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This text discusses the discovery of planets outside our solar system and the formation of black holes through the collapse of massive stars. It explores concepts such as neutron stars, event horizons, and gravitational red shift.
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It was discovered in the early 1990’s that the pulse period of a millisecond pulsar 500 parsecs from earth varies in a regular way.
It fluctuates on two time scales: 67 days and 98 days. This may be caused by the Doppler effect as the pulsar wobbles in space.
This wobble may be caused by the combined gravitational pull of two planets with 67 and 98 day orbital periods.
This is the first evidence for planets outside our solar system.
These planets were probably not formed the same way as Earth because the supernova would have destroyed them.
Neutron stars rest in an equilibrium: gravity vs. the pressure the squeezed neutrons.
There is a situation where the gravitational pull is too great for the neutrons to withstand the pressure.
Low mass stars (less than 1.4 solar masses) leave behind a white dwarf at the end of the star’s life.
High mass stars (between 1.4 and 3 solar masses) produce a neutron star.
Above a solar mass of 3, even the packed neutrons cannot hold up vs. gravity.
Once this pressure is exceeded, no force known can counteract gravity. The core collapses forever.
Gravity around the core is so great that light can’t escape. This object emits no light, no radiation; nothing escapes.
This is a black hole. The density and the gravitational field become infinite. It is called a singularity.
Two key facts from Einstein’s relativity theories help us understand black holes: • 1. Nothing can travel faster than light. • 2. All things, including light, are attracted by gravity.
Escape velocity is inversely proportional to a star’s radius. The smaller an object becomes, the higher escape velocity becomes.
Eventually escape velocity can exceed the speed of light. This would occur if the Earth was compressed to the size of a grape.
A similar compression occurs in a black hole, but with a much larger beginning mass.
The critical radius at which escape velocity equals c, is the Schwarzchild Radius.
The Schwarzchild radius is proportional to the mass. • For Earth’s mass it is 1 cm. • For Jupiter’s mass it is 3 m. • For the Sun’s mass it is 3 km. • For 3 solar masses it is 9 km.
The Schwarzchild radius is the radius to which an object would have to be compressed to become a black hole.
The surface of an imaginary sphere with radius equal to the Schwarzchild radius and centered on a collapsing star is called the event horizon.
The event horizon defines the region within which no event can be seen or known by anyone outside. It is the “surface” of a black hole, but no matter is associated with it.
A 1.4 solar mass neutron star has a radius of 10 km and a Schwarzchild radius of 4.2 km. Increasing a neutron star’s mass increases its Schwarzchild radius, but the physical radius is unchanged.
When a neutron star’s mass exceeds about 3 solar masses, it surface would lie just within its own event horizon and the star would collapse beyond the Schwarzchild radius to a point singularity.
So, if at least 3 solar masses remain after a supernova, the remnant core will collapse to a black hole in less than one second.
At 1.5 Schwarzchild radii from the center of the star, photons emitted perpendicularly travel in a spherical orbit forming a photon sphere.
Relativity states that matter “warps” (curves) space in its vicinity. The greater the mass, the greater the warping. Close to a black hole, the mass is so great that space “folds over” on itself causing objects within to disappear.
Tidal forces at a black hole are greater than any known forces. Any object would be stretched vertically and horizontally squeezed. This plus collisions among the debris produce tremendous frictional heating.
This frictional heating produces radiation in the form of x-rays before the matter reaches the event horizon.
Light emitted by an object motionless near the event horizon would be more and more redshifted the closer it moved to the event horizon.
This is gravitational red shift caused by the huge gravitational field and is a clear prediction of Einstein’s general theory of relativity.
Photons lose energy to escape a black holes gravity, so they go to a lower frequency and longer wavelength. Photons at the event horizon lose all their energy and go to an infinite wavelength.
