BLACK HOLES
BLACK HOLES
Recall that when the core of a collapsing star has between 1.4 and ~3 solar masses (the whole star was between 8 and 20 solar masses) it will end as a neutron star.
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If the core is greater than ~3 solar masses (whole star greater than 20 solar masses) no force can stop the collapse.
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The core collapses to a mathematical point (no height, width, or depth) with infinite density; a black hole.
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What quantum mechanical principal is violated by this collapse?
Pauli Exclusion Principle
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The sphere around the black hole from which light �(or anything else) cannot escape is called the �event horizon.
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Since light cannot escape once inside this sphere the area looks like a black hole in space; hence the name.
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Black holes come in different sizes.
A black hole of 3-12 solar masses is called a stellar mass black hole and is formed from the collapse of a massive star as described thus far.
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Super Massive Black Holes are found and the center of galaxies and are though thought to be important in the formation and life of galaxies.
e.g. A 4.6x106 solar mass black hole is at the center of the Milky Way.
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How big are these black holes? The answer may surprise you!
Recall: What we call a “black hole” is the event horizon. Its radius is determined by the mass of the black hole. It can be calculated with this formula:
Radius of the event horizon (m)
Mass of the black hole (kg)
Speed of light squared (m/s)
Universal gravitation constant
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Radius of the event horizon (m)
Mass of the black hole (kg)
Speed of light squared (m/s)
Universal gravitation constant
Let’s try one: The first black Hole discovered is Cynus X-1 with a mass of about 15 solar masses. How big would it appear (how big is its event horizon)?
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Let’s try one: The first black Hole discovered is Cynus X-1 with a mass of about 15 solar masses. How big would it appear (how big is its event horizon)?
44.5 KM….about the distance from Reno to Carson City. Smaller than most asteroids!
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Let’s try another: The SMBH at the center of the Milky Way has a mass of about 4.6x106 solar masses. How big would it appear (how big is its event horizon)?
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Let’s try another: The SMBH at the center of the Milky Way has a mass of about 4.6x106 solar masses. How big would it appear (how big is its event horizon)?
1.35x1010 KM….about the distance from Venus to the Sun!�Big difference!
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Let’s try another just for kicks: The largest known SMBH at the center of galaxy NCG1277 has a mass of about 1.7x1010 solar masses. How big would it appear (how big is its event horizon)?
5x1013 KM….about the 10x the orbit of Neptune!�Truly a monster!
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Let’s try another just for kicks: The largest known SMBH at the center of galaxy NCG1277 has a mass of about 1.7x1010 solar masses. How big would it appear (how big is its event horizon)?
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The difference between a stellar mass black hole and a super massive black hole is NOT based primarily on size; the distinction is based on how the black hole formed.
However, black holes observed at the centers of galaxies tend to be thousands or millions of time larger than black holes that formed from a single star.
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A black hole may act like a lens; bending light from behind it into a new image. This effect has been seen to occur with several known black holes.
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Black holes are often strong X-ray sources and radio sources. If matter is falling into a black hole the disk of matter around it will be very hot and so give off radio waves. Some of this matter forms jets at the poles traveling at nearly light speed; these will give off X-ray light.
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This is similar to the SMBHs at the centers of galaxies.
When a stellar mass black hole is viewed edge-on it will appear as a radio source.
When viewed from its north or south pole it will appear as an x-ray source.
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Misconceptions:
The Sun will never be a black hole, it simply does not have enough mass.
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Misconceptions:
Black holes are not cosmic vacuum cleaners sucking up everything. Their gravity (anything’s gravity) diminishes the farther from it you get. A planet could orbit a black hole without falling in.��e.g. In “Interstellar” astronauts visited two planets in orbit around a black hole.
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Black holes are often detected because one or more objects orbit around them.
If one detects a strong radio or x-ray source and it appears that a companion star is orbiting ‘nothing’; this ‘nothing’ is a good candidate for a black hole.
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Tidal Force (aka tide): A differential force of gravity due to different distances.
e.g. High tide on Earth is roughly beneath the moon because the moon pulls the ocean to it.
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With their enormous gravity black holes create much greater tidal forces.
e.g. If you fell into a black hole feet first the gravity on your feet would be about 106 times greater than the gravity on your head.
You would be stretched into a long, thin string. This process is called spaghettification.
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Stars (or anything) orbiting very near a black hole would be warped and torn apart by this tidal force.
After it is ripped apart it forms what is known as an “accretion disk” around the black hole.
This accretion disk is the matter that gives rise to the radio and �x-ray emissions noted previously.
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Einstein calculated that gravity actually warps time the same as it does space.
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For example, we have actually measured the difference in the passage of time between the surface of the Earth and clocks on the ISS(Inter. Space Station) due to a difference in gravity. It’s small but real.
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Let’s calculate this time change for a real black hole: Cygnus X-1 with a Schwarzschild radius of 44.5 km (calculated earlier).�At 2x this distance what is the time dilation?
For every minute that passes on your watch you would see only 42 seconds pass for a clock 89 km from the BH’s center.
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Let’s calculate this time change together using the formula:
That’s the Schwartzschild radius rs�so we can simplify
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Let’s try again, but for a clock only 1km above the Schwarzschild radius�What is the time dilation?
For every minute that passes on your watch you would see only 8 seconds pass for a clock 1 km from the BH’s center.
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Think on this…
What would happen to the clock when it is exactly at the event horizon?
Time would stand still. t0 = 0
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It is important to note that this difference is not due to gravity’s effect on the clock; rather time itself is progressing at different rates.
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If someone watched you fall into a black hole they would see your time get slower and slower. It would stop when you got to the event horizon.
From your perspective time in the rest of the universe would speed up, reaching infinity when you are at the event horizon.
Weirdly, you would see the passage of all time at once.