Chapter 1: Outline of Universe

• Solar System
• Nearby Stars, Our Galaxy
• Galaxies and the Universe
• Lengths : AU, light year, parsec
• Angles : degree, arcmin, arcsec
• Units, Powers of 10 (Appendix A)

Chapter 6.1 : Nature of Light

• Speed of light = c = 300,000 km/s (Roemer).
• Spectrum (blue = 400nm, red = 600nm)
• Electromagnetic waves
• Electromagnetic Spectrum :
  • Radio, microwave, infra-red, optical,
  • ultra-violet, X-ray, gamma-ray
• Atmospheric windows (transparency/opacity)
• Wavelength (lambda), frequency (f), c = f × lambda
• Photons carry energy : E = hf = hc/ lambda
  • h=Planck's constant = 6.6× 10^-34 Joules sec.

Chapter 7 : Light and Spectra

• Creation of light : accelerated charge
• Thermal : hot solids, liquids, dense gases
• Temperature scales : Kelvin (K),
  • Celsius (C), Fahrenheit (F) [0 K = -273 C]
• Blackbody (perfect) emitter/absorber
• Blackbody spectrum shape
• Stars (dense gas) approximate blackbody spectra
• Higher Temp, shorter (bluer) peak,
  • lambda_peak (nm) = 2.9× 10⁶/T (Wein's Law)
• Star color --> Star Temperature
• Higher temp, more emission
  • E per unit area = sigma T⁴ (Stefan-Boltzmann Law)
• Line radiation created by atoms
• Atomic structure : protons, neutrons, electrons
  • protons and neutrons in nucleus
  • electrons in orbits
  • number of protons ---> element
  • number of neutrons + protons ---> isotope
  • number electrons = number protons (neutral atoms)
  • number electrons not equal to number protons ---> ions
• Bohr picture of electron orbits
  • only certain permitted orbits
  • orbit levels ---> energy levels
  • electrons can jump between levels
  • jump up ---> absorption of photon
  • jump down ---> emission of photon
  • jump out (lost) ---> ionization
• Hydrogen atom energy levels (n=1,2,3...)
  • Lyman (n=1), Balmer (n=2), etc series of lines
• Kirchoff's Laws : conditions for
  • creating Emission/Absorption lines
• Stellar spectra
• Absorption lines from photosphere
• Hydrogen Balmer series changes in strength :
  • weak at low temp : all in ground state (n=1)
  • weak at high temp : all ionized
  • strongest at about 10,000K (A0 stars)
• Classification of absorption spectra
  • O B A F G K M
  • subdivided by numbers 0 to 9
• Temperature sequence
  • O stars 50,000K, M stars 2000K
  • T decreasing : ions ---> atoms ---> molecules
• Composition of stars : 74% H, 24% He, 2% everything else
• Doppler shift : v/c = (lambda - lambda_o)/ lambda_o
  • v is radial velocity (RV) only
  • redshift (away), blueshift (towards)
  • no shift (gransverse)
• Collisional line broadening
  • small (large) stars ---> high (low) pressure atmospheres
  • high (low) pressure ---> wide (narrow) lines

Chapter 8: The Sun : an ``average'' star

• Global properties
  • size, mass, density, luminosity,
  • temperature, composition, rotation
• Photosphere (`surface') : where light comes from
• Granulation : results from sub-surface convection
• Chromosphere : low density, pink, hotter, He discovery
• Corona : large, very low density, very hot
• Solar wind : aurora, comet tails pushed back
• Solar activity, sunspots, magnetic fields, cooler
• Sunspot cycle, magnetic field cycle, differential rotation
• Prominences, flares, coronal mass ejections
• Helioseismology : observations and internal structure
• The sun's energy source
• Inadequacy of chemical or gravitational energy sources
• Binding energy curve for all elements :
  • Fusion of light elements & Fission of heavy give energy
  • Iron (element 26) is the most stable nucleus
• Nuclear (hydrogen) fusion, p-p chain
• E=mc²: energy from mass
• 4H ---> ⁴He + Energy (0.7% efficient)
• Solar neutrinos; detectors; discrepancy

Chapter 9 : Stars

• Star distances :
  • stellar parallax (p)
  • d(pc) = 1/p(arcsec)
  • 1pc = 3.26 light years
  • works for d < 1000 pc
• Star luminosity, L, intrinsic (Watt)
• Star brightness, b, at earth (Watt/m²)
  • brightness depends on distance
  • inverse square law : b proportional to 1 / distance² : L = 4 pi d² b
  • E.g. Sun : L = 3.8×10²⁶ Watt, b = 1400 Watt/m²
  • Sirius : L = 9.1×10²⁷ Watt, b = 1.14 × 10^-7 Watt/m²
• Apparent magnitude, m
  • Hipparchus, 1 ---> 6 (brighter ---> fainter)
  • difference of 5 mag is × 100 in brightness
  • difference of 1 mag is × 2.512 in brightness
• Star sizes : large range
  • Area of star (sphere) = 4 pi R²
  • Luminosity of star: L=4 pi R²sigma T⁴
• H-R diagram (Luminosity vs Temp)
  • Main sequence (MS), giants, white dwarfs
• Also luminosity/size classes
  • large R ---> low pressure ---> narrow lines
  • ---> Luminosity Class (LC) & star size
  • LC I, III, V = supergiants, giants, main sequence
  • e.g. Sun : G2V, Arcturus : K2III
• Binary Stars : (very common)
  • Visual; astrometric; spectroscopic binaries
• Star Mass determination from binary orbits :
  • k (M₁ + M₂) = a³/P² (Kepler's 3rd Law)
  • the constant k=1 if M in M_sun, a in AU, P in years
  • range of star masses : 0.08 - 100 M_sun
• Mass-Luminosity relation for Main Sequence stars
  • L ~  M ^3.5, eg M0 = 0.5 M_sun; A0 = 4M_sun
  • MS lifetime shorter for higher Mass
• Luminosity Function (census by brightness)
  • lower luminosity stars more common
  • night sky stars usually luminous

Chapter 10: Interstellar Medium

• Very low density gas and dust
• Galactic ``atmosphere'', ~5% mass in stars
• Dust : absorption & reddening of light
  • cold, so thermal emission in IR
• HI : electron spin flip -----> 21 cm (radio) photon
• Molecules : e.g. CO ``visible'' in radio (not H² )
• Four phases (approximate pressure balance) :
  • 1) cold (~20K) ``dense'' (~  10 ³ /cm ³ ) molecular clouds
  • 2) warm (~500K) neutral hydrogen, HI clouds
  • 3) hot (~   10 ⁴ K) ionized hydrogen, HII regions
  • 4) v. hot (~   10 ⁶ K), low density (0.01/cm³), pervasive
• Cycle : gas ---> stars ---> gas

Chapter 11: Star Birth

• Gas (molecular) clouds usually supported :
  • thermal+magnetic pressure/turbulence/rotation
• Can collapse if shocked
  • trigger : supernovae, stellar winds, spiral arms
  • core heating from gravity : "protostars"
  • hidden cocoon phase (IR sources), disks & jets
  • planets form; discovering extrasolar planets
• Hydrogen fusion begins : star is "born"
  • evolutionary tracks on H-R diagram
  • Zero Age Main Sequence (ZAMS)
  • location on MS mass dependent (O high, M low)
  • formation time mass dependent (O short, M long)
• Brown dwarf : ``failed'' star, M_star < 0.08 M_sun, no fusion
• HII regions, O&B stars ionize H, pink (H-alpha) color
• Star winds & supernovae remove gas ---> young star cluster
• Star Structure :
• Energy source : p--p chain; CNO cycle
• Energy transport :
  • radiation, convection, (conduction)
• Hydrostatic equilibrium :
  • gravity inwards = pressure outwards
  • stability : stellar thermostat

Chapter 12: Stellar Evolution

• Computer model of Sun's interior :
  • centrally concentrated (core/envelope)
  • nuclear reactions in core ($<20$\%)
  • inner 80\% radiative
• Life on the Main Sequence (MS)
  • core H fusion (4H ---> He)
  • p-p chain (low mass), CNO cycle (high mass)
  • longest stage of life (e.g. Sun 10¹⁰ yrs)
  • MS lifetime : Lower mass ---> Longer lifetime
• Leaving MS, up Red Giant Branch (RGB) first time
  • H fuel exhausted in core
  • core contracts, H burns in shell, powerful
  • envelope expands & cools
  • Red Giant (R_star ~ 1 AU), luminous (L_star ~   10³ L_sun)
• Beyond RGB
  • He ignites in core, 3He ---> C (triple alpha)
  • (M_star < 2 M_sun Helium flash)
  • lands on "Horizontal Branch" (HB)
  • He fuel exhausted in core
  • He & H shells burning, very powerful
  • envelope expands and cools ---> up RGB second time (AGB)
  • red supergiant (R_star ~ 5 AU, L _star ~ 10 ⁴ L_sun )
• Star Clusters : groups of the same age
  • Globular clusters : old, halo, metal poor
  • Open clusters : young, disk, metal rich
  • Cluster H-R diagrams : isochrones (same age)
  • Young cluster isochrones
  • Main Sequence Turn Off point (MSTO)
  • measuring cluster age from MSTO
• Variable stars
  • instability strip on H$-$R diagram
  • stellar pulsation, periods $1-90$ days
  • RR Lyrae (fainter, lower mass)
  • Cepheids (brighter, higher mass)
  • period$-$luminosity relation
  • distance estimates

Chapter 13: Star Death

• Low mass stars (eg the Sun) :
• Large size ---> low surface gravity ---> mass loss
• Planetary nebula
• White dwarf (WD)
  • = inner core revealed
  • earth size, carbon/oxygen, hot (white), faint
  • density ~  5 × 10 ⁵ g/cm³
  • electron degenerate pressure support
  • degeneracy pressure independent of temperature
  • more massive WDs are smaller
  • limiting mass 1.4M_sun (Chandrasekhar mass)
  • slow cooling down ---> black dwarf
• Mass accretion onto WD from companion :
  • Nova : hydrogen detonation of surface layer
  • Type I supernova : carbon detonation of entire star
• High mass stars (M_star > 10 M_sun ) DIFFERENT
  • short MS lifetime
  • heavier elements burn (He--->C/O---> etc)
  • higher core temps & densities, shorter durations
  • onion shell structure, core + shells
  • iron core : no more energy (minimum in mass defect)
  • core collapse (0.2 seconds; radius 3000km --->10 km)
  • protons + electrons ---> neutrons + neutrinos
  • huge neutrino release
  • core bounce ---> rising shock ---> star explodes
• Type II supernova (eg SN 1987A)
  • total energy 10 ⁴⁶ Joules (gravity origin)
  • energy emerges : 99% neutrinos, 1% kinetic, 0.01% light
  • neutrino burst detected from SN 1987A
  • light outshines galaxy for a week
  • fades with decay ⁵⁶Co ---> ⁵⁶Fe (half life = 77 days)
  • nucleosynthesis (origin of elements)
  • expanding shell (supernova remnant)
  • recycle into ISM ---> new stars (and planets and us!)
  • gradual element enrichment of galaxy
• Neutron stars
  • remaining core after Type II Supernova
  • size ~  10 km, density 10 ¹⁴ g/cm³
  • neutron degenerate pressure support
  • mass limit about 3M_sun
• Pulsars :
  • rotating magnetized neutron stars
  • conservation of angular momentum ---> rapid spin
  • lighthouse model
  • Crab nebula powered by pulsar (synchrotron)
  • slowing down (young pulsars spin faster than old)
• Mass accretion onto NS from companion :
  • He detonation of surface ---> X-ray burster
  • rapid spin-up ---> millisecond pulsars
• Black Holes :
  • escape velocity, V_esc² = 2GM/R
  • for V_esc = c, we get R_s = 2GM/c²
  • R_s= Schwarzchild radius = event horizon = 3M/M_sun
  • M > 3M_sun collapse unstoppable ---> singularity
• Near BH : time slows, light redshifted, strong tides
• Spinning black holes (Kerr), drag space around.
• Searching for black holes :
  • rapid X-ray variability ---> small size
  • Cyg X-1, accreting binary, M_BH ~  few M _sun

Chapter 15: Our Galaxy

• Appearance of Milky Way (MW) ---> slab geometry
• Star counts ---> sun at center (Herschel)
• Globular cluster distribution ---> sun off-center (Shapley)
• Discrepancy : dust absorption in ISM (Trumpler)
• Galaxy shape :
  • radius ~15 kpc, Sun ~8.5 kpc from center
  • disk of stars + ISM, bulge, nucleus,
  • large spherical halo with globular clusters
• Disk rotates :
  • Sun's speed ~200 km/s
  • Sun's orbital period ~200 million yrs
  • about 70 rotations since birth of galaxy
  • Kepler's law ---> M ~   10 ¹¹M_sun inside of Sun's orbit
• Rotation curve :
  • rapid rise, then constant (at ~200 km/s)
  • differential rotation (inner stars overtake)
  • dark matter extends beyond stars (unknown)
• Stellar Populations :
  • Pop I : young, disk, enriched by heavy elements
  • Pop II : old, halo, depleted in heavy elements
• Galaxy Formation :
  • collapse of protogalactic cloud
  • + interactions/accretion of dwarf companions
• Spiral structure :
  • seen in HI 21cm maps
  • seen in distribution of star formation regions
  • (seen in other galaxies)
  • arms follow star formation ---> brighter/bluer
• Theories of spiral origin
  • NOT simple rotation ---> windup too tight
  • self-propagating star formation
  • density wave theory : slow pattern speed
  • density wave triggered by bar or passing neighbor
• Radio 21 cm HI observations
• Galactic Nucleus, possible black hole (~ 10 ⁶M_sun)

Chapter 16: Other Galaxies

• Shapley-Curtis debate: nature of spiral nebulae
  • Cepheids in M31 ---> external galaxy (Hubble)
• Galaxy shapes : Hubble's classification
  • ``tuning fork'' diagram
  • spirals : Sa--->c : big--->small bulge, tight--->open arms
  • barred spirals : SBa,b,c ; have inner bar of stars
  • ellipticals : smooth, round (E0)---> flat (E7), no ISM
  • lenticular : like E plus disk but no arms or ISM
  • irregulars (often smaller)
• Galaxy distances
  • Cepheid variables (ok to ~ 1 Mpc)
  • further, need bright ``standard candles''
  • eg brightest stars, HII regions, supernovae
• Velocity of galaxies (almost all redshifts)
• Hubble diagram : velocity (km/s) versus distance (Mpc)
  • straight line, v ~ d, or v = Hd (Hubble Law)
  • H : Hubble's constant ~75 km/s/Mpc (20 km/s/MLY)
  • (nearby galaxies don't follow the law)
  • current uncertainty for H : 50-100 km/s/Mpc
  • use to estimate distance (v ---> d)
  • caused by universe expanding; no center
• Galaxy masses and mass/light ratios
  • rotation curves
  • dark(missing) mass
• Galaxy interactions/collisions/mergers :
  • gravitational perturbations ---> distortion
  • gas clouds collide ---> strong star formation
  • no stars collide (too much space)
  • spiral + spiral ---> elliptical
  • ---> clusters contain more ellipticals
• Clusters of galaxies :
  • can contain thousands of galaxies
  • few big galaxies, many more smaller ones
  • Doppler shifts ---> ~ 500 km/s ---> 10 ⁸ yr to cross
  • velocities ---> mass ---> dark mass dominates
  • often large central galaxy ---> cannibalized others
• Large scale structure : walls, voids
  • uniform on large scales (cosmological principle)
• Dark Matter exists on all scales
• Galaxy Evolution
  • study distant (therefore younger) galaxies
  • star formation, chemical enrichment, gas dispersal
  • ? early times; top down or bottom up ?

Chapter 17: Active Galaxies

• Seyfert galaxies : bright variable nucleus
• Radio galaxies : jets and lobes
  • Synchrotron emission : fast electrons in magnetic field
• Supermassive black holes (10⁷-10⁹ M_sun) in galactic nuclei
• Accretion disk releases gravitational energy ---> luminous
• High speed bipolar jets often created
  • jets can appear superluminal
• Even non-active galaxies may have nuclear black holes
• Activity triggered by galaxy interactions ---> gas inflow
• Quasars :
• Discovery history :
  • bright radio sources but faint galaxies or ``stars''
  • (``quasars'' : quasi-stellar radio source)
  • redshifts ---> very distant ---> VERY luminous
  • some brighter than 100 galaxies
  • variable (timescales dt ~   months) ---> tiny source (R < c dt)
  • energy source puzzle ---> distances doubted
• Evolution; quasars more common in past (further away)

Chapter 18: Cosmology : The Big Bang

• Hubble law : cosmic expansion (cake & balloon analogies)
• Cosmological (not Doppler) redshift : spacetime expands
• No center : everyone sees same expansion
• Shape & size of universe :
  • matter curves spacetime (curvature k)
  • curvature depends on density
• Expansion implies Big Bang : when all together
• Time since BB : t ~   d/v ~ 1/H, eg H=75 km/s/Mpc ---> t ~ 13 Gyr
• Lookback time = light travel time (eg 1Gly ---> 1Gyr ago)
• Current limits are 80% lookback to BB (adolescent galaxies)
• Particle horizon at 100% lookback to BB
• Microwave background :
  • Penzias & Wilson (1963); COBE (1990); WMAP (2003)
  • whole sky : black body spectrum, T=2.7K
  • recombination in 3000K gas; hot fog cools & clears
  • redshift factor ~ 1000; 380,000 yrs after BB
• Early History :
  • t ~ 10^-6 s : gamma rays produce particle/antiparticle pairs
  • t ~ 10^-4 s : protons freeze out (10¹²K)
  • t ~ 4 s : electrons freeze out (10¹⁰ K)
  • t ~10 - 180 s : hydrogen fusion to helium; 25%
    • 25% He observed everywhere
  • t ~ 50,000 yr : matter density > radiation density
  • t ~ 380,000 yr : electrons captured ---> H,He atoms
    • fog clears; 3000K; redshift ~1000 ---> Microwave background (MWB)
• Future of the universe
  • matter decelerates expansion
  • three cases : expand for ever, turn around, balance
  • depends on density of universe
  • critical density ~   2.4× 10^-29 gm/cm³
  • current estimates ~ 4% atoms, ~25%dark matter
• Recent Developments
  • Flatness problem; Horizon problem; Structure problem
  • Inflation may solve all these
  • The age problem
  • An accelerating universe; dark energy
  • our visible universe was smaller and connected
  • Microwave Background Fluctuations :
    • sound in the early universe
    • origin of galaxies and large scale structure
• Exciting times !