THE STARS AS SUNS
The physical properties of stars:
Distances:
Trigonometric parallax (heliocentric parallax)-stellar triangulation.  Stellar parallax (shift in position compared to nearby stars) is determined from two positions in space 2 AU apart (6 months orbit around the sun).  The distance between the Earth's two positions is called the baseline.  Half of the measured angular shift is the astronomical parallax of a star.
The smaller the angular shift the greater the distance of the star.
The larger the angular shift, the smaller the distance.
Parsec (pc)-distance a star would be to produce a shift of 1 arcsecond using a baseline of 1 AU.  Equal to 3.26 light years or 206,265 AU.
Inverse square law for light-brightness decreases as the square of the distance.
If two stars have the same luminosity, the brighter one will be closer.
Flux (amount of energy passing through each unit of area in a second) is inversely proportional to the distance squared.
We can only measure out to 100 pc because of our limited baseline.

Surface temperature:
The different colors in stars suggests different surface stellar temperatures.
The hotter the star, the shorter the wavelength of the peak in the star's continuous spectrum.  The different colors in the spectrum where the star's wavelength peak (Planck curve) determines it's surface temperature.  The hottest stars peak in the ultraviolet.  Eg. the sun is in the green-yellow (5800K).
-A star's luminosity is also related to it's color and temperature.  A star that is has a low surface temperature, but a high luminosity can only be accounted for by a large surface area.  Likewise, if a star has a high surface temperature and a low luminosity, it must have a very small surface area.

Chemical composition:
The absorption (dark lines) spectra can be used to infer photospheric composition.  Stars that are somewhat hotter than the sun show darker Balmer (hydrogen) lines.  But, stars that are MUCH hotter than the sun have weak Balmer lines.  The reason is that at a higher temperature electrons will become excited and jump up to the second energy level of hydrogen.  At an even higher temperature, electrons are violently knocked out of the atom, leaving protons behind.

Diameter: Lunar occultations-the moon occults a star as viewed from earth.  Because we know the moon's angular speed in the sky, we can find out a star's angular diameter from and accurate timing of the occultation.
A star's luminosity is related to it's surface temperature and it's surface area.

Luminosity:
First you must measure the star's flux (the amount of energy passing through each unit of area in a second), find the earth-star distance in km, construct an imaginary sphere around the star and the earth and add up the flux over the total area.
Absolute magnitude (M) takes distance out of the equation and compares all stars at a distance of 10 parsecs.  Eg. apparent magnitude of the sun is -26.6m but at 10 parsecs it is +5M.  Vega, by comparison is 0M
Measure the star's flux (the amount of energy passing through a unit of area each second) to determine visual luminosity.

The Hertsprung-Russell Diagram (H-R diagram)-pattern of stars according to their spectoral class.  Temperature vs. luminosity for stars in the solar neighborhood (r=100 parsecs).
90% of stars fall of the main sequence line.

Determining distance with a H-R diagram:
1. Determine the spectoral type (O, B, A, F, G, K, M).
2. Look on the H-R diagram to find the absolute luminosity.
3. Measure the flux from earth and use the Inverse-Square Law for light to find the distance from the luminosity and the flux.
4. The widths of certain absorption lines will aid in determining the specific star in a spectoral type.
Luminosity Classes-Stars that have the same spectoral type, but absorption lines have different degrees of sharpness.
-Fuzziest lines are on the main sequence (m-s) and are the densest.
-Sharpest lines are giant stars and are the least dense.
Ia Bright supergiants
Ib Supergiants
II Bright giant
III Giant
IV Subgiant
V Main sequence
White dwarfs have a different classification.
Luminosity Law
1. Bright but cool stars must have large radii and low density.  Eg. red giants.
2. Hot but dim stars must have small radii and high density.  Eg. white dwarfs.

Mass: Binary stars
1. Angular size and orbital period of the binary system.
2. The distance to the binary system to convert their angular separation into a physical one.
3. Account for system's orbital tilt.
4. Newton's revised form of Kepler's third law to find the sum of the masses.
5. To find the individual masses the center of mass of the system must be known.
Each star orbits the center of mass at a distance inversely proportional to its mass.
In visual binaries, the stars cycle around their center of mass which is a straight line.  The stars distance from this line gives us the systems combined mass.  This can be seen through a telescope.
Spectroscopic binaries can determine wavelength shifts that can be turned directly into radial velocity shifts by using the Doppler effect.  The radial velocity (Doppler shift along our line of sight) and the orbital period to get the circumference of the orbit.  From that information the radius can be calculated and thus the separation of the two stars.  Using this information along with Kepler's third law will get the star's individual masses.
Eclipsing binary stars are the only way to determine the tilt of the systems orbit, which is the essential information for determining the individual masses.  Eclipsing binaries also tell us the diameters of the individual stars as they pass in front of each other.

The mass-luminosity relation-a star's luminosity is roughly proportional to the fourth power of its mass for stars with mass greater than 0.4 solar mass.  This relation tells us that the masses of most other stars do not differ widely from the sun's mass.  Stars with masses greater than about 100 solar masses are unstable, and bodies with masses less than roughly 0.1 solar mass cannot become hot enough to start nuclear reactions and become stars.

STARBIRTH AND INTERSTELLAR MATTER
Emission (bright) nebula emit light.  It is not their own though, clouds of gas and dust (mainly hydrogen and helium and oxygen) reflect light from O or B type stars nearby.
Ionized gas around the O star is called an H II region.
Neutral atom-H I (atomic hydrogen)
Atom with one electron removed-H II (ionized)
Atom with two electrons removed-H III (doubly ionized)
Radio telescopes can also detect interstellar gas by 21cm radiation.  This happens whenever a hydrogen atom's electron flips from spinning parallel with the proton to spinning in the opposite direction.  Ultraviolet observations above earth's atmosphere show very good evidence for a very hot gas of oxygen stripped of five electrons, permeating from interstellar clouds.  Polyatomic molecules have been discovered with radio waves.  Molecular hydrogen, the most abundant of molecule in the galaxy does not admit or absorb at radio wavelengths.  It absorbs and emits ultraviolet and infrared wavelengths.  The emission lines of molecular hydrogen have been observed from heated interstellar clouds by spectroscopic observations.

Interstellar dust called dust clouds significantly blocks light from stars behind it.  Extinction is the dimming of starlight and reddening is when dust scatters the starlight.  It can also reflect light causing reflection nebulas.

Dust is made of small, solid particles called grains composed of hydrogen, oxygen, oxygen, carbon, nitrogen, and silicon.  The grains are composed of silicates, iron, or graphite with mantles of ice.  Some of the mantles of grains contain organic compounds.

Hydrogen molecules form on interstellar grains, and molecules of up to four atoms form in the interstellar gas.  The formation of more complex molecules may be the product of chemical reactions, driven by ultraviolet light, in grain modules.  Dense dust grains are probably made in the atmospheres of cool super giant stars.  Ices likely condense on cores in the deep interiors of dense molecular clouds where they are protected from ultraviolet radiation.

A cloud with enough mass and a low temperature will naturally contract from its own gravity.  As gravitational potential energy becomes kinetic energy, the material in the cloud heats up.  Eventually the temperature and density builds up to a point that the outward pressure brings down the rapid collapse to a slower contraction.  Greater pressure halts the collapse and the temperature finally begins fusion reactions.  The collapse occurs fast because of free-fall controlled by gravity.  Once a core has formed, it accretes material from the infalling envelope of material surrounding it.  One model has a large spinning cloud of gas that forms smaller blobs (knots) whose masses are protostar cores.

Massive star formation from giant molecular clouds: the hot stars have heated the gas around them, ionizing it and destroying the molecules there.  The hot gas of the H II region slowly expands and runs into the cold, dense molecular cloud.  A shock wave forms and prompts gravitational collapse and star formation out of the molecular cloud.  It will finally self-destruct by a chain reaction shock wave that will create more OB stars.

Solar-type star formation: the observational evidence for the formation of sunlike stars involves molecular clouds.  Dark clouds are the observed nurseries for solar-mass stars.  They form fragments throughout the cloud rather than at the edges like the massive stars do.  The birth of massive stars sweeps away the gas and dust to make smaller stars.  T-Tauri stars are a type of young stellar objects that have low mass and are surrounded by dark clouds.  They are the only young variable stars.  They provide evidence for the star formation theory.  About ten new stars are born each year in the Milky Way.

Bipolar outflows are high-speed outflows of gas in opposite directions from a young stellar object (YSO); the result of a magnetized accretion disk around the YSO, collimating its stellar wind.   The accretion material is hot enough to produce ultraviolet photons to ionize some of the gas nearby.  If the star has formed with a magnetic field, the ionized outflow follows along the magnetic field lines.  The outflow creates a shock front that backs up the material in two lobes.
Starbirth sequence: a star forms in the gravitational collapse of part of a rotating molecular cloud; the central part gathers into the protostar, which appears as an infrared source surrounded by a dense disk.  Next, the star develops a powerful wind that breaks through the disk in opposite directions.  The wind carries along clumps of molecular material and strikes the cloud, producing shock waves.  Cavities carved by the outward flow enlarge and push away more of the dark cloud, eventually revealing the star.

STAR LIVES
The main sequence on the Hertsprung-Russell diagram marks stars at the stage of converting hydrogen to helium in their cores; stars remain at the stage for the greatest part of their lives.  Therefore, a red giant must be a shorter stage because their are less of them.  A star's mass determines how the star will evolves.

Requirements for a stable star model:  in must be in hydrostatic equilibrium, star must generate energy internally, a star must transport energy from it's core to it's surface (conduction, convection, radiation).  A star's opacity directly affects its radiative energy transport.  Opacity depends on a star's chemical composition, density, and temperature.  We need to know exactly the thermonuclear processes that produce energy, and the mass and chemical composition of a model star.

Gravity ignites the birth of a star.  A protostar gets its energy from gravitational contraction, not fusion reactions.  Once the dense core of the cloud has formed the protostar, the remaining cloud accretes upon it.  For a time the protostar has a larger radius and lower temperature than it will have a s m-s star, and because of the larger radius it will also have a higher luminosity.  Convection then transports energy outward so a protostar is completely convective, a bubbly mass.  As the protostar shrinks, its luminosity decreases and the core continues to heat up.  When the core hits 10 million kelvins, thermonuclear reactions begin and a star is born.  At this stage it is called zero-age main sequence.  The star's mass will determine where it ends up on the H-R diagram.  In the main-sequence lifetime the star's energy is transported through its interior mainly by radiation.  The more massive a star, the faster it burns hydrogen (15 solar-mass star would last only 5 million years).  The m-s phase ends when almost all of the hydrogen in the core has been converted to helium.  The temperature in the core decreases gradually and luminosity increases because of the greater flow of energy to the surface.  The star becomes a red giant.  Thermonuclear reactions stop in the core, but continue in the shell around the core, where fresh hydrogen still exists.  Gravity takes over in the core and it contracts, heating up the hydrogen in the outer shell causing the luminosity to increase.  The star's radius increases, temperature decreases, and opacity increases.  The red giant core becomes a degenerate electron gas where electrons produce a degenerate gas pressure which depends only on density, not temperature.  This makes it possible for the core to attain and preserve a balance even though no fusion reactions are going on.  Then the degenerate core begins a triple-alpha reaction where helium burns to create carbon and energy.  This process is called helium flash.  The star decreases its radius and luminosity a bit to adjust.  Eventually the core is converted to carbon, core reactions stop, but the outer layer still burns hydrogen.  The star expands again as a red giant.  Thermal pulses, thermonuclear explosions in the shell can cause the star's luminosity to rise and dip up to 50%.  A superwind, a very strong outflow of mass from the surface, blows off the envelop of the star in gusts.  A hot core is left behind and the hot material left behind forms an expanding shell of gas heated by the core, called a planetary nebula.  The leftover core finally becomes a white dwarf and then a black dwarf.

Stars with smaller percentages of heavy elements and less mass than the sun make a horizontal line on the H-R diagram called the horizontal branch during the phase of burning helium in their cores.  Theses stars have a lower mass than when they were m-s stars.

Massive stars differ in their evolution because they can reach higher temperatures in their cores and throughout their interiors.  While in the m-s the star burns hydrogen by the CNO cycle.  The star's m-s lifetime is shorter, the higher temperatures kindle fusion of carbon and heavier elements in the core.  The helium-rich core does not become degenerate and energy is transported through the interior mostly by convection rather than radiation.  The star will still become a white dwarf.

For observational evidence, stars must be seen at the different life cycle stages.  Galactic (open) star clusters have a loose array of stars.  They have an average of about 100 stars within a diameter of 10 yr or 0.1 star per cubic light year.  Globular clusters contrast dramatically with open clusters.  They have distant spherical shapes with stars as close as a hundred per cubic light year.  The H-R diagram of a globular cluster shows the m-s turns off to the red giant branch and the upper end of the m-s disappears. It instead, makes a horizontal branch that indicates that globular clusters are very old (15 billion years).  The horizontal branch indicates also that globular stars are less massive and have fewer heavy element than the sun.

The stars in a open cluster are called Population I stars.  The brightest PI stars are blue-white and have 100 x the luminosity of PII stars.  Population II stars occur in globular clusters with their brightest stars being red giants.  Spectroscopic observations shows that PI stars have essentially the same composition as the sun-1 to 2% by mass of heavy elements.  PII stars contain only about 0.01 to 0.02% of the mass.  This shows that PI stars are younger than PII stars.  When a massive star dies it spews a lot of material back into the interstellar medium.  This blown off material has been enriched with heavy elements and from it new stars will be born.  As a cluster ages, the m-s will gradually shorten as the stars peels off, in order of mass, and evolve over into the red giant region.  This turnoff point gives the age of the cluster, when compared to the evolutionary tracks of theoretical models.  The comparison also confirms the general validity of star models.

Variable stars are in the later stages of life that have rapidly varying luminosities.  They lie above the m-s on the H-R diagram because they are post m-s, burning helium.
Periodic (regular variables)-change in luminosity with time follows a regular cycle over a certain period.  RR Lyrae stars have a typical period of 12 hours.  They are P II stars and have about 100x the sun's luminosity.
Cepheid variables have periods of 5-10 day period for P I stars and 12-20 day periods for P II stars.
Red variables have irregular cycles of light variation that range from 100 to 2000 days.  They are red giant and supergiant stars, both P I and P II, with luminosities about 100x that of the sun.

Nucleosynthesis:  when a star first becomes a red giant, thermal pulses, sparked by the triple-alpha process, burn helium and carbon, which is then transformed to oxygen.  The convective zone that develops as a result of the pulses reaches down to the star's core and pulls up elements that have been made with hydrogen burning.  This whole process is called dredge-up.  For medium-mass stars (5 solar masses), the second phase of nucleosynthesis takes place after a star has burned up all of its helium in it's core.  Thermal pulses then convert helium to carbon, carbon to oxygen, nitrogen to magnesium, and iron to certain neutron-rich isotopes (more neutrons than protons in the nucleus) of heavier elements.  The convective zone brings these to the surface, in a process called second dredge up.

STARDEATH
White Dwarf is a small dense star that has exhausted its nuclear fuel and shines from residual heat.  The only force working against gravity is called a degenerate electron gas where pressure is not related to temperature and depends only on density.  The electrons can only resist the force of gravity in stars that are less than 1.4 solar masses.  The stored thermal energy in the star flows to the surface by conduction because of the density.  The more massive the white dwarf, the smaller its radius will be, in contrast to a m-s star where a more massive star has a larger radius.  Chandrasekhar limit is the point at which degenerate electron matter is crushed by gravity-1.4 solar masses.
Brown dwarfs are objects without enough mass to ignite thermonuclear reactions in their core.  They have surface temperatures of about 3000K.
Neutron stars are extremely dense stars with radius of about 10 km or less.  They form from more massive stars where the inward pull of gravity is greater.  The force of gravity is balanced by inverse beta decay where a proton and a electron form a neutron and a neutrino (energy).  The neutrons provide degenerate gas pressure to allow a stable star composed mainly of neutrons.  They have three layers: a core of neutron fluid, followed by a crust of fluid or solid lattice with a thick solid crystalline crust and an atmosphere of iron atoms.  Like a white dwarf the larger the mass of neutron star, the smaller the radius.  A neutron stars limit is about 2-3 solar masses.

A nova is a star that has a sudden outburst of energy, temporarily increasing its brightness by hundreds of thousands of times.  Light curve is the plot of a nova's rise and fall in brightness.  The star's photosphere expands dramatically to about 100-300 solar radii.  Second, the photosphere collapses back onto the star.  Third, a shell of material is blown off the star and rapidly expands away from it.
Observations indicate that all novas occur in close binary systems.  The stars are so close together that matter may flow between them.  The nova occurs on the white dwarf companion of the system when the matter from the donor star flows onto an accretion disk around the companion white dwarf.  It does this by existing within the Roche lobe, a region between the two stars that gravity dominates.
Supernovas are cataclysmic explosions that spew out energy in extraordinary amounts (10 billion times the sun's luminosity) that signals the death of a massive star.  Type I supernovas have sharp maximums on the light curve (10 billion solar luminosities) and die off gradually.  Type II have a broader peak at maximum (1 billion solar luminosities) and die away rapidly.  The features of spectra are the best way to differentiate the type of super- nova explosion because Type II show strong hydrogen lines, and Type I do not.  Most SN output is in the form of neutrinos rather than electromagnetic radiation.  O and B stars are expected to become supernovas after they evolve off of the m-s and become red supergiants.
A supernova explosion sends out a blast wave into the interstellar medium.  The shell of material creates a shock wave the plows through interstellar gas and dust.  The shock wave's collisions with the cool clouds of the interstellar medium can excite the interstellar material, making it glow and produce emission lines.  The luminous material marks a supernova remnant.  Radio astronomers recognize supernova remnants by a special property of their radio emission.  A plot of intensity versus frequency displays a nonthermal spectrum, showing that it is a supernova remnant and not a thermal hot gas.  The nonthermal spectrum produces high speed electrons that accelerate to form synchrotron radiation, radiation from an accelerating charged particle (usually an electron) in a magnetic field.  The intensity and wavelength range of this radiation depend on the intensity of the magnetic field and the kinetic energy of the electrons.

The Crab Nebula is a supernova remnant.  It appears in a spot where Chinese and Japanese astronomers observed a bright star in 1054 A.D.  Doppler shifts show that the gas is expanding.  It is also polarized, the planes of its vibrating motion tend to be oriented in the same direction.  A large amount of energy is added to the nebula over a time of only a few years emitting from a pulsar in the nebula.

When the core of a star ends up as iron, its fusion reactions stop.  Gravity squeezes the core to higher temperatures and densities.  The photons gain so much energy that they penetrate the iron nuclei and break them down into helium.  As the iron disintegrates into helium, large amounts of heat are used up.  Photons that normally would provide the radiation pressure to support the star are splitting iron nuclei instead.  The pressure in the core no longer supports the star, and it collapses suddenly.  The gravitational collapse rapidly pumps heat into the material.  In the collapse protons and neutrons released by the disintegration of nuclei in the core pelt and penetrate the remaining nuclei.  If these particles capture neutrons, they can be transformed to heavier elements.  Then, the layers above the core plummet inward toward the core and heat up.  Suddenly, ignition temperatures of many fusion reactions are reached.  They turn on explosively and neutrinos are produced.  Finally, the inner core's collapse creates a neutron star; degenerate pressure stops its collapse, and the material rebounds outward.  As infalling matter from the outer core crashes in the rebounding inner core, a shock wave forms; it blasts its way outward from the core in tens of milliseconds.

Pulsars are rapidly rotating neutron stars found in the remnants of supernovas.  Pulsars were discover by radio observations because of their regular rate of pulse.  The duration of the pulse can determine the size of a pulsar by timing its on/off rate.  Rotation accounts best for the clock mechanism of pulsars.  The lighthouse model for pulsars says that the rotation provides the pulse period and the magnetic field generates the electromagnetic radiation.

A black hole is created when the overwhelming pressure of gravity crushes a star into infinite density.  Photons of light are trapped by the intense gravitational field in an orbit around the star.  The escape velocity from the star is greater than the speed of light.  The Schwarzschild radius is the critical size that determines the size of a black hole.  1 solar mass-3km, 2 solar masses-30km, etc.  Runaway gravitational collapse and a supernova can cause a black hole.  For someone falling into a black hole, time would speed up as they passed the event horizon and they would witness the end of the universe before they fell into the singularity, the theoretical end to runaway gravitational collapse.  Matter is squeezed so tightly that it occupies no space or volume.  From the viewpoint of an outside observer, the person journeying into the black hole would be frozen in time just before they reach the event horizon.

The only way we can get evidence of the existence of black holes is by observing binary star systems where they interact with visible matter.  Cygnus X-1 is a binary system that emits x-rays from a hot accretion disk around a suspected black hole.  It has a mass of at least six solar masses.  A sign of a possible black hole is a rapidly varying x-ray source, which must be eclipsed at regular intervals in a binary system.  The high temperature of the accretion disk would produce x-rays and be an indication of a black hole sucking off mass from it's companion star.

Cosmic rays are particles that travel close to light speed through the interstellar medium.  Their origin probably relates to star deaths for they carry much of the energy of the interstellar medium.  They are charged particles-usually protons of hydrogen, helium nuclei, electrons, and light nuclei.  Supernova explosions, pulsars, sources outside the Milky Way, and intergalactic magnetic fields and supernova shock waves can all accelerate particles to such high speeds.