05.08 – Innermost Stable Circular Orbit

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From the course by University of Alberta

Astro 101: Black Holes

4 оценки

University of Alberta

Astro 101: Black Holes

4 оценки

What is a black hole? Do they really exist? How do they form? How are they related to stars? What would happen if you fell into one? How do you see a black hole if they emit no light? What’s the difference between a black hole and a really dark star? Could a particle accelerator create a black hole? Can a black hole also be a worm hole or a time machine? In Astro 101: Black Holes, you will explore the concepts behind black holes. Using the theme of black holes, you will learn the basic ideas of astronomy, relativity, and quantum physics. After completing this course, you will be able to: • Describe the essential properties of black holes. • Explain recent black hole research using plain language and appropriate analogies. • Compare black holes in popular culture to modern physics to distinguish science fact from science fiction. • Describe the application of fundamental physical concepts including gravity, special and general relativity, and quantum mechanics to reported scientific observations. • Recognize different types of stars and distinguish which stars can potentially become black holes. • Differentiate types of black holes and classify each type as observed or theoretical. • Characterize formation theories associated with each type of black hole. • Identify different ways of detecting black holes, and appropriate technologies associated with each detection method. • Summarize the puzzles facing black hole researchers in modern science.

From the lesson

Approaching a Black Hole

What would you see as you approached a black hole, using a black hole binary as a vehicle to explore black holes? In this module students will follow material as it is transferred from a companion star to a black hole via Roche lobe overflow or wind fed accretion. They will then follow that material down through the accretion disc to explore tidal forces to learn about the ways in which black holes can rip apart surrounding material. This material will then pass through the innermost stable orbit of the disc, before falling in. Students will also get the opportunity to look at jets - the outflow of material from the innermost regions of this structure. Module Objective: Introduce properties of black holes from the outside in, through the context of a journey into the event horizon of a black hole. What would we see as we are far away? What will we see and experience as we get closer? What is a disc? What is a jet?

05.01 – Journey to a Black Hole2:54

05.02 – Jets6:44

05.03 – Black Hole Companions1:09

05.04 – Mass Transfer in Binaries8:20

05.05 – Have a Corona!2:31

05.06 – So What is Accretion?8:32

05.07 – Spinning Through the Disc10:08

05.08 – Innermost Stable Circular Orbit4:44

05.09 – Teetering on the Edge1:05

Meet the Instructors

Sharon Morsink
Associate Professor
Department of Physics, University of Alberta

After a thorough investigation

of the accretion disk around the black hole,

we'll end this module teetering at the edge of stability.

Note, we're not discussing the black holes event horizon just yet.

But we can stay indefinitely in a stable orbit around a black hole as

long as we don't cross a boundary called the Innermost Stable Circular Orbit.

If Cygnus X-1 were not rotating,

it would permit stable orbits about three times the distance from its event horizon.

We'll learn in module six what happens when a black hole

rotates but this would allow stable orbits as

close as 130 kilometers from the center of

Cygnus X-1 or 90 kilometers from its event horizon.

The Innermost Stable Circular Orbit is

the boundary that distinguishes between stable orbits,

which don't require energy for an object to stay in orbit there and unstable orbits,

which will pull you in towards the black hole's event horizon.

Unless you have very powerful engines,

like the Enterprise and Star Trek.

The Innermost Stable Circular Orbit,

which we will henceforth just call the ISCO or ISCO defines the inner edge of

the accretion disk beyond which material will

fall freely and become captured by the black hole.

Somewhere between the accretion disk and the event horizon,

Newtonian gravity stops being a good approximation and

the gravitational field becomes much stronger than Newtonian gravity predicts.

This increased strength of the gravitational field is due

to corrections by Einstein's theory of general relativity.

The result is that the gravitational pull becomes much stronger within the region

bounded by the ISCO and stable orbits

predicted by Newtonian gravity are no longer stable.

Since the gravitational potential around a black hole

is represented by a Schwarzschild potential,

there are five kinds of orbits that we can find.

There are Stable and Unstable Circular Orbits,

orbits that we call Bound Processing Orbits,

Scattering Orbits, and Plunging Orbits.

For a Schwarzschild black hole,

the solution to the equations of

general relativity tells us that the peak of the potential

occurs at a radius equal to six GM divided by C squared,

which should be looking pretty familiar right now.

Recall that we've already encountered the radius of

a Schwarzschild black hole when we were experimenting with the Escape Velocity formula.

The Schwarzschild radius, which describes the event horizon of a black hole occurs

at a radius of two GM over C squared, quite the coincidence.

The only difference between the Innermost Stable Circular Orbit

and the event horizon is a multiple of three.

Actually, this makes life quite a bit easier for us since we can simply state

the Innermost Stable Circular Orbit of

a non-rotating black hole is three times further from the black holes event horizon.

The key here is that it's not rotating.

We haven't discussed much about rotating black holes

yet and we'll get more into it in module six,

but I just can't help myself here because the ISCO will

actually change when we're considering a rotating black hole.

This is apparent in the movie Interstellar,

when the crew of the endurance visit Miller's

planet very close to Gargantua's Event Horizon.

Gargantua is an oldest spinning black hole.

It's what we call a gentle singularity.

Gentle?

They're hardly gentle. The title gravity is so quick that something

crossing the horizon fast might survive. Approte.

What happens after you cross it?

After the horizon is a complete mystery.

They were able to do it safely because a rotating black hole can

actually have an ISCO that's much closer to the event horizon.

In an extreme case,

a rotating black hole could have an ISCO coincident with the event horizon.

But we'll see more about that in an upcoming lesson.

Now one final note about the Innermost Stable Circular Orbit,

we've only covered matter interacting with the gravitational field of the black hole.

If instead we looked at light,

we would have found a different result.

The ISCO for light orbiting a non-rotating black hole

can be a factor of two closer to the event horizon.

Photons can get trapped in circular orbits at

the light ISCO radius and orbit many times before escaping.

We can then detect these photons which would look like they're

coming from a sphere of light surrounding the black hole,

which scientists sometimes call, the Photon Sphere.

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