Author: Steve Willner <swillner@cfa.harvard.edu>,
 	Ken Croswell

There are lots of different ways to classify stars.  The most important
single property of a star is its mass, but alas, stellar masses for most
stars are very hard to measure directly.  Instead stars are classified
by things that are easier to measure, even though they are less
fundamental.

There are three separate classification criteria commonly used: surface
temperature, surface gravity, and heavy element abundance.  The familiar
"spectral sequence" OBAFGKM is a _temperature_ sequence from the hottest
to the coolest stars.  Strictly speaking, the letters describe the
appearance of a star's spectrum, but because most stars are made out of
the same stuff, temperature has the biggest effect on the spectrum.  O
stars are hotter than 30000 K and show ionized helium in their spectra.
M stars are cooler than 4000 K and show molecular bands of TiO.  Others
are in between.

The ordinary spectral classes are divided into subclasses denoted by
numbers; thus G5 is a medium temperature star a little cooler than G2.
The Sun is generally considered a G2 star.  Not all the subclasses are
used, or at least generally accepted; G3 and G4 are absent, for example.

For historical reasons, hotter stars are said to have "earlier"
spectral types, and cool stars to have "later" spectral types.  An
"early A" star might mean somewhere between A0 and A3, while "late A"
might denote roughly A5--A8.  Or "early type stars" might mean
everything from O through A or F.  There's nothing terribly wrong with
this bit of jargon, but it can be confusing if you haven't seen it
before.

There are several spectral types that don't fit the scheme above.  One
reason is abnormal composition.  For example, some stars are cool enough
for molecules to form in their atmospheres.  The most stable molecule at
high temperatures is carbon monoxide.  In most stars, oxygen is more
abundant than carbon, and if the star is cool enough to form molecules,
virtually all the carbon combines with oxygen.  Leftover oxygen can form
molecules like titanium oxide and vanadium oxide (neither of which is
particularly abundant but both of which have prominent spectral bands at
visible wavelengths), but no carbon-containing molecules other than CO
can form.  (This is only approximately true.  Weak CN lines can often be
seen, for example, and all kinds of stuff will show up if you look hard
enough.  This article just gives a summary of the big picture.)  In a
minority of stars, however, the situation is reversed, and there is no
(or rather very little) oxygen to form molecules other than CO.  These
stars show lines of CH, CC, and CN, and they are called (not
surprisingly!) "carbon stars."  They are nowadays given spectral
classifications of C(x,y) where x is a temperature index and y is
related to heavy element abundance and surface gravity.  These stars
were formerly given "R" and "N" spectral types, and you occasionally
still see those used.  Roughly speaking, R stars have temperatures in
the same range as K stars and N stars in the same range as M, though the
correspondence is far from exact.

Another interesting group is the S stars.  In these, the atmospheric
carbon and oxygen abundances are nearly equal, and neither C nor O (or
at least not much of either) is available to form other molecules.
These stars show zirconium oxide and unusual metal lines such as barium.

There are other stars with unusual abundances: CH, CN, SC, and probably
more.  They are rare.  There are also stars that are peculiar in one way
or another and have spectral types followed by "p."  The "Ap" stars are
one popular class.  And finally, some stars have extended atmospheres
and show emission lines instead of the normal absorption lines.  These
get an "e" or "f."

The second major classification is by surface gravity, which is
proportional to the stellar mass divided by radius squared.  This is
useful because spectra can measure the gas pressure in the part of the
atmosphere where the spectral lines are formed; this pressure depends
closely on surface gravity.  But because surface gravity is related to
stellar radius, it is also related to the stellar luminosity.  Every
unit of stellar surface area emits an amount of radiation that mostly
depends on the temperature, and for a given temperature the total
luminosity thus depends on surface area which is proportional to radius
squared hence inversely proportional to surface gravity.  The upshot of
all this is that we have "dwarf" stars of relatively high surface
gravity, small radius, and low luminosity, and "giant" stars of low
surface gravity, large radius, and high luminosity _and their spectra
look different_.  In fact, many "luminosity classes" are identified in
spectra.  For normal stars, these are designated by Roman numerals and
lower case letters following the spectral class in the order: Ia+, Ia,
Iab, Ib, II, III, IV, V.  Class I stars are also called "supergiants,"
class II "bright giants," class III "giants," class IV "subgiants," and
class V either "dwarfs" or more commonly "main sequence stars."  By the
way, not all luminosity classes exist for every spectral type.

The importance of all this is that the luminosity classes are closely
related to the evolution of the stars.  Stars spend most of their
lives burning hydrogen in their cores.  For stars in this evolutionary
stage, the surface temperature and radius, hence spectral type and
luminosity class, are determined by stellar mass.  If we draw a
diagram of temperature or spectral type on one axis and luminosity
class on the other and plot each star as a point in the correct
position, we find nearly all stars fall very close to a single line;
this line is called the "main sequence."  (This kind of diagram is
called a "Hertzsprung-Russell" or "H-R" diagram after two astronomers
who were among the first to use it.)  Stars at the low mass end of the
main sequence are very cool (spectral type M) and are called "red
dwarfs."  This term is not very precise and may include K-type stars
as well.

As stars age, they expand and cool off; stars in this stage of evolution
account for the brighter luminosity classes mentioned above.  If they
happen to be cool, they are called "red giants" or perhaps "red
supergiants."  One interesting special case is for the hottest stars,
spectral classes O and early B.  Normally main sequence stars are hotter
if they have more mass, but not once they reach such high temperatures.
Instead more massive stars have larger radii but about the same surface
temperature, so an O I star is likely more massive but no more evolved
than an O V star.  These stars are called "blue giants" or "blue
supergiants."

After stars finally burn out their nuclear fuel, any of several thing
can happen, depending mainly on their initial mass and perhaps on
whether they had a nearby companion.  Some stars explode and are
entirely destroyed, but most leave remnants: white dwarfs, neutron
stars, or black holes.  

White dwarfs have high density because they are supported by "electron
degeneracy pressure."  This is a kind of pressure that arises from the
Fermi exclusion principle in nuclear physics.  A white dwarf has roughly
the radius of the Earth but a mass close to that of the Sun.  No white
dwarf can have a mass greater than the "Chandrasekhar limit," about 1.4
solar masses.  White dwarfs are given spectral type designations DA, DB,
and DC according to the spectral lines seen.  These lines represent the
composition of just a thin layer on the star's surface, so the spectral
classifications aren't terribly fundamental.

White dwarfs radiate solely by virtue of their stored heat.  As they
radiate, they cool off, eventually turning into "black dwarfs."  Because
their radii are so small, though, white dwarfs take billions of years to
cool.  There may be few or no black dwarfs in our galaxy simply there
has not been time for many white dwarfs to cool off.  Of course it's not
obvious how one would detect black dwarfs if they exist.

Neutron stars are even more compact; the mass of the Sun in a radius of
order only 10 km.  These stars are supported by "neutron degeneracy
pressure," in which Fermi exclusion acts on neutrons.  Neutron stars
have a maximum mass of around 2 solar masses, although the exact
theoretical value depends on properties of the neutron that are not
known terribly accurately.  Because the radius is so small, these stars
don't emit significant visible light from their surfaces.  They may emit
radio energy as pulsars.

Some properties of black holes are discussed elsewhere in the FAQ.

All types of "compact remnants," white dwarfs, neutron stars, and black
holes, may emit energy from an accretion disk around them if a nearby
companion is transferring mass to the compact remnant.  The emission
often comes out at X-ray and ultraviolet wavelengths.

The third classification is by composition and specifically by "heavy
element abundance."  In astronomy, "heavy elements" or "metals" refers
to all elements heavier than helium.  Since heavy elements are created
in stars, stars formed later in the life of the galaxy have more heavy
elements than found in older stars.

The term "subdwarf" or occasionally "luminosity class VI" refers to
stars of low metallicity.  Because they have so few metals, they look a
little hotter than they "ought" to be for their masses or equivalently
have lower luminosity than main sequence stars of the same color.
Physically, these stars are burning hydrogen in their cores and are
similar to main sequence stars except for the lower metallicities.
Since all these stars are old, they are of low luminosity.  Their higher
luminosity counterparts no doubt existed but have long since evolved
away, most of them presumably into some form of compact remnant.


The following material is adapted from Ken Croswell's book The Alchemy
of the Heavens (Doubleday/Anchor, 1995) and is reprinted here with
permission of the author.

The terms "Population I" and "Population II" originated with Baade,
who in 1943 divided stars into these two broad groups.  Today, we
know the Galaxy is considerably more complicated, and we recognize
four different stellar populations.  To make a long story short, the
modern populations are:

      THIN DISK      metal-rich, various ages
      THICK DISK     old and somewhat metal-poor
      STELLAR HALO   old and very metal-poor; home of the subdwarfs
      BULGE          old and metal-rich

To make a long story longer: as astronomers presently understand the
Milky Way, every star falls into one of these four different stellar
populations.  The brightest is the thin-disk population, to which the
Sun and 96 percent of its neighbors belong.  Sirius, Vega, Rigel,
Betelgeuse, and Alpha Centauri are all members.  Stars in the thin
disk come in a wide variety of ages, from newborn objects to stars
that are 10 billion years old.  As its name implies, the thin-disk
population clings to the Galactic plane, with a typical member lying
within a thousand light-years of it.  Kinematically, the stars revolve
around the Galaxy fast, having fairly circular orbits and small U, V,
W velocities.  (These are the intrinsic space velocities with respect
to the average of nearby stars.  Zero in all components means rotating
around the center of the Galaxy at something like 220 km/s but no
other motion.)  Thin-disk stars are also metal-rich, like the Sun.

The second stellar population in the Galaxy is called the thick disk.
It accounts for about 4 percent of all stars near the Sun.  Arcturus is
a likely member.  The thick disk is old and forms a more distended
system around the Galactic plane, with a typical star lying several
thousand light-years above or below it.  The stars have more elliptical
orbits, higher U, V, W velocities, and metallicities around 25 percent
of the Sun's.

The third stellar population is known as the halo.  Halo stars are old
and rare, accounting for only 0.1 to 0.2 percent of the stars near the
Sun.  Kapteyn's Star is the closest halo star to Earth.  These stars
make up a somewhat spherical system, so most members of the halo lie far
above or far below the Galactic plane.  Kinematically, halo stars as a
group show little if any net rotation around the Galaxy, and a typical
member therefore has a very negative V velocity.  (This is a reflection
of the Sun's motion around the Galactic center in the +V direction.)
The halo stars often have extremely elliptical orbits; some of them may
lie 100,000 light-years from the Galactic center at apogalacticon but
venture within a few thousand at perigalacticon.  Metallicities are even
lower than in the thick disk, usually between 1 and 10 percent of the
Sun's.  Subdwarfs are members of this population.

The fourth and final stellar population is the bulge, which lies at the
center of the Galaxy.  Other galaxies have bulges too; some can be seen
in edge-on spiral galaxies as the bump that extends above and below the
galaxy's plane at the center.  The Galactic bulge is old and metal-rich.
Most of its stars lie within a few thousand light-years of the Galactic
center, so few if any exist near the Sun.  Consequently, the bulge is
the least explored stellar population in the Milky Way.

References:

Ken Croswell, _The Alchemy of the Heavens_ (Doubleday/Anchor, 1995)
(See http://www.ccnet.com/~galaxy)

James B. Kaler, _Stars and their Spectra: an Introduction to the
    Spectral Sequence (Cambridge U. Press, 1989)

Most any introductory astronomy book.