Stellar Death

High Mass Stars

 

Part I

 

The Main Sequence lifetime for the high mass stars is much faster.  Larger mass means higher gravity.  The strong gravity is capable of compressing the core to higher temperature and higher temperature accelerates the reaction.  A fifteen solar mass star will live less than one-thousandth the lifetime of the Sun.

 

The high mass star will finish helium fusion above the Chandresakhar limit, so that heavier nuclear fuels can be processed.  Likewise the high mass stars can reach higher and higher temperature without the core material becoming degenerate.  In the evolution of the fifteen solar mass star, notice that each heavier nuclear fuel requires higher temperature and goes by in a shorter period of time.  Heavy element processing continues as long as it is energetically feasible to do so.  Hydrogen fusion returns the biggest amount of surplus energy and drives the main lifetime of the star.  By the time that star is using iron in the core, the situation has become energetically unfavorable.  The reactions of iron require more energy than is released in the reaction.

 

A self-accelerating process takes place when iron is in the core:

 

…

Etc……

 

The core is now in uncontrollable gravitational collapse.  All the material can do is make room for the collapse.  Several steps are taken to save space:

 

 

The collapsing core is now so dense that the neutrinos cannot escape.  The neutrinos bounce off of the outer core (core bounce) and implode the core.  Meanwhile the momentum transfer of the core bounce causes the rest of the star to explode in a supernova.  The supernova produces the total energy production of the Sun throughout its entire lifetime in just a few short days.  During the first seconds active fusion reactions take place in the exploding star, producing all of the heavy elements of the universe through uranium.  The heavy element content of the universe is due solely to the supernovae.  During the first days of the event, a single supernova can outshine the entire galaxy is which it occurs.

 

There is abundant evidence for historical observations of supernovae.  The most famous is the event that occurred on or about July 4, 1054 in the constellation of Taurus.  It was visible in the daytime sky for 23 days and bright enough to read by at night.  At the site of the event is the Crab Nebula.  We shall examine the Crab in detail shortly since we know it is a supernova remnant.  There have been other supernovae in the Milky Way throughout history, but none since 1604.  A nearby galaxy called the Large Magellenic Cloud had a supernova event 1987 and much was learned about supernovae by its study.  Sites of known supernovae all seem to have rapidly expanding gas clouds, pushing shock waves in front of them, and shocking the interstellar medium to emit X-rays.

 

Part II

 

The core of our massive star was in a state of implosion.  Is there anything that can halt the collapse?  In the low mass stars the mutual repulsion of all the electrons caused a degenerate electron pressure (essentially the action of the electromagnetic force).  If the mass is less than the Chandresakhar limit, the electron degeneracy pressure can halt the collapse.  But the massive stars we are now considering are beyond the limit.  The core of this massive star is composed mostly of neutrons (see above) and there is another kind of degeneracy that can occur.  When the neutrons are compressed to the density of an atomic nucleus, the neutrons fill in all the energy state allowed to them, and a neutron degeneracy pressure results.  This pressure is essentially the action of the strong nuclear force.  If the mass of the core is greater than 1.4 solar masses, but less than 3 solar masses, the neutron degeneracy pressure can halt the collapse.  The object is called a neutron star.

 

We can predict that it will be small (radius about 10 km).  In order to conserve angular momentum, the neutron star must be very rapidly rotating (about 1000 rotations per second).  The magnetic flux must also be conserved in the collapse, leading to the prediction of a powerful magnetic field for the neutron star (one trillion gauss).

 

By 1967 radio astronomers discovered a new class of objects - extremely regular pulsations separated by a few seconds or less.  Some originally thought this must be an artificial signal.  We can argue against this hypothesis as follows:

 

 

The objects became known as Pulsars.  The Light Time Argument tells us that the period of variation of an object is limited by the size and the speed of light.  An object can be no larger than the distance light can travel in the shortest period of variation.  The shortest period for the pulsars is about 1/40 second, which is the turn on time.  So the object associated with the pulsar can be no larger than 1/40 light-second, much smaller than any normal star.  The only candidates for pulsars from this argument are white dwarfs and neutron stars.

 

To decide between these candidates, we must look at the pulse mechanism.  There are only three mechanisms:

 

 

Binary stars and stellar oscillations can be eliminated either due to a mismatch of the predicted and observed rates or the prediction of an effect that is not observed.  Rotation had to be the mechanism, but until 1969 astronomers could not determine whether white dwarfs or neutrons stars were responsible for the pulsars.

 

Part III

 

In 1969 a pulsar was discovered in the Crab Nebula.  The pulse period of this pulsar is 0.033 seconds.  This short period eliminated the white dwarf from consideration.  Pulsars are rotating neutron stars.  They emit their pulsars much like a lighthouse.  We receive a pulse from regions near the magnetic poles each time a pole comes into viewed.  We may see two pulses per rotation, if we can see both poles.  Theory was also supported by the fact that the Crab Pulsar was located in a known supernova remnant.  Supernovae should result in the production of neutron stars.

 

Pulsars are now known to occur in binary star systems.  If the two components of the system are close together, then the neutron star can distort and pull material off the surface of the normal stellar partner.  Centripetal forces will cause this material to form a thick accretion disk, which heats up as it approaches the neutron star.  Temperatures in the inner disk are high enough for X-ray emission in a bi-polar jet. 

 

Neutron stars should also be the source of synchrotron radiation, which is highly beamed light produced when charged particles are moving close to the speed of light in a magnetic field.  Synchrotron emission is observed from pulsars, which tells us that the predicted strong magnetic field must indeed exist.

 

The pulse period of all pulsars are increasing - the pulsars are slowing down.  The energy lost to the pulsar from the slowing of its rotational period is gained by the supernova remnant that may exist in the region. Occasionally, sudden period decreases have occurred, which seem to be redistributions of mass within the pulsar - "starquakes."  Thus pulsars are useful in probing nature at extreme conditions impossible to reproduce in the laboratory.

 

Main Sequence Mass        Final Core Mass       Supporting Force        Name of endpoint

 

< 10                                       < 1.4                      Electromagnetic              White Dwarf

 

10 - 40                                 1.4 - 3                     Strong Nuclear                Neutron Star

 

> 40                                       > 3                               None                            Black Hole

 

Part IV

 

If the star is so massive (greater than 40 solar masses on the Main Sequence) that it reaches the end of its lifetime with more than three solar masses, then no known force can halt the ultimate gravitational collapse.  The star collapses into a point and is called a Black Hole.

 

The understanding of black holes requires general relativity, a new theory of gravity due to Einstein.  Here the universe is viewed as four-dimensional, the three spatial dimensions and time.  A universe with no mass has no distortions in space-time.  Mass distorts space-time.  For example the space-time around the Sun is distorted by the presence of the Sun.  Planets are moving in the straightest possible paths given the distorted space-time in which they move.  The predicted orbital shapes are ellipses, just like in Newtonian physics.  New theories must be able to predict all of the known facts as well as make new predictions to be tested.  General relativity does each.

 

 

 

If we could view the vicinity of a collapsing star, as it becomes a black hole, we would notice that the gravity from the star is increasing as the collapse proceeds.  At first the gravity is weak and the light is bent very little.  As the collapse proceeds the bending becomes greater and greater until light is bent so much that it orbits the star.  The orbital radius is called the photon sphere.  An exit cone may be defined such that light projected inside the cone is bent, but escapes.  Light moving just along the edges of the cone orbits the star, and light projected outside the exit cone is bent so much that it falls back onto the star.  As the collapse continues gravity gets stronger and the exit cone narrows.  General relativity predicts that the exit cone disappears when the escape velocity becomes equal to the speed of light.  Nothing can move faster than the speed of light, so when the gravity has increased to make the escape velocity equal to the speed of light, nothing (not even light) can escape.  The surface of the collapsing object at this moment is called the event horizon and its radius is the Schwarzschild radius.  The object is truly black.  The collapse continues inside the event horizon, but observers on the outside can never see it.  The object collapses into a mathematical point called the singularity.  The Schwarzschild radius is three times the mass of the collapsed object measured in solar masses.  For example a three solar mass black hole has an event horizon of radius 9 km.

 

Near a black hole space-time is severely distorted and time itself is affected.  As measured by an outside observer, time stops on the event horizon.  Because the original object is no longer accessible from our universe, we cannot know very much about a black hole.  In fact, theoretically only three things are knowable about a black hole:

 

 

Black holes are frustrating to astronomers - they don't emit any light.  Perhaps the only way of finding a black hole is if one formed in a binary star system.  If the black hole and the normal star are close enough, material will be pulled off of the normal star and an accretion disk will form.  As the material in the disk moves closer to the event horizon of the black hole, it heats up.  Just before dipping within the event horizon and disappearing from the universe, the disk gas is hot enough (several million K) to emit X-rays.  We may be able to find black holes by looking for X-ray sources.  Objects emitting enough X- radiation to be observed at a distance are all compact objects - white dwarfs, neutron stars, or black holes.  We could distinguish between these choices if we knew the mass.  Fortunately, the binary star allows us to determine the mass.  So far several promising candidates have been found, Cygnus X-1 being the best known.