A review of main sequence (MS) stars and how they work, although much
applies to stars in general:
1. Stars shine because they're hot and dense: emit a thermal
spectrum modified by absorption lines; this absorption line spectrum is
produced at its surface (called a photosphere).
- the result of the gravitational collapse of a gas cloud
- pressure - gravity balance
- given their mass relative to their size, this means stars must
be and remain hot
- sets up structure within star: pressure (P), temperature
(T), number density of particles (n) - in order for
star to support itself against its own weight, all three of these must
their highest values within the star's core, and then diminish in value
the star's surface. Recall that gas pressure P is proportional to the
of the number density of particles n and temperature T.
2. If core T exceeds 107 K: 4 Hydrogen nuclei fuse
into 1 Helium nucleus + energy (gamma-rays) + 2
neutrinos at a rate sufficient to balance off the loss of energy in the
form of light at the star's surface (i.e., it's luminosity). In
our Sun, the central temperature is at present about 15.7 million K,
million metric tons of H are fused into 609.5
of He each second. By the way, what happens to the other 4.3
tons of matter processed per second?
- energy generated by the star's core is transported through
through the star's envelope (the portion of the star outside of its
core), and then to the surface by radiation
(photons) or by convection. Photons stream out of the
star's photosphere into dark, cold space - that which we call star
- energy balance & energy transport: energy lost at
in the form of light (luminosity L*) is replaced precisely
energy released via fusion (Lfusion) within star's core,
L*= Lfusion. In this case, the star need not
to remain hot enough to generate sufficient pressure to avoid
under its own weight.
- pressure-temperature thermostat regulates fusion within
(keeps star from exploding like a thermonuclear bomb), & together
energy transport regulate the energy balance of star
3. so...higher mass main sequence stars:
- require higher T at every layer within for sufficient pressure
- T at the star's surface (Ts) dictates star's
(thermal radiation spectrum modifed by absorption lines)
- T within core sets energy released by fusion - higher central T
greater Lfusion, thus balancing a more massive star's
- are larger in radius R for the following reasons. If all MS stars
had the same density (i.e.,
the ratio mass/volume which scales as ~ M/R3), then the size
of the star would be
larger for a larger mass, scaling like R ~ M1/3. However, a
that is supported against its weight by pressure that depends on
temperature (such as gas pressure) cannot
have both more mass
and an equal
or higher density. Therefore, higher mass MS stars must be less
dense than lower mass ones. In fact the sizes of main sequence stars
scale more rapidly
with mass, as R
~ M0.6 (with a power on mass of 0.6), than do masses of
equal density (with a power on mass of 1/3). During a
star's formative stage as a
gravitationally contracting protostar
of a given mass M, it contracts gravitationally while balancing
pressure and gravity, to a size R, so that its central core temperature
becomes great enough to make Lfusion = L*, in
converting hydrogen into helium in its core.
that L* is
to R2x Ts4 , the hotter, larger, more massive MS stars
are therefore much more luminous than MS stars of lower mass.
In fact the luminosities of these stars scale with their mass as L ~ M3.5.
This greater surface luminosity is precisely balanced by their greater
fusion energy generation rate, Lfusion, meaning that MS
stars are in
a state of energy balance.
- have, therefore, disproportionately rapid consumption
of fuel supply (H
within the central core) to
sufficient energy to keep itself hot enough to remain in
balance, and so have much shorter life times
- All of these characteristics are in contrast to the situation for
mass main sequence stars.
4. If pressure - gravity balance is established with central
less than 107 K, the full set of fusion reactions converting
into helium + energy cannot occur. The object never achieves energy
balance (it radiates energy away in the form of light from its surface,
but has no way to replace that lost energy), and thus this object never
full-fledged star, and is instead called a brown dwarf (a
`still-born' star). This occurs for objects2 whose masses lie below 0.08
Msun. There are now thousands of "brown dwarfs" known, and
they are suspected
be nearly as numerous as all normal stars in the Milky Way Galaxy
Remember, you can compare the structures of only those stars that
the same energy source in their cores. For main sequence stars, this is
fusion of hydrogen into helium in their central most regions. Can
you see how the many known
facts of main sequence stars are logically and causally linked together
the laws of nature?
1Strictly speaking, this is
true when averaged over the characteristic time required to transport
the energy through the star. If for any reason the star
in energy balance, you can bet that it is adjusting its structure
(expanding/cooling or contracting/heating) until it is.
2By this time these
objects' densities have become so high that a weird
quantum mechanical pressure known as "electron degeneracy pressure"
becomes important. Since this kind of pressure does not depend on
temperature, it can balance against the force of gravity even though
the object continues to radiate energy away as light from its surface.
As a consequence the object does not contract, and without contraction
no more gravitational potential energy can be released to raise the
temperature, and so the temperature slowly falls over the eons of time.
Professor of Astronomy
Department of Physics
Western Michigan University