University of California, San Diego
Physics 7 - Introduction to Astronomy

H. E. Smith   Winter 2007

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:

As shown in the figure above the place where a star reaches the Main Sequence is directly related to the star's mass.

Massive Stars

We may crudely distinguish between stars more massive than the sun and solar type stars in their evolutionary characteristics:

  1. 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:

    L M3.5

    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!)

  2. 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.

  3. 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.

  4. 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.

  5. 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 massive
    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 are
    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
    from Seeds Horizons © Wadsworth 1994

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.

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Conducted by Gene Smith, CASS/UCSD.
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Prof. H. E. (Gene) Smith
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Last updated: 16 April 1999