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9.7 OPTION - ASTROPHYSICS
CONTINUED PAGE 3
Numbers appearing in parentheses at the end of sentences or paragraphs refer to
the references provided in the Bibliography at the end of these notes.
are six main types of binary systems: visual, spectroscopic, eclipsing,
astrometric, spectrum and optical (1).
The first four of these are required for study by the current syllabus.
Let us now describe these four different types of binary star systems.
OF STELLAR MASSES
An astrometric binary is observed to have a period of 44.5 years and an
orbit with an average distance of separation between the component stars of 100
AU. Determine the sum of the masses
of the stars in this binary. (Data:
1AU = 1.5 x 1011 m) (Answer:
1.012 x 1033 kg)
An eclipsing binary has a period of 44.5 years and an average distance of
separation between the component stars of 3.9 AU.
Determine the combined mass of the binary system.
(Answer: 6.0 x 1028 kg)
OF VARIABLE STARS
A variable star is one that varies in brightness (5).
As at January 2004, the total number of designated variable stars was
38622 according to the “General Catalogue of Variable Stars”, 4th
Edition, by P N Kholopov et al, Moscow (1985) and its published updates (also
available on the Internet). There
are two broad categories of variable star: (a) Extrinsic Variables, which
vary in brightness for some reason external to the star; and (b) Intrinsic
Variables, which vary in brightness due to changes in the star itself.
Certain stars may vary in brightness due to both of these reasons. (5)
OF CLASSIFICATION OF VARIABLE STARS:
POSITION OF VARIABLE STARS
ON HR DIAGRAM:
The following figure shows where certain types of variable stars are
found on the HR Diagram. Cepheid
variables and RR Lyrae variables are located in the Cepheid
(between the dotted lines on the diagram), which occupies a region between the
main sequence and the red giant branch. A
star passing through this region along its evolutionary track becomes unstable
and pulsates. (3)
The diagram above is an amalgamation of similar diagrams
from Ref. 3 p.530, Ref. 12 p.327 and Ref. 9 p.47.
on re-arrangement we have:
which yields d = 177.8
parsecs, when m
= 3.75 and M =
-2.5 are substituted into the above equation.
Thus, the distance to our Cepheid variable is 177.8pc.
PROCESSES INVOLVED IN STELLAR FORMATION
ON THE MAIN SEQUENCE
By definition, a main
sequence star is one that produces energy by the fusion of hydrogen nuclei
(protons) to helium nuclei in its core.
This fusion reaction produces energy by the conversion of some of the
hydrogen nuclei mass into energy according to Einstein’s equation, E = mc2.
Note that astronomers are notorious for referring to fusion reactions as “burning”. So they speak of “hydrogen burning” instead of hydrogen
fusion and “helium burning” instead of helium fusion, and so on.
Two different fusion
mechanisms are responsible for the helium production and consequent release
of energy in main sequence stars. Both
mechanisms can occur simultaneously in a main sequence star. However, for stars whose core temperatures are below 16
million K the proton-proton chain reaction is the main mechanism, while for
stars whose core temperatures are above this, the carbon-nitrogen-oxygen (or CNO)
cycle predominates (3). Let us
now have a brief look at these two mechanisms.
Proton-Proton Chain Reaction
This reaction predominates in
stars like our Sun. Originally
proposed by the American physicist Charles Critchfield, this reaction has three
branches (3). Since the primary
branch PP I, accounts for the production of 85% of the Sun’s energy, we will
consider only this branch of the reaction in detail.
PP I consists of three steps:
For those not familiar with
nuclear equations, refer to the Key above.
In step 1, two protons combine to form a deuterium nucleus (an isotope of
hydrogen), a positron and a neutrino. In
step 2, another proton combines with the deuterium nucleus to form a nucleus of
light helium and a gamma ray photon, which carries energy away from the
reaction. In step 3, two light
helium nuclei combine to produce a nucleus of ordinary helium and two protons.
Thus, the overall reaction is to
convert four protons into a nucleus of helium with the release of some energy.
In the PP II and PP III branches
of the reaction the light helium produced in step 2 above suffers different
fates. Details of these branches
can be found in Refs. 1 & 3.
Carbon-Nitrogen-Oxygen (CNO) Cycle
This reaction mechanism
predominates in stars whose core temperatures are above 16 million K. Hans Bethe and Carl von Weizsacker discovered it
independently (3). In the CNO cycle
the carbon-12 nucleus acts as a catalyst and the following six-step
reaction takes place (10).
Overall, in this reaction four
protons are converted into a helium nucleus, two positrons, two neutrinos and
high-energy gamma ray photons (10). Again,
for those not familiar with nuclear reactions the following Key is provided.
For the CNO cycle to proceed,
there must be carbon-12 nuclei present. Obviously,
as the carbon-12 is returned at the end of the cycle, it is not actually used in
by the reaction.
Throughout the lifetime of the
main sequence star, the helium produced by the proton-proton chain reaction
and CNO cycle accumulates in the centre of the star, since it is denser
than the hydrogen. Also as the main
sequence star ages, changes occur in its luminosity, surface temperature and
radius (3). Hydrogen burning
decreases the total number of atomic nuclei in the star’s core (four hydrogen
nuclei are used up to make each single helium nucleus).
The resulting decrease in internal pressure causes the core to contract
slightly under the weight of the star’s outer layers.
In turn, this contraction increases the core’s density and temperature,
which effectively raises the pressure in the core to a level higher than it was
The increased core pressure
pushes outwards on the star’s outer layers, causing the star’s radius to
increase slightly. Also, the
increased density and temperature in the core cause hydrogen nuclei in the core
to collide more frequently, causing the rate of hydrogen burning to increase.
Hence the star’s luminosity increases.
Since the star’s surface temperature depends on the star’s luminosity
and radius, it changes as well. Thus,
as the star ages, its core shrinks and its outer layers expand and shine more
brightly. As an example, over
the last 4.6 x 109 years, our Sun has become 40% more luminous, grown
in radius by 6% and increased its surface temperature by 300K.
As a main sequence star ages and
evolves, the increase in energy outflow from its core also heats the material
immediately surrounding the core. As
a result, hydrogen burning can begin in this surrounding material.
This is called shell hydrogen burning since it is happening in the
shell surrounding the core. By
tapping this fresh supply of hydrogen, a star manages to last a few extra
million years on the main sequence. (3)
A star’s lifetime on the main
sequence depends critically on its mass.
The more massive the star, the shorter its main sequence lifetime.
This is because the more massive the main sequence, the more luminous it
is. In order to emit energy so
rapidly, these massive stars deplete their hydrogen stocks very much more
quickly than less massive stars. High
mass O and B stars completely exhaust their hydrogen supplies in only a few
million years, whereas low mass M stars take billions of years to use all their
hydrogen. A star of around one
solar mass will spend roughly 1010 years on the main sequence. So, our Sun, which has been on the main sequence for about
4.6 billion years, should have about another 5 billion years left to enjoy the
main sequence status. (3)
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