Parallax:

-What is the formula and what is it measured in?

-How are both nearby and faraway stars involved?

• d=1/p
• d: distance in parsecs
• p: parallax angle in arcseconds
• Measures distance of nearby stars compared to far away star

Luminosity:

-define

-what it's measured in

Apparent brightness:

-define

-what it's measured in

-where its mesaured

-formula

• Total light output of a star
• Measured in Watts, but usually given in reference to sun's luminosity

• How much solar radiation a star gives out in a certain area
• Watts per square meter: W/m²
• Measured outside Earth's atmosphere because not all solar radiation makes it to the ground
• B = L/(4∏d²)
  • L: luminosity in Watts
  • d: distance in meters

Stellar Magnitudes

-define

-how do the values relate to its brightness?

-what type of scale is it

-does it measure luminsoity or apparent brightness?

-What is absolute magnitude?

• a scale that gives the apparent brightness (not luminosity) of stars
• The lower the value of stellar magnitude, the brighter the star is
  • Arranged like a race: #1 is better!
• Logarithmic scale
  • A difference of 5 magnitudes corresponds to a brightness ratio of 100:1
• APPARENT BRIGHTNESS

• Brightness of a star if it were 10 parsecs from us

Ratio of Apparent Brightness

B₁/B₂ = 2.512^{(M₂−M₁)} = 100^{(M₂−M₁)/5}

-Should B1 or B2 be dimmer in order to keep the exponent positive?

-How would you phrase a sentence to describe which is brighter than which and by how much?

• B₂ should be dimmer, thus M₂ is a greater number that M₁--keeping the exponent positive
• B₁ is ______ times brighter than B₂

Absolute magnitude
-What does it relate to?

 -What do we know about the sun's absolute magnitude?

• related to luminosity
• Sun's absolute magnitude is +5
  its luminosity is L_sun

• Side note: A star with luminosity 100L_sun will have a magnitude of 0

• Visual binary- one way of determing the physical behavior of stars which leads us to find their mass

• Orbital periods of visual pairs are determined observationally in cases where the stars can both be resolved

• Eclipsing binary - one way of determing the physical behavior of stars which leads us to find their mass

• One star passes in front of the other
• Overall brightness decreases when star is eclipsed
• Looking at plot of (apparent) brightness over time can determine the orbital period of the stars

• Spectroscopic binary - one way of determing the physical behavior of stars which leads us to find their mass

• Looking at Doppler effect in the spectral shifts
• leads to determining relative velocity of star toward or away from us

• Kepler's 3rd law!!!
  • Using the modified version of the law we can find out the mass of the whole system
  • If we know the relative speeds of each star
    • ex. Star A is 4 times faster than Star B
  • we can use that to figure out the masses
    
    • Star B is 4 times more massive than A--
    • divide their total mass into 5 parts
    • A gets 1 and B gets 4

• Absorption spectral lines

• spectra produced by gasses in the photospheres of stars
• prominence of lines depends on temp
• determining temp involves comparing spectrum with a catalog of known spectra and determining its spectral type

• main sequence stars are densest (not counting white dwarfs) and have wide spectral lines
• giants are least dense and have thin spectral lines

OBAFGKMLT

-What is this? and what does it classify?

-Which is hottest/coolest?

-How is the classification furthered?

Oh Be A Fine Guy/girl Kiss Me Later Tonight

• Spectral classification, classifies stars by temp
• Type O is hottest and Type T is coolest
• Furthered by numbers 0 (hottest) to 9 (coolest)

Measuring stars

-What issues are encountered when trying to measure star diameters?

-What technique has been developed for giants and supergiants?

• Atmospheric blurring and telescopic effects smear light

• Interferometry
  • combining light from 2 or more telescopes to pick out detail; very advanced, very new
  • Speckle interferometry: multiple images from same telescope to increase resolution and eliminate random occurrences

Size of stars in eclipsing binary systems

-What do we graph against what to to help determine time?

-How does velocity factor in?

• Graph of brightness vs. time is takes star to pass in front of the other
• Using velocities (found from Doppler shift) we can determine their size

Update Stephan Boltzman Law:

L = σ A T⁴ = 4Π σ R² T⁴

-How is this used to find size of a star?

-What else must we know first?

• Luminosity proportional to area and temperature to the 4th -- knowledge luminosity and temp = knowledge of area = knowledge of radius
• Most common way to determine star size

• So here's how we determine the size of a star:
  
  • use its apparent brightness and distance to
    determine the luminosity from the inverse square law.
  • Use its spectral type to determine
    its temperature.
  • From the Stefan-Boltzmann law, the luminosity and temperature of a star can tell us its radius

H-R Diagram!

(Hertzsprung-Russell Diagram)

• Vertical axis: Luminosity of the star
• Horizontal axis: Temperature (L:highest, R:lowest)
• LOGARITHMIC SCALE

Stellar Radius

• Using Stefan-Boltzman law (luminosity=temp⁴x radius²) we get straight lines on a logaritmic scale

• Green lines = lines of constant radius
• Slope of line tells us that for a given radius hotter stars are brighter and cooler stars are dimmer

• Hot but dim stars: small radius
• Cool but bright stars: large radius

Stellar Mass

• Luminosity=Mass^3.5
• Magic formula!!!!!
  • Luminosity in solar luminosities
  • Mass in solar masses
• Note: formula only works for main sequence stars

Luminosity Class

• For a given temperature...
  • brightest stars have thinnest spectral lines
  • dimmest stars have thickest spectral lines

• Reasoning for this...
  • Effect is caused by density of photosphere
  • Denser the gas >>
    greater # of atomic collisions >>
    less well-defined the atomic energy levels >>
    wider range of photo wavelengths for a given transition in high density compared to low density

• Class I stars = large, diffuse (low density), supergiants
• Class V = main sequence stars

Spectroscopic "parallax"

-What can we determine with it?

-What steps are followed?

• Distance of stars with distances too great to be measured by actual parallax
• Isn't really parallax as we would think of it, but called that because it determines distance
• Generally used for stars 500 parsecs or more away

• Know spectral class (temp) and luminosity class (size) from observed spectra
• Read graph for luminosity
• Use luminosity and apparent magnitude to find distance through inverse sq. law

Evolution of low-mass star

1. Star forms from collapse of gas and dust in nebula
2. As star heats up, some energy is ejected in bipolar flows
3. Core of star becomes hot enough for fusion to start; main sequence (stays here for a while, ie billions of years)
4. Core shrinks and heats up when fusion stops--outer parts of star expand to red giant stage
5. Helium fusion stars in the core, core stabilizes and star shrinks to yellow giant stage
6. When Helium fusion stops, the core shrinks and outer layers expand again for 2nd red giant stage
7. High stellar winds blow outer materials away from core--planetary nebula forms
8. Degenerate helium/carbon core of star forms in the middle--white dwarf. Same mass of Sun but size of Earth, start out hot and slowly cool off

Evolution of high-mass star

1. Star forms from collapse of gas and dust in nebula
2. As star heats up, some energy is ejected in bipolar flows
3. Core of star becomes hot enough for fusion to start; main sequence (stays here for a while, thought not as long as low mass stars
4. Once fusion in the core stops, the core will shrink and the surface will expand until helium
   fusion starts in the yellow giant stage.
5. This star will "pulsate" in radius and brightness,
   yet its surface will continue to expand and cool as different types of fusion take place
   in and outside of its core.
6. Once fusion in the core ceases, the core will collapse violently, releasing a great deal of
   energy as a supernova.
7. The core of the star will have collapsed to a neutron star or even a black hole.

-How are stars born?

-What happens if they are 8% the mass of the sun?

-What is a brown dwarf?

-What if their mass is 150 solar masses?

-What is the common size of stars?

• Born of nebulae
• Cloud collapses and increases rotation (to conserve angular momentum)
• More it condenses--becomes hot enough to glow

• Larger than 8%: becomes hot and dense enough for fusion

• Brown dwarf: hot, small never-developed small; happens when the mass is less than 8% solar mass

• Prostelar winds blow away excessive material
• 150 solar masses is like an upper limit on star size

• 30 solar masses
• rare for there to be enough material to form super-massive stars

-How do stars balance gravity and pressure?

-Is this like or unlike the Sun?

-What are the two types of hydrogen fusion?

-Which one is common for smaller stars?

-For larger stars?

-What is the general process for both?

-How is the CNO cycle different?

• Proton-proton chain
  • smaller stars 
  • four hydrogen nuclei (protons) are eventually fused into a helium nucleus through direct
    fusion

• CNO cycle
  • larger stars with hotter cores
  • two hydrogen nuclei into a single helium nucleus
  • procedes by fusing the protons to various other nuclei in the process (Carbon, Nitrogen and Oxygen)

t = M/L×10¹⁰ years
t = M^−2.5×10¹⁰ years

Explain this formula

-What does it tell us?

-What are the units?

• Lifetime of a star on the main sequence

• M in solar mass units
• L in solar luminosity units

• The more massive a star, the more fuel is available in the core for fusion to take place.
• On the other hand, the more luminous the star, the faster it emits fusion energy and burns up the core fuel.

• Once stars leave the main sqeuence, their cores will shrink and the surfaces will expand as they become red giants.

• Very massive stars will procede roughly horizontally along the main squence, as the increased brightness due to expansion is balanced by the decreased brightness due to cooling temperatues.

• Low mass stars, on the other hand, will get rather much brighter as they expand

• Once the cores of stars shrink sufficiently, hydrogen fusion can actually initiate in the shell.
• This shell fusion will cause the surface of the star to continue expanding to the red giant or red supergiant stage.

• Only a star M>.5M_sun can do this

• Once the core shrinks to a sufficiently high density and temperature, helium fusion can occur in the core
• Helium fusion in the core mostly procedes by the "triple-alpha" process,
  • three helium nuclei (alpha particles) are utimately fused into carbon nuclei.

Concerning helium fusion, what happens with the following stars:

• M<0.5M_sun
• M>0.5M_sun and M<2M_sun
• M>2M_sun

• M < 0.5 Msun
  • Core shrinks, no helium fusion
  • shell fusion eventually stops and the star
    cools off

• 0.5 Msun < M < 2 Msun
  
  • "Helium flash" initiates fusion,
  • yellow giants live around one hundred million years
  • grow bright until helium fusion stops

• M > 2 Msun
  • Helium fusion begins stably.
  • Eventually heavier element fusion can occur.

Planetary Nebula

-How were they named?
-What are they really?

White dwarfs

-What are they made of?

-How do they change over time?

Planetary Nebula

• Astronomers with crude telescopes thought they looked like planetary disks
• wispy clouds of gas and dust illuminated by the white dwarf at the center.
  
  • UV radiation from the white dwarf excites atoms and molecules in the nebula
  • This causes them to fluoresce with colors characteristic of each element or compound.

White dwarfs

• Core of carbon and helium; about mass of Sun but the size of Earth (super dense!)
• Glows in UV spectrum at beginning of its life; slowly cools off and cannot grow due to lack of fusion in its core

Nuclear Reactions

-What two types are there?

-What element do reactions go towards?

• Fussion
  • light nuclei release energy when they fuse to form heavy nuclei
• Fission
  • Heavy nuclei release energy when they are split

• Iron
  • lowest energy per nucleon
  • end point of typical fusion processes

Death of Massive Stars

-What happens to the size of the star?

-Why does this occur?

-What is the order of elements in the core?

-How long does the star have to live once it leaves the main sequence?

• Shrink
• When a fusion processes stops in the core, it shrinks
• Hydrogen > Helium > Carbon > Neon > Oxygen > Silicone > Iron--nothing fuses with iron!!
• over 1 million years

Core Collaspe Supernova

-How do outer layers respond when the core collapses?

-How bright can the supernova be?

-What type of energy is released?

-How do nuetrinos play a part?

• They collapse, faster and faster as core collapses
• When they can't collaspe any further, they bounce back in an explosion

• Bright as billions of suns
• electromagnetic energy at all frequencies: UV, gamma rays, x-rays, etc

• Nuetrinos carry away most of the energy
• Form elements heavier than iron
• Iron quickly fuses for even heavier elements
• This is origin of all heavy elements on earth-radioactive elements por ejemplo

Nuetron Stars

-When are they formed and out of what?

-What kind of magnetic fields do they have?

• Resulting object of a star going supernova
• Made of neutrons (duh)
  • electron degeneracy pressure is overwhelmed
  • electrons and protons are forced to combine
  • super super dense, extreme gravity

• Strong magnetic fields
• charged particles emited in field lines that don't line up with their rotational axis
• cause a lighthouse beam effect that we call pulsars--very fast and very regular, good for keeping time

Black Holes

-How do they form?

-Why are they so dense?

-Why are they so bright? What part of spectrum?

• Some stars are so massive that the core does not stop at the neutron star stage when it collapses.
• The core will become so dense as to form a black hole, a region of space in which gravity is so strong that nothing, not even light, can escape

• No nuetron star core--matter doesn't bounce back to mave supernova; it sticks instead

• Infalling matter heats to really high temperatures--gamma ray spectrum
• Radiation flies out along jets; show up as "gamma ray bursts" if we are in the path of the jets

Standard Candles

-What are they?

-What do we need to know to find its distance?

• An object whose luminosity is known/can be determinded without measuring distance

• To find distance:
  • Use Brightness = Luminosty/(4Π(distance)²)
    .
  • Thus distance = luminosity/(4ΠBrightness)^1/2

How are star clusters used to determine distance?

• Because all of the stars in the cluster are near each other, all are roughly the same distance from us
• Can use the distance of one cluster to approximate the distance of another cluster-taking apparent brightness into consideration as well

Variable stars

-How do they change over time?

The 2 types are RR Lyrae and Cepheid

-How do we distinguish them from the sun?

-What size are RR Lyrae?

-How are Cepheid different and how are they used as standard candles?

• Size changes dramatically over a period of days--causes oscillation in brightness

• The shape of their light curves is different than the physical behavior of the sun

• RR Lyrae: 40 times size of sun even during their (short) oscillation period

• Cepheids are brighter and thus better standard candles
• We can get 'reasonably precise' measures of their luminosity from meauring their periods
• Since some are super bright and can be seen in other galaxies we can get intergalactic measurements

White dward (Type Ia) Supernova

-When do they occur

-What is the Chrandrasekhar limit?

-Why are they excelent standard candles?

• when a white dwarf is in a star system with another star. The white dwarf can gravitationally pull matter off the companion star.

• around 1.4 solar masses
• When the star collects enough material to reach the Chandrasekhar limit, the dwarf will collapse and initiate fusion that ultimately blows the star apart
• results in an extremely bright star with a luminosity of around 10 billion times that of the sun

• Because they occur when a white dwarf reaches the Chandrasekhar limit, the all should have roughly the same peak luminosity.
• This makes them excellent standard candles that are visible in even very distant galaxies

Special Relativity

-What are the fundamental postulates?

-What are the consequences of these postulates?

1. the laws of physics are the same for all non-accelerating observers
2. the speed of light is the same for all non-accelerating observers

• Consecuences:
  • Nothing can move faster than the speed of light
  • Re-imagining of universe: SPACETIME
  • time moves slower for people in motion,
  • moving objects are shorter in the direction they are moving
  • that two events that appear simultaneous to one observer will not appear simultaneous to another observer moving with respect to the first one.

Length Contraction and Time Dilation

• Rocket at 87% the speed of lightwill appears ½ as long 
• Friend's clock on the rocket will tick one second for every two seconds your clock ticks
• Earth shrunk by half in one direction according to person on rocket and that your clock will tick off one second for every two of hers.

Lorentz Factor

γ = 1/(1−v²/ c²)^1/2

Einstein's General Theory of Relativity

-What does it treat gravity as?

-How is the shortest distance between two objects?

• Curvature of spacetime instead of a force
• Curved

Effects of Curvature

• Planetary orbits "precess"
  • aren't eliptical and curve doesn't quite close
• Gravity bends path of light from stars
  • observable during eclipses: stars that should be visible near sun appear farther away
• Light is "red-shifted" due to gravity
• Time runs slower when deeper in the gravity well
  • Relevant for GPA signals--time goes faster for satellites that are farther from Earth

• Denser the object--more curved it is near the surface

Black holes:

• Escape velocity is greater than speed of light
• Once you get past event horizon, you can only get closer to the center of the black hole---can never get out
• Event horizon is NOT a surface
• Schwarzschild Radius:
  • R_S = 2 G M/c²
• Time slows down as you get near the horizon
• Light is redshifted as it escapes
  and it is blueshifted as it approaches

• Intense spacetime curvature causes extreme tidal forces
• stretch and squeeze: spaghettification
• Tidal forces for a 3 M_sun black hole would be lethal, but they wouldn't be as bad for a super massive blackhole

Gravitational Waves

-What are they/when do they occur?

-How do they relate to energy?

-Weak or strong?

-How do we see gravity waves in binary pulsars?

-What is LIGO?

• Changes in curvature of spacetime, move at the speed of light
• Created any time there is a moving mass; especially in a binary system which is constantly changing -- changes act like waves

• Carry energy away from systems
• In a binary system--energy of system continuously decreases as gravitational waves carry away energy

• Very weak -- rarely relevant
• Would be bigger for two nuetron stars or black holes orbiting each other

• 2 nuetron stars orbiting each other emit a lot of g. waves that we don't observe them on Earth
• Cumulative effect: They should lose energy as they emit waves and spiral towards each other, speeding up as they do so

• Observatory in Louisiana and WA
• Directly detect existence of gravitational waves
• If a wave passes, one arm gets shorter and the other gets longer
• Goal: detect waves produced by big events (two black holes colliding)

• Hubble recognized that spectral lines from elements of galaxies are redshifted
• Appling Doppler effect means they are moving away from us at a speed relative to the amount of redshift

• Linear relationship from graph of recession speed v. distance gives Hubble's Law:
  • velocity = H_o x distance
  • H_o = 70 km/s/Mpc
  • distance in Mpc gives us velocity in km/s

• Conclusions drawn from this:
  • All galaxies (except those neighboring us that are bound by gravity) are moving away from us
  • Universe in its entirety is expanding

• Einstein could have figured this out but he was determined that universe was static and changed his equations to account for this...sucks

Hubble's view of redshift

-What steps are followed to get from Doppler effect to Hubble's law?

• Redshift from Doppler Effect
  • z = Δλ/λ
• Velocity determined from redshift
  • v=c*z
• Distance found from Hubble's law
  • d=v/H_o

Distance and faraway galaxies

-What term do astronomers use instead of distance?

-What does it mean?

• lookback time
• We are speaking of how long ago the light left the galaxy to reach us when we talk about the distance to a galaxy
• If it took 400 million ly for light to reach us from a galaxy, it doesn't mean the galaxy was 400 million ly away when the light was emitted. Because we are expanding away from the galaxy as the light is coming towards us, we actually would have been closer when the light first started

• photon wavelengths are expanded
  • not redshifted because galaxy is moving away
  • redshifted because expansion stretches them
• Amount of redshift is related to the universal expansion since the photon is released

Redshift and the size of the universe

R₀/R = z + 1

-What does this mean?

-What does it tell us?

• R = "size" of universe when light was emitted from a galaxy (avg. distance is btwn galaxies is a good measure of size)
• R₀ = "size" of universe today
• z > 1 does not mean it's moving faster than speed of light but instead means universe has more than doubled size since light was emitted

• Amount the universe has expanded in terms of redshift

Age of the Universe

-How does Hubble's constant relate to this age?

-Is it exact?

-What is the best estimate for the universe's age?

• Tells us age bc it relates velocity and distance
  • Age = distance/velocity = 1/H_o
  • Must convert units to get to years instead of Mpc/km/s
  • gives age of 14 billion years
• Depends if universe expansion is constant, speeding up or slowing down
• Best average: 13.7 billion years

Evidence for the Big Bang Theory

-Characterize the universe when it was much smaller

-How would light have functioned?

-What would have happened as it cooled?

• Smaller: hotter and denser
• 3,000 K means too hot for atoms--instead filled with plasma

• Light constantly emitted and absorbed
• Universe not "transparent" to light

• Cooling below 3000 K -- atoms form
• Any light that existed would have been a blackbody around 3000K and it would continue traveling through the universe, undisturbed by matter: cosmic background radiation
• With expansion of universe, this would have become more redshifted to longer wavelengths. Would have "cooled" as universe expanded

Cosmic Background Radiation

How do Gamow, Dicke, Penzias and Wilson play parts?

Gamow

• 1st to predict existence of cosmic background radiation

Dicke

• set out with research group at Princeton to find CBR
• Atom formation should have happened 400,000 yrs after big bang, meaning universe has expanded 1000 times since then
• Radiation now would be about 3K, 1000 times smaller than the 3000K original temp.
• 3K radiation would have a peak wavelength of 1 millimeter--microwave part of spectrum

Penzias and Wilson

• Accidently discovered it first from a hum in their radio telescope

We now know that the universe is filled with radiation characteristic of a blackbody with a temperature of around 2.7 K.

This is strong evidence that the universe once existed in a hot dense plasma state around 13.7 billion years ago

Verification of an important prediction of the big bang model

Anisotropy & Cosmic Microwave Bckg Radiation

-What was the problem with graniness?

-How was it resolved?

• Blackbody spectrum is so uniform that astronomers initially didn't unverstand "graininess" of galaxy clusters
• Uniform gas should expand uniformly, meaning no galaxies would form, right?

• Microwave telescopes in space measure slight variations in the temp (therefore density) of cosmic background radiation
• Experiments proved that radiation is not perfectly uniformed but has graniness consisten with observed structure of universe