For example, red dwarf stars spend several hundred billion years as a main sequence star, whereas the
much more massive stars at the top of the main sequence spend only a few million years as a main sequence
star.  Stars with a masses similar to that of the Sun have a main sequence lifetime of about 10 billion years.

Gravity is always trying to contract the star while  gas pressure is trying to  expand the star.   If gravity is
greater than the gas pressure, a star  contracts and heats up.  If gravity is weaker than gas pressure, a star
expands and cools.  If gravity and gas pressure are equal at every point in a star, the star is said to be in
hydrostatic equilibrium, it neither expands or contracts.

    The mass of a star determines how strong gravity is. The greater the mass of a star the stronger gravity
is and the greater the compression of a star.  The greater the compression of the star, the higher its
temperature. The temperature of a star determines how strong the gas pressure is and the rate at which any
thermonuclear reactions take place. The faster the TNF reactions take place, the faster a star evolves.

    The exact sequence of evolutionary stages also depends on the mass of a star. Stars similar in mass to
that of the Sun follow the following sequence of stages:

T Tauri star, M-S (main sequence stage), RG (red giant), Horizontal Branch, He TNF, Planetary Nebula
Stage, and WD (white dwarf).

    For a star that is 10 times more massive than the Sun, the sequence is:

     T Tauri star, M-S, RS (red supergiant), various other TNF reactions, supernova, and then either WD,
neutron star, or black hole, depending on the remaining mass of the star after the supernovae even.

^{B. Stages of Stellar Evolution:}

1. Nebular Stage:
    Stars form from gas and dust clouds in the interstellar medium of a galaxy called nebulae.  This happens when
random motions within the cloud leads to the formation of knots in the cloud. The knots are regions of higher
density and gravity begins to dominates over gas pressure.  Gas pressure is small because the temperature in a
nebula is very low. The cloud then slowly begins to contract and heat up. Any random motions within the cloud
become organized and the protostellar cloud  begins to rotate.

   Dark globule/ Bok Globule: The stellar nebula gravitationally contracts, gets denser and becomes
opaque.  These objects are seen in silhouette against a background of fluorescing gas
(mostly hydrogen).  See Fig. 61.2 in S&A.

2. Protostar :
    The contracting cloud is  converting  gravitational potential energy into heat or thermal energy, some of
which is converted into EM radiation.

Protostars are living on their gravitational potential energy

The cloud  remains opaque until the temperature in the central region  become sufficiently high that the  radiation
from this core  ionizes the gases and vaporizes the dust particles that are located in an envelope surrounding the
central region.  Light from the core then penetrates the cloud or envelope and  is able to reach an observer.
Hence, the central region or core begins to shine as a star. However,  it does so erratically, but the core of our
cloud  is now a protostar.

    Stars identified in the later stages of the protostar stage are called T Tauri stars. Such stars are said to be in a
state of quasi hydrostatic equilibrium, because they contract very slowly now.  However, they can not stop
contracting completely because they  lose heat by radiation faster than they can generate heat by contraction.

3. Main Sequence:
     A star enters this stage when it initiates TNF of hydrogen nuclei into helium nuclei in its core.  This happens
when the core of the contracting protostar reaches about 5 million Kelvins.  This is because at this temperature,
the collisions between protons are so intense that  the particles are able to overcome the repulsive force of the
positive charges and get sufficiently close for the strong or nuclear force to become effective.   The first step in a
series of steps that ultimately produces a helium nucleus, is when 2 protons merge and form a deuterium nucleus.
During this reaction, one of the protons converts to a neutron by emitting a positron.  A deuterium nuclide then
consists of one proton and one neutron.  See page 416 in the textbook for furter detaiils of the
steps for hydrogen fusion in what is called the pp-chain. The thermonulear fusion of H into He
reactions release a tremendous amount of energy that percolates its way up through the star, heating it, and
increasing the gas pressure to the point that it balances gravity.  Stars that are beginning the main sequence
stage define what is called the Zero Age Main Sequence or ZAMS, which is a unique curve or locus in the H-R
diagram . Main  sequence stars are characterized by:

      a. TNF of H into He in the core of the star.
      b. Hydrostatic equilibrium: At every point in the star, gravity is balanced by gas pressure. This happens
           because the star does not radiate away its heat at the surface faster than it generates it by TNF.

     Some main sequence lifetimes for different stellar masses (Ms means solar masses):

            25.0 Ms:   4 million years
            15.0 Ms : 10-15  million years
             5.0  Ms : 65 million years
             3.0  Ms:  800 million years
             2.25 Ms : 480 million years
             1.5   Ms:  4.5 billionn years
             1.00 Ms : 7-10 billion years
              0.5  Ms:   25 billion years
             0.10 Ms : 100 billion years

    Objects with a mass less than 0.06 solar mass units (the Kumar Limit) never initiate TNF,  and never
become true stars.  These objects are called Brown Dwarfs. Since brown dwarfs are intrinsically faint objects,
it is difficult to detect them.   However, several nearby ones have been detected recently, so their existence
has been verified.  Brown dwarfs, like stars, are comprised mostly of hydrogen and helium, whereas
terrestrial-like planets are comprised  mostly of metals and silicates (rocks).    Jupiter, Saturn, Uranus, and
Neptune are comprised mostly of hydrogen and helium, like stars, but they are planets.  To be a brown dwarf,
an object must be at least 17 times more massive than Jupiter but be below the Kumar Limt.
    It may be that brown dwarfs could be found to orbit a true star.   If this is so, a new class of satellites
orbiting stars, like the TNOs and comets, would have to be recognized.
 

4. Red Giant or Supergiant stage:
   This depends on the mass of the star. Upon exhaustion of H in the core, the star begins to contract and get
hotter.   TNF of H into He then begins in a shell around the core. Meanwhile, the He core continues to contract
and get hotter. The energy released from the H fusion shell  and the much hotter core heats the outer layers of
the star thereby causing these layers to greatly expand. The star then becomes a red giant or supergiant.

5. Core He fusion stage.

    At 100 million Kelvins, He nuclei in the core collide and fuse to form C, then O,  and then Ne. The ignition of
He-fusion happens almost explosively (helium flash), and the star  undergoes a rapid change to enter a stage of
hydrostatic equilibrium again as it undergoes helium fusion in the core.  The star is then said to be a horizontal
branch star, because stars of different mass in this stage of evolution define a locus in the H-R diagram that is
is horizontal.

6. Other stages of TNF:

    When all the He is exhausted in the core, the star begins to contract again until He fusion  occurs in a shell
around the core, while hydrogen fusion occurs in a layer above that. The star then expands to  become even
larger and enters the asymptotic giant branch stage.

However,  a star may stop contracting before it can reach the ignition temperature of these other fusion
reactions. How does this come about?  The temperature in a stellar cores is so  large that the gas is highly
ionized.  The free electrons now act as another gas in the star, separate from that of the nuclei,  and exerts
a separate pressure called

This pressure results from the mutual repulsive forces between electrons and other quantum theory aspects of
the energy states that the electrons occupy when crowded close together.  So, as the core contracts and
heats up, the electron pressure  increases.  Depending on the mass of the star, there will be a temperature at
which electron pressure may eventually balance gravity and the star halts its contraction.

At  600 million K, C fuses into Mg. At higher temperatures, Mg undergoes TNF to form Si and then Si fuses
to  become Fe.  This last reaction happens only for very massive stars.
 

The following figure shows the post main sequence evolutionary tracks for stars with several different masses.

7.  Planetary Nebula Stage:

    For the Sun, this happens before the carbon in the core reaches its fusion ignition temperature.  However,
the Sun is much hotter and smaller now.  The hot core now emits very intense radiation that causes the Sun
to loose gravitational  control of its outer envelope.  The envelope now begins to undergo  pulsations that
grow larger and larger.  Eventually, the outer hydrogen envelope of the Sun drifts away into space.  The Sun
then enters what is called the  planetary nebula stage.  This name arose from the fact that these expanding
shells appeared like fuzzy  planets to early telescopic observers, but they are not planetary phenomena.   More
massive stars will reach the  ignition temperatures of other nuclear reactions before electron pressure  can
stop further  contraction.

The diagram below summarizes the evolution of a star like the Sun in a temperatur luminosity diagram, from the
main sequence to the white dwarf stage.  Not shown are the pre main sequence stages such as the T Tauri
stage and other protostar stages.

8.  The Supernova Event:

    Very massive stars that convert Si into Fe run into a problem.  Fe will not undergo TNF.   Instead, as the
iron core slowly contracts and heats up, the iron nuclei absorb the gamma radiation, which is now very intense.
This causes the  iron nuclei to undergo photodisintegration into He, some neutrons, and copious amounts of
a very weakly interacting particles called neutrinos.  In addition, many electrons are also forced to combine with
protons at the enormous pressure inside the core of the star.  This reactions also releases copious amounts of
neutrinos. The neutrinos quickly escape into space, taking with them a large amount of thermal energy from the
core.  So the core cools very quickly with  a concomitant reduction of pressure.  This brings about a sudden
collapse of the core which then rebounds, and bumps into the outer layers of the star which are also collapsing
onto the core.   The result is  a shock wave that travels up through the star .  The shock wave also compresses
the upper layers of the star to the ignition point of any nuclear fuels that are present in these layers.
The released energy from these reactions adds to the luminosity of the star. This all happens very quickly, like an
explosion.  The star then brightens by millions of times so that, observationally, there appears to be a
super bright new star in the galaxy to which it belongs.  Hence the name supernova.  Nova means new in Latin.

Remember, this only happens for very massive stars. The Sun will not become a supernova.  It and other low
 mass stars will slowly shed their outer layers as they evolve to their final stage. The shedding of the outer layer
 non explosively is called the planetary nebula stage.

 In a supernova explosion, the outer layers of the star blow off at very high speed, leaving behind the core
of the  star, which is sometimes referred to as a supernova remnant.  However, the term supernova remnant
is sometimes meant to refer to the blown off layers.   The latter  continue to expand and eventually enrich the
interstellar medium with the heavy elements that the star produced. So stars are slowly causing a change in
the chemical composition of a galaxy. Successive generations of stars will then have a higher abundance of
heavy  elements than earlier generations or older stars. In this way, the age of a star may be determined. Some
of the heavy elements in the supernova remnant form microscopic particles that are called "dust".  Only in this
way does it become possible to make planets and people. So we are made of "stardust."

9.  Final Stages:

    When a star is prevented from collapsing so that it can not ignite another TNF reaction it enters into a final
stage where it slowly cools off and dies as a star. The possible final stages, depending on what stops further
contraction are:   a. white dwarf, b. neutron star, and c. black hole.

    Which final stage a star eventually reaches depends critically on its mass. Very massive stars may undergo a
supernova explosion and then become either white dwarfs,  neutron stars, or black holes, depending on how
much mass the star has after the explosion.  Stars like the Sun and those less massive than the Sun evolve
to become white dwarfs.

White Dwarfs :

    In a white dwarf, the repulsive forces between free electrons acts like a pressure in the star.  This pressure
can be very significant because highly evolved stars are so hot that the gases are  almost completely ionized.

The electron pressure is strong enough to balance gravity if the star's mass is less than 1.4 times the Sun's
mass.  This is known as the Chandrasekhar limit.  White dwars are about the size of the Earth or somehat
larger.  They have an averge density 100 million times the density of water.

White dwarfs eventually cool to become black dwarfs, but  this takes about 50 billion years.  The universe is
insufficiently old for this to have occurred for any star yet.

Neutron Stars

    Stars slightly more massive than 1.4 solar masses, but less than 3 solar masses,  contract to the point where
all electrons are forced into the nuclei to combine with the protons and form neutrons.

    The repulsive force between neutrons now acts as a pressure that balances gravity.  When this happens,
the star becomes a  neutron star.

    Neutrons stars are very small, have intense magnetic fields, and spin very rapidly.  Charged particles in the
atmosphere of a neutron star move along the magnetic field lines are focused towards the magnetic pole
the star.  As they spiral towards the magnetic poles, the partilces emit all kinds of EM radiation, even
radio waves.  The radiation emitted along the magnetic axis of a neutron star is very intense. If the magnetic
axis is tilted with respect to the rotational axis, one could observe the radiation coming from the magnetic
poles of the star to be in pulses, much like a rapidly  rotating lighthouse. Such objects have been detected and
are called "pulsars". Hence, pulsars are evidence that neutron stars really exist.  The first pulsar was detected
in 1967 by Jocelyn Bell, a grduate student in radio astronomy.   Later, pulars were discovered to be emitting
synchrotron radiation over the entire EM spectrum.  Read Units 62.1 and 62.2 in the textbook.
The explanation of the pulsar phenomenon as a rapidly rotating neutron star was made by Pacini and Gold.

Black Holes

   Stars that enter the final stage of evolution with more than 3 solar masses become black holes. Here the
gravity of the star is so strong that light can not escape from the star, so it is said to be black.  Black Holes
are stars that have collapsed inside their critical or "Schwarzschild Radius."  Once this happens, there is no
known force that can stop the star from contracting and this is an untenable  problem. Ordinary classical
physics can not explain what happens in a black hole and we must turn to the general theory of  relativity.
In  general relativity, very massive objects distort space and time.  Gravity is then interpreted as the curvature
of space-time.

Go to Chapter 11, which discusses General Relativity and Black Holes in more detail.

End of file

Copyright 2003, 2009, by R. J. Pfeiffer