Introduction to Stars
A star can be defined as a body that satisfies two conditions:
(a) is bound by self-gravity;
(b) it radiates energy supplied by an internal source.
From the first condition it follows that the shape of such a body must be spherical,
for gravity is a spherically symmetric force field.
By this definition,a planet,for example, is not a star, in spite of its stellar appearance,
because it shines (mostly) by reflection of solar radiation. Nor can a comet be
considered a star, although in early Chinese and Japanese records, comets belonged
with the “guest stars” - those stars that appeared suddenly in the sky where none had
previously been observed. Comets, like planets, shine by reflection of solar radiation
and, moreover, their masses are too small for self-gravity to be of importance.
A direct implication of the definition is that stars must evolve: as they release energy produced
internally. changes necessarily occur in their structure or composition, or both. This is precisely
the meaning of evolution.
From the above definition we may also infer that the death of a star can occur in two ways:
●
●
violation of the first condition — self-gravity — meaning breakup of the star and
scattering of its material into interstellar space, or
violation of the second condition — internally supplied radiation of energy — that could
result from exhaustion of the nuclear fuel.
In the latter case. the star fades slowly away,while it gradually cools off radiating the energy
accumulated during earlier phases of evolution. Eventually, it will become extinct, disappearing
from the field of view of even the most powerful telescopes. This is what we call a dead star.
We shall therefore start pursuing the evolution of a star from the earliest time when both
conditions of the definition have been fulfilled, and we shall stop when at least one condition has
ceased to be satisfied, completely and irreversibly.
STAR BIRTH
●
●
●
Birthplace of Stars – Molecular cloud (Nebula)
A nebula is a giant cloud of dust and gas in space. Some nebulae (more than one nebula) come
from the gas and dust thrown out by the explosion of a dying star, such as a supernova. Other
nebulae are regions where new stars are beginning to form For this reason, some nebulae are
called "star nurseries.".
There are three types of nebulae: Emission nebulae, Reflection nebulae and Dark nebulae.
Omega Nebula
Horsehead Nebula
Eagle Nebula
How do stars form in a nebula?
●
●
●
Nebulae are made of dust and gases—mostly
hydrogen and helium. The dust and gases in a
nebula are very spread out, and exist in
equilibrium state.
The equilibrium state can be disturbed by factors
such as collision with other clouds or shock
waves from nearby supernova event. These
factors trigger a collapse of the molecular cloud
and initiate the burst of star formation.
The condition for the cloud to collapse is that it
must exceed a certain mass above which
gravity dominates.
https://youtu.be/4kJUsNmwwDE
How do stars form in a nebula?
● The collapsing cloud region undergoes fragmentation into
even smaller clumps that are dense and cold. Gravity of the
core of the clumps causes it to collapse and pull in more gas
– protostars form.
● As the gas/dust falls in, it picks up speed and energy. It is
slowed by friction and the energy is converted to heat. The
protostar keeps contracting under it own gravity. It is
powered by gravity via contraction - not by fusion.
● The protostar becomes a star when it has contracted so
much that it is dense and hot enough to begin nuclear fusion.
https://youtu.be/4kJUsNmwwDE
Life Cycle of Stars
○
○
○
Main Sequence: Hydrogen burning and stability
Red Giant Phase: Helium burning and expansion
End Stages: Planetary nebulae, supernovae, white
dwarfs, neutron stars, black holes
Tutorial
Describe in detail the pre-main sequence stages of stars, highlighting the characteristics of
each.
●
●
Evolutionary Time Scales
Changes in a star may take place on quite different time scales at different evolutionary phases.
There are three important basic time scales: the nuclear time scale tn , the thermal time scale tt
and the dynamical or freefall time scale td .
●
The Nuclear Time Scale
●
The time in which a star radiates away all the energy that can be released by nuclear reactions.
●
●
●
An estimate of this time can be obtained if one calculates the time in which all available
hydrogen is turned into helium.
It is known that only just over 10% of the total mass of hydrogen in the star can be consumed
before other, more rapid evolutionary mechanisms set in. Since 0.7% of the rest mass is turned
into energy in hydrogen burning, the nuclear time scale will be:
For the Sun one obtains the nuclear time scale 1010 years, and thus
●
●
●
●
●
The Thermal Time Scale
The time in which a star would radiate away all its thermal energy if the nuclear energy
production were suddenly turned off. This is also the time it takes for radiation from the centre
to reach the surface. The thermal time scale may be estimated as:
The Dynamical Time Scale
The time it would take a star to collapse if the pressure supporting it against gravity were
suddenly removed. It can be estimated from the time it would take for a particle to fall freely
from the stellar surface to the centre.
The dynamical time scale of the Sun is about half an hour. td << tt << tn
Gravitational lifetime for a star
M⊙ = 2 x 1033 gm;
R⊙ = 7 x 1010 cm;
L⊙ = 4 x 1026 Watt;
G⊙ = 6.67 x 10-8 dyn cm2/g2; This is a lifetime of 20 million years.
However, we know from geological evidence that the Earth
has been around for over four billion years.
This means that the Sun must be at least that old. Therefore,
the Sun (and other stars) cannot exist in a stable
configuration on stored gravitational energy.
Nuclear energy for stars
●
●
When a star is on the main sequence, its basic source of energy is the conversion of hydrogen
into helium. We start with four protons and end up with one 4He nucleus.
We can calculate the energy released by converting four protons to one 4He by comparing
their masses. We find that:
●
●
●
4mp - m(4He) = 0.007(4mp)
This means that 0.007 of the mass of each proton is converted into energy.
If 0.007 of the mass of each proton in the Sun is converted into energy, and if we assume that
most of the mass of the Sun was originally in the form of protons, then 0.007 of the Sun’s total
mass is available for conversion into energy. The total energy available is therefore:
●
●
E = 0.007 Mʘ c2
= (0.007)(2.0 Χ 1033 g)(3.0 Χ 1010 cm/s )2
= 1.3 Χ 1052 erg
The lifetime is this energy divided by the luminosity:
●
However, only 10% of the mass of the Sun is in a region hot enough for nuclear
reactions – the core, so we must lower our estimate by a factor of ten.
This leaves us with a lifetime of ten billion years. We think that the Sun has already
lived half of this time.
Internal Equilibrium Conditions
tion
a
u
eq m.
e
th ilibriu
is
equ
s
c
i
i
Th rostat
hyd
of
The derivative dT/dr is negative, since the temperature
increases inwards. Clearly there has to be a temperature
gradient, if energy is to be transported by radiation.
If the radiative transfer of energy becomes inefficient,
the absolute value of the radiative temperature gradient
becomes very large. In that case motions are set up in the
gas, which carry the energy outwards more efficiently
than the radiation.
In these convective motions, hot gas rises upwards into
cooler layers, where it loses its energy and sinks again.
The rising and sinking gas elements also mix the stellar
material, and the composition of the convective parts of a
star becomes homogeneous. Radiation and conduction,
on the other hand, do not mix the material, since they
move only energy, not gas.
Introduction to Stellar Clusters
Definition:
A star cluster is a group of stars that share a common origin and are bound together by gravity.
Types:
❖
Open (Galactic) Clusters:
Contain a few to thousands of stars.
Often found in the spiral arms of galaxies.
❖
Globular Clusters:
Dense clusters (compact spherical appearance) containing
thousands to millions of stars.
Orbit the cores of galaxies in a spherical distribution.
Open Clusters
●
Definition:
Open clusters are loose, irregularly shaped groups of stars that were
formed from the same molecular cloud and are bound together by mutual
gravitational attraction. They typically contain a few hundred to a few
thousand stars.
●
Characteristics:
○ Age: Generally younger, ranging from a few million to a few
billion years.
○ Metallicity: Tend to have higher metallicities (more elements
heavier than hydrogen and helium) compared to globular
clusters, reflecting their more recent formation from
interstellar material enriched by previous generations of stars.
○ Distribution: Found mainly in the galactic plane and the
spiral arms of galaxies, often associated with regions of active
star formation.
Globular Clusters
●
Definition:
Globular clusters are dense, spherical collections of hundreds of
thousands to millions of stars. They orbit the galactic core and
are thought to be some of the oldest stellar populations in the
galaxy.
●
Characteristics:
○ Age: Typically very old, ranging from 10 to 13 billion
years, making them among the oldest stellar objects in
the galaxy.
○ Metallicity: Generally have lower metallicities
compared to open clusters, reflecting their formation
in the early universe when heavier elements were less
abundant.
○ Distribution: Found in the halo of galaxies, including
the Milky Way, often in globular clusters orbiting the
galactic core.