After its formation, the star starts generating energy through nuclear fusion, and becomes stable. An internal hydrostatic equilibrium is established (that is the pressure of external layers equals that of the radiation produced inside) and an energy balance holds (the energy that is produced equals that emitted). It takes the star several tens of million years to reach a central temperature of 10 million degrees. This is the temperature required in order to convert hydrogen into helium.
In the internal thermonuclear reactions, two or more atomic nuclei merge into a heavier nucleus. The resulting nuclear mass is slightly lower than the sum of the initial nuclei. The mass difference M is converted into energy (E), according to the well known Einstein law
E = M c 2
where c is the speed of light. Atomic nuclei are made of protons and neutrons, so they are positively charged. The mutual electrostatic repulsion then obstacles their fusion. The nuclei will then merge only when the gas has very large pressures and temperatures, that is a large kinetic energy. The larger are the atomic nuclei, the larger is the electric force, and the larger is the required temperature.
Every star begins its life burning hydrogen in its nucleus, and converting it into helium, but the later evolution depends on the initial mass.
As a first point, their lifetimes are different. The luminosity of a star depends on its mass: for the lower main sequence, it is proportional to the squared mass. For the more massive stars, it depends on the mass raised to the third or fourth power. The mass of a star also determines the amount of fuel that is burnt in nuclear reactions, and its luminosity gauges the rate of mass consumption. The lifetime of a star is the time that it takes to exhaust all its fuel, so its is almost equal to the ratio of its mass over its luminosity. Since its luminosity grows faster than its mass, this ratio is smaller for more massive stars. The hotter, more massive, and more luminous stars, those which populate the higher part of the main sequence, are therefore those which live shorter. The largest stars only burn hydrogen for just a few million years, while the smaller stars in the sequence can keep on burning even for 100 billion years. The lifetime of our Sun, which is a rather small star, is about 10 billion years, and five of them already passed.
Moreover, the larger is the star mass, the larger is the central temperature
that it generates. The atomic fusion requires larger temperatures to burn
heavier nuclei. Only the more massive stars are therefore able to synthesize
the heavier elements. Finally, the larger is the temperature, the faster
is the fusion.
As the star exhausts successive fuels, the process becomes faster and
faster.
The evolution of the stars is also determined by the physical status
of the gas. In relatively low density conditions, the ions and electrons
gas is in a normal state. If density grows and becomes larger than a particular
limit, the gas becomes degenerate. In the fist case, its
pressure is proportional to its temperature. A temperature increase will
cause a pressure increase. The gas will then expand and cool again. In
such way, pressure and temperature are self regulated, and a temperature
increase does not accumulate energy inside the gas.
Conversely, in a degenerate gas pressure no longer depends on temperature.
If the gas temperature raises, the gas does not expand and the energy that
gets trapped cannot be dissipated. Beyond a certain limit, this accumulation
of energy makes the star unstable and makes it explode.
During the hydrogen burning, the star has a well defined temperature,
luminosity and color. These quantities define a position in the H-R
diagram. All the stars that are in the hydrogen burning phase (which
is the longest phase in the star's lifetime) are comprised within a band
in the H-R diagram, which is called main sequence . The mass of
the star determines the position of its point within the sequence. The
larger is the mass, the larger are its temperature and luminosity in the
hydrogen burning phase, and vice versa.
During this phase the star is stable. Depending on the mass, the phase
can last from a few million to several billion years. When the nuclear
hydrogen is almost exhausted, the hydrostatic equilibrium no longer holds,
since the energy produced by the fusion is not enough to counterbalance
the pressure of the star's external layers. As a consequence, the central
temperature rises, so that the remaining hydrogen is burnt faster, and
later the fusion of helium into carbon starts. The star is then overheated,
so the external layers expand, in order to dissipate the excess energy.
The surface temperature drops, so the star's color gets redder and redder,
and the luminosity increases, since the emitting surface got larger. In
other words, the star becomes a red giant, that is a
star which is cooler and brighter than the stars which are on the main
sequence. Its representative point in the H-R diagram moves up and to the
right, climbing the so-called "red giant branch". At the same time, the
star starts loosing mass, by the expulsion of its surface layers. The mass
lost during this phase can be a significant fraction of the original total
mass of the star.
When the central temperature of the star reaches 100 million degrees,
the helium nuclei start merging, three at a time, to form a carbon nucleus.
The star moves from the red giant region towards the main sequence.
If the mass of the star is lower than about two times that of the Sun,
its active evolution stops here. Indeed, smaller stars are more compact
than larger stars, and the gas in their nucleus is so dense that it gets
degenerate. The nucleus cannot further contract, and carbon cannot be ignited.
When helium is almost exhausted, the nucleus contracts and the external
layers expand, since less energy is produced at the center. The point in
the H-R diagram climbs along the red giant branch. The star now becomes
unstable, and the external layers start pulsing, until they are expelled.
The hot and dense nucleus of the star is exposed, so it now becomes a white
dwarf. The central star plus the expelled gas is called a planetary
nebula.
The more massive stars will go several times through the contraction
and expansion cycle. Each time the central fuel exhausts, a heavier element
burning is started. At the same time, the nucleus gets hotter and hotter.
The fusion of carbon nuclei starts at 800 million degrees, and it generates
elements such as oxygen, magnesium, neon. At 1.4 billion degrees the oxygen
nuclei merge, and they form silicon, sulfur, phosphorus, and so on.
The chain of nuclear burnings is broken when the nuclear gas gets degenerate.
At this time, the fusion of the next fuel releases a large amount of energy
into the gas, and this makes the star explode as a supernova.
The gas, enriched in heavy elements, is given back to the interstellar
medium. The supernova explosion is the main process chemically enriching
the galaxies. The external layers of the star are expelled into the space,
while its nucleus collapses under its own gravitational pull, so an extremely
dense and compact object is formed.
Only stars whose mass is larger than 12-13 times that of the Sun are
able to go through the whole cycle of nuclear burnings. The last element
that can be synthesized is iron, and after that the chain is broken. In
fact, the fusion of iron into heavier elements requires energy, instead
of releasing energy.
The iron synthesized in the stellar core then undergoes an instability:
the iron nuclei break due to the enormous pressure exerted by the external
layers, and collapse upon themselves. The core contracts, seeking a new
hydrostatic equilibrium. The external layers drop upon the core at a large
speed, hitting its surface. The shock wave that is generated, heats the
gas up to very high temperatures. These conditions ignite very fast nuclear
burnings, which release a large amount of energy into the gas layers. The
star then explodes as a supernova.
The destiny of the core now depends on its mass. If it is smaller than
some critical threshold (a few solar masses), the nuclei merge with the
electrons, forming a very dense and compact "sea" of neutrons. This new
object finds an equilibrium, and is now a neutron star.
If the core mass is larger than the previous limit, nothing can stop
its collapse. As the core contracts its mass is constant, so the surface
gravity increases. According to the theory of general relativity, the space
around the star is distorted, it curves and modifies the paths of the bodies
that pass nearby. The star disappears, since even light gets trapped inside
its enormous gravitational field. A black hole is born.
Red giant and supergiant stars are among the brightest bodies of the
sky. They are formed by the expanded and rarefied envelope of evolved stars.
The envelope surrounds a hot and compact core. Even though their masses
are small, the largest red giant stars have radii hundreds of times larger
than that of the Sun. Their atmospheres extend for million kilometers,
and inside the atmosphere the densities are lower than 10-5
grams per cm3. Just think that, when the Sun will become a red
giant, its external layers will expand beyond the orbit of Mars, and they
will swallow the innermost planets, including the Earth.
The surface temperatures of red giants have values around 3,000 degrees,
so their spectra are of type K and M. Antares in Scorpio and Betelgeuse
in Orion are among the better known red giants.
These celestial bodies keep losing gas, which is blown away as a stellar
wind; this mass loss is a key factor for the later evolution of the
star.
 |
The first direct image of the atmosphere of a star which is not the Sun. This is Betelgeuse, the brightest star in the Orion constellation. It is a red supergiant. The image reveals a spot, hotter and brighter than the rest of the surface. Its size is ten times that of the Earth, and its origin is still unexplained. (HST) |
This kind of nebula is made by a very hot, compact, and small central
star surrounded by a gaseous luminous disk or ring. The size of the system
is relatively small, generally lower than a light
year. The first planetary nebulae that were observed, were then compared
to the planet Saturn and its rings, and this explains their name. The star
at the center of a planetary nebula is the remnant of a low mass star,
which is seen during its terminal evolutionary phases. Its temperatures
are very high, between 30 thousand and 150 thousand degrees, so its mainly
emits in the ultraviolet spectral region. It is also rather small and compact,
since its size is lower than one fifth that of the Sun.
We think that planetary nebulae descend from red supergiant stars,
which expel the outermost layers (composed by hydrogen and helium) into
the interstellar space. This gas then forms a spherical shell, which expands
at lower and lower rates. It is ionized by the radiation coming from the
central star. When electrons recombine with ions, the gas emits radiation.
As time passes, the nebula is dispersed into space. The hole process
probably lasts shorter than 100,000 years. It is another way through which
stars give back to the interstellar medium part of the gas that was trapped
inside them. Its heavy elements content is higher than the original one,
so this is another process that enriches the medium.
 |
NGC 6543, also known as "Cat's eye" nebula, is one of the most complex
planetary nebulae ever observed. One can recognize high speed gaseous jets,
concentric gas layers and shock wave remnants. The age of this nebula is
estimated around 1,000 years.
(HST) |
The planetary nebula M57,
in the Lira constellation. (SEDS)
White dwarfs represent the final stage in the life of low mass stars.
The prototype is Sirius B, the companion of the better known star Sirius.
The two stars form a binary system. During and
after the red giant phase, the star releases its external layers and the
remaining structure rapidly collapses. If the remaining mass is lower than
some critical limit (1.44 solar masses), at some time the collapse stops
and the star finds a stable configuration, and the star is now a white
dwarf.
The higher is the stellar mass, the smaller is the final radius of
the white dwarf. This type of star is very small, dense and compact, and
it rotates fast. Its name comes from the fact that its radius is much smaller
than that of a normal star. Since this dwarf is very hot, its light is
mostly emitted at short wavelengths, corresponding to white colors. The
mass of a white dwarf is comparable to that of the Sun, and its size is
comparable to that of the Earth. The gas inside is completely degenerate,
apart from a very thin surface layer. This layer is in an ordinary physical
status, and it is mainly composed by hydrogen and helium. The degeneracy
of a gas sets in when it is compressed beyond some critical density. Inside
a degenerate gas, the space normally filled by a single atom is instead
populated by hundreds of thousands of particles. Inside a white dwarf,
its matter is compressed to densities of 106 - 107
grams per cm3. If a sugar tablet were so dense, it would weigh
more than a car on the Earth's surface! In spite of this high compression,
the matter inside a white dwarf is gaseous, while at such high pressures
normal matter would get solid.
A degenerate gas can strongly resist a further compression, since itself
exerts a very high pressure. This is what supports the white dwarf. This
star cannot contract and ignite further nuclear burnings. It is then a
"dead" star, that will shine at the expense of its internal energy, which
will not be renovated. However, the initial temperature of a white dwarf
can reach 100,000 degrees, and it will take several billion years to bring
it down to values close to zero. Since the age of the Universe is 15-20
billion years, probably no white dwarf has yet reached its "thermal death".
If, in a binary system, one of the two stars is a white dwarf, a nova
can be generated.
 |
Left. An image of the globular cluster M4, which contains more than
100,000 stars. Many of them are red giants. Right. An image of part of
the cluster, where 8 white dwarf sare marked. The Hubble Space Telescope
revealed 75 of them in a small spatial region.
(HST) |
The appearances of "new" stars were reported since ancient times. These
stars shined for a few week or month, and afterwards they got fainter and
disappeared. Their name "novae", that is new stars, comes from this behavior.
Now we know that this phenomenon is not caused by actual new stars. Instead,
already existing but very faint stars explode, so they get suddenly much
brighter and can be recognized. This kind of explosion is much less violent
than that of a
supernova, and does not completely disrupt
the star. It is caused by a mechanism that appears during the evolution
of the star.
Normally, novae are compact, not very bright, and high temperature
stars (typically, white dwarfs), that are part of a binary
system. Their companion is an evolved and expanded star, such as a
red giant. This star loses gas towards the white dwarf, and the gas forms
and an accretion disk around the compact
star. The gas slowly falls upon the white dwarf and accumulates. The mass
transfer goes on until the white dwarf reaches a limiting mass. At that
time the falling matter generates an explosive reaction, which releases
part of the energy that it acquired.
The luminosity of the star increases up to 11-12 magnitudes,
going from a typical value around +4 or +5 up to about -7.5 at maximum
brightness. During the explosion, the external layers are expelled at speeds
as large as 3,000 km/s. As they move away from the star, the initial temperature
of the gas (about 10,000-15,000 degrees) decreases. The expelled gas becomes
less dense and slows down, until it forms a small nebula.
The explosion of a nova releases as much energy as that emitted by
the Sun in 100,000 years. The mass that is expelled is instead a small
fraction of the total mass of the star, about one hundred thousandth. After
some year, the star that exploded is back to its initial status.
The nova phenomenon can repeat, if suitable conditions are met. In
this case these objects are called "recurrent novae". However, not all
novae behave the same way. Some of them suddenly reach their maximum luminosity,
and afterwards get faint within a few months. In other cases, the star
takes more time to reach the peak brightness, then it shows multiple explosions
and takes several years to go back to its minimum brightness.
 |
This image illustrates the mechanism beneath the cataclysmic variable phenomenon. We have a binary system of close stars, composed by a white dwarf and a normal low mass star. The gas flows from the normal star towards the white dwarf, forming an accretion disk, and falls upon its surface. Hydrogen accumulates on it and heats up until the nuclear fusion is ignited. This causes the explosive "nova" phenomenon. (HST) |
 |
Nova Cygni, which exploded on February 19, 1992. Right. The Hubble Space Telescope image reveals a ring like elliptical structure. It is the very thin remnant of the explosion. An image taken on May 31, 1993 (left) delivered the first information on the ring and on a strange structure which has the shape of an unresolved bar. (HST) |
When a star explodes as a supernova, it offers one of the most spectacular
events that the sky can show. The explosion comes at the end of the nuclear
burning sequence of a massive enough star. In that case the core collapses,
the external layers fall upon the core and they heat up, and suddenly thermonuclear
fusion reactions are ignited. They produce a very large amount of energy,
which is delivered to the gas as kinetic energy. The layers are expelled
at very large speeds (tens of thousands kilometers per second), in a huge
explosion. The energy released by a single supernova is so large that,
for a few weeks, it emits as much light as a whole galaxy! The light emitted
by the supernova dims and disappears after a few years. What is left, is
a gas cloud whose expansion is slowing down. The supernova remnants, that
is the gas expelled during the explosion, make some of the most beautiful
nebulae that we know.
At the center of a supernova, a black hole or a
neutron
star is left. The explosion releases very high temperature, strongly
ionized, gas into the interstellar medium, and cosmic rays. The free electrons
and ions carry an intense magnetic field. When interstellar gas is present
around the supernova, it is compressed by the expelled material, which
at the same time slows down. The interstellar gas is heated and emits radiation.
The expanding gas gets an irregular filament structure, which gets thinner
and thinner. The supernova remnant emits optical, radio, infrared, and
also X and gamma radiation. Even when it cools down, it emits synchrotron
radiation, caused by a rapid motion of its electrons around the magnetic
field. The X emission is instead produced during the interaction of the
ions and electrons with the interstellar gas.
Since the high mass stars are just a small fraction of the total number
of stars, the explosion of a supernova is a quite rare event. It is currently
estimated that in our Galaxy, an average of 3 supernovae per century do
explode. The last two supernovae that exploded in our Galaxy are that of
1572, in Cassiopeia constellation, and that of 1604 in Ophiucus. However,
supernovae are well visible also in external galaxies, and indeed represent
one of the best ways to estimate their distance.
Some supernovae entered the history of Astronomy. A very well know
one is that of 1054. Chinese astronomers recorded their observations, and
it was so bright that for some time it could be seen during the day. Its
remnant is today the Crab Nebula, which owes its name to the interlaced
structure.
Another supernova remnant is the Cygnus Loop, which is what remains
of a star that exploded about 50,000 years ago, and which is still producing
an emission line spectrum. Supernovae have a key role in the evolution
of galaxies. They enrich the interstellar medium with heavy elements, and
they compress this same gas causing the formation of dense clouds, and
thus of new stars.
 |
NGC 1952, better known as the Crab Nebula, is the remnant of a supernova
that exploded in 1054. This event was observed by ancient Chinese astronomers.
At the center of the nebula, which is 6,000 light-years far away, there
is a pulsar. The pulsar rotates with a 1/30
sec period.
(Courtesy Bill Arnett) |
 |
The Vela Nebula, in the Cygnus constellation, is the remnant of
a supernova that exploded about 15,000 years ago. This image shows only
a part of it.
(Royal Observatory, Edinburgh) |
 |
The evolution of the supernova 1987A remnant, from February 1994 to February 1996. The supernova exploded in the Large Magellanic Cloud on February, 1987. Its relics are now expanding at a speed of more than 10 million kilometers per hour! Ten years after the explosion, the remnant is large enough so that the Hubble Space Telescope can resolve it. The supernova is 167 thousand light years from the Earth, in the Large Magellanic Cloud. Its explosion represented an important chance to test the stellar evolutionary theories. (HST) |
 |
The image shows supernova 1994I in the M51 galaxy, 20 million light years from us. The arrow indicates the position of the supernova, some 2,000 light-years from the nucleus. (HST). |
 |
The light curve of supernova SN93J, plotted in 5 spectral bands.
(The Electronic Universe Project) |
 |
Infrared image of supernova SN1994D.
(The Electronic Universe Project) |
 |
Light curve of supernova SN1994D.
(The Electronic Universe Project) |
These unusual objects are formed during the final evolutionary phases
of a star whose core mass is comprised between 1.44 and about 3 solar masses.
After the nuclear burning chain has come to an end, the star suddenly contracts,
pulled by its own gravitational force, while its external layers expand.
The star undergoes such a violent collapse that it cannot regain the equilibrium
as a white dwarf. Equilibrium will instead be reached in an even more extreme
status, when it becomes a neutron star. In fact, the collapse goes on until
the atomic nuclei break up and the protons merge with the electrons, so
that a a "sea" of degenerate neutrons is formed. The density is very high
(1013 - 1014 grams per cm3). The degenerate
neutrons provide the pressure that prevents a further collapse.
Little is still known on the internal structure and the physical status
of such a star. It must have very strong gravitational and magnetic fields.
Furthermore, a neutron star must be very rapidly rotating, just due to
its own contraction. Just like an ice skater rotates faster when she moves
her arms closer to her body, so a star or a gas cloud start rotating around
an axis, if they contract.
A mass comparable to that of the Sun shrinks to the size of a big asteroid.
The typical dimensions of a neutron star are indeed about 30 km in diameter!
At these densities, a volume of matter as small as a sugar tablet would
have a mass as large as that of the whole mankind...
Neutron stars do not emit light as normal stars, so they cannot be
"seen". However several ones have been identified, on the basis of indirect
evidence. They in fact produce the pulsar phenomenon. In 1967, radio
astronomers recognized a few strange sources, some kind of radio light-houses
emitting radio pules on very regular and short time intervals. Later this
phenomenon was explained as a rapidly rotating neutron star. It should
also posses a very strong magnetic field, which could generate a strong
electric field. Within this electric field, ions and above all electrons
are pushed out from the magnetic poles of the star. They spiral around
the magnetic field lines, so they are decelerated and emit synchrotron
radiation. If the magnetic field axis (which does not necessarily coincide
with the rotation axis) is inclined with respect to us, each time a magnetic
pole aligns along our line of sight we observe a radiation flash.
The pulsars emit not only in the radio band, but also in the optical,
ultraviolet, X and gamma bands. And the period is just the same of the
radio pulses. These radiations are emitted at the expense of the star's
energy, so its rotation becomes slower and slower. The period goes from
a fraction of a second to a few hours or days.
If the stellar core mass, at the end of the nuclear burning sequence,
is larger than about 3 solar masses, then not even its particles are able
to stop its collapse. It goes on, generating a black hole, a monster like
object that swallows all the matter that happens to be within a given distance.
Nothing can escape from it. The gravitational force is so large that it
compresses the particles up to a practically "infinite" density. Matter
is converted into an unknown physical status.
Einstein's general relativity theory predicts the existence of black
holes. During the collapse, the star "folds" upon itself, and its enormous
gravity curves the surrounding space-time. The surface gravity of a black
hole is so large that not even light can escape, so this object is totally
dark and it cannot be revealed in a direct way.
The escape speed at a given distance D can be defined for a
black hole, just like for each star or planet. This is the minimum speed
that a celestial body must have at the distance D, in order to escape
the gravitational attraction exerted by the black hole at that same distance.
Conversely, for any given velocity, we can find the minimum distance from
the black hole that a body can reach, without being captured. If this speed
is set equal to that of light (the maximum possible speed), then we find
the distance beyond which not even light can escape the black hole. This
limit is called "event horizon" and defines the inner region of the black
hole. From this region no signal can reach the outside world, so we cannot
have any news of what goes on inside.
A real surface cannot be defined for the black hole, nor a volume or
density. This object is characterized by its mass and its Schwarzschild
radius, that is the distance from the center to the event horizon (Schwarzschild
was the first theoretician who studied black holes). These two quantities
are related by the expression
RS = 2GM/c2
where RS is the Schwarzschild radius, G is the universal
gravitational constant, M is the black hole mass, and c is the speed of
light. The larger is the black hole mass, the farther its "influence" can
reach. Using the values of the constants, we find that RS is
equal to 3 times (M/MS) Km, where MS is the mass
of the Sun. Until a few years ago, there was no evidence of the real existence
of black holes. In fact, they can only be revealed by the gravitational
effects on the surrounding matter. For example, if the black hole is part
of a binary system, then its presence can be revealed by the motion of
the normal star around the common baricenter. If the star evolves as a
red giant and expands, then part of its external gas can form an accretion
disc around the black hole. The gas slowly drops from the disk onto
the black hole. The friction grows towards the inner edge of the disk,
it heats the gas and the gas generates a wide radiation spectrum, mostly
in X and ultraviolet bands. The presence of a compact object plus an accretion
disk can be revealed by this radiation.
When the first satellites carrying X ray detectors were launched, many
X sources were discovered, both inside and outside our Galaxy. Indeed,
our atmosphere blocks most of the X radiation coming from the outer space.
The sources that were discovered emit more X radiation than optical one,
and their spectrum is not thermal. That is, it cannot be emitted by a star,
or a group of stars. Some of these X sources have a "stellar" nature, such
as Cygnus X-1, Scorpio X-1 or Hercules X-1. It looks like Cygnus X-1 is
a binary system of the type that was described previously. It could be
made of a black hole whose mass is about 6 solar masses, and a star whose
mass is 20 solar masses. Other X sources are pulsars, and other ones are
superposed to galaxies or quasars.
The gravitational field of the black hole is so strong that it curves the nearby space-time. One of the main consequences is that a light beam passing near the black hole, is curved and changes its path. Actually, this happens for any large mass concentration. This phenomenon explains the gravitational lenses. If the light beam passes at the distance RS, it gets so curved that it starts going round the black hole! The presence of a very massive black hole between us and a light source such as a distant galaxy, could then also be revealed by the gravitational lens effect on the radiation coming from the source.
It seems that supermassive black holes exist, or existed, inside the
nuclei of active galaxies, and that matter accretion
onto these objects represent their central energetic engine.
 |
A dust disc with a diameter of 800 light years is found inside the
nucleus of the galaxy NGC 4261, as well as a probable black hole whose
mass is 1.2 billion solar masses!
This image represents the hypothetical view from a planet inside the dust disc, when looking towards the black hole. The white light coming from the very hot gas falling onto the black hole, is reddened by the dust, which absorbs high frequency light and re-emits it at lower frequencies. Illustration by J. Gitlin (Space Telescope Science Institute) |
 |
Image of the dust disc surrounding the central black hole in the
spiral galaxy NGC 4261. Astronomers measured the speed of the gas rotating
around the black hole, and from this speed they could gauge its gravitational
field and its mass, which is about 1.2 billion solar masses.
(HST) |
