134 9. STELLAR EVOLUTION
there are a lot of stars to study! But even more important are the existence of star clusters. For a
star cluster is a place where many stars—of different masses—formed at roughly the same time
out of the same cloud of gas and dust. And so the stars in a star cluster, although they have a range
of masses, are all nearly the same age and chemical composition.
is means that Nature has performed for us what are, in effect, controlled experiments in
stellar evolution. A given star cluster shows us the progress along the evolutionary tracks of stars
up to a particular point in time, for many different masses at once. Study a different star cluster and
you will find the same thing, but it will likely show the results after a different amount of time
has passed. us, taken as a whole, the star clusters show us snapshots in the evolution of stars.
If we plot the stars of a particular star cluster on the H-R diagram, we have what is in
essence an isochrone—a diagram of constant time. We can then calculate theoretical isochrones
using our theoretical models of the physics of stellar evolution, and compare them to the H-R
digrams of known star clusters. To the extent that this provides self-consistent results, we can
accept our theory, and then use it to determine the age of the star cluster.
Since clusters are groups of stars that are all the same distance from Earth, differences
in apparent brightness correspond directly to differences in luminosity. Figure 9.10 shows the
observed H-R diagram for two different open star clusters, M 67 and NGC 188, with the stars
from each cluster plotted with a different color. Both clusters show the lower main sequence,
but for each the upper main sequence is missing. at is because those stars, with much shorter
main-sequence lifetimes, have long ago ended their visible lives. ere is a portion of the main
sequence that seems to be bending off to the right. is is called the turnoff point and it tells us
that those stars are just now leaving the main sequence. ere are also a small number of red
giants on the upper right of the diagram.
e location of the turnoff point is an important clue to the age of the star cluster; its age
is equal to the main-sequence lifetime of stars that are just now leaving the main sequence. If
the turnoff point is higher up on the main sequence, the star cluster is younger; stars higher on
the main sequence have a shorter main sequence lifetime. And so it is clear from this comparison
that M 67 is younger than NGC 188.
9.10 WHAT REMAINS
All stars that start out with a mass greater than about 0.3 M
@
eventually become red giants or
supergiants. is is followed by a brief period of mass loss—much of the outer layers of the
star are ejected away. For stars with a range of masses at the middle of the main sequence, this
ejection is comparatively gentle, and briefly forms a beautiful planetary nebula. For upper-main-
sequence stars, it is a violent supernova explosion.
But in all of these cases, the core of the star is thought to remain, and it will be some
kind of small compact object—perhaps difficult to detect—that can simply cool off over time.
ese are the ultimate fates of stars, and I list them below in order of increasing initial mass of
the original star:
9.10. WHAT REMAINS 135
M 67
NGC 188
← Temperature
← Absolute Magnitude
Figure 9.10: H-R diagrams for two star clusters, shown in two different colors. e lower main
sequence is evident for both, as is the turn-off point. Since the turn-off point for M 67 is higher
on the main sequence than that for NGC 188, M 67 is a slightly younger star cluster than
NGC 188. (Graphic created by User:Worldtraveller, CC BY-SA 3.0.)
• M less than 0.0125 M
@
Hot Jupiter: If the initial mass is too low, then the contracting ball of gas will never become
hot enough inside to initiate any kind of nuclear fusion. It will be heated by gravitational
contraction alone. Eventually it will contract, cool, and liquefy and become an object some-
thing more like the planet Jupiter than a star.
• M greater than 0.0125 M
@
but less than 0.08 M
@
Brown dwarf: In this range of masses, the central core becomes hot enough to initiate
some minor fusion reactions, but such a star will not be able to stablize and become a
main sequence star. It will glow very dimly in the infrared.
• M greater than 0.08 M
@
but less than 0.3 M
@
Helium white dwarf: ese stars never become red giants, and after leaving the main se-
quence contract directly to a white dwarf made of almost pure helium. But this has not
happened yet, because these stars have main sequence lifetimes longer than the age of the
universe so far.
136 9. STELLAR EVOLUTION
• M greater than 0.3 M
@
but less than roughly 10 M
@
White dwarf made of carbon, neon, and oxygen, as well as helium: Stars with this range of
initial masses become red giants or supergiants, and then go through a brief planetary
nebula phase that ejects much of their mass. What is left is a white dwarf with a more
complex composition than for the lowest mass stars. Higher temperatures in the cores of
these stars has resulted in fusion of heavier elements.
• M greater than about 10 M
@
Either neutron star or black hole: ese most massive of stars end in a supernova explosion.
What remains after the explosion clears is either a neutron star or a black hole.
e ultimate fate of a star depends on its initial mass, but there are also mass restrictions
on the final product, which is often much less mass than the original star; many stars lose much
of their initial mass in either the planetary nebula phase, or in a supernova explosion. Below I
list the ranges of possible mass for these end products themselves.
1. White dwarfs: M greater than 0.08 M
@
but less than 1.4 M
@
A white dwarf cannot be less massive than 0.08 M
@
, because it would not have enough
self-gravity to squeeze it to the high densities that characterize a white dwarf. But a white
dwarf cannot be more than 1.4 M
@
. is is the so-called Chandrasekhar limit. If one were
to try to make a white dwarf with a greater mass than this, it would collapse and become
a neutron star. Stars up to perhaps 10 solar masses eventually become white dwarfs, but
they get rid of most of this mass in the planetary-nebula phase.
2. Neutron stars: M greater than 1.4 M
@
but less than about 3 M
@
A neutron star cannot have a mass less than the Chandrasekhar limit, simply because its
gravitational contraction would stop at the white dwarf stage. A neutron star can withstand
more weight than can a white dwarf, but there is a limit. e calculation is less certain, but
if one tried to make a neutron star with a mass more than roughly 3 M
@
, it would instead
collapse to a black hole.
3. Black holes: M greater than about 3 M
@
but less than about 10 M
@
A black hole cannot form if the contracting mass is less than about 3 M
@
, simply because
the collapse would stop and become a neutron star instead. e upper limit is less certain.
e most massive stars possible are roughly 100 M
@
, but it is unknown just how much of
that mass is ejected in the supernova explosion.
Note that we are talking here about black holes formed as the end products of the evolution
of stars. e supermassive black holes found in the centers of galaxies—with millions of times
the mass of the Sun—are a different matter.
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