Physics 101 Study guide for Exam 4

Physics 101 - Astronomy

Study guide and notes for Exam 4

Here are some factual statements that you might want to know for the exam. This gives you an idea of similar important ideas that you might review. You should know the definition of items that are in boldface.

Characterizing the Stars

See figures in the book or my PowerPoints to review the idea of parallax. This is used to measure the distances to the stars. Accurate measurement of the position of a star is needed in order to use parallax, so the satellite Hipparcos was launched to obtain parallax measurements of over two million stars. A more recent spacecraft called Gaia is now getting better data on many more stars. The definition of the parsec is a result of these ideas.

Luminosity is the total energy given off by a star, per second, so it would be a huge number of Watts, a very big number, in fact, so we often use the luminosity of the Sun as the basic unit, one Solar luminosity.

Apparent magnitude is the classification of the apparent brightness of the stars on a system that originally had 6 magnitudes. The brightest stars were supposed to be a 1, and the dimmest that could be seen by eye are magnitude 6. Of course, with telescopes we can see to much higher magnitudes, which are much dimmer than visible stars. The apparent magnitude depends on the actual luminosity of the star, and also its distance, since the brightness will decrease in a way that is proportional to the inverse of the square of the distance from us.

The color of the star is related to the temperature of the star through the blackbody curve. I had a list of colors for various temperatures in my PowerPoint. You should be aware that stars can be classified by the details of the spectra, as well as the color and temperature, but you aren't expected to remember the OBAFGKM scheme or the detail in the tables.

Luminosity is related to size (bigger is more luminous) and temperature (hotter is more luminous) so we can estimate the size of a star if we can determine its luminosity and temperature. This is done by using the apparent magnitude and the distance to estimate the luminosity, or in some cases, by using the spectral classes to estimate the luminosity. Sizes range from bigger than 300 times the radius of our Sun to under 1/100th the size of our Sun.

Look at the H-R diagrams in the book or PowerPoints. You should be able to point out some types of stars: blue giants, red dwarfs, white dwarfs, red giants, main sequence, and you should know what quantities appear on the axes: luminosity on the vertical axis, and temperature (reversed) on the horizontal axis. The sun is near the center, and is a fairly common type of star.

Stellar masses can be determined by studying binary stars, which are two stars in orbit around each other. Three methods are used to study these: direct observation to photograph these over a period of years (visual binaries), or by measuring the Doppler shift of the spectra of the two stars, or by observing a smaller companion star transiting its bigger companion (which is rare, since they usually aren't lined up so that we can see this happen). Along the main sequence of stars, the masses tend to increase for more luminosity, and higher temperature. Giant stars are actually fairly rare. Most stars are less massive than our Sun. The lifetime of a star is also related to the mass: more massive means shorter life. The Sun's estimated lifetime is about 10 billion years.

The Lives of Stars

Interstellar medium

The interstellar medium is mostly gas and dust. Dust grains are about 10^-7 m in diameter, about the size of smoke particles. Dust causes reddening of the light that passes through it, but NOT redshift, so if light from distant stars passes through a dust cloud which is not too thick, it will be reddened. This is due to absorption of the blue components of light (more-so in UV than visible, and much less in infrared). Since infrared is not absorbed so well by dust clouds, it might be possible to see "through" dust clouds if you use an infrared telescope or camera. Even the densest dark dust clouds are still mostly gas, not mostly dust.

The interstellar gas is very dilute, about ONE atom per cubic centimeter. In some places it is much denser. The distribution of gas is very uneven. It is mostly Hydrogen (90%), Helium (9%), and everything else (1%). The ultraviolet light from nearby hot stars (that emit lots of ultraviolet light) causes hydrogen to glow with a pinkish color. This is the origin of the pinkish or reddish color of the emission nebulae.

EGGs – Evaporating Gaseous Globules - discussed in class, these can be seen as pillars and egg-like objects in some nebulae.

The density in molecular clouds can be a million times the average density of the interstellar medium, or about one million molecules per cubic centimeter. The molecules in these clouds are mostly hydrogen molecules, which are two hydrogen atoms bonded together by a chemical bond. These are very dark in visible light, and emit mostly in the radio frequency range of the spectrum, the so-called 21 cm radiation, named after the wavelength of the radio waves.

Formation of stars proceeds in seven stages:

1 – an interstellar cloud becomes unstable because of a passing star or supernova explosion
2 – the shrinking molecular or dust cloud breaks up into fragments
3 – a fragment of the shrinking cloud is about the size of our solar system
4 – the protostar which formed at the center reaches 1,000,000 K and continues to radiate heat at the same time that it shrinks
5 – the protostar is now at about 10 times the solar radius, and the surface is at 4000K, it now looks like a star
6 – ignition of fusion in the core starts when the core reaches 10 million K, and the object is now defined to be a star
7 – after settling into a steady state, the star reaches the main sequence and stays there for most of its lifetime

The minimum mass needed to get nuclear fusion and produce a real star is about 0.08 solar mass, or about 80 times the mass of Jupiter. With less mass all we get are “brown dwarfs”.

We believe that most stars form in clusters from a single large cloud that fragments.

An example of an Open Cluster is the Pleiades cluster (M45, a.k.a. “the seven sisters”). These contain no more than a few hundred stars and have stars that lie all along the main sequence, including a few bright, blue giants. Open clusters are usually only a few million years old, and will eventually come apart as the stars move around in the Milky Way.

An example of a globular cluster is Omega Centauri. These contain hundreds of thousands or even millions of stars, but are very old, about 10 billion years old, and only stars less massive than our Sun are left, so only part of the main sequence of stars is seen in these globular clusters.

It is important to know the H-R diagram: what is plotted on the horizontal axis and vertical axis, the location of the main sequence, and the locations of red giants, white dwarfs, and the horizontal branch. Notice the diagonal lines for the stellar radius. You do not need to remember OBAFGKM.

Core hydrogen burning is the source of energy for main sequence stars for most of their lifetime. This is Stage 7, and it doesn't end until the hydrogen is mostly burned up and converted to helium, which remains in the core. Even though the helium is a very hot gas, we sometimes call it helium "ash" because it is the residue of fusion of hydrogen.

Stage 8 and 9 occur when the hydrogen in the core is burned up and burning continues in a shell around the core. The hydrogen-shell burning causes the star to expand into a Sub-giant and then a Red Giant. You should be looking at the H-R diagrams to understand how the star expands during these stages.

The helium flash is a rapid nuclear reaction that occurs for some red giants, after which there is a carbon core. The star will stay on the horizontal branch after this event, then slowly become a giant again. Now there are two burning shells, the hydrogen-burning shell and the helium-burning shell.

In stage 11, the red giant is burning hydrogen and helium at a high rate, and it becomes very large. This stage can end in two different ways, one for low-mass stars like our sun, and a different way for high-mass stars.

Low mass stars can form various planetary nebulae as the envelope is blown off by the hot core. The result is a white dwarf, which is small and mostly made of hot carbon. This white dwarf is the source of a nova that is due to a nuclear explosion of hydrogen, which might accrete on the surface of the white dwarf if it happens to be in a binary system. The accretion disk is a swirling cloud of hot material around the white dwarf in a binary system, and is the source of X-rays and other radiation that we can sometimes see. After enough mass is accreted, the white dwarf can explode in a carbon-detonation supernova (also called Type I) which completely destroys the white dwarf.

Deaths of Stars and stellar remnants

High-mass stars evolve differently, because they can fuse heavier elements than helium and hydrogen. See the H-R diagram for massive star evolution. These stars form a series of shells, like an onion, with different types of fusion reactions occurring in each shell. This whole process eventually ends in a core-collapse supernova (also called Type II).

Supernova remnants are clouds of material left after the supernova explosion. They expand rapidly and crash into material in the surrounding interstellar medium to produce a visible nebula-like object in the sky.

Stellar clusters are excellent places to look for confirmation of our theories, since they show the main-sequence turnoff clearly.

Stellar remnants - Neutron Stars and Black Holes

Neutron stars are a solid sphere, made entirely of neutrons, about 20 km across, with a density similar to the density of the nucleus of atoms. The neutron star spins rapidly, which can cause a pulse of radiation to come in the direction of observers on Earth. Neutron stars are created in the core collapse that causes the Type II Supernovae. The exterior of the star is blown off, and only the neutron star remains.

Pulsar Model: As the neutron star rotates, the emission is not aligned with the poles, so it sweeps across the sky, this is called the “lighthouse” model, this shows “hot spots” that sweep by our direction as the neutron star rotates. As a consequence, we see pulses of radiation, which might be radio, light, or X-rays. Accretion disks are sometimes seen around neutron stars, if they are in a binary system.

Black holes probably form during supernova explosions, when the collapse of the core continues past the density of neutron stars. They have a huge amount of mass, possibly as massive as a million stars, and will attract nearby mass just like any other large mass. But any mass (or light!) falling past the event horizon is lost forever, and will never escape. Black holes are completely invisible, because light cannot escape. However, the accretion disk will be very hot, and will radiate large amounts of X-rays, UV, visible light, radio, etc. We believe that there is a massive black hole in the center of the Milky Way galaxy, with an accretion disk.

For more material, see the notes in http://faculty.wiu.edu/BM-Davies/phys101notes/

In the OpenStax online textbook, to prepare for the fourth exam, read sections
17.1-4, 18.1-4, 19.1-2, 20.1-6, 21.1-3, 22.1-5, and 23.1-4 (and skim Ch. 24).
Skip the biographical notes and other extra material in the boxes if you don’t have time.
Review the Key terms and Summary sections at the end of each chapter.