Back in 1975, it was theorized by astrophyscists Kip Thorne (U.S.A.) and Anna N, Zytkow (Polish then British) that a super Giant Star like Betelgeuse could have a neutron star at the core rather than nuclear fusion like that of our local star, the Sun. These objects are also known as Thorne-Zytkow Objects after the authors. They are known as Hybrid Stars because they are a creation of two types of other stars.
A Neutron Star is one possible end of a star once it has run out of fuel to sustain itself. At the end of its life, a star will grow in size many times larger than it was once like as what has happened with Betelgeuse. The growth in side is due to the outward pressure overcoming the inward pressure caused by gravity. Eventually the star will explode and create a neutron star or a black hole.
A super giant star can be many hundreds or thousands the size of the Sun. The current holder of the largest star in the universe is UY Scuti which is about 1,708 times the size of the Sun. If at the centre of our solar system, it would stretch out to about the orbits of Jupiter or Saturn and Earth would not exist.
At the other end of the scale, a neutron star is the tiny, its can be about 10km in diameter. A neutron star could be no bigger than the size of Manhatten Island in New York. A teaspoon of a neutron star would weigh as much as a house because the neutrons are so tightly squashed together.
A giant star on the other hand being made of hydrogen and helium would be light. As a neutron star is a tough nut to crack, sorry for the clichè but it is and therefore could survive being inside a gas giant.
The first such object was discovered in 2014 and the star was HV 2112 which is located in the Small Magellanic Cloud, a satellite galaxy that is orbiting our own galaxy, the Milky Way. HV 2112's light spectrum contained evidence of rubidium, lithium, and molybdenum, all chemicals which a Thorne-Zytkow object would contain.
The only way you would be able to identify one is by looking at the light spectrum as you're never going to build a probe to enter a star to examine the centre or slice a star open.
The authors of the paper did notice that the star could actually not be a T.Z.O. but instead be a Super Asymptotic Giant Branch star (SAGB) which is something else. S.A.G.B. stars are stars with an Oxygen/Neon core supported by electron degeneracy and undergoing thermal pulses with third dredge up. Both T.Z.O.s and S.A.G.B. stars are pretty rare so either way, what they have found is pretty special. Their paper can be read at Research Gate
A paper discounted the star as being a T.Z.O., instead it referred to the star as being a foreground Galactic S Type Stars. An S-Type star is a star that has roughly the same amount of Oxygen and Carbon in their spectrum.
A T.Z.O. could be created is when a neutron star orbiting a main sequence star accretes hydrogen from the main star and cause the neutron to be engulfed in the hydrogen that has been sucked from the main star. The neutron star could then be classes as a Symbiotic Star or to use the more exotic name or more familiar term, Vampire Star. (Taam et al, 1978). A T.Z.O. accreting sufficient mass could turn into a black hole first before turning into a stable T.Z.O. (Fryer et al 1996)
Another way in which the T.Z.O. could be created is by being fired into the heart of a large giant star. The cause of the the star being fired into the other star is the result of a supernova explosion that pushes the neutron star. (Leonard et al, 1994)
A third way is when the main sequence star simply grows and encompasses the neutron star, nothing as dramatic as being a vampire or a being fired into the other star.
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