Red Giants & White Dwarfs - Sirius A & Sirius B - The Binary Star System
Image credit: Wikimedia Commons , Image source
Red Giants & Dark Companions
Planets and stars differ in a few ways- Planets are cold and lustreless
- Planets are not as enormous as stars in size
- Stars are hot and emit visible radiation.
However, because a star preserves its structure at the expense of something inside that is always changing, stars are in a state of dynamic equilibrium. Although the gravitational pull inward is virtually unchanging, nuclear reactions that consume hydrogen and make helium are what drive the temperature to push outward at the Sun's center, counteracting that pull. Only at the cost of continuously turning 600,000,000,000 kilograms of hydrogen into 595,800,000,000 kilos of helium every second , the Sun continues to be in its current state.
Thankfully, even at this rate of conversion, there is so much hydrogen in the Sun that we don't need to worry about something catastrophic occurring very soon. Even after the Sun's nuclear furnace has been burning hydrogen for around 5 billion years, there is still enough left over for at least another 5 to 8 billion years.
Even five to eight billion years, however, is not an eternity. When the hydrogen runs out, what happens?
As far as astronomers can tell from their research on nuclear processes and the characteristics of the different stars they can observe, the depletion of hydrogen appears to be the precursor to significant structural changes in stars.
For example, when the Sun's core collects helium at the center and consumes up all the hydrogen, the core will continue to contract as heavier nuclei further concentrate at the inner part of the gravitational field. The core is going to get hotter and heavy enough. The Sun's core will eventually start to heat up quite a lot, and the extra heat will cause the outer segments to expand dramatically. Even while the Sun's outer segments will have a far higher overall temperature than they do now, it will be dispersed over a much bigger surface area. In comparison to the current surface, the new surface will be cooler and each piece of surface will be having lesser heat. The surface temperature of the expanded Sun will be no higher than 2,500° Celsius, where the Sun's surface temperature is currently 6,000°. It will shine only in red color at that lower temperature. "Red giant" is the name given to this stage of a star's life cycle because of its enormous size and crimson brilliance. Betelgeuse and Antares are two stars that have currently attained this stage.
The red giant that our Sun will eventually transform into will be big enough to swallow up Mercury's or possibly Venus's orbit. At that point, life on Earth would have been impossible due to the early phases of the Sun's expansion, making the planet completely inhospitable. (Perhaps humanity, if it still exists, will have departed from the Earth by then and relocated to artificial territories constructed far out in space or to worlds orbiting other stars.)
The Sun will have become diminished to the last remnants of its hydrogen by the time it attains its maximum expansion as a red giant. However, the Sun's core will have warmed up to a temperature of at least 10,00,000000°C by that point, which will cause the helium atoms that had been created from hydrogen atoms over the previous ages to merge into even larger nuclei, and those into still larger nuclei, until iron nuclei—each consisting of 26 protons and 30 neutrons—are formed.
About 6% of the initial energy accessible from the fusion of hydrogen to helium is now available by the additional transformation of nuclei. Also, things stop moving forward after iron is made. The energy from nuclear reactions has run out.
Therefore, the red giant's left-over life as a nuclear-powered object must be fewer than a billion years, if not less, after the hydrogen is depleted and it has reached its maximum development.
Furthermore, nothing will be able to withstand the unstoppable inward pull of the gravitational field when the nuclear processes fade and die. For billions of years, gravity has been pulling steadily and relentlessly , and now ultimately, resistance to that pull has finally broken down, the blown-up Sun—or any red giant—can not do anything other than shrinking to a smaller size.
It does diminish, and that is what gets us right onto the high road to the black hole, with two places to halt along the way (stopping points).
Friedrich Wilhelm Bessel, a German astronomer who lived from 1784 to 1846 discovered the first stopping point . His attempt to determine the distance between stars was the first to be successful.
Stars appear to have very little motion because they are so distant from us. But they do have appreciable motion. (Consider how much slower an aircraft appears to be moving against the sky when it is very aloft in the air as opposed to when it is very low.)
Along with the proper motion, stars should appear to locomote as an outcome to the shift in angle from which they are observed from the Earth as it revolves in its elliptical orbit around the Sun. As the Earth revolves around the Sun in this manner , a star should imprint a very diminutive ellipse in the sky as a result of this motion by the Earth (as long as you ingnore the proper motion and other interfering factors). The ellipse gets tinier as the star gets farther away, and the distance of the star can be estimated if the size of the ellipse (known as parallax) can be ascertained at the telescope using highly exquisite work.
Bessel proclaimed in 1838 that he carried the task through for an extremely faint star called 61 Cygni which is located almost 150 trillion kilometers from the Earth. Even light can not traverse such a vast distance quickly , traveling at 3 lakh kilometers per second. Light originatin at 61 Cygni will reach us after 11 years. So 61 Cygni is decidedly 11 light-years away from the Earth.
After that, Bessel continued his attempts to find out the distance to other stars. He took upon Sirius which looked more proximate than 61 Cygni for various reasons. Evidently, Sirius is the most luminous star in the sky which may be on account of being near to the Earth.
Bessel cautiously examined the location of the Sirius night after night and marked out the way in which it very slowly locomotes relatively to the other stars over several days. He supposed the movement of the Sirius to shift in a particular way the would lead to the formation of an ellipse as a result of the revolution of the Earth around the Sun. The ellipse had formed but he noticed a fluctuation on it that had nothing to do with the movement of the Earth around the Sun.
After observing the enigmatic motion of the Sirius thoroughly and painstakingly, He came to know that it orbits in an ellipse of its own and finishes each revolution around that ellipse in around 50 years.
It is only a gravitational field that can cause a star to locomote in an ellipse like that. There was nothing known in his time that could cause it. Additionally, a gravitational field that is big enough and forceful enough to cause a star to move in an ellipse can be generated only by a start that is large enough to contain the corrresponding mass
Bessel did not find anything at in the vicinity of the Sirius that could act as a gravitational source but he suspected that something should be there. He concluded that there really was a mass that could account for a star that was creating the gravitational field. But this star was not shining but was dark. It was a huge planet that was nearly of the size of a star. So physicists named it as the "dark companion" of the Sirius.
Bessle continued his research and found out that another star named Procyon had a similar disorderly motion. So he thought this star also must have had a dark companion. It looked like the dark companions are present all over. but they are not susceptible to be detected because we can not see them directly.
A dark companion was not enigmatic at all to Bessel and his generation of physicists. It was a star that ceased emitting light for some reason. it had exhausted all its energy reserve (Bessel was not aware of nuclear reactions at that time) and was wandering around. But it remained as big as ever and exerted a gravitational field that was as strong as ever in its life time. But it was dark and cold.
The "dark companion" that Bessel discovered was nothing but the "red giant".
Super Density Of Sirius B
The puzzle about the dark companions was resolved in 1862 when Alvan Graham Clark (1832-1897) prepared a telescope for the University of Mississippi. When he finished preparing the lens, he wanted to give it a try by looking through it at the sky. He pointed in the direction of the star Sirius while trying his telescope and noticed a small spark of light in its neighbourhood which was not shown or identified in any of the star maps at that time.At first, Clark thought that the tiny bit of light was because of some fault in the lens or else that part of the light emitted by Sirius was deflected. But upon additional testings of the lens, he found that there was no fault in the lens. The position of the spark was exactly where the dark companion of the Sirius was expected to be around that time.
So it was concluded that what Clark was beholding was a dark companion. it was very faint emitting only a small amount of light and appearing only 1/10,000 as luminous as the Sirius. But it was not entirely dark. The dark companion of the Sirius is now named "Sirius B" while Sirius itself is referred to as "Sirius A". Physicists refer to the Sirius now as a "binary" or double star system.
The binary star system of Sirius A and its diminutive blue companion, Sirius B
Image credit: NASA , Image source
Image credit: NASA , Image source
The German American astronomer John Martin Schaeberle (1853-1924) discovered a flash of light near to the Procyon. Its dark companion was also a dim one. It is referred to as "Procyon B" now.
These findings did not change much for the astronomers. They are not "totally dead stars", but they are about to die and so they are shining forth. But when Schaeberle saw the dim companion of the Procyon , things were changing in the field of astronomy and physics.
The German physicist Wilhelm Wien (1864-1928) proved in 1893 that the characteristics of light emitted by any warm object (whether it is a star or a large outdoor fire) changes with temparature. It is possible to examine the wavelengths of the light given off and the characteristics of the dark lines in the spectrum and determine correctly the temperature of the object giving off light.
According Wien's law, any star that is glinting out and diminishing in temperature (thus cooling down) on its way to become dark must be red in color. But Sirius B and Procyon B appear white -dim.
Examination of the companion stars just by eye was not enough. A spectrum was required to be formed so as to study the wavelengths and dark lines. it was not so easy as the companions are so close to the bright stars (which can muffle them out) and are so dim.
However the American astronomer Walter Sydney Adams (1876-1956) succeeded in 1915 in letting the light of Sirius B go through a spectroscope forming a spectrum that could be analyzed. Once its spectrum was analyzed, He came to know undoubtedly that Sirius B is not glinting out. It is hot , nearly as hot as Sirius A and exceedingly hotter than our Sun.
Sirius A has a temperature of 10,000°C on the surface where as Sirius B has 8,000°C. The surface temperature of the Sun is just 6,000°C.
It was calculated that the Sirius A should emit 35 times as much light as the Sun does and it should be almost 1.8 times as wide as the Sun or should have a diameter of 2,500,000 kilometers.
However Sirius B was a puzzle to solve. Considering its surface temperature of 8,000°C, it must be emitting almost as much light as does the Sirius A. To give a reason for why it is so dim, we have to come to an agreement that Sirius B has a less surface area (quite a smaller surface area). Taking its temperature into view, its surface must be only 1/2,800 of that of Sirius A.
If Sirius B has only that much of surface area, its diameter must be only 1/53 of that of Sirius A or 47,000 kilometers. If this is correct, then the size of the Sirius B is similar to that of a planet because its estimated size is more or less equal to the size of Neptune or Uranus. Its diameter is only 1/3 of that of Jupiter and its volume only 1/30 of that of Jupiter. In fact , it is measured to have a diameter of only 3.7 times that of the Earth.
The discovery made by Adams implied that Sirius B was a totally different class of star which has white-hot temperature and also absolutely shorter size than usual stars like our Sun. So Sirius B is considered to be a "white dwarf" and it became evident later that Procyon B is also a white dwarf.
If Sirius B were to have not only planetary size but also a planetary mass, then it was not possible for it to shine away so hotly. There would absolutely be no required amount of pressure at their cores to inflame the nuclear reactions for objects containing the size and mass of Neptune or Uranus.
Undoubtedly, Sirius B is having only a planetary mass, with its size left aside. It could not impel a huge star like Sirius A to veer away from its straight-line path if it were not having a mass similar to that of a star. At least not such a noticeable veer away.
We know the distance of Sirius A and B from the Earth and their evident separation in the sky. With this data, we can compute how far apart they are. It was found out that Sirius A and Sirius B are separated by a distance of roughly 3,000,000,000 kilometers. So their separation distance is only scarcely larger than that of the planet Uranus from the Sun. However in contrast to the planet Uranus taking 84 years to complete a revolution around the Sun, It takes only 50 years for Sirius B to complete a turn around the Sirius A.
From this, Sirius A and Sirius B are estimated to have the intensity of their gravitational fields 3.4 times those of the Sun and Uranus respectively. This implies that Sirius A and Sirius B put together are almost 3.4 times as massive as the Sun and Uranus put together.
In reality, Sirius B does not revolve around the Sirius A. These two stars revolve around the center of gravity of their combined system. They can be compared to the two ends of a dumbbell spinning rapidly around some point which is the center of gravity along the woody rod that join them together. If the two ends are having exactly equal mass, then the center of gravity will be exactly in the middle between them. If one of them were heavier than the other, the center of gravity will be closer to the heavier one and proportionately to the degree by which it is heavier.
If we consider the combined system of the Sun and any of its planets, the Sun is much more bigger than the planets that the center of gravity is always close enough to the center of the Sun, so it is fair to say that the planet is revolving around the Sun. The same is true in the case of the Moon orbiting around the Earth as the Earth is 81.3 times more heavier than the Moon. So the center of gravity of the combined system of the Earth and the Moon is 81.3 times as near to the Earth as to the Moon.
In case of the Sirius A and Sirius B, the mass is distributed more or less equally. So the center of gravity is lies almost in the midway between them. Both stars revolve around that center and change their positions appreciably as they orbit around. If this were not the case, Bessel would not have observed the definite variability in the path of the Sirius across the sky.
Keeping in view the position of the center of gravity for the two stars, it is calculated that Sirius A should have 2.5 times more mass than Sirius B. As the mass of the two stars combined together is 3.4 times that of the Sun, we can conclude that Sirius A has 2.4 times the mass of our Sun and Sirius B which looks like a small flicker (almost unnoticeable) in the sky, has a mass that is trivially less than that of our Sun.
It is not surprising to know that Sirius A should have 2.4 times the mass of our Sun. In reality, it looks brither, hotter and larger than the Sun. But Sirius B however is evidently unusual. Where as its size is equal to that of Neptune or Uranus, its mass is almost equal to that of the Sun
It means that Sirius B should be very compact undoubtedly. Its average density should be in the range of 35,000 g/m3 which is 3,000 times as dense as the material at the core of the Earth and 350 times as dense as the material at the core of the Sun.