Review Kirchhoff's laws
Doppler Effect equation (change in wavelength divided by wavelength = relative velocity (in the line of sight) of the object divided by velocity of light). Motion toward us is blue shift (shorter wavelength), away is red shift (longer wavelength). These terms (red shift and blue shift) are used even for wavelength regions where "color" has no meaning, e.g., radio region.
The class named various properties of stars, such as
Light becomes dimmer proportional to the distance squared of the observer from the source.
The fundamental method of determining distances to stars is parallax. A parsec is the distance of an object whose parallax is one second of arc.
The absolute magnitude of a star is the magnitude it would have if it were 10 parsecs from the sun. Another term to indicate the intrinsic brightness of a star is luminosity = how much energy a star emits in Joules/second. The sun is one solar luminosity and sets the standard for other stars.
The Hertzsprung-Russell diagram is a plot of stellar surface temperature versus absolute magnitude or luminosity. The luminosity = 4 pi Radius^2 times sigma Temperature^4. (Sigma and pi are constants.) That is, it depends both on the diameter of the star and the surface temperature.
H-R diagram.... Plot of surface temperature (or spectral type) versus luminosity (or absolute magnitude)
Luminosity = how much energy a star emits in Joules/second. The sun is one solar luminosity and sets the standard for other stars. Luminosity includes ALL radiation emitted by the star, while absolute magnitude is just the magnitude is one wavelength range.
Luminosity Class-- giant versus Main Sequence stars -- determined from the width of the spectral lines for two stars of the same temperature
spectroscopic parallax -- not a "parallax" at all, but a method to use the calibrated H-R diagram and spectral type and luminosity class to get an estimate of the absolute magnitude. When compared to the apparent magnitude, you get the DISTANCE.
Binary stars are the path to masses -- the barycenter is the balance point
Astrometric binary (where both stars are seen revolving about the barycenter)-- use Kepler's laws to get SUM of masses is proportional to a^3/ p^2 where a = average distance between the two stars
Then get ratio of masses by ratio of distances of each star from the CENTER OF MASS.
Spectroscopic binary stars show two sets of spectral lines together which separate and come together as the stars orbit.
Eclipsing binary stars occur when the orbiting stars are lined up in our line of sight such that one passes in front of/behind the other.
eclipsing binary stars give stellar diameters also...one passes in front of the other. We can watch how the amount of light changes to time the passage across. The spectral of the star gives the velocity of the stars as they orbit each other. The time of passage can then be turned into real distance units to get diameters for the stars.
Binary stars teach us that the main sequence is a sequence of masses -- see figure 8-20 of text There is a mass-luminosity relation
When examining patterns along the supergiants, giants, main sequence, and white dwarfs, we find a relation with density.
DENSITY = mass/volume.
Figure 8-23 and 8-24 show H-R diagrams for nearest and brightest stars. Note that most of the near stars are dwarf stars (red dwarfs and white dwarfs)
CHAPTER 9: BIRTH OF STARS:
Stars exist because of GRAVITY. Interstellar gas and dust is birthplace of stars. 75% is H and 25% He with traces of others (C, N, O, Ca, ...) with density of 10-1000 atoms/cc
What's in the nebula: interstellar reddening (scatter blue light) and interstellar absorption lines. Hot stars will ionize gas in a nebula and then the gas glows.
How can we tell interstellar reddening is occurring? Compare color of star as expected from spectra and compare to measured color. The star appears dimmer and redder because of the cloud between us and it.
Giant molecular clouds of about 1000 atoms/cc and temperatures of 10K held together by gravity - shock wave (like a sonic boom that compresses material) ...form a protostar. Several stars may be formed, and the radiation from the larger ones can trigger more star formation.
We can indicate on an H-R diagram the changes the protostar makes as it ages and contracts, and heats up.
Protostar -eventually becomes a star. It has an evolutionary
track on an H-R diagram. The time it takes for a protostar to contract
from a cool gas cloud to a ms star depends upon its mass.
Figure 9-9 shows a very young star cluster NGC 2264 - many lower mass stars
have not yet reached the main sequence. Blue tracks are from models, showing
what different masses might do.
Class 22: 8 March - Dr. Robbins (cancelled class)
Class 23: 10 March - Dr. Robbins
Proton-proton cycle occurs with core temperature of about 10 million degrees K.
CNO cycle (see overhead) for stars 1.1 solar masses or more, with temp of 16 million K. Like the proton-proton cycle, it also turns 4 H into 1 He
Heavy element fusion (He fusion requires at least 100 million K) = triple alpha process:
4 He +4 He -> 8 Be + gamma ray
8 BE + 4 HE -> 12 C + gamma ray
Carbon can fuse to even heavier elements if the temperature is at least 600 million
When the interior of a star heats up, it begins to expand -- and therefore cool down. As it cools, gravity pulls it and allows more heat (and more reactions) to occur).
Energy Transport: Energy flows from hot to cool regions by
Conduction = direct motion, molecule to molecule or atom to atom
Radiation = photons are absorbed and re-emitted in random directions as they work their way out. Higher energy photons are gradually converted to many lower energy ones. The flow depends on how difficult it is for a photon to move through the gas -- if the gas is dense, they are more likely to be absorbed. The opacity of the gas is a measure of its resistance to the flow of radiation.
Convection If opacity is high and radiation can't get through; it backs up and heats the mass of gas, which then rises.
Stellar models: build model of a star by making concentric shells and write down equations relating temperature, mass, density, and energy flow for each shell. The shells have to match each other at each interface.
Main Sequence Stars = stars spend 90% of their lives on the main sequence Eventually, it runs out of hydrogen in the core. The amount of time this takes to happen depends upon the mass of the stars
Giant Stars
If the core of a star is cooler than 100 million degrees, it can't fuse helium - which is all that is left there. The core contracts and turns gravitational energy into thermal energy - which heats the surrounding hydrogen (and it begins to fuse). This flood of energy moving outward pushes the atmosphere of the star outward -- expanding it to become a giant.
Degenerate matter- what happens to very dense matter when squeezed - the ideal gas law is no longer obeyed.
Electrons at dense conditions fill all lowest allowable energy states and can not slow down (that would decrease energy) nor compress further. Pressure depends on speed of electrons, but if this gas is heated, the nuclei move faster and few electrons move to higher energy states...pressure is very dense and won't change - no expansion nor contraction. Changing temperature has almost no effect on the pressure. On earth, a teaspoon of degererate matter would weigh as much as an automoblile.
Helium fusion at 100,000,000 K, He can fuse to make Carbon. The degenerate gas in the center become hot enough and it FLASHES with new fusion.... a few hours. Stars from 0.4 Solar mass to about 3 solar masses do this.
Stars greater than 3 solar masses can fuse He without going through degeneracy.
Stars more massive than 3 solar masses reach 600,000,000 and can fuse higher elements.
Stars less than 3 Solar Masses experience He flash, but those greater than 3 have their non-degenerate cores begin He fusion gradually
Stars less massive than 0.4 solar mass never get hot enough to fuse He.
After He begins to fuse, there is still H-shell fusion occurring. The flash occurs in a very short time (minutes) in which a great deal of energy is produced suddenly. This releases the degeneracy, and the process is under control. The envelope of the star contracts and grows hotter. What does this mean in terms of the H-R diagram?
Questions: Contact Mary Kay Hemenway, Ph. D.