In the case of the earth, the baseline is the
diameter of the earth's orbit around the sun, i.e. 1011 m, and the
technique has been refined to determine distances as large as 1018m, i.e.
100 light years (a light-year, commonly used astronomical unit, is the distance
covered in one year when moving at the speed of light, i.e. about 1016 m.).
If you gradually heat a piece of metal, it will first radiate in the (invisible)
Infrared range, then it will show a red glow that will
eventually become bluish-white (this is where the expression "white heat" comes
from). Further temperature increases will then shift the emission to the
UltraViolet region, etc. Consequently, we can determine the temperature of an
object simply by analyzing the distribution of the wavelengths of the emitted
radiation. This can equally be done for stars, so that we have a rather reliable
way of estimating a star's temperature.
The explanation for the existence of such main classes of stars could not
be found, until the processes responsible for the stars' energy production were
understood. Today we can fit the existing
data within our understanding of the stars "life cycle".
A more catastrophic fate is reserved for stars larger than at least 10 solar
masses. When such a large star exhausts its fuel and starts collapsing, the
gravitational pull is strong enough to overcome the electron's degeneracy
pressure. The star catastrophic implosion squeezes electrons and protons
together, giving origin to a neutron star. The process of implosion
generates in a very short time tremendous amounts of energy, in a series of
collisions between layers of materials bouncing back and forth. To a
distant observer, the phenomenon will manifest itself as a sudden increase
in brightness of a previously ordinary star, maybe even of a star previously
invisible to the naked eye. Understandably, in ancient days this phenomenon was
interpreted as the birth (rather than the death) of a new star, hence
the name nova, or supernova when the event was particularly
powerful. As for the case of White Dwarves, pressure degeneracy will intervene
to stop the star's collapse, but this time Pauli's principle applies not to
the electrons but to the neutrons. In a neutron star, matter is packed together
with the same density as nuclear matter, which, as we have seen is 100,000 or
so more dense than ordinary matter. If we could gather a spoonful of neutron
star material, it would weigh many thousands of pounds !!!
Evidence for Neutron Stars: Pulsars.
if the signal is due to a rotating
body, then a point on the surface of the body must move with a velocity given by
Black Holes
We have already discussed how, in the sun, fusion reactions can form elements
as heavy as Carbon. It turns out that in more massive stars, thanks to the
larger values of gravitational pressure, fusion processes can proceed even
further, and all the elements up to Iron can successively be created. It should
be clear that energy producing fusion processes will stop at Iron, since,
as we have learnt when studying nuclear stability and binding energies,
Iron corresponds to the maximum of the binding energy curve.
Fusing elements to form nuclei heavier than Iron will not produce but
consume energy, and this is not believed to be happening during the normal life
of a star. On the other side, it is believed that the explosive processes
associated with the death of a star can provide enough energy to initiate
even the endothermic reactions required to make nuclei heavier than Iron. Upon
explosion, all the elements that were in one way or another generated inside
the star are scattered into space, until they eventually aggregate to form
another star, a planet, your body, etc...
Lecture 21
In spite of the limitations on the data we can gather from the stars, the
combination of Astrophysics, Nuclear and Elementary Particle Physics has
allowed us to gain a fair understanding of the inner workings of stars and the
factors controlling their life and death. You have all heard terms like Red
Giants, White Dwarves, Supernovae, Pulsars, Neutron Stars and Black Holes. In
this lecture we will learn what they all are and how we were able to explore
their properties. To start, let us understand how we can gather information
on some of the most basic star parameters, like their distance, size and
temperature.
The Stars
Measuring Star Distances
How can we determine the distance of a star ? It is not easy, but a few
techniques have been devised that can be applied to some specific situations.
The most direct procedure is the same one used by surveyors to map the land.
Using Trigonometry, the distance of a faraway object can be determined by
measuring the angle at which it is seen from two different locations.
It is easy to convince oneself that this procedure will only work as long as
the distance to be measured is not too large with respect to the
baseline, i.e. the distance between the two locations from
where the angles are measured.
Outside the geometrically attainable range, other techniques have been devised,
the most fruitful of which is given by the Cepheid variables. These stars,
so called because first observed in the Cepheus constellation, portray a
periodic pattern of increasing and decreasing brightness. Painstaking
observation revealed that the period of variation is directly related to the
star's absolute magnitude. Combining the knowledge of the absolute with the
apparent magnitude allows then to deduce the distance.
Star Families
Another piece of information we can gather about the stars is their surface
temperature. This can be done since extensive experimentation on earth has
shown that, regardless of their composition, different bodies will emit a
spectrum of radiation that depends uniquely on their temperature, with
increasing temperatures corresponding to shorter and shorter wavelengths
of emitted radiation.
As a next step, the correlation between temperature and luminosity (the total
amount of emitted energy) can be studied (remember that luminosity can be
determined combining the information on apparent magnitude with distance, hence
the importance of estimating the distance). The result of such a study is
contained in the Hertzsprung-Russell diagram, showing that most stars have a
rather regular behaviour, as they fall on a well defined curve in the diagram,
the so called main sequence. In addition, the diagram is populated
by two more categories of stars, exhibiting respectively high luminosity with
low temperature and low luminosity with high temperature. The interpretation
for these two categories is the following:
Life and Death of the Stars.
Throughout most of its active life, a star generates energy by the Hydrogen into
Helium fusion process, as we have learnt to happen within the sun's core.
During this stage,
the star's energy production and temperature are consistent with the main
sequence of the H-R diagram. For a given amount of material, the size of a star
is a consequence of the dynamical equilibrium between the inward pull of
gravity and the kinetic agitation of the molecules determined by the energy
production (think of a ping-pong ball suspended in an air stream....). The
actual rate of Hydrogen burning will depend on the overall size of the star. The
gravitational pull will be stronger for a bigger star, therefore more energy has
to be produced in order to balance it: bigger star are less long lived, since
they have to burn more fuel in order to avoid gravitational collapse.
Bur for any star the day must come when the supply of Hydrogen runs low:
when fuel starts being scarce, the first effect is the collapse of the star
to a smaller dimension. This collapse has two immediate consequences:
This renewed energy production will cause the star to expand to a much larger
volume: during this phase, the star will have the characteristics of a Red
Giant. We can then think of a Red Giant as a rather old, but not yet dying star.
The final destiny of a star depends on its original size, and its end will be
the more catastrophic the more massive it was to start with. For a star of
small to intermediate size, consumption of the Helium fuel will cause it to
collapse to rather modest proportions: a sun-sized star will collapse to
dimensions comparable to the Earth's size. As usual, the collapse is
accompanied by a strong increase in temperature, and the collapsed star will
assume the charateristics of a White Dwarf. When in this state, the star is not
producing any more energy, but it gradually cools off, experiencing a slow
and peaceful death.
What determines the size a star will reach upon collapse?
The answer is given by Pauli exclusion
principle, the same principle that controls the maximum number of electrons in
the atomic shells. Pauli's principle, whose deep origin is not fully understood,
will prevent the electrons contained within the star from getting closer than
a certain distance, and this effect will be enough to counteract the
gravitational pull and will then put a stop to the star's shrinking. The
resistance to collapse due to Pauli's principle is called degeneracy
pressure, from a term in Quantum Mechanics, since different states
possessing the same energy are said to be degenerate.
As you can understand, all of the above ideas about the life and death of stars
are based on theoretical models and calculations, where the laws and rules
learnt from the sudy of elementary particles and the forces among them are
applied rigorously. Do we have any experimental evidence to support such
theories? A nice match between observation and theory did occur in recent
years.
About 30 years ago, even before the idea of neutron stars was fully developed,
astronomers had discovered a puzzling phenomenon. A graduate student,
Jocelyn Bell Burnell, reported to her supervisor the detection of a pulsating
radio signal, "beeping" with extreme regularity at about 1000 pulses per second.
The scientists were puzzled, and for a while they did not even discard the
possibility of radio broadcasts from a faraway civilization. As an internal
half-joke, the first discovered pulsating radio source was identified by the
code LGM-1, with LGM standing for "Little Green Men", the hypothetical senders
of the radio signals. Further investigation revealed more pulsating sources,
then globally referred to as pulsars, and the possibility
of them originating from distant civilizations was abandoned, and
some natural explanation was sought. But what celestial object could generate
such a regular signal at such a high frequency? When dealing with periodic
signals, the first thought goes towards rotation, but it is very easy to
estimate that, in order not to violate relativity, the pulsating object has to
be extremely small. Here is the argument:
, where T is the time to perform one rotation and r is the
radius of the (spherical) object. Relativity tells
us that v must be less than c ; the observed pulsars were emitting signals at
a frequency of 1000 Hz, therefore the rotation time T had to be of the order
of 1/1000 s. Substituting in the above equation, one finds that, to satisfy
relativity, r must be 50 km or less, an incredibly small radius for a stellar
object producing so much energy (for comparison, the radius of the earth is
about 6000 km).
The puzzle was resolved with the realization that the newly hypothesized
neutron stars could have the required characterisitics in terms of size,
rotational speed and energy emission. What we detect on earth is a radiation
beam emitted by the rotating neutron star magnetic field, the same way a ship
at sea detects the periodic signal from a rotating lighthouse mirror. The
association of pulsars and neutron stars with the end product of stellar
collapse was confirmed by the observation that a pulsar was found at the
location corresponding to the sighting of a supernova 1000 years ago !!
In the case of even more massive stars, the gravitational pull can be even
stronger than the neutron pressure degeneracy. In such cases, the collapse can
reach a state that cannot even be properly described, both because of our
residual limitations in understanding the properties of matter and since the
mathematical equations describing the phenomenon
produce unphysical infinite results. This very exotic state is what
we call a black hole, a massive, unimaginably dense object whose
gravity is so strong that not even light can escape (remember that, according
to General Relativity, light is affected by gravity).
Being so mysterious and
so exotic, black holes have intrigued both scientists and science fictioners,
and their properties and behaviour are far from being fully understood. What
we can say for sure is that the existence of black holes is a necessary and
unescapable consequence of the laws of Physics applied to the collapse of a
super-massive star. More research, both theoretical and experimental, will
probably improve our understanding in the future years.
What are we made of ? Stardust!
The study of the stars has given us the answer to another very basic
question: what is the source of all the elements, including the heaviest
Uranium etc., that are found on earth, form our own bodies and anything else
we see around us? The answer is that all of these elements were originally
manifactured either inside a star or during the catastrophic processes of a
supernova explosion.