University of California, San Diego
Physics 7 - Introduction to Astronomy
||Physics 7 - Lecture Summary #10
Stellar Evolution II - Massive Stars
Review evolution of a solar type star.
The evolutionary history of a star may be considered a story of the inexorable
battle of the star against the force of gravity which, once the star begins
its contraction out of the interstellar medium, attempts to pull it ever
smaller into a more compact, more tightly bound sphere. Stars of solar-type
masses will come to a compromise with gravity as they end their lives as
compact, dense white dwarf stars with diameter about the size of the earth and
density of order 1 ton/cm3. The most massive stars will lose this
battle in spectacular fashion.
The Russell-Vogt Theorem
It follows that the single most important determinant of the life-history
for a star is its
mass; this principle is called the Russell-Vogt Theorem.
Important mass regimes for stellar evolution:
- M* < 0.01 M -
Planet. Jupiter, for example, has a mass of about 0.001 x
M. Jupiter's temperature is
slightly warmer than would be expected from the amount of solar energy it
receives; this is interpreted as due to gravitational potential energy
stored as heat from Jupiter's contraction out of the proto-solar nebula.
But the energy balance for Jupiter and other planets is largely determined
by the energy received from the sun and central temperatures never come close
to the 1 million K required for even the simplest nuclear reactions.
- 0.01 M < M* <
0.085 M -
these objects will never become hot enough in their cores to ignite the P-P
Chain. Release gravitational potential energy will cause them to heat up
to core temperatures as hot as 3 million K, hot enough for the first stages
of nuclear reactions, perhaps, but never hot enough to establish stable
hydrogen burning. With atmospheric temperatures
Tsurface < 2000K, brown dwarfs will be very faint,
radiating the vast majority of their luminous energy in the infrared, and
very hard to detect. A new near-infrared survey of the sky called 2MASS
has detected a large number of cool stars, now classified as
which are likely to be brown dwarfs. Here's a
press release of another
possible brown dwarf detected at Palomar and the Hubble Space Telescope.
- 0.085 M < M* <
0.4 M - these stars will be very
long lived, but will never reach temperatures hot enough for the Triple-alpha
process to occur. They will not have a helium flash in the red giant stage
nor a helium-burning main-sequence phase.
- 0.4 M < M* <
1.2 M - these stars
like the sun will burn hydrogen to helium via the P-P Chain and will burn
helium to crabon via the Triple-alpha process following a path through the
H-R Diagram essentially like that outlined in Lecture 9
- M* > 1.2 M - these
stars will reach high enough core temperatures to burn hydrogen via the CNO
- M* > 8 M - stars
more massive than about 8 solar masses (this number is very uncertain compared
with those above) will have a larger number of nuclear burning cycles and
their cores will be more massive than the limiting mass of
1.4M, the largest mass that can be
supported by electron degeneracy, and thus the largest possible mass for a
white dwarf. As we shall see these stars end their lives with a cataclysmic
explosion called a supernova.
As shown in the figure above the place where a star reaches the Main Sequence
is directly related to the star's mass.
We may crudely distinguish between stars more massive than the sun and solar
type stars in their evolutionary characteristics:
- Massive stars live their lives more rapidly than do solar-type stars --
they "live fast and die young." One can determine relatively
straightforwardly from the balance between gravity, pressure and temperature
that the luminosity of a star will be approximately
proportional to the Mass3.5. This is the Mass-Luminosity
Relation which applies to all phases of stellar evolution:
Since the available fuel is effectively the mass of the star, the lifetime
will be approximately proportional to 1/Mass2.5. A star of 10
solar masses can thus be expected to go through its life cycle about 300 times
faster than the sun, with a main sequence lifetime of about 30 million years.
(The most massive stars have lifetimes shorter than about a million years,
while stars with masses less than about
3/4M have lifetimes longer than
the age of the Universe!)
- As described above massive stars require higher central temperatures to
balance the greater pull of gravity. This means that massive stars produce
helium from hydrogen via the CNO cycle rather than the P-P Chain.
- Higher central temperatures and pressure dictate that the stellar core
will not become electron degenerate at the onset of helium burning, so there
will be no helium flash.
- Because a massive star will reach higher core temperatures, massive stars
will experience more advanced nuclear burning stages producing a wider range
of nucleosynthesis products, up to iron.
- As already mentioned, stars whose core is greater than 1.4 solar masses
exceed the "Chandrasekhar limit" to the mass for a white dwarf. They will end
their lives with a dramatic explosion, becoming either neutron stars or white
dwarfs. Because stars lose considerable mass due to stellar winds in the
later stages of evolution and in the planetary nebula phase, it is currently
believed that stars with M < 8M
end their lives as white dwarfs.
Confirmation of Stellar Theory -- Hertzsprung-Russell Diagrams
The "filmstrip" to the left shows the development of the H-R Diagram for a
cluster of stars formed at a single epoch.
At an age of 1 million years the most massivefrom Seeds Horizons © Wadsworth 1994
stars have contracted to the Main sequence,
lived out their hydrogen-burning lifetimes and
are evolving off the Main Sequence. Lower
mass stars like the sun are still in the
Pre-Main Sequence phase. The youngest
clusters observed in the Milky Way are
estimated to have ages of a few million
- At 10 million years stars of 1 solar mass are
still above the Main Sequence, just beginning
nuclear reactions. They will be observed as
T-Tauri stars. Stars with M ~ 20M
just moving off the Main Sequence. Such
clusters will still be associated with regions
of gas & dust from which they formed.
- At 100 million years most stars are on or
nearing the Main Sequence, but stars with
M > 5M are now moving
off the Main
Sequence. The Pleiades cluster is estimated
to have an age of about 100 million years.
- With an age of a billion years, cluster stars
with masses between 2--3 M are moving
off the Main Sequence. The Main Sequence
location at which stars are just beginning to
exhaust the hydrogen fuel in their cores and
move toward the Red Giant region is called
the Main Sequence Turnoff
- The oldest clusters in the Milky Way, the
globular clusters, are estimated to have ages
of the order of 10-15 billion years and
show H-R Diagrams like that at the left.
Because the globular cluster stars have
very low abundances of the elements heavier
than helium (C,N,O ...) some corrections
need to be made to compare their H-R
diagrams to younger clusters with higher
The theoretical H-R diagrams above can be compared with the schematic H-R
Diagrams of a selection of clusters shown below.
Schematic H-R Diagrams for star clusters in the Milky Way.
The "Main Sequence Turnoff" is used to estimate the cluster age.
Globular Cluster H-R Diagrams
The H-R Diagram for a Globular Cluster, M3,
in the galactic halo.
From considerations of the way in which the Milky Way
formed, we believe that the globular clusters formed some 10-15 billion
years ago, consistent with their ages determined from their H-R Diagrams.
Supernovae & Neutron Stars
Stellar Evolution #1
Physics 7 Lectures
Physics 7 Home
Conducted by Gene Smith, CASS/UCSD.
You may send email to email@example.com
Prof. H. E. (Gene) Smith
CASS 0424 UCSD
9500 Gilman Drive
La Jolla, CA 92093-0424
Last updated: 16 April 1999