Whittle : EXTRAGALACTIC ASTRONOMY

 
       
 

1 : Preliminaries	6 :   Dynamics I	11 : Star Formation	16 : Cosmology
2 : Morphology	7 :   Ellipticals	12 : Interactions	17 : Structure Growth
3 : Surveys	8 :   Dynamics II	13 : Groups & Clusters	18 : Galaxy Formation
4 : Lum. Functions	9 :   Gas & Dust	14 : Nuclei & BHs	19 : Reionization & IGM
5 : Spirals	10 : Populations	15 : AGNs & Quasars	20 : Dark Matter

(1) Introduction

For reasons not yet fully understood, matter in the universe is organized into three basic structures:

• Atoms
• Stars
• Galaxies     -- the subject of this course

• ~1750 - 1850 :   recognition of basic existance
• ~1850 - 1930 :   recognition of basic properties
• ~1930 - present :   deeper understanding (structure, creation, evolution, sociality)

• atoms & stars :   understanding now mature
• galaxies :   becoming mature; now 30 yrs is a golden time.

    currently fertile area (astronomy is prominent amongst physical sciences)
    your careers will witness significant growth
    these notes will be of limited use when you teach the course, in ~20 yrs.

Let's first look briefly at some historical hightlights.

(2) Discovering Galaxies : Ours & Others

(a) Early Aims

• Early thinking (before 1923) focussed on two main questions :
  • What is the Milky Way   (Latin : Via Lactea)
    • initially : what is its shape and where is the sun
    • later : what is its size and internal motion

  • What are the Nebulae   (Latin : clouds)
    • initially : use "large" telescopes to find, catalog, and describe them
    • later : are they unresolved star groups, or genuinely nebulous (gaseous)
    • finally : are they internal to the MW, or external "island universes"

• As telescope apertures increased, the methods developed :
  • Visual photographic visual spectra photographic spectra

• The path of discovery was NOT linear, with discussion often polarized and ambiguous.

• Here are some simple time-line sketches identifying the key people/work

  1750 - 1900      [ figure ] 1900 - 1950      [ figure ] 1950 - present  [ figure ] all combined:    [ figure ]

(b) Before 1850 : Search & Discovery

• before 1750 :   essentially no references to galaxies, except :
  Australian dreamtime narratives include "Magellanic" Clouds
  ~ 950 al-Sufi (Persian) includes M31 in star charts : [ images ]

• 1610 :   Galileo Galilei (Italian) uses early telescopes
  realises Milky Way is composed of many stars

• 1750 :   Thomas Wright (English) : [ images ]
  Publishes "An Original Theory of the Universe" in 1750
  giant spherical shell; we see tangent plane; God @ center
  stars orbit around, preventing them falling onto God
  

• 1755 :   Immanuel Kant (German)
  
  writes : "General Natural History & Theory of the Heavens"
  (1) rejects spherical shell
  (2) MW like huge solar system, rotating
  (3) stars far from plane on different orbits
  (4) disks (like MW) project to ellipses
  (5) oval nebulae (seen by de Maupertius) = separate galaxies
    remarkably precient, but not widely accepted through 1800s

• 1780s :   William Herschel (English) : [ images ]
  
  star counts MW = flat disk with sun @ center
  no size estimate
  ultimately recognizes wrong assumptions & retracts

• 1781 :   Charles Messier (French) completes first catalog of nebulae (109) [image]

• 1770 - 1810 :   William & Caroline & John Herschel (English) : [ images ]
  all-sky survey     2500 nebulae
  used 18" (20 foot) reflecting telescope, diurnal sweeps
  extended to southern skies by son John at Cape of Good Hope (1834-9)
  some resolve into stars (clusters) others dont (gas?)
  speculation : uniform distribution of stars will gravitationally cluster
  

• 1845 :   William Parsons (3^rd Earl of Rosse) : [ images ]
  
  English Lord resident in central Ireland : Birr Castle
  36" then 72" (Leviathan of Parsonstown; largest until 100" Mt Wilson, 1917)
  spiral structure (eg M51, M33, M101)
  some have stars and gas (eg M42)     supports Kant's rotation idea
  1840s potato famine stops work; never achieves its potential

• 1864-68 :   William Huggins (English) : [ images ]
  telescopic visual spectra of nebulae
  1/3 emission lines (gaseous); 2/3 continuous (stellar)

• 1885 :   Nova (actually Supernova) in M31
  10% brightness of entire nebula
  seen as strong evidence against "island universes"

• 1888 :   John Dreyer (Danish) [image] working at Birr Castle, compiles
  New General Catalog (NGC) :   7840 nebulae
  Index Catalog (IC) :   5086 more

• 1900s :   James Keeler and Herber Curtis (USA, Lick) use photography
  36" Crossley reflector @ Lick : [ images ]
  estimates ~120,000 nebulae accessible; ~50% are spiral

• 1910 :   E. Fath (USA, Lick) and Max Wolf (Germany, Heidelberg)
  photographic spectra of many spirals
  many have absorption lines     stellar systems     external?

• 1906-22 :   Jacobus Kapteyn (Dutch) : detailed study of MW : [ images ]
  surveys 200 areas :   star counts, proper motions, radial velocities
  concludes :   MW = thick disk, 5kpc radius, sun @ center
  considers absorption and finds some reddening, but
  assumes Rayleigh scattering so infers (wrongly) absorption unimportant

• 1912 :   Henrietta Leavitt (USA, Harvard) : [ images ]
  Period-Lumimosity relation for Cepheids in Magellanic Clouds
  tool for measuring distances

• 1913 :   Ejnar Hertzsprung (Danish) and Henry Russell (USA, Princeton)  [image]
  first color-magnitude (CM) diagrams for stars

• 1914 :   Vesto Slipher (USA, Lowell) : [image]
  spectra of spirals (take 80 hours!)
  finds large velocities (eg M31 is -300 km/s)
  much larger than any MW stars

• 1916 :   Adriaan van Maanen (USA, Mt Wilson) :
  finds proper motion rotation in M101 (!!)
      must be local to avoid super-luminal speeds

• 1917 :   Herber Curtis (USA, Lick [PhD Virginia!]) :
  measures more novae in spirals     100 x farther than galactic novae
  suggests 1885 "nova" in M31 was anomalous

• 1918 :   Harlow Shapley (USA, Princeton/Harvard) :
  uses Globular Clusters (GCs) to infer "Big Galaxy"
  diameter 100 kpc, sun ~15 kpc off-center
  10 x Kapteyn's galaxy; suggests absorption was the problem

• 1920 :   Shapley (no) - Curtis (yes) Debate :   "Are Spiral Nebulae Island Universes"   [image]
  public debate @ National Acadamy of Science, Washington DC.
  Short (30min) presentations, but summary articles published 1921
  surprisingly, Shapley "won" the debate, though Curtis was right.
  Shapley :
  new MW so big, inconceivable universe so much bigger
  van Maanen rotation rules out distant spirals
  Curtis :
  doubted Shapley's MW size
  range in size (0.01-2 deg) range in distance (1000x more than MW)
  Novae in M31 100 kpc away and size of Kapteyn's MW
  spectra show large doppler shifts, yet no proper motions
  some edge on spirals have dust lanes similar to MW (zone of avoidance) external

• 1923 :   Edwin Hubble (USA, Mt Wilson) :   uses the new 100"
  finds Cepheids in M31 300 kpc (now, 770 kpc) external galaxy
  (centennial review of Hubble's career by Sandage : [ o-link ])

(d) 1925 - 1950 : Expanding Horizons

• 1927 :   Bertil Lindblad (Sweedish) and Jan Oort (Dutch) :
  Lindblad predicts differential rotation near sun; Oort find it
  supports Shapley's MW with sun off-center (against Kapteyn's MW)
  however, derives smaller size than Shapley
  suggests disk flattened by rotation + spherical system non-rotating
  resembles bulge/disk of external galaxies

• 1929 :   Edwin Hubble and Milton Humason (USA, Mt Wilson) :   galaxy spectra
  Finds redshift-distance relation (Hubble's Law)   (Original paper: [ o-link ])
  already expected from de Sitter's solutions to GR
  looked for by others; Hubble used distance ladder, including Cepheids
  1931 - includes many more galaxies
  H ~ 530 km/s/Mpc     2 Gyr age (less than earth !?)
  attempts (failed) to find alternative to Hubble Law

• 1930 :   Robert Trumpler (USA, Lick) :
  compares sizes and CM diagrams of open clusters
  concludes absorption pervasive (~0.5mag/kpc, close to correct)
  nail in the coffin of Kapteyn's Milky Way

• 1932 :   Carl Jansky (USA) :   detects radio from MW
  (HI predicted 1945; observed 1951; map of MW plane 1958)

• 1936 :   Hubble : publishes galaxy classification (tuning fork)
  uses names (early, late) influenced by Jean's theory of gravitational collapse
  eg E's = large gas cloud, evolves into spiral

• 1930s :   Fritz Zwicky (Swiss/USA, Cal Tech) : [ images ]
  measures galaxy velocities in Coma;
  infers dark matter needed if clusters are bound
  no one believes him

• 1944 :   Walter Baade (German/USA, Mt Wilson) :
  observes Spiral bulges & Ellipticals (war time black-outs help)
  uncovers stellar populations :
  • Pop I :   blue supergiants in disks
  • Pop II :   red giants in bulges and Ellipticals

• 1939 :   Hans Bethe (German/USA, Cornell) :   p-p chain
• 1946 :   Fred Hoyle (English) :   SN generation of elements
• 1957 :   Burbidge, Burgidge, Fowler & Hoyle (B²FH) :   Nucleosynthesis

(e) 1950 - Present : Modern Developments

• 1952 :   Baade :   uses 200" to recalibrate Cepheid P-L relation
  depends on Pop I or II; previous work used wrong relation
    all distances doubled
    M31 is similar in size to MW
    Universe doubles in size (!)

• 1955 :   Edwin Salpeter (USA, Cornell) :
  introduces Initial Mass Function (IMF) for frequency of star masses

• 1962 :   Eggen, Lynden-Bell & Sandage (ELS) :
  Collapse model for formation of MW galaxy
  Accounts for position/kinematic/metallicity gradients
  Importance of ELS picture still debated

• 1963 :   Maartin Schmidt (German/USA, Cal Tech) :
  Discovers Quasars

• 1965 :   Arno Penzias & Robert Wilson (USA, Bell Labs) :
  Discover Cosmic Microwave Background (CMB)
  Strong support for Hot Big Bang model

• 1972 :   Leonard Searle & Wal Sargent (USA, Cal Tech) :
  measure 24% He basiline in low metallicity Dwarfs
  consistent with Big Bang nucleosynthesis

• 1970s :   Vera Rubin et al. (USA, Carnegie) :
  infers dark matter from spiral rotation curves
  inspires Cold Dark Matter (CDM) models of 80s-90s

• 1992 :   COBE (NASA) :
  measures stunningly accurate black body spectrum
  finds slight (10^-5) anisotropies in CMB     pregalactic structure

• 1996 :   HST's HDF (NASA) :
  galaxies down to 29^m; out to z~3; total ~10¹⁰
  young galaxies visibly different
  early star formation rate is high ("Madau" plot)

• 1998 :   High-z SN Projects (USA, Berkeley & Harvard) :
  Two groups use Type Ia SN as standard candles out to z ~ 1
  Both find evidence for non-zero cosmological constant (universe accelerating)

• 2003 :   WMAP (NASA) :
  CMB power spectrum measured; includes accoustic peaks 1,2,(~3)
  inspires concordance model with "high" accuracy (few %)
  combines : WMAP;   SN-1a;   2dFGRS;   HST-H_o;   BBNS; to find :
  • flat geometry
  • 70% Dark Energy; 26% Dark Matter; 4% Baryonic Matter
  • age 13.7 Gyr
  • initial fluctuation spectrum is power law, index -1 (consistent with inflation)
  • epoch of reionization starts near z ~ 20

(3) Preliminaries

(a) The Big Picture

The following diagrams help integrate a wide range of physical processes into a whole.
You probably "know" most of what's in them, but it is good to grasp the bigger picture.
Usually, our intuition spans only a small fraction of what Nature offers.

• Remind yourself, using simple scale models, just how BIG the Universe is.

• A more physically revealing diagram plots Size vs Mass on exponential axes.

• The Universe is incredibly dynamic; as seen in a Time-Energy diagram.

• See the atomic and nuclear cycles in a Density-Temperature diagram.

• Regain a sense of your own significance in a Mass-Complexity diagram.

  In a course of this type, it can be too easy to develop myopia.
  Keep trying to see your subject in a "global" context -- see where it fits on the grandest scales.
  

(b) Galaxies are Multicomponent Systems

• Three constituents, with rough mass ratio 1/10/100 : Gas / Stars / Dark Matter
  
  The first two have complex identity :
  • Gas:     different phases; dynamics; composition; (like "weather")
  • Stars:  different ages; locations; kinematics; metallicities; (like "cars")
  The third is simpler but more enigmatic:
  • DM:      collisionless "gas" (of WIMPs?); huge; ~smooth; centrally concentrated

• Several components, with varying prominence depending on galaxy type
  • Nucleus: dense; star formation; supermassive black hole
  • Bulge:     spheroidal; mixed ages; kinematically "hot" & little rotation
  • Disk:       gas & stars; younger; star formation; spiral arms; kinematically "cold" & rotates
  • Halo:       low density; GCs present; old; Dark Matter dominates; [sketch]

    Note :   Dark Matter dominates on large scales only
                 bulge & disk dynamics determined by stars & gas alone

(c) The Milky Way - A Typical Large Spiral

To get oriented, let's look at the basic properties of the Milky Way
NGC 891 & NGC 6744 are thought to be Milky-Way look-alikes [images]

Masses and luminosities are in solar units (V band; B&T Tables 1-1, 1-2, 1-5)

• Global Properties:
  • Type:  Sbc/SBbc, with weak bar.
  • Total luminosity:  1.4 x 10¹⁰ L;  disk / bulge 1.2 / 0.2 x 10¹⁰ L
  • Disk: exponential scale length: 3.5 kpc;  mass: 6 x 10¹⁰ M;  M/L_v: ~5
  • Spiral structure is difficult to identify with certainty, but 2-3 arms known.
  • Like many spirals, the MW probably has a large HI disk.

• Milky Way Coordinates and Rotation:
  • The North Galactic Pole (NGP) and Galactic Center (GC) have RA, Dec (J2000):
                  6^h35^m, +46.4^o             and           6^h35^m, +46.4^o.
  • These define galactic longitude and latitude (l, b):   l = 0^o towards the GC
    increasing eastwards: 0 (Saggitarius) 90 (Cygnus) 180 (Lyra) 270 (Grus).
  • The MW rotates clockwise viewed from the NGP
          (opposite to the direction of earth's rotation and orbit around the sun).
  • The rotation curve is normal for a spiral of our type and luminosity.

• Solar Neighborhood and the LSR:
  • The sun resides ~8.5 kpc from the GC, and is slightly above the plane, z ~ +40 pc.
  • Mass & luminosity volume density :   0.18 M pc^-3   &   0.067 L pc^-3
  • Mass & luminosity surface density :      75 M pc^-2   &       15 L pc^-2
  • The circular rotation rate and period of the solar neighborhood are ~220 km/s  &  240 Myr
  • The Local Standard of Rest (LSR) is a frame moving at 220 km/s towards l, b = 90^o, 0^o.
  • The local velocity coordinates are: U,V,W (towards l = 180^o; 90^o; NGP):
          Relative to the LSR, typical disk star random velocities are ~40 km/s.
          The sun's motion is: U;V;W = -10; 20; 7 km/s (16.5 km/s towards Leo: l = 53, b = 25).

• Galaxy Center Properties :
  • Core radius :   ~1pc     (human cell in middle of
  • Stellar density :   5 x 10⁶ M pc^-3
  • Velocity dispersion (1-D sigma) :   ~150 km/s
  • Total mass : 10⁸ M
  • Black Hole Mass (MW) :   3.4 x 10⁶ M

(d) A Wide Variety of Size, Mass & Form

Pretty galaxy posters give a very biassed view of the galaxy population.
• Huge range in mass, size, and luminosity : (in units of MW)

  Type	Mass	Diameter	Luminosity
  Spirals	0.005 - 1.5	0.2 - 2.0	0.005 - 10.0
  Ellipticals	10-4 - 5.0	10-2 - 5.0	5×10-5 - 5.0
  Irregulars	<5×10-4 - 0.15	0.01 - 0.25	5×10-5 - 0.1

  Note that spirals span a narrower range in all three parameters.
  See M87 (Giant E) and M32 (dwarf E) at same physical scale [images]

• Relative numbers of galaxies described by :
  luminosity functions   (e.g. the Schechter Function: [Topic 4])
  mass functions   (in practice, more difficult to evaluate)
  Typically, these are steep functions, increasing for smaller galaxies
    dwarfs far outnumber large galaxies (by 100s to 1)

• Many galaxies do not have cleanly defined Hubble type
  Galaxies (particularly disks) are fragile and easily disturbed
    many cluster galaxies are "pecular"
    disturbed/interacting field galaxies are not uncommon
    many high-z galaxies look peculiar (not yet relaxed/assembled)

(e) Useful Units

Calculations of galaxy properties are greatly simplified with sensible units (see also: Toolbox).
Rather than "mks" or "cgs" for length/mass/time, we can use:

"psm" :   parsec,   solar mass,   Megayear   :   pc, M, Myr

There are a number of nice features to this system:

1. Velocity in psm units, pc/Myr, is the same as km/s (within 2%; 1pc/Myr = 0.9778 km/s)
   (recall the pnemonic: "a kilometer per second is a parsec in a million years ")
2. Newton's constant: G = 4.50 × 10^-3   (4.49846 × 10^-3)
   its units are:   (pc³/M) Myr^{-2     -1} Myr^-2       (km/s)² pc M^-1
3. Equations, such as   M = R V² / G,   directly accept and yield observational values
4. Densities, _psm, are in M/pc^-3 = 6.76 × 10^-23 gm cm^-3 = 40.4 m_p cm^-3 = 3.60 × 10⁶ h²_crit
5. Frequencies, Myr^-1, are also velocity gradients: km/s/pc
6. Crossing/collapse times: R(pc) / V(km/s) = 1 / (G )^½   are in Myr.
   

Some examples illustrate psm units, and introduce basic galaxy properties :
(see homework for further examples).

• Estimate the mass interior to the sun's orbit (R~8kpc; V~220 km/s)
  use (3): M ~ RV² / G     8000 x 220² / 4.5 x 10^-3 ~ 8.6 x 10¹⁰ M

• Whats the density at the galactic center, where V ~100 km/s @ R ~1pc?
  use (6) : R²/V² = 1 / (G )
    = V²/(G R²)   = 100² / (4.5x10^-3 x 1²)   =   2.2 x 10⁶ M/pc^-3

• What's the Schwarzchild radius of a 10⁸ M black hole ?
  use R_s = 2GM/c² = 2 × 4.5 × 10^-3 × 10⁸ / (3 × 10⁵)² = 1.0 × 10^-5 pc = 2 AU

• What's the Hubble time for H_o = 75 km/s/Mpc ?
  use (5) : t_H(Myr) = 1 / (75 km/s/Mpc) = 1 Mpc / (75 km/s)
  = 10⁶ / 75 = 1.33x10⁴ Myr = 13.3 Gyr

There are a few extensions to the psm system which can, at times, be useful:

7. psm energy units: peu (Mpc²Myr^-2) = 1.89 × 10³⁶ Joules
8. psm luminosity units: plu (peu/Myr) = 5.97 × 10²² Watt = 1.56 × 10^-4 L
9. mass/luminosity units: M/plu = 3.33 × 10⁷ kg/Watt = 6400 (M/L)
10. linear momentum: pmu (Mpc/Myr Mkm/s) = 1.85 × 10³³ kg m s^-1  
11. angular momentum: pamu (Mpc²Myr^-1 M km/s pc) = 5.71 × 10⁴⁹ kg m² s^-1
12. force (momentum flux): pfu (Mpc/Myr² Mkm/s/Myr) = 5.86 × 10¹⁹ N
13. acceleration: pau (pc/Myr² km/s Myr^-1) = 3.09 × 10^-11 m s^-2

A few more examples help illustrate:

• What's the gravitational luminosity of a galaxy merger (M ~ 10¹¹M in R ~ 10 kpc)
  Use (6) for collapse time ~ (G)^-½ ~ (4.5 × 10^-3× 10¹¹/20000³)^-½ ~ 130 Myr
  Energy of collapse ~ GM²/R ~ 4.5 × 10¹⁵ peu
  Gravitational luminosity = 3.5 × 10¹³ plu = 5.4 × 10⁹ L
  (much less than ~10¹¹ L from typical star formation).
• What's the ejection velocity of a 10 M supernova envelope of energy 10⁴⁶ J ?
  Energy is ~5 × 10⁹ peu ~ ½MV² V ~ 32,000 km/s
• What's the mechanical luminosity and force of a 1000 km/s AGN jet carrying 10 M yr^-1 ?
  L = ½ Mdot V² = ½ × 10⁷ × 10⁶ = 5 × 10¹²   plu  =  3 × 10⁴² erg s^-1
  F = Mdot V = 10⁷ × 10³ = 10¹⁰ pfu  =  5.9 × 10³⁴ dyne

(f) Magnitude Systems and Surface Brightness

The previous section deals only with dynamical variables : V, R, t, M.
Let's introduce starlight into the mix, not least because it is easy to measure.

Astronomers use two systems: magnitudes and fluxes (each with apparent and intrinsic)
it can sometimes be tricky jumping back and forth between these systems.

• Magnitudes: 
  The generic magnitude is defined:

  m  =  const  -2.5 log10[flux]  =  -2.5 log10[flux / flux_0]

  (1.3f - 1)

  
  where flux_0 is a reference flux for a star with m = 0.0 (usually Vega), and is filter-specific.
  Typically, m ~ 12 - 14 (nearby galaxies); 16 - 18 (distant galaxies); 21 - 25 (very distant galaxies).

  Absolute magnitude (M) is defined as the apparent magnitude (m) were the object at 10pc, hence:
  

  M  =  m  -  5 log dpc  +  5

  (1.3f - 2)

  
  
  Typically, M ~ -10 to -17 (dwarfs); -18 to -21 (normal galaxies); -22 to -24 (giant galaxies & QSOs).

• Solar magnitudes and fluxes: 
  Often, we express luminosities relative to the sun (e.g. 3 × 10⁸ L_V,)
  The sun's absolute magnitude in band X = U,B,V,R,I is M_X, = 5.66, 5.47, 4.82, 4.28, 3.94.
  Hence, an object with absolute magnitude M_X, has luminosity:

  LX  =  dex[ -0.4(MX - MX,) ]   LX,

  (1.3f - 3)

• Surface Brightness: 
  Extended objects have surface brightness, µ in mag arcsec^-2   (mag/ss; sometimes written )
  Since µ is independent of distance it immediately gives the surface luminosity density, I L pc^-2
  e.g. using M_,B from above, we find (see homework) :

  µB  =  27.04  -  2.5 log(IB)

  (1.3f - 4)

  
  
  and in general, for U,B,V,R,I, the constant is: 27.23, 27.04, 26.39, 25.85, 25.51.

• Example: 
  M87 has a central surface brightness µ_V = 17 mag/ss.
    the core has projected luminosity density: dex[ -0.4(17 - 27.04)]  =  10,400 L_V, pc^-2.
  if the core radius is 10 arcsec, what's the core's total luminosity?
    m_core  ~  17 - 2.5 log [×10²]  =  10.75, giving L_core  =  3.26×10⁶ L_V,
  for a distance of 15 Mpc, what's the luminosity density in M87's core?
    10 arcsec = 730 pc, so j_core ~ I_core / 2 r_core ~ 7.1 L_V, pc^-3.
  to find the mass density requires a mass-to-light ratio, which is our next topic:

(g) Mass to Light Ratios

Light and dynamics are coupled using "Mass to Light Ratios (M/L)".
• "Mass to Light" (M/L) ratios are important for two reasons :
  • they allow us to estimate mass (important but difficult to measure)
    using light (easy to measure)

  • they tell us about the content of a system,
    eg (M/L) values differ :   pop I < pop II < galaxy+halo < clusters

• Solar units are used :   where (M/L)     M/L     1
  Physical units :   kg/Watt are not generally used
  [ convertion : (M/L)_,bol = 5173 kg/Watt = 0.5173 gm/(erg/s) ]
  (M/L) is expressed at a given waveband, most commonly B,V,I,K, or bolometric (all ).
  e.g. for waveband "X", using absolute magnitudes :

  (M/L)X  =  M/M  /  LX/L,X  =  M/M  /  dex[ -0.4( MX  -  M,X) ]

  (1.3g - 1)

  
  where M_X & M_X are X-band absolute magnitudes of the object & sun;
  and L_X & L_X are X-band luminosities of the object & sun
  and X = U,B,V,R,I,K,bol   and   M_X = 5.66, 5.47, 4.82, 4.28, 3.94, 3.33, 4.74
  note : (M/L)_X is the same for all X only if the object and sun have the same colors
  (careful : M used for both mass and absolute magnitude here - sorry)

  One can also use luminosities (usually only bolometric)
  L_,bol = 3.84 x 10³³ erg s^-1   and M_bol = -2.5 log(L_bol / L_,bol) + 4.74

• For main sequence stars, we have L M^3.5, giving :   (M/L) M^-2.5 L^-0.71
  showing, as one expects, later spectral types have higher M/L.
  eg K stars : M ~ 0.5M     M/L ~ 10; A stars : M ~ 2.0M     M/L ~ 0.1

• For composite systems, M/L reflects the average M/L over the population
  • Pop I (young) :   massive stars dominate light; low mass stars dominate mass
    
  • Pop II (old) :   giants dominate light; M.S. stars dominate mass
    Typical galaxy (& solar neighborhood) has M/L_V ~ 6 , M/L_B ~ 10
    In general : M/L increases with age and metallicity
    Maximum range : 2 < M/L_B < 20.

  Dark components further increase these values, eg

  • SMBH in galaxy nuclei
  • Dark Matter in galaxy halos

  More specifically, for main sequence stars and composite systems in V :

  Type M / M MV LV / L,V (M/L)V O5 60 -5.7 16,140 0.0037 B5 5.9 -1.2 255 0.023 A5 2.0 +1.95 14 0.14 F5 1.4 +3.5 3.4 0.41 G5 0.92 +5.1 0.77 1.19 K5 0.67 +6.4 0.23 2.87 M5 0.21 +12.3 0.001 206

  System (M/L)V Reason HII region 0.3 - 1 Pop I only Spiral Disk 2 - 5 Pop I + II Bulges / Ellipticals 8 - 15 Pop II Nucleus (no AGN) 10 - 50 BH present Galaxy + halo 20 - 50 DM important Clusters 100 - 500 DM dominates Universe ~1000 DM dominates

• Surface brightness to surface mass density:

  From 3f above, surface brightness µ mag/ss yields surface luminosity density, I L / pc².
  adopting a value for (M/L) now gives the surface mass density _M, in M pc^-2
  Combining M/L and the relation between µ and I, we have (for the B band):

  M  =  (M/L)B × dex[ -0.4 × (µB  -  27.05) ]     M pc-2

  (1.3g - 2)

  
  e.g. the cores of giant E's have µ_B ~18 mag arcsec^-2, (M/L)_B ~10, R_c ~1kpc,
    _M ~4 x 10⁴   M pc^-2   &   ~20   M pc^-3 (taking depth ~2R_c)

  Note that nowhere did we need distance to obtain this important parameter.
  Another example : M32 & M87 have cores with µ_V ~11 & ~17 V mag/ss (Topic 7.4cii)
    M32 is a much denser system : _M ~250× higher (in fact, ~10⁵× higher)

(h) Gas in and Between Galaxies

Despite its small total mass, diffuse gas is an important component of galaxies.
• Gas (and dust) comes in a wide range of phases :
  
  Within galaxies :
  
  • Molecular cold "dense" clouds (DMCs) :   (eg CO 2.6mm);   (pre)-star formation regions
    
  • Dust (~1µ graphite/silicates):   (IR);   DMCs; diffuse ISM; old star winds.
  • Atomic warm neutral gas :   (eg HI 21 cm);   disk ISM; outer disk
    
  • Ionized gas @ 10⁴K :   (eg H);   HII star formation regions; diffuse ISM; cooled SNRs
    
  • Ionized gas @ 10⁶K :   (eg X ray);   SNRs; diffuse ISM
    
  • Relativistic magnetoionic plasma :   (eg synchrotron);   SNRs; widespread; AGN-jets.
  
  Between galaxies :
  
  • Almost no neutral atomic or molecular gas
    
  • Superwinds :   energetic multiphase global outflow, driven by a starburst (or AGN);
    
  • Intracluster gas (ICM) :   (X-ray);   M ~ 1-5x M(gals); Z ~ 1/3 solar; primordial + superwinds
    
  • Intergalactic gas (IGM) :   v. low density; UV (AGN+SF) ionized; Ly clouds (X_e ~ 10^-5)

• Gas cooling enables the formation of dense systems (see 3l below)
  stars & DM undergo dissipationless collapse     low density endpoint
  gas, however, can radiate energy during collapse     high density endpoint
    gas plays a fundamental role in giving galaxies their present day form
  
  The efficiency of gas cooling depends on three factors :
  • density :   almost all radiation mechanisms are collisional, hence ×
    
  • temperature :   this defines the state of the gas (molecular / atomic / ionized),
            which in turn determines the particular radiation processes which can operate
    
  • metallicity :   since most radiation comes from elements other than H or He.
  Some examples :
  ICM gas cannot cool easily :   too low
  DMC gas cools efficiently :   high; moleular lines; dust IR
  10⁵K gas is rare :   strong resonance line cooling in, eg, OV & OVI
  primordial star formation unusual :   no metals, just H and H₂ cooling
  
  All complexities are absorbed in cooling curves :   efficiency as f(T,Z)
  
  
• Two kinds of ionization :
  • photoionization :   photon energy > electron binding energy   (UV - Xray).
    typically found near OB stars (thermal UV) or AGN (non-thermal UV)
    ionization degree depends mainly on ratio (ionizing flux / gas density)
    typically, T(e) << T(ionization degree)     ions and electros not in LTE

  • collisional ionization :   thermal energy > electron binding energy   (T > 10,000K).
    typically found in shocks; accretion disks; ICM;
    usually, T(e) = T(ions) = T(ionization degree)

    Note: in most circumstances, ISM/IGM gas is optically thin.
    Inside stars, of course, the high density makes the gas optically thick,
    and we have full LTE :   T(e) = T(ions) = T(ionization degree) = T(photons)

• Gas provides access to chemical evolution
  emission and absorption produced by diffuse gas can yield abundances, eg
  within galaxies :   ISM gas participates in the star/gas evolutionary cycle
    abundance gradients; comparisons between galaxies; low Z (~primordial) galaxies.
  outside galaxies :   gas is sensitive to superwind pollution history
    high-z QSO metal absorption gives halo abundances in young galaxies.
    primordial D/H & He³ abundances     BBNS constraint on _b

(i) Collisionless Components

Stars fill galaxies very sparsely
They never collide and rarely experience large deflections. Here's why :
Consider the solar neighborhood. A typical star size/separation is:
• size ~D(sun) ~1/100 AU (sun ½ deg);   sep ~1pc ~10⁵AU
    size/sep ~10^-7 filling factor ~10^-21   (note, for air : 10^-1.5 & 10^-4.5)
  Illustration :   star=sand grain (~0.1mm) typical galaxy ~10¹¹ = cubic yard of sand
  but, each separated by ~1km (10m in nucleus)     fills Earth     very empty.
  [amusingly, since dynamical time t ~ 1 / (G )^½   & _sand ~ _star, then
  the sparse sand model & MW galaxy have the same gravitational timescale :   ~100 Myr ]

• Pathlength : 1/n = sep³/size² = (sep/size)² x sep = 10¹⁴pc ~10⁹ orbits !
  Collision time : ~10¹⁷yrs @ 200 km/s (~10¹⁸yrs @ disk dispersion).
  Hence the famous statement : when two galaxies collide, no stars collide.

• Alternate perspective : typical star-star encounter deflection ~½ arcsec
  hence, star orbits follow smooth potential
    long range forces dominate, and physics tends to be global
  since potential determined by distribution of all stars, behaviour can be complex.

• Dark Matter (elementary particles) also behaves in a collisionless manner.
  strange : usually view particles as bouncing around, but these move on smooth orbits
    to first order, DM particles and stars share similar dynamics.
  however, DM currently more extended, so how did this arise ?
    gas behaves differently (see 3g below)   settles before forming stars.

(j) Thermal & Fluid Character of Stellar Dynamics

It may be useful at this time to plant some seed thoughts about Stellar Dynamics,
let them germinate before starting the subject proper in Topic 8.
• Consider a gas of atoms :
  unlike stars in a galaxy, the atoms collide frequently, having small free path
  quickly, an isotropic Maxwell-Boltzmann velocity distribution is established
  if there is bulk flow, a mean velocity is added to the random thermal motions.
  Thus, much physics is local, and most memory of initial conditions is lost
  if the gas is bound by its own gravity (eg a star), thermal motions "match" the potential

• Now consider our galaxy of collisionless stars :
  in each region (dx,dy,dz at x,y,z) we have stars with a range of velocities
  ie a distribution function : DF(V_x,V_y,V_z,x, y, z) dV_xdV_ydV_zdx dy dz
  this is analogous to the Maxwell-Boltzmann DF, but it usually has different form
  typically, there is a mean velocity and a random dispersion
  these are analogous to the bulk flow and thermal motion for atoms in a gas
  eg if dispersion velocity is ~same everywhere, one speaks of an isothermal system

• There are further similarities with fluids :
  stars & atoms are neither created nor destroyed     their DF's obey continuity equations
  star & atom ensembles obey energy and momentum conservation equations
  star & atom movement is affected/defined by the total gravitational field

  these similarities are sufficient that :
    the equations governing the stellar DF look like fluid equations
    hence, we speak of the "equations of stellar hydrodynamics"

• Stellar dynamics can be more complicated/interesting for several reasons :
  Because no strong collisions, the memory of former conditions can persist, eg
    the MW has tidal streams from cannibalized infalling dwarfs
    many galaxies have counter rotating cores, formed from an accreted companion
        (note that smooth looking galaxies can hide structured velocity distributions)

  Dispersion velocities can be anisotropic (and non-Gaussian), eg
    can have mainly radial dispersion, with little azimuthal or polar dispersion
    since dispersion defines scale height, then anisotropy can cause non-spherical shape
    the analogous thermal property is anisotropic pressure (impossible for gas)

  Stellar systems are gravitationally bound     they have negative specific heat
    remove energy system contracts star velocities increase = hotter
  note, same for single stars   when cores contract(expand) they heat(cool)

(k) Support: Rotation vs Dispersion

Since galaxies are empty and gravity attracts, why don't they just collapse: what "supports" them?
There are two extreme situations, and everything in between :
• Pure rotation :
  like the solar system, circular orbits hold stars "up" very effectively
  in a pure rotationally supported disk, all stars follow circular orbits.
  at each radius V_rot = V_circ   (the "circular velocity" which balances gravity).
  note, there is zero velocity dispersion     the system is kinematically "cold"

• Pure dispersion :
  because stars never collide, their orbits are free to intersect one another
  a "swarm" of random orbits could have only dispersion and zero net rotation
  with no collisions, stars continue on their orbits, and the galaxy "stays up"
  we say the system is dispersion supported     it is kinematically "hot"
  in this case, velocity dispersion acts like a pressure, giving hydrostatic support
  since the orbits follow gravity, then V_disp ~ V_circ, as one might expect

• Intermediate cases :
  not surprisingly, one can have intermediate cases, for example :
  • The MW disk near the sun has < V_rot > ~220 km/s, and V_disp ~40 km/s
    it is mainly rotationally supported, but has a small dispersion component
    note that < V_rot > is slower than V_circ   (an effect called asymmetric drift)

  • The MW bulge rotates slowly
    it is mainly dispersion supported, with a small rotational component

  • As expected, rotation and dispersion combine to provide the full support needed :

    Vcirc2     Vrot2 + Vdisp2

    (1.3k - 1)

• Rotational flattening :
  if a galaxy of stars behaves like a fluid, then a rotating galaxy should flatten
  conversely, flattened galaxies should rotate accordingly
  it came as a great surprise in 1977 when this was found not to be the case
    flat-ish (luminous) ellipticals do not rotate
  so, what flattens them ?

  Unlike atoms in fluids, stars can have anisotropic velocity dispersions
  since dispersion acts like "pressure", it sets the scale height against gravity
  thus, one can have different scale heights in different directions
    non-rotating Ellipticals can be oblate, prolate, or even triaxial

(l) Dissipationless vs Dissipational Collapse

Before galaxies formed, the Universe had roughly uniform low density
somehow, parts of it collapsed to form much denser systems (galaxies, bulges, stars).
It is not immediately obvious how this can happen :
• Consider first the collapse of a collisionless system (stars or dark matter) :
  
  it starts large and motionless, falls radially, at the bottom of the hill nothing collides
  so, out it goes again, getting larger and slower, back to its starting point.

  In practice, small irregularities grow, causing "orbit scrambling" (violent relaxation)
  we say the system "virializes"   it settles down, relaxed and unchanging
  the final system is ~half the original size & supported by random motions
  it therefore has low-ish density   still not dense enough to be a galaxy.

  We need to remove energy from the system to allow further collapse.
  In a smooth collisionless system this cannot happen.
  The only "cooling" possible is ejection of "hot" stars (or DM) by scattering.
  However, 2-body scattering never occurs & large scale scattering needs inhomogeneities
  hence the collapse is termed dissipationless :  no energy is dissipated.

• Consider now the collapse of gas :
  this proceeds quite differently :   atoms collide, so free fall is halted by pressure
  as before, the binding and kinetic (thermal) energies are equal ("virial theorem")
  but there is a crucial new aspect :   the gas can lose energy by radiation (photons)
  this allows the gas to cool, lose pressure, and contract
  this is dissipational collapse (energy is dissipated), and creates much denser systems
    an obvious example: stars form from collapsing gas clouds.
  if the compact gaseous region then forms stars, we finally achieve high stellar densities.

• Rotation complicates both types of collapse :
  the previous discussion ignored angular momentum (AM)
  conservation of AM (V x R) prevents efficient collapse ("AM barrier")
  for efficient collapse, one needs efficient AM transfer/loss mechanisms to operate
  two such mechanisms have recently been identified :
  • MHD torques operating in gas (accretion) disks
    
  • gravitational torques operating between stars and gas during galaxy mergers
  these allow dissipational collapse to proceed and build the dense systems we find.

(m) Concordance Cosmology

• Our subject is explicitly and implicitly cosmological
  We will need to frame questions within a chosen "World Model"
  Contemporary models (GR + FRW + more) involve several important parameters :
  • _tot = the total density, determining global geometry (1.0=flat) :   _tot = _m +
  • _m = total matter density, including dark matter and baryons :   _m = _DM + _b
  • = density of dark energy (cosmological constant). Exerts "pressure".
  • H_o = current rate of expansion (sets basic age, modulo de(ac)celeration)
  • Primordial perturbation spectrum :   creates structure (Pow Law :   index & amp)

• We approach this subject at an ideal time
  Before ~1995 :   fundamental ambiguity in parameter values
  eg uncertainty in H_o (50 - 100); Omega (~0.3 & 1.000); the age problem (t_U < t_GCs); etc..
  Since ~1995 :   astounding progress, culminating with WMAP in Feb 2003.

• Cosmologists now combine about 5 datasets to constrain all the parameters :
  • WMAP :   power spectrum of CMB fluctuations [ _tot; _b ; index & amp ]
  • HST-H_o :   local Cepheid distances and radial velocities [ H_o ]
  • High-z SN Ia :   Hubble diagram using bright standard candles [ H(t) ; ]
  • BBNS :   Helium and light element abundances [ _b ]
  • 2dFGRS/SDSS :   large scale structure [ _m ; index & amp ]
  These yield a single self-consistent framework : the concordance model

• Parameter values are now known (reliably?) to a few %
  _tot = 1.0     = 0.7     _m = 0.3     _DM = 0.26     _b = 0.04
  H_o = 72 km s^-1Mpc^-1     t_age = 13.7 Gyr     t_CMB = 380 kyr
  z_reion ~ 20     index ~ -1.0 (consistent with inflation)

• Here are some useful time-line diagrams for the concordance world model.

  Full history :           Parameters   and   Events The first Gyr :         Parameters   and   Events The first 500 kyr :   Parameters   and   Events

  etc....

• A few key facts :
  • z ~ 1 is ~60% lookback time (LBT), with cosmic age ~6 Gyr
  • coasting (changover from de to ac-celeration) occurs at z~0.65 or ~45% LBT
  • high-z galaxies and QSOs at z~4-6 are at ~90% LBT, age ~1Gyr
  • recombination is at z~1100, T~3300K, age~380 kyr, ~10³ cm^-3
  • at recombination, 10kpc subtends ~2.8 arcmin, or 1 deg ~170 kpc
  • matter/energy equality occurs at z~3300, T~10,000K, age~50 kyr, ~10⁵ cm^-3

• Using a normalized Hubble constant :   "h"
  For decades, H_o was uncertain to ~50%
  it was/is useful, therefore, to set H_o to 100h km/s/Mpc with h kept explicit
  h appears once for each redshift-distance, with a power of opposite sign : eg
  
  The distance to Coma, cz ~ 6000 km/s, is 60h^-1 Mpc
  The luminosity of 3C 123 is 3x10⁴⁴h^-2 erg/s
  3C 123 has M_B ~ -24.5 + 5log(h)   [recall m - M = 5log(d) - 5]
  The jet in 3C 123 has length 150h^-1 kpc   [length = angle x distance]
  The core mass of NGC 1234 is 2x10¹⁰h^-1 M   [M ~ RV²/G, & R d]
  Its luminosity density is 1.6h L pc^-3   [h^-2 / h^-3]
  Its M/L ratio is 10h solar units   [h^-1 / h^-2]

  Note that h does not appear for non-redshift distances (eg Cepheid distances).
  Although we now know h=0.72 (with ~5% uncertainty), its good to keep using it.