Physical Universe Chapter 18

Neutron star (4)

• ball of neutrons left over after a massive star supernova

• electron degeneracy pressure goes away as electrons combine with protons to form neutrons and neutrinos

• the newly formed neutrons collapse to the center, forming a neutron star

• neutron degeneracy pressure now supports the star from collapsing under gravity

Neutron star size (1)

roughly the size of small city

Discovery of Neutron stars (2)

• in 1967, Jocelyn Bell noticed regular radio emission pulses coming from a point in space

• they were emitted from a spinning neutron star, aka a pulsar

Pulsars (3)

• a neutron star that beams radiation along its magnetic axis

• this axis is not aligned with its axis of rotation

• these beams sweep through space as the star rotates

x-ray bursts (1)

• the sudden onset of fusion from the heated accreted matter on a neutron star produces these

Pulsars spin fast because (2):

• conservation of angular momentum

• the speed of the core’s rotation increases as the star collapses into a neutron star

Accretion Disks and Neutron stars (3)

• matter falling towards a neutron star forms an accretion disk

• this matter adds angular momentum, increasing rotation speed

• this is much like a white dwarf binary system

Spacetime (3)

• as per Special Relativity, space and time are not absolute

• rather, they are linked in a 4-D combination coined ‘Spacetime’

• gravity comes from the distortion of spacetime

Key Ideas of General Relativity (5)

• Gravity arises from distortions of spacetime.

• Time runs slowly in gravitational fields.

• Black holes can exist in spacetime.

• The universe may have no boundaries and no center but may still have finite volume.

• Rapid changes in the motion of large masses cause gravitational waves.

The Equivalence Principle (2)

• Einstein preserved the idea that all motion is relative

• he pointed out that the effects of acceleration are exactly equivalent to those of gravity

Dimensions of Spacetime (3)

• We can move through three dimensions in space (x, y, z).

• Our motion through time is in one direction (t).

• Spacetime, the combination of space and time, has four dimensions (x, y, x, t).

Rules of Geometry in Flat Space (4)

• A straight line is shortest distance
between two points.

• Parallel lines stay the same distance apart.

• Angles of a triangle add up to 180°.

• Circumference of a circle is 2πr.

Geometry on a Curved Surface (1)

• the great circle connecting two points is the shortest distance between them

Gravity: Newton vs. Einstein (2)

• Newton viewed gravity as a mysterious
  “action at a distance.”

• Einstein removed the mystery by showing that what we perceive as gravity arises from curvature of spacetime.

Curvature Near Sun

• Sun’s mass curves spacetime near its surface.

• If we could shrink the Sun without changing its mass, curvature of spacetime would become greater
  near its surface, as would strength of gravity.

Curvature Near Black Hole (3)

• if the sun continued to shrink, the curvature of spacetime would become so great that it would form a “bottomless pit,” aka a black hole

• the curvature of spacetime near a black hole is so great that nothing can escape its gravity

• Event Horizon: “point of no return,” a three dimensional surface

Time in an Gravitational Field (2)

• effects of gravity = effects of acceleration

• time moves faster at higher altitudes in a gravitational field

Black Hole (1)

an object whose gravity is so powerful that not even light can escape it

“Surface” of a Black Hole (2)

• spherical surface called the Event Horizon, the radius where the escape velocity equals the speed of light

• this radius is called the “Schwarzschild Radius”

“No escape from a black hole” (3)

• Nothing can escape from within the event horizon because nothing can go faster than light

• no escape refers to completely losing contact with something that falls in, the object loses its identity

• this increases the holes mass and can change its spin/charge

Singularity (2)

• beyond the neutron star limit (TOV), no force can resist the crush of gravity

• gravity crushed all matter into a single point called this

Neutron Star Limit (3)

• stated by quantum mechanics: neutrons cannot occupy the same state at the same time

• if the mass of a neutron star exceeds roughly 3M Sun, neutron degeneracy pressure can no longer support the star from collapse

• some massive star supernova can create a black hole if enough mass falls into the core

Black Hole Verification (3)

• Mass is measured by using orbital properties and measuring the velocity and distance of orbiting gas

• if the mass exceeds the neutron star limit, and its not a star, its a black hole

• some x-ray binaries contain objects of mass exceeding 3MSun, meaning they are likely to be black holes