1. Black Hole & Schwarzschild Radius for the Remnant of a Supermassive Star. Con
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Question
1. Black Hole & Schwarzschild Radius for the Remnant of a Supermassive Star.
Consider an “extremely massive star” with a mass M = 100M (that is, 100 solar masses,near the upper limit of stability for stars).
Then, answer the following questions.(a) After leaving the main sequence, the star’s core would turn into a black hole.
Briey explain why.Note: The main sequence is the stellar equivalent of adulthood.
(b) While all the mass falls into a central point or singularity, the black hole is surroundedby a “sphere of darkness” or event horizon, with a Schwarzschild radius
RS (3 km) M
where M is measured in solar units (masses).(This is the same as saying that RS/(3 km) = M/Msun.)
Assuming that, before “death,” the core consisted of 20% of the progenitor star’s mass,calculate the radius of the event horizon in kilometers; how many miles is this?
(c) What would happen to you if you crossed the event horizon?
2. Supermassive Black Hole in the Milky Way.
(a) What is the mass of the supermassive black hole at the center of the Milky Way galaxy?
Hint. Mentioned in class or look it up.
(b) How far away is it from our solar system (in light-years)?Hint. Look it up.
(c) Is it “dangerous” at the moment?
(d) Determine the Schwarzschild radius of the supermassive black hole at the center of theMilky Way Galaxy (Note: assuming its mass known, as in your answer above). Howdoes it compare in size (radius) with the Sun?
Hint: You can use again RS (3 km) M, when M is measured in solar units (masses).
Explanation / Answer
a) the main sequence stars are the stars like our sun in which the core has the fuel hydrogen which converts into Helium by fusion after the core run out of the fuel it will starts to compress and it temperature starts to rise which in turn ignites the surrounding hydrogen and this will increase the radius of star turning it into a red giant star.stars greater than chandrasekhar limit i.e greater than 1.4 times mass of sun will tend too explode in a supernova whereas the smaller stars will shrink until they become a black hole in this case the star wheather turn into blackhole or supernova the star is huge size, it will not shed most of its mass in a supernova (not like smaller stars) due to the fact that its huge gravity will pull all its mass to its center at the ending of its life cycle.
b) "sphere of darkness" is formed because the mass forms into that condition of singularity in which it creates sufficient gravitational pull to warping the light, so it prevents the photon to escape & thus creates a "black hole."
c) Event horizon is the boundary of the black hole its an imaginary boundary there is nothing tangible there.nothing can escape from it everything falls towards its center which is called a singularity. whats beyond the event horizon, we knows that at the center of the black hole there will be singularity. at this point were all of the matter and energy falls Since it's infinitesimally small, you wouldn't be able to see it, even if light were able to escape.
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