Astronomy 162: Professor Barbara Ryden
Monday, January 27
THE MAIN SEQUENCE
``Everything should be made as simple as possible -
but not simpler.''
- Albert Einstein
- A main sequence star is powered by fusion of
hydrogen into helium in its core.
- Fusion is stabilized by a natural pressure-temperature
- High-mass main sequence stars have shorter lifetimes
than low-mass main sequence stars.
(1) A main sequence star is powered by fusion of hydrogen
into helium in its core.
Recall that a `Hertzsprung-Russell' diagram is a plot
of the luminosity of stars versus their temperature.
The main sequence on a Hertzsprung-Russell
diagram is a diagonal band, running from cool, dim, small,
low-mass stars (in the lower right corner) to hot, luminous,
big, high-mass stars (in the upper right corner):
All main sequence stars (including the Sun) are powered
by the fusion of hydrogen (H) into helium (He). Fusion
of hydrogen requires temperatures of more than 10 million Kelvin.
Above this temperature, the fusion rate is strongly
dependent on temperature: a small increase in temperature results
in a MUCH higher fusion rate. Because fusion is so
temperature-sensitive, in a main-sequence star, fusion
of hydrogen into helium occurs only in the hot, dense
All main sequence stars (including the Sun) are in
hydrostatic equilibrium. That is, the inward force of
gravity, which tends to compress the star, is balanced
by the outward force due to the pressure. (For a review
of hydrostatic equilibrium within the Sun, you can
go to the lectures for
Wednesday, January 8.)
The observable properties of main sequence stars, such
as their surface temperature, luminosity, and radius,
are all dictated by the mass of the
star. Thus, the main sequence is a MASS sequence.
Consider taking a star and increasing its mass
by pouring a little extra hydrogen gas onto it.
Because of the extremely sensitive dependence of the
fusion rate on temperature, a small change in mass leads
to a small change in the central temperature, but a
very large change in the luminosity. Expressed mathematically,
- Higher mass leads to
- Higher compression, which leads to
- Higher central density and temperature, which leads to
- MUCH faster fusion, which leads to
- MUCH higher luminosity.
L = M3.5
where L is the luminosity of a main sequence star (in units
of the Sun's luminosity) and M is the mass of a main sequence
star (in units of the Sun's mass). For instance, a star
with a mass of M = 2 Msun will have a luminosity
L = 23.5 = 11 Lsun
(2) Fusion is stabilized by a natural pressure-temperature
Also humans cannot manufacture stars, they have figured
out how to make bombs powered by nuclear fusion. In
a fusion bomb, the fusion reactions last for only a
tiny fraction of a second. In the Sun, fusion reactions
have been going on for 4.6 billion years. This leads to
Why doesn't the Sun explode like a hydrogen bomb?
The main reason why the Sun doesn't blow itself to
bits in a runaway fusion reaction is that the physical
relation among the pressure,
temperature, and fusion
rate creates a natural thermostat which
keeps the center of the Sun (and the center of
any other main sequence star) at a steady temperature.
A thermostat is any feedback device which acts to
keep the temperature of a system nearly constant.
(If you've ever been curious how the thermostat
in a home heating system works, you can go to the
``How Stuff Works'' web site.) Basically, when
the temperature drops too low, the thermostat increases
the rate at which heat is generated. When the temperature
rises too high, the thermostat decreases the rate at
which heat is generated.
How does a star's natural thermostat work? Consider what
would happen if you increased the fusion
rate in a star's core:
Thus, increasing the fusion rate sets a chain of events
into action whose end result is to decrease the fusion
- (1) Core temperature increases
- (2) Core pressure increases
- (3) Core expands
- (4) Core density & temperature decrease
- (5) Fusion rate decreases
Now consider what would happen if you decreased
the fusion rate in a star's core:
- (1) Core temperature decreases
- (2) Core pressure decreases
- (3) Core contracts
- (4) Core density & temperature increase
- (5) Fusion rate increases
(3) High-mass main sequence stars have shorter lifetimes
than low-mass stars.
A star's ``lifetime'' on the main sequence is how long
it takes to use up the hydrogen in its core. The luminosity
(L) of a star is a measure of rapidly it is using up
its hydrogen. The mass (M) of a star is a measure of how
much fuel it has. The time it takes to use up the fuel
is proportional to its amount of fuel (M) divided by
the rate of fuel consumption (L). Expressed more mathematically,
t = M/L ,
where t = lifetime (in units of the Sun's lifetime)
M = mass (in units of the Sun's mass)
L = luminosity (in units of the Sun's luminosity.
Note that since L = M3.5,
t = M/L = M/M3.5 = 1/M2.5.
The Sun will not be able to convert all its mass into helium.
For one thing, the Sun was not made of pure hydrogen when
it formed 4.6 billion years ago. For another, only the hydrogen
in the Sun's core is able to be fused; the hydrogen in the
Sun's outer layers is at too cool a temperature to fuse.
Mathematical models of the Sun's interior lead to the
conclusion that the Sun will run out of hydrogen in its core
after a lifetime of tsun = 10 billion years.
(Thus, the Sun is middle-aged, nearly halfway through its
main sequence lifetime.)
Consider a star of mass M = 0.2 Msun.
Its lifetime will be
t = 1 / (0.2)2.5 tsun = 56 tsun =
560 billion years.
Similar calculations can be done for stars of other masses.
Very hot and luminous stars (of spectral type `O' and `B')
have short lifetimes; if you see an `O' or `B' main sequence
star, you know it must be much younger than the Sun. However,
cool and dim stars (of spectral type `K' or `M') have long
lifetimes; if you see a `K' or `M' main sequence star, it
might be older than the Sun. (On the other hand, it might
Prof. Barbara Ryden
Updated: 2003 Jan 27
Copyright © 2003, Barbara Ryden