demonic star”. Its name is probably due to the behavior that ancient astronomers observed in it. In times past it was considered that the heavens were immutable so the variability of a star could only be the work of the Devil .
In the constellation Perseus , it represents the eye of the gorgon Medusa , the being that the hero beheaded in the famous mythological story. The physical explanation for his behavior was given in 1782 by the Englishman John Goodricke. Radio astronomical observations have led, in 1971, to the discovery that Algol is a source of radio emissions due, it seems, to exchanges of gaseous substances between the two main components of the system. Algol is the prototype of the Eclipse Variables, double stars in which one component periodically hides the other, causing a decrease in luminosity. In the case of Algol, the brightest star in the system is eclipsed every 68.8 hours by a weaker star, which is 10 million kilometers away from the first.
Algol brightness curve
At the end of the 18th century the English amateur astronomer John Goodricke noted that the brightness of Algol varies regularly over a period of 20 hours and 49 minutes. In order to characterize the period of a star, the concept of phase is implanted: the phase in a time expressed in fractions of period P. The phase is calculated taking a certain instant as the initial instant and assigning it a phase equal to zero. It usually matches the minimum brightness of the star. After the observation time is recorded, the initial instant is subtracted, and the result is divided by the period. The rest of the division is the phase.
The brightness of a variable star is calculated relative to the constant brightness of a star that is in its vicinity. The graph of the brightness of a star, as a function of its phases, is called a brightness curve.The Algol brightness curve, calculated by Goodricke, had two minimums in the same period: the main minimum, or primary, in the zero phase ; and the secondary minimum in phase 0.5. To understand this curve, Goodricke deduced that Algol was actually a binary system where the components were hidden one after the other, with respect to the line of sight, in its orbital period of 2.9 days. Then the question arose as to why one minimum was more pronounced than the other.
Outside of the eclipse the stars are seen at the same time. So the brightness that is perceived is the sum of the brightness of both stars. When one star hides the other, the brightness decreases in proportion to that radiated by the area of the eclipsed star. To calculate the amount of energy radiated by the covered part of the star’s surface, the energy radiated by the unit of surface must be multiplied by the area of this surface. From this it can be deduced that the difference between the depth of the minima is due to the difference in the energy radiated per unit area of the stars. That is, in phase zero the eclipsed star is the brightest, and therefore the hottest.
Algol-type curves are very common among variable stars. In fact, these types of variables are called “Algol-type variables” since this star was the first of this kind studied. These curves are characterized by the presence of two minima separated by almost constant brightness intervals. And why almost constant? By the reflection effect. It would be logical to think that if the two stars are seen in their totality between the two eclips, and if the brightness of the system is the sum of the brightness of the stars, then the intervals should be constant. But in a brightness curve it is observed that after the primary minimum, the brightness of the system gradually increases as it approaches the 0.5 phase, and in the absence of the secondary eclipse, there would be a maximum here.
The increase in brightness is explained by the phenomenon of reflection. Taking into account that one star in Algol is hotter than the other, this causes the hottest star to illuminate one side of the colder star, and therefore, the side of the cold star facing the hotter increases in temperature. and consequently of brightness. A reflection of light does not actually occur, without a re-emission in which the colder star acts as if it were a mirror, reflecting the light from the hotter star.
The reflection effect depends on the phase. In phase zero, the cold star outshines the hot one, which means that the coldest part of the less bright star is seen. As the revolution passes, it orbits, that is, as the phase increases, an increasing part of the lit side of this star is seen. In this way, the overall brightness of the system slowly increases, with the cold star in phase 0.5 showing its hotter side. Subsequently, the brightness of the system decreases symmetrically until reaching phase 1. In the Algol system the reflection effect plays a very small role, but in other systems, the only variation in brightness that is seen is due to this phenomenon since the stars , from one point of view, they do not overshadow each other.
The brightness curve allows to find the period of the system and the relative radii of the stars. During a period the star travels a distance 2pia. Since the period is already known, it is possible to find out what part of the total length of the orbit the star travels during the eclipse.
Radial velocity curve
By photographing the spectrum of a star in different orbital phases, the speed of motion of binary stars can be determined. The dependence of velocity as a function of phase is called the radial velocity curve. As the star moves through the orbit, the projection of the star’s velocity varies periodically with respect to the visual beam. It should be noted that for the components of the binary system these changes occur in phase opposition. The spectra show how the lines of the stars in the system “shift” as the stars, in their orbits, move closer and farther.
Now we know the radial velocity and the period of the system. With these data, knowing the size of the semi-major axis, a, and with the help of Kepler’s third Law, the sum of the masses of the system can be found. Recalling that the quotient of the orbital velocities of the stars is equal to the inverse of the quotient of their masses, the relationship between the masses of the stars can be found.
By analyzing the curve of light and the radial velocity of a double system, it is possible to determine the dimensions of the orbit of the binary system, the masses and the dimensions of the stars. This is only possible if the lines of the two stars are seen in the spectrum, since often only those of the brighter star are perceived. The system also needs to be viewed from the side.
Algol paradox
In the 50s of the twentieth century astronomers they discovered that the Algol system contradicted the accepted theories of stellar evolution, what was called Algol Paradox. Soviet astronomers AG Masièvich and PP Parenago showed that the most massive star in this system is in the main sequence, and that the least massive one left it and became a subgiant star.
Theories say that binary stars are born at the same time. The more massive a star is, the faster it consumes its fuel, so massive stars evolve much faster than less massive ones. It was observed that the more massive Algol A is still in its main sequence, while the less massive Algol B is a sub-giant star that is in a later stage of its development, which contradicts the theories. How can this phenomenon be explained?.
The Algol Paradox is a very common phenomenon in double stars, so at first it was assumed that these stars had a different evolution from that of isolated systems. The paradox could only be resolved by assuming that the masses of the stars in a binary system were variable. This could have happened in the following way: that the least massive star in Algol was previously the most massive, so it left the main sequence earlier, later losing part of its mass for some reason until it became its partner in the most massive star . The American physicist J. Crawford proposed an evolutionary scenario to explain this phenomenon.
The lone star theory of evolution states that a star expands upon leaving the main sequence. A binary system made up of two main sequence stars. The mass of star 1 is greater than that of star 2. At the beginning of their lives, both stars evolve without the other star interfering in their evolution. Star 1 is the first to leave the main sequence so it begins to dilate, filling its Roche lobe. and initiating a mass transfer towards star 2. The amount of matter transferred was such that star 2 acquired more mass than star 1. In this way the stars exchanged their roles, star 2 becoming the most massive in the system, obtaining a system in which the most massive star remains in the main sequence, and the less massive one expands until it acquires the dimensions of a subgiant.
Binary systems that undergo a mass exchange during their evolution are called compact binary systems. The study of these objects is still far from complete, since in the 70s it led to the appearance of X-ray astronomy in which it was discovered that many of these binaries could evolve into exotic systems.
