NS102: The Physical Universe
Prof. Bechtold
Fall 2000

PROPERTIES OF STARS

The Spectral Class (OBAFGKM) is a sequence of surface temperature, ranging from hot (T=20,000K) for O stars to cool (T=2500K) for M stars.

The H-R diagram, or Hertzprung-Russell diagram is a plot of luminosity or absolute magnitude versus spectral class or surface temperature.

In the H-R diagram, many stars, including the Sun, fall on the MAIN SEQUENCE. Stars on the main sequence shine because they are converting hydrogen to helium in their cores by fusion: either by the proton-proton chain (for cooler stars, M<1.1 solar masses) or the CNO cycle (for hotter stars, M>1.1 solar masses). The CNO cycle has the net result of turning hydrogen to helium, but requires C, N and O atoms for intermediate steps of the fusion chain.

In addition to the Main Sequence on the HR diagram there are "Red Giants" and "Red Supergiants" which are bright for their surface temperature. These are stars which have evolved off the main sequence and are bright because they are so large.

White dwarfs are hot, dim stars on the HR diagram.

The spectral class OBAFGKM is also a sequence of mass , with O stars the most massive (30-50 solar masses) to M stars the least massive (few tenths of a solar mass).

Masses of stars have been measured directly in a few cases when the star is a member of a binary star system. Then the doppler shifts of the spectral lines in the stellar spectra can be used to measure the velocity of the stars, and then you can compute the mass required to keep the stars from flying apart. Binary stars can be "visual binaries" meaning that you can see each member of the binary separately, or "spectroscopic binaries" meaning you can't see each member of the binary separately but you see spectra of two types of stars and one set of lines moves one way and the other another way.

Massive stars have shorter main sequence lifetimes than less massive stars. This can be understood qualitatively by recalling that a star on the main sequence is in HYDROSTATIC EQUILIBRIUM meaning that the force of its gravity (which tends to make it collapse) is balanced by gas pressure. More massive stars require higher temperature gas to avoid collapsing than less massive stars. At higher temperatures the CNO or proton-proton fusion process runs faster and the star uses up its hydrogen quicker. O and B stars have short lifetimes: a few million years. M stars have very long lifetimes: 100 billion years. The Sun's main sequence lifetime is about 9-10 billion years.

Photons produced in the center of stars by fusion slowly make their way out of the star by a "random walk" process. Stars are very opaque. This means that a photon travels a short distance (in the center of the Sun on average a few cm) before interacting with an atom. It takes a typical photon several hundred thousand years to make it from the center of the Sun to the surface. If it flew straight out at the speed of light (ie if the Sun were transparent) the trip from the center to the surface would take only a few seconds.

If you took a random sample of a million stars in our galaxy: 900,000 would be main sequence stars, 95,000 would be white dwarfs, 4000 would be red giants and 1 would be a red supergiant. On the main sequence, O and B stars are rare, and less massive stars are common.

BROWN DWARFs are substellar objects, with masses in the range of 0.1 - 0.01 solar masses, or 10-100 Jupiter masses. They are not quite massive enough to make their centers hot enough to have fusion going on. Just how Brown dwarfs relate to planets like Jupiter and very low mass stars (like M stars which are shining by fusion) is an interesting question of current research.

STAR FORMATION

Stars are forming today, in the disk of the Milky Way and other spiral galaxies.

The INTERSTELLAR MEDIUM (ISM) refers to the gas and dust in interstellar space. Although the mass of the ISM in the Milky Way is only about 5% of the total mass, the ISM is important because new stars form out of the ISM, and the ISM also can be opaque to optical light, making it hard to see very far in the disk of our galaxy.

DUST GRAINS are small particles of 10^6-10^9 atoms, containing a core of silicates, iron, and graphite (carbon), and a mantle of ices, such as H2O, NH3 and CH4. Dust grains are opaque to optical photons, and appear as black regions in optical pictures. IR photons can pass through dust relatively unattenuated (remember the 10 micron camera demo). So IR photographs are useful for seeing deep into star-forming regions.

MOLECULAR CLOUDS are clouds of gas which are so cold (T=10 K) that most of the gas is molecular. Molecular hydrogen (H2) is the dominant molecule, but there are many molecules detected including diatomic molecules like CO and much more complex molecules like alcohol and even orgainics. Molecules are detected with milimeter and radio telescopes, since molecules vibrate and rotate and produce spectral emission lines, which have wavelengths in the mm and radio.

Stars form in molecular clouds when a perturbation such as a supernova shock wave causes the cloud to collapse. The collapsing cloud fragments and forms a cluster of stars of different masses. The massive O and B stars are hot, and produce a lot of UV photons which ionize the atoms in the remaining ISM. The red color in pictures of star-forming clouds (also called nebulae) is the result of hydrogen atoms recombining. The green color is from oxygen atoms where the electrons have been excited to a high energy state by motions in the gas and then decay back down to the ground state. Reflection Nebulae (e.g. the Pleides) have dust which reflects the optical and UV light. We looked at a lot of magnificent pictures of star-forming regions such as Orion and the "Pillars of Creation".

As individual stars collapse, they go through a phase before they reach the main sequence when they have a large, rotating disk of infalling material (remember the demo on conservation of angular momentum). Perpendicular to the disk they have jets of OUTFLOWING material which eventually clears out the surrounding ISM. The disk eventually forms planets, asteroids, etc. Several proto-planetary disks have been imaged directly, e.g. Beta Pic.

Eventually the cluster of stars moves away from its place of birth, and the stars are mixed in with the other stars in the disk of the Galaxy.

Before it reached the main sequence it was fainter and cooler. This pre-mainsequence phase lasted about 50 million years. The Sun has been on the main sequence (burning H to He) for about 4.5 billion years.

As the Sun burns hydrogen in its core it gradually gets hotter and brighter. In about 1.1 billion years it will be 10% brighter than it is today. This will cause enough of a greenhouse effect on Earth that the water will evaporate out of the oceans. In 3.5 billion years, the Sun will be 40% brighter and conditions on Earth will be similar to the conditions on the present-day surface of Venus.

After about 11 billion years on the main sequence, the Sun will have exhausted the hydrogen in its core and the core, which is mostly helium, will collapse. Fusion continues in a shell outside the core, the Sun's outer regions will expand, and the Sun will be a red giant. We don't know exactly how far the Sun will expand -- some calculations indicate that the outer atmosphere of the Sun will extend as far as the present-day orbit of Mars. In that case, the inner planets, including the Earth, will be INSIDE the solar atmosphere and will quickly spiral in (due to friction) and be engulfed in the core.

During the red giant phase, fusion continues in shells around the core, and Helium is fused to C, O, Si, and heavy elements up to Fe (iron). Eventually the star becomes unstable and pulses, expelling a Planetary Nebula. What is left is a hot core, which lights up the Planetary Nebula, so you see the same red and green colors as in a star-forming region. The core is a White Dwarf, a hot (T=100,000) dense star the size of the Earth which subsequently cools and becomes dimmer and dimmer.

What happens after the main sequence depends on the mass of the star. Stars with mass < 6 Solar masses become white dwarfs (and shed their outer layers as planetary nebulae). Stars with mass = 6-20 solar masses become neutron stars (and explode as supernovae). Stars with mass > 40 solar masses become black holes (with the explosion of a supernova also).

A WHITE DWARF is a compact object, where the gravitational collapse has been halted by ELECTRON DEGENERACY PRESSURE. They are typically about a solar mass, and have a radius R = 0.01 R(sun). The Chandrasekhar limit (the maxiumum mass a white dwarf can have ) is 1.4 M(sun).

If the core mass is greater than the Chandrasekhar limit, then electron degeneracy pressure is not sufficient to halt gravitational collapse, and the star collapses further. The star eventually is so dense that protons + electrons are squished and become neutrons, and then NEUTRON DEGENERACY PRESSURE stops the collapse. When this happens the outer layers still falling in "hit a brick wall" and bounce, being ejected in a bright supernova explosion. For a brief time, the supernova is billions of times more luminous than the Sun.

Supernovae are so bright that nearby ones are naked eye objects, visible in some cases during the day. We estimate that one occurs in a galaxy like the Milky Way once every 100-1000 years. In 1054, the Crab SN exploded, and was seen by Native Americans, and the Chinese, who dubbed it the Guest Star. In 1604, Tycho saw one, which bears his name. SN1987a was a supernova in the Large Magellanic Cloud, visible from the southern hemisphere. It was notable because neutrino telescopes, built to measure solar neutrinos, detected neutrinos from it.

PULSARS are rotating neutron stars. They were discovered in 1967 by graduate student Jocylyn Bell with radio telescopes in England. Pulsars exhibit pulses of radio waves, thought to be produced when a hot spot or beam of radiation associated with the magnetic field of the neutron star rotates past us. The radio hot spot is produced by synchrotron radiation, the result of relativistic electrons orbiting in magnetic field lines.

Black Holes are the result of a collapsing stellar core with core mass > 3 solar masses. The black hole is a "singularity", and has zero radius and infinite density. If anything enters the event horizon of the black hole it cannot escape -- the escape velocity is greater than the speed of light. A famous theorem in general relativity is "black holes have no hair", that is, once a black hole is formed, you can't tell what it's made of. Black holes can be detected by their gravitational effects. They curve space near them. When they are in a binary star system, material from the companion can fall on the black hole and form a rotating accretion disk. The accretion disk emits X-ray photons, and several objects believed to be black holes have been discovered in our galaxy: e.g. Cygnus X-1. A white hole is the (theoretical, never observed) opposite of a black hole, connected to a black hole by a worm hole. Black holes were originally called "frozen stars" because someone falling into one would appear to an outsider to move more and more slowly as they approached the event horizon.

NUCLEOSYNTHESIS

A profound result of the scenario for stellar evolution we have described is the star-gas-star cycle. Molecular clouds collapse and form stars; the stars fuse H, He into C, Si, Fe and other elements in their centers; and then the stars die as planetary nebulae and supernovae, dispersing the newly made elements into interstellar space. New stars form out of the contaminated interstellar gas, and have more C, Si, Fe etc. Thus, with time, stars that are being made start out on the main sequence with more heavy elements than earlier generations of stars. The Sun, for example, cannot be the oldest star in the Universe, since it is relatively rich in C, Si, Fe etc. The atoms that make up most of the Earth and the bodies of living things, were produced by fusion by previous generations of stars.

Fusion is effective in building up nuclei up to iron. Heavier nuclei are not stable and fission tends to make them split into less heavy nuclei. The most stable element is iron.