STARS

• Next we want to consider other stars. Are they similar to or different from our Sun? How do we learn about stars which are so far away?

• We already learned that we can measure masses of stars which are in binary systems using our understanding of gravity. From observations of many different systems, we find that stars come in a wide range of masses; there are stars both less massive and more massive than our Sun.

• The fact that stars have different masses imply that they may have a different evolutionary history from that of the Sun. The reason for this is that different amounts of mass imply different strengths of gravity in the different stars, and this implies that different stars will reach different temperatures in their cores when they initially form.

• Stars form when a parcel of gas in the interstellar matter starts to come together under the force of gravity. The gravitational attraction acts to accelerate the gas, thus heating it up. More massive protostars heat up more than less massive ones because they experience more gravitational acceleration. Consequently, the life history of a star depends on its mass.
  • Since we know that we must have a minimum temperature in order that nuclear reactions can occur, this implies that there is a minimum mass for stars. Models of how the physics of gas balls work suggest that if a protostar has less than about 1/10th the mass of the Sun, that it will never get hot enough for nuclear reactions to start. Observations seem to confirm this, in that we do not see stars with masses much less than this.

  • For stars which are more massive than this, up to stars with masses somewhat larger than that of the Sun, the evolution is similar to that of the Sun. During most of their lifetimes, these stars convert hydrogen to helium and the pressure generated by the heat in their cores balances the gravitational pull which tries to compress the star. As with the Sun, the hydrogen eventually runs out, gravity acts to compress the star until a new nuclear reaction which converts helium to carbon starts up. Eventually, the helium runs out, the star stars to collapse again, but the collapse is halted by electron pressure when the carbon core takes on a degenerate form.
    • Different stars take different amount of times to go through the stages of evolution.
    • The most massive stars get the hottest in the cores, so they are the ones that use up their fuel quickest; even though they have more fuel (since they are more massive), the rate of consumption is much faster, so they live shorter.
    • The more massive the star, the brighter it is during most stages of evolution.

  • For stars which are much more massive than the Sun, a somewhat different evolutionary path is followed. These have the same stages of hydrogen and helium nuclear reactions as the less massive stars. But after the helium is converted to carbon, these stars collapse and even the conversion of the carbon into degenerate matter does not provide enough pressure to stop the gravitational collapse, which is stronger in these more massive stars. The core continues to collapse until a new series of nuclear reactions set in which convert the carbon into successively heavier elements until the entire core is converted into iron. Iron is a special element from the point of view of nuclear reactions, because there are no nuclear reactions involving iron which can produce energy. Consequently, once an iron core is reached, the star collapses under its gravitational force and no nuclear reactions can stop it. Several things can happen to these very massive stars:
    • If the star is not extremely massive, the collapsing core can turn into a different state of matter called neutron degenerate matter, in which protons and electrons fuse together to create an incredibly dense star known as a neutron star. Neutron degenerate matter produces a sort of pressure called neutron pressure which can balance the gravitational force. We observe actual neutron stars when we see a sort of object called a pulsar.

    • For the most massive stars, even neutron pressure cannot hold the star up after nuclear reactions have finished running their course. We know of no other force which can hold up these stars, so we suspect that these stars may collapse into an infinitely dense point which has such strong gravity at its surface that even light cannot escape from it. Such is object is called a black hole, and there are indications that such objects actually exist in the Universe.

    • Many, if not all, massive stars experience a massive explosion as they near the end of their life which expels a large fraction of their mass back into the interstellar medium. These explosions are called supernova explosions. Different stars probably expel different fractions of their mass back into space.
      • The end stages of stellar evolution, and supernovae explosions in particular, are very important for the existence of life in the Universe because they are the means by which heavy elements are distributed into the interstellar matter.

      • We think that when the Universe original formed, it contained only hydrogen and a tiny bit of other light elements. There were no heavier atoms such as carbon, nitrogen, and oxygen which are so important for our existence today (we are made of these!).

      • The first stars converted some of the light elements into heavier ones by the process of nuclear reactions. Some of these heavier elements were distributed back into the interstellar matter by ejection of matter at the end of the lives of stars (planetary nebulae for lower mass stars and supernovae explosions for higher mass stars). These elements mixed with the original light elements, and a new generation of stars were born which had some heavier elements. This process has continued up to the current time; stars are successively formed with more and more heavier elements, which are deposited into the interstellar matter by supernovae explosions.
      • Planetary nebulae gallery
      • Stingray
      • NGC 7027
      • M2-9
      • MyCn18
      • NGC 6543
      • Final stages of massive star evolution: Eta Car
      • Supernovae remnant: Cygnus
      • Supernovae remnant: Crab

      • Some of the heavier elements form into planets around new stars, and it is from this material that life evolved. We believe that the heavy elements which we are made of were originally created inside of massive stars! In a literal sense, we are all made of stardust.

• All of this description of what goes on inside of stars comes from our stellar models, which predict what stars will look like and how they evolve based on our understanding of the physics of gas balls and nuclear reactions. These models, however, are quite well verified by observations of real stars, and we now turn to the demonstration of why we think that these models are correct.

• When we study stars, all that we get to study is the light they emit, since they are too far away for us to go to them and study them hands-on. Consequently, we need to understand the properties of light and find out what we can infer about objects from the light they emit.

• What can we observe when we look at stars, and what can we infer from these observations?
  • Color. From the color of stars, we infer the temperature - hotter stars are bluer and cooler stars are redder.

  • Brightness. The brightness of a star depends on three things: its distance, temperature, and size. More distant stars are fainter, cooler stars are fainter, and smaller stars are fainter.

  • Spectral absorption lines. The absorption lines which are present in the spectra of stars depend on the composition of a star and its temperature.

  • The Doppler shift allows us to measure something about the radial velocity of a stars.

• When we make these observations of stars, we find:
  • Most stars have similar compositions, namely: mostly hydrogen, some helium, and a little bit of everything else.

  • Stars come in a wide range of temperatures. The different temperatures make the stars have different spectra, and stars are classified by spectral type (OBAFGKM), which is a temperature sequence. O stars have surface temperatures around 30000 degrees, M stars around 3000 degrees. The Sun is a G star with a surface temperature around 5500 degrees.

  • Stars also come in a wide range of brightnesses. Brightnesses are harder to interpret because they are affected by three things: temperature, size of star, and distance. We can measure the temperature from the spectrum but we have a problem separating the effects of size and distance. We can pose the question: are different brightnesses a result of different distances, or different intrinsic brightness? Alternatively, are all stars the same size?
    • We are greatly aided in our study of stars by the presence of clusters of stars, which are groups of stars in the sky. These clusters are real physical associations of stars, meaning that all stars in a cluster are at about the same distance from us.

    • When we observe clusters, the effect of distance is the same for all stars. We find that stars in a cluster have different brightnesses, and this is caused by a combination of different temperatures and different sizes.

• When we look at a cluster, or, alternatively, when we look at a bunch of isolated stars and correct for the effects of different distances (by measuring distances using parallax, as we talked about long ago), we find that there is an interesting relation between the size of stars and their temperatures. A very useful tool for understanding stars is a diagram which plots the color against the luminosity. In such a plot, stars are only found at several locations:
  • Most stars are found along a line in this diagram, known as the main sequence. The hotter stars along this sequence are brighter, even more than expected from their temperature: they are also bigger.

  • Some stars are found which are cool but bright. The only way this can be is if such stars are very large. Consequently these stars are known as red giants. They are red because they are cool, and bright because they are very large.

  • Some stars are found which are hot but faint. These stars are known as white dwarfs.

• There are many more fainter stars than there are brighter stars.

• We can now pose the question: why do different stars have different appearances? Several possibilities come to mind: do stars with different appearances have different masses, ages, or compositions?
  • We already learned that we can measure composition from the spectra of stars and we find that most stars have similar compositions. So this is not responsible for the different appearances.

  • We can measure masses of stars in binary systems, and we find that stars of different masses lie in different locations along the main sequence. The hot, bright stars on the main sequence are much more massive than the cool, faint stars. The main sequence is a mass sequence.

  • Red giants are more complicated, however. We find red giants of a variety of masses. We believe that red giants are older stars. To understand this, we can consider what our stellar models predict for the appearance of stars as they age.

• Our stellar models use basic physics to predict what is going on both inside and on the surface of stars. These models predict that stars of different masses will have different internal and external temperatures after they are formed, depending on their mass: massive stars will be hotter than less massive stars. Our understanding of nuclear reactions and the balance between pressure and gravity also allows us to predict sizes of stars, and we find that we expect more massive stars to be larger than less massive stars. These predictions are exactly what we observe along the main sequence.

• The stellar models predict that as hydrogen is depleted, the outer parts of a star will expand and the star will get cooler at its surface. This happens roughly independently of the mass of the star. Consequently, our stellar models predict that we will observe red giants of a range of masses, just as we see.

• The stellar models predict that when the nuclear reactions finally convert all of the core helium to carbon, all that will remain of most stars (all except the most massive ones) is a small, hot core. This is exactly what is observed as white dwarfs.

• Our models also predict how long it will take for stars of different masses to go through their evolutionary stages. We find that massive stars will go through these stages much faster than less massive stars. This occurs because they are so hot in their cores that nuclear reactions proceed at a much faster pace, and the nuclear fuel runs out much faster than in less massive stars, even though the more massive stars have more fuel.
  • This understanding leads to predictions about the appearance of stars in star clusters of different ages which is spectacularly confirmed by observations. It turns out that the stars in star clusters are not only at the same distance from us, but they are also all about the same age.

  • When we look at a very young star cluster, stars of all masses are still converting hydrogen in their cores. Consequently, all stars are still on the main sequence.

  • As a cluster gets older, the more massive stars run out of hydrogen and become giants. At this point we no longer see the bright end of the main sequence, because these are the stars which have evolved to become the giants.

  • As the cluster ages further, stars are depleted from the upper end of the main sequence as they run out of hydrogen in their cores. We get more and more giants. After a certain age, we begin to see white dwarfs in the clusters, because these are the remnants of stars which have gone all the way through their nuclear reactions.

  • These predictions for the appearance of the color-magnitude diagram are verified by observation. Consequently, we have a very strong feeling that we understand the physics of stars.

• Note that our understanding of stars and our ability to match the observations very accurately provides strong evidence that some stars must be very old. We see some young clusters, but we also see clusters that must be 10-20 billion years old in order for us to be able to match the observations with our models. This provides independent evidence that the Universe is old (the other evidence came from studying radioactive decay of specimens within our Solar System).