The Lives of Stars

Last: 9. How Far the Stars? Next: 11. The Origin of Elements

Stars are born inside giant clouds of cool gas and dust. Such a cloud may contain thousands of denser gas blobs; some of these blobs collapse under their own weight. Gravitational compression heats the gas until thermonuclear reactions occur. When the production of nuclear energy matches the rate of energy escape into space, the collapse halts and a main-sequence star is born. Eventually, the hydrogen in the star's core is used up, and the star flares up in last burst of brilliance before it dies.



  12.1 Starbirth   p. 278-281
  11.1 Colors, Temperatures, and Spectra of Stars   p. 245-249
  11.4 Temperature-Luminosity Diagrams   p. 252-256

Giant Molecular Clouds

The space between the stars is not empty -- it's filled with a thin, mostly hot gas of hydrogen and helium atoms. Embedded within this gas are giant molecular clouds of cold gas and dust. These clouds may be more than 100 pc in diameter and contain as much mass as a million Sun-like stars. They can be detected in different ways: they absorb starlight, and they emit microwave radiation from CO and other molecules.

One such cloud is only 600 pc away in the constellation of Orion...


Optical and CO Views of the First Galactic Quadrant [CfA]

Orion in Visible and Infrared

Barnard's loop nebula
Orion Molecular Cloud Complex [Wikipedia]

IRAS View of the Constellation Orion [IPAC]

The Sword of Orion

Astronomy Picture of the Day [NASA]

The Orion Nebula


The Infrared Hunter [Caltech]

The Orion Nebula in IR Light

Astronomy Picture of the Day [NASA]

Star Formation in Molecular Clouds

2MASS Picture of the Week [UMass]

This picture shows a cluster of new-born stars deeply embedded in the molecular cloud which formed them. Dust in the cloud dims and reddens the light of background stars as well as stars in the cluster itself. All star formation takes place in molecular clouds.

Question 10.1

Why are there no stars in part of this picture?

  1. Stars are scattered randomly, and it just happens that none fall in the middle of this image.
  2. This is a window out of the Milky Way and into intergalactic space. It's dark because there are no stars beyone the Milky Way.
  3. The dark region is a nearby molecular cloud, which absorbs light from more distant stars. Since it's nearby, there are few stars between it and the Earth.
Barnard's dark nebula #68
Astronomy Picture of the Day [NASA]

Gravitational Contraction

A sphere of gas held together by gravity heats up as it radiates. This paradoxical behavior is the key to the life-cycle of stars.

An ordinary object -- for example, an iron sphere -- cools off and fades from blue-hot to red-hot as it radiates energy.   A sphere of iron cooling down

A gas sphere held together by its own gravity heats up as it contracts.   A sphere of gas heating up

Gravity & Temperature

The remarkable fact that a gas sphere heats up as it radiates energy can be understood from a few very basic facts:

Now consider what happens as a gas sphere radiates energy into space. This energy comes from the motions of individual atoms, which slow down. As they slow down, they no longer have the speeds needed to stay in orbit, so they fall inward toward the center -- in other words, the sphere contracts. This contraction releases gravitational energy, and by the time pressure balance is restored the atoms are moving faster than they were before.

Question 10.2

Consider a gas sphere sitting quietly in pressure balance, and suppose we add energy to it (for example, by exposing it to a sudden blast of intense radiation). In response, the sphere will change its radius and temperature, and find a new balance. Will the sphere

  1. contract, and heat up?
  2. expand, and heat up?
  3. contract, and cool down?
  4. expand, and cool down?

(Hint: ignore for the moment the gradual escape of radiation which normally takes place.)

Question 10.2

Consider a gas sphere sitting quietly in pressure balance, and suppose we add energy to it (for example, by exposing it to a sudden blast of intense radiation). In response, the sphere will change its radius and temperature, and find a new balance. Will the sphere

  1. contract, and heat up?
  2. expand, and heat up?
  3. contract, and cool down?
  4. expand, and cool down?  ←  Correct!

(Hint: ignore for the moment the gradual escape of radiation which normally takes place.)

Orbital Speeds

Let's work out the speed of a circular orbit of radius R about the Sun. Using Kepler's third law, the orbit's period P is:

P = √(R 3 yr2AU3) .

The orbit is a circle, so the distance traveled in one orbital period is the circumference C = 2πR. Speed is distance divided by time, or

v  =  C 

 =  R 

√(R 3 yr2AU3)

 AU ⁄ yr .

If we set R = 1 AU, we get v = 6.28 AU ⁄ yr = 30 km ⁄ sec, which is the Earth's orbital speed around the Sun. The key point, however, is that orbital speed is inversely proportional to the square root of the radius:

v  ∝  1 


Radius & Temperature

We can use the equation just derived to work out the speed of an orbit which just skims the surface of the Sun; seting R = 0.0047 AU, which is the Sun's radius, we get

v = 92 AU ⁄ yr = 440 km ⁄ sec .

A gas of hydrogen atoms moving with this speed turns out to have a temperature

T = 1.1×107 K .

Recall that the Sun's core temperature T = 1.5×107 K; our simple calculation yields a pretty good guess for the average temperature within the Sun!

More generally, the temperature of a gas is proportional to the square of the atomic speeds; combining this fact with our previous result on the relationship between speed and radius, we have

T  ∝  v 2   ∝  1 



Within a giant molecular cloud there are thousands of small blobs of higher-density gas. If the density is high enough, the self-gravity of a blob may overcome the turbulent motion of the gas and compress it even further, and a protostar is born.

The formation of a protostar involves two distinct phases: collapse and contraction.

  Dark globules in IC 2944
Thackeray's Globules in IC 2944 [STScI]


Although completely opaque to visible light, a protostar is initially transparent to microwave radiation. As a result, the gravitational energy released as the gas blob falls inward can be radiated away rapidly, and the temperature of the gas remains low -- about 10 or 20 °K.

The collapse phase is relatively brief, lasting about 105 yr.


Eventually, the collapsing protostar becomes so dense that even microwaves can't escape. When this happens, the center of the cloud begins to warm up, and soon reaches pressure balance. The outward pressure of the gas then halts the rapid collapse, and a gas sphere forms within an infalling envelope. This gas sphere is several times the diameter of the star it eventually becomes. It slowly contracts, steadily heating up as it does so.

This phase lasts several 106 yr for a star like the Sun; more massive stars contract more rapidly.

Rotation & Disks

Rotation adds a new level of complexity to the process of star formation. Much of the infalling gas settles into a disk instead of falling directly into the central protostar. Such disks can be easily seen silhouetted against the bright background of the Orion Nebula.

Some of these disks may be forming planets as well as the central stars seen in these images.

Protostellar disks on Orion Nebula
Dust and Gas Disks Around Young Stars in Orion Nebula [STScI]

Disks & Jets

The rapid rotation of protostars is actually a barrier to star formation; unless some angular momentum can be lost, much of the gas may never reach the central star!

Although the details are unclear, it appears that jets flowing out along the axis of a protostellar disk carry away angular momentum. Jets like the one shown here are common in star-forming regions. Jets may carry away about 10% of the infalling gas; the other 90% eventually reaches the central star.   Protostellar disk and jets
Protoplanetary disc [Wikipedia]
Protostellar disk and jets
Herbig-Haro object [Wikipedia]

A Jet in Action

Time-lapse movie of a jet
Herbig-Haro object [Wikipedia]

This animation spans 5 years and shows a jet squirting away from its protostar (left). Typical jet speeds are 100s of km ⁄ sec.

A Star is Born

A protostar continues its slow contraction for several million years. All the while, the central temperature is increasing in inverse proportion to the star's radius. When the core gets hot enough, nuclear reactions begin to occur. Eventually, the energy released by these reactions balances the energy escaping from the star's surface, and stable star is born.

The Proton-Proton Chain (Review)

In the Sun's core, nuclei of hydrogen atoms (protons) are converted to nuclei of helium atoms:
  1. Two protons (p) fuse, forming one deuteron (d)
  2. One p and one d fuse, forming He3, a light helium nucleus
  3. Two He3 fuse, producing one He4, two p, and energy.
This process converts mass to energy with an efficiency of 0.7%; for example, 1000 gm of H burn to produce 993 gm of He. The missing 7 gm are converted to energy (~150 kT).
  Nuclear fusion in the sun
Proton-proton chain reaction [Wikipedia]

Main-Sequence Stars

Once nuclear reactions -- specifically, the ``burning'' of hydrogen to helium -- generate just as much energy as escapes from a star's surface, the star becomes part of the main sequence. The Sun is a main sequence star. Not all main sequence stars are like the Sun, but all have one key property in common:

All main sequence stars produce energy by burning hydrogen to helium in their centers.

To define the main sequence from observations, we need to measure two stellar properties: luminosity and surface temperature...

Luminosities of Stars

Using the inverse-square law in the form L = 4 π D 2 B, we can determine the luminosities L of stars of known distance D and apparent brightness B. We find that stars span a huge range of luminosity; for example, the 150 stars nearest the Sun have this distribution of luminosities:

of Stars
  10.0   100.0   4   Vega: L=50LSun
  1.0   10.0   14   αCen: L=1.5LSun
  0.1   1.0   25   τCet: L=0.46LSun
  0.01   0.1   21     
  0.001   0.01   57     
  0.0001   0.001   29     
  View of the solar neighborhood

Spectral Type

Spectra of stars, types O to M

A star's spectral type is a measure of its surface temperature. From hot to cool, the types are O, B, A, F, G, K, M -- ``Old Bread And Fruit Get Kinda Moldy''. (Each type is further subdivided into 10 subtypes.)

Temperature Indicators

Most stars have the same composition as the Sun, but their spectra vary a great deal due to differences in surface temperature.

Surface temperature determines the visibility of spectra lines. All these stars have the same amount of hydrogen, but H lines are strongest for type A (T = 10,000 K). Likewise, lines of ionized calcium (Ca II) are weak in hot stars and strong in cooler ones, and so on.

  Blue spectra of stars

The Temperature-Luminosity Diagram

If we plot surface temperature versus luminosity for a large sample of stars, we can see that these two properties are related. In particular, the main sequence emerges as a continuous band running from cool dim stars to hot luminous ones.

What determines where on the main sequence a given star appears? It turns out that a star's mass is the key...

HR Diagram of Hipparcos stars
Hertzsprung-Russell diagram [Wikipedia]

The Main Sequence is a Mass Sequence

On this temperature-luminosity diagram, the main sequence is highlighted in red. The numbers next to the main sequence give stellar masses.

Stellar mass increases along the main sequence; cool dim stars have low mass, while hot luminous stars have high mass. (This diagram does not include the smallest stars, which are only 8% the mass of the Sun.)

As stars age, they eventually move off the main sequence toward the upper right, as shown by the thin black tracks. Stars within the shaded region near the main sequence are still powered by hydrogen burning.

  HR diagram with models & tracks
Galaxies in the Universe, Ch. 1, Fig. 4

Stability of Main Sequence Stars

The hydrogen burning reactions which power main sequence stars are extremely temperature sensitive; a tiny increase in temperature yields a large increase in energy release. This might seem a recipe for disaster:

  →   burn
  →   temperature
  →   burn
  →   ...   →   BOOM!

This is basically what happens when a thermonuclear bomb explodes. Of course, main sequence stars are not nearly so ill-mannered. How do stars regulate their energy production?

In fact, we've already found the answer: adding energy to a star causes it to expand and cool down. When it does so, it burns hydrogen more slowly, breaking the vicious circle and restoring a balance between energy production and energy escape.

  Thermonuclear explosion
Operation Castle [Wikipedia]

Stability: a Simple Analogy

To understand the stability of main sequence stars, an everyday analogy helps:

  A running toilet

A toilet ``runs'' if there's a small leak in the flush valve at the bottom of the tank. As the water level drops, the float drops with it, the refill valve begins to open slightly, and fresh water starts to flow into the tank. Eventually, the flow into the tank exactly balances the flow out, the water level stops dropping, and your water bill goes through the roof.   Toilet anatomy

How the Analogy Works

Water level in tank = Energy content in star
Leak in flush valve = Energy radiated by star
Flow through refill valve = Energy production in star
Height of float = Temperature in core

As a star radiates energy it contracts and its core gets hot. When the core is hot enough, nuclear reactions begin to replace the energy radiated away. Temperatue continues to increase until nuclear energy release exactly balances the energy radiated into space. At this point the star is stable -- any increase or decrease in nuclear energy production is corrected by a readjustment of the core's temperature.

Question 10.3

Suppose that the energy production in a star decreases slightly. In response, does the star's core

  1. contract, and cool down?
  2. contract, and heat up?
  3. expand, and cool down?
  4. expand, and heat up?

History of the Sun

What could reduce the rate of energy production? As hydrogen is burned into helium, the amount of fuel decreases, and the core must heat up to bring the star back into balance.

This is exactly what has happened in the Sun. Studies of solar vibrations imply that about half the hydrogen initially present in the core has been converted to helium. In response, the core has slowly contracted, and its temperature has increased.

One side-effect of this increasing temperatute is a gradually increasing rate of energy flow from the core and through the Sun's surface. The Sun is growing brighter by about 6% every billion years.

  H and He fractions vs radius in Sun
The Astronomy and Astrophysics Encyclopedia, p. 866
Last: 9. How Far the Stars? Next: 11. The Origin of Elements
Joshua E. Barnes (
Last modified: October 26, 2006
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