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

• Wide range in morphological appearance:
  eg classification bins : simple E0-6 compared with all the spiral types
  not just smooth, considerable fine-scale details
• Wide range in stellar populations:
  
  old, intermediate, young and currently forming
    ongoing chemical enrichment
• Wide range in stellar dynamics:
  
  "cold" rotationally supported disk stars
  "hot" mainly dispersion supported bulge and halo stars
• Significant cold ISM:
  
  note : the cold and warm components are dissipative, and therefore :
  influences dynamical evolution (eg helps spiral formation)
  influences stellar density distribution (eg creates dense cores & black holes)

(b) Review of Basic Components [image]

• Disks :
  Metal rich stars and ISM
  Nearly circular orbits with little (~5%) random motion & spiral patterns
  Both thin and thick components
• Bulge :
  Metal poor to super-rich stars
  High stellar densities with steep profile
  V(rot)/ ~ 1, so dispersion support important.
  
• Bar :
  Flat, linear distribution of stars
  Associated rings and spiral pattern
• Nucleus :
  Central (< 10pc) region of very high density (~10⁶ Mpc^-3)
  Dense ISM &/or starburst &/or star cluster
  Massive black hole
• Stellar Halo :
  Very low SB; ~few % total light; little/no rotation
  Metal poor stars; GCs, dwarfs; low-density hot gas
  
• Dark Halo :
  Dark matter dominates mass (and potential) outside ~10 kpc
  Mildly flattened &/or triaxial
  

(2) 3-D Shapes

• Distribution of (projected) b/a : [image]
  Approximately flat over wide range, from 0.3 to 0.8
  Rapid rise at b/a ~ 0.1 - 0.3; and rapid fall at b/a > 0.8
  

• Interpretation :
  • Randomly oriented thin circular disks give N(b/a) = const
      observed N(b/a) consistent with mostly flat circular disks
  • Drop at low b/a due to bulge. Note: slower rise for big bulge S0s, and faster rise for small bulge Scs.
  • Minimum b/a ~ 0.05 - 0.1 for ~bulgeless Sdm   disks can be highly flattened
  • drop at high b/a ~ 0.8 caused by non-circular disks
      dark matter potentials slightly oblate/triaxial ( < () > ~ 0.045)
  
  
• Warps: [image]
  
  • starlight almost always flat (if undisturbed)
  • however, HI is often warped, with warp starting beyond D₂₅
    
  • 180 degree symmetry: "integral sign" when seen edge-on.
  • 75% of warped galaxies have no significant companion
      probably response to non-spherical halo potential misaligned with disk
    

Not as easy as ellipticals because of other components
Study edge-on spirals to minimise contamination
Results :
• oblate spheroids, flattened by rotation
    probably similar to low-luminosity ellipticals

• Axis ratios from 2.5 to 5.
• Probably flat, since they aren't visible in edge-on spirals
• However, "peanut" bulges thought to be thickened (unstable) bars seen edge-on [image]
  

(3) Surface Photometry

• 1-D fits to elliptically-azimuthally averaged light profile
• 2-D fits to full image: better, since bulge & disk have different ellipticities

(a) Radial Profiles

(i) Bulge

deVaucouleurs R^1/4 Law, first in flux units:

(5.1a)       (5.1b)

or in magnitudes per square arcsec:

(5.2a)       (5.2b)

where

• Effective radius, R_e, contains half the light; [Note: I(R_e) I_e, etc ]
• R_e ~ 0.5 - 4 kpc (larger for early Hubble types)
• I(0) = 2140 I(R_e)
  
• Integrating to infinity: L_tot = 7.22 R_e² I_e

(ii) Disk

Exponential fits well (first flux units, then mag/ss):

(5.3a)       (5.3b)

where

• R_d is the disk scale length, ie I(R_d) = 1/e I(0)
• Typically, R_d ~ 0.25 R₂₅ ~ 2 - 5 kpc   (R₂₅ is 25^th mag/ss isophote)
• In practice, disk light falls sharply beyond 3 - 5 R_d
• R_d > R_e always (eg MW : R_d ~ 5 kpc, R_e ~ 2.7 kpc)
• Integrating to infinity: L_tot = 2 R_d² I(0)
• µ_B(0) ~ 21.65 ± 0.3 mag/ss (Freeman 1970 "Law" of ~const µ(0) for normal spirals)
  However, a few Low Surface Brightness (LSB) galaxies have much fainter µ(0) [image]
  
  

(iii) Stellar Halos

• MW and M31 have resolved halos with metal poor stars, and globular clusters
  Both of these systems contain significant substructure [image]
    tidally stripped dwarf galaxies and globular clusters.
  However, M33 does not have a significant stellar halo

• Extremely difficult to see as integrated light in other galaxies [image]
  Stacking ~1000 SDSS edge on galaxies shows extended red light out to µ_i ~ 29 mag/ss:
  Implied density: (r) r^- with ~ 3.
  Consistent with moderately flattened spheroid: c/a ~ 0.6

• Overall, still unclear yet:
  How much of stellar halo is in form of tidal streams
  How many galaxies have stellar halos .

Studies of edge on disks suggests exponential distribution: [image]

(5.4)

Where z_o is the scale height of the disk, ie I(z_o) = I(0) / e
At large z, excess light sometimes reveals a second "Thick Disk" of larger z₀
(see 4d(ii) below for further discussion of vertical disk structure)

(4) Disk Velocity Field

Typical rotation curve comprises [image]
• rise from zero at the nucleus
• V_max peak at R_max
• extended region close to flat
Many rotation curves have now been measured
Some systematic trends are noticable :

(i) At Large Radius

• V_max increases as L increases (T-F relation, see below)
• Outer slope increases as L decreases [image]
  for V(r) R ^m we find m in the range -0.2 to 0.2 (m = 0, flat, for M_B ~ -22.5)
  Drop in massive early types caused, in part, by high V_max from bulge

(ii) At Small Radius


• For luminous early type spirals, V(r) rises very rapidly (often unresolved)
  dense bulge core( &/or black hole?) [see Milky Way rotation curve: image]

• For low luminosity later type spirals, V(r) rises more slowly
  often V(r) r     "solid body"
  However: sometimes, when V(r) drops, (r) increases, so V(r) is not the full V_c
  i.e. rotation and dispersion both provide support
  

Disks are faint     stellar LOSVD (Line Of Sight Velocity Dispersion) is difficult to measure
Also, brighter central regions are confused by bulge component
Nevertheless, some results are emerging.

(i) Rotation

For disk stars, V_los >> _los so stars are cold and have ~ circular orbits
Usually, V_stars follows V_gas which is close to V_c [image]
• Sometimes, star orbital rotation velocity can be slower than the gas
  this is called asymmetric drift and indicates a higher stellar dispersion
        support beginning to be shared with dispersion
        stars at r likely to be at apogee, so have V < V_c

• In S0s, ~30% have counter-rotating gas disks [image]
  a few spirals even have two counter-rotating stellar disks
        both indicate external origin postdating primary disk formation

  (ii) Vertical Dispersion

  Face-on galaxies yield _z : the vertical stellar dispersion

• As a function of radius, _z decreases exponentially, with scale length 2R_d
  This agrees with simple stellar dynamics theory:
  An isothermal disk gives _z² = 2 G z_{o M}
  where _M is the surface mass density and z_o is the scale height
  Hence _{z     M}^½     I(r)^½     exp(-R/2R_d),     as found.

• Consider the Milky Way disk: observations near the solar neighborhood:

  The inferred mass density within the disk suggests dark matter does not dominate the disk.

  It turns out there are several components of different z_o and _z [image]

  • gas and dust,     z_o ~   50 pc ;   _z ~ 10 km/s
  • young thin disk, z_o ~ 200 pc ;   _z ~ 25 km/s
  • old thick disk,     z_o ~ 1.5 kpc ; _z ~ 50 km/s

  The astrophysical origin of this is thought to be _z increasing with age

  • stars born "cold" from molecular clouds with _z ~ sound speed, and corresponding small z₀
  • stars gradually "heated" by scattering off DMCs and spiral arms, and/or
  • heating of the disk over time by satellite passage and/or minor mergers

A circular disk tilted by angle i (0 = pole on) projects to an ellipse.
The photometric major axis (PMA) of this ellipse is called the line of nodes

Contours of projected velocity, V_los, give a spider diagram [image]

Kinematic Major Axis (KMA): line through nucleus perpendicular to velocity contours
Kinematic Minor Axis (KMI): V_los contour at V_sys through the nucleus

These spider diagrams reveal much about the detailed form of the disk velocity field:

• Circular velocity in an inclined circular disk: [image]
  KMA aligned with photometric major axis (PMA)
  KMI aligned with photometric minor axis (PMI)
  
• Flat V(r) (beyond initial rise) gives:
  V_los contours are approximately radial at large R
  If V(r) declines past V_max, then V_los contours close in a loop.
• Solid body i.e. V_c(r) r in near-nuclear regions, gives:
  equally spaced contours across nuclear KMA, with spacing 1/slope
• Warped disks have: [image]
  Twisted V_los contours in outer parts
  Note: model galaxies as a set of rings with different V(r), PA(r), i(r)
• Bars often show:
  evidence of radial motion over bar region
• Oval disks (e.g. arising from non-axisymmetric halo)
  KMI and KMA not perpendicular
  KMA not aligned with PMA, and KMI not aligned with PMI
• Spiral arms yield: [image]
  small perturbations to V_los contours near arm positions

(5) Scaling Relations

There are a number of correlations between the global parameters of galaxies:

Luminosity; Size; Surface Brightness; Rotation Velocity;
Such relations are called "Scaling Relations".
They are important for several reasons:
They reveal the internal properties of galaxies
They must arise naturally in theories of galaxy formation.

In the case of disk galaxies, the most important is between V_rot and Luminosity:

• V_max = maximum rotation velocity (inclination corrected), derived from: [image]
  • Major axis optical (often H) rotation curves (half the full amplitude)
  • HI 21 cm integrated (single dish) profile width, W₂₀: W₂₀ / sin i   =   2V_max
    

• Tully & Fisher (1977) recognised that V_max correlates with galaxy luminosity
  • L   V_max     ~ 3 - 4

• As for the Faber-Jackson relation, the T-F relation stems from virial equilibrium:
  V_c² M/R     and     L I(0) R²
  L (M/L)^-2 I(0)^-1 V_c⁴
  T-F relation holds if (M/L)^-2 I(0)^-1 ~ const     (roughly true)

• Usually, choose longer wavelengths (eg I & H bands rather than B & V): [image]
  • smaller scatter on the T-F relation, and slightly steeper gradient ( larger)
  This is because, at ~1-2µm :
  • L_1µ is less sensitive to star formation and dust
  • L_1µ tracks older population which dominates mass and has a more homogeneous M/L ratio

• The T-F relation is one of the key methods of distance determination
  • First calibrate on nearby galaxies with Cepheid distances [image]
    this yields the following relations :

  (5.5)

  • Then for more distant galaxies, measure V, inclination, and apparent magnitude:
    V_max and TF relation gives M, which gives m - M, which gives distance.
  • These greater distances can now be used with redshifts to derive H_o [image]

(6) Mass Estimates and Dark Matter Halos

For centrifugally supported circular motion, V_c(r) yields the mass distributions.
In general (not assuming spherical symmetry):

(5.6)

where is a geometry factor 0.7 <     < 1.2
Sphere:   =   1.0,     Flattened :   ~   0.7

For an exponential, thin disk, one can show that :

(5.7)


Where I_n and K_n are modified Bessel functions of the first and second kind.

This rotation curve has peak: V_max at R_max ~ 2.2 R_d [image]
for R   >   3 R_max   V_c(R) falls ~ R^-½   (Keplerian)

• 1960s (Burbidge's) gathered H rotation curves and assumed Keplerian fall-off beyond their data.
    quote well defined galaxy "masses"

• 1970s & 80s (Rubin et al) went deeper : ~ flat out to ~ 2 - 3 R_d [image]
    conclude dark matter (careful : exponential disk still ~flat here)

• Kent (1986) images same galaxies and derives rotation curves directly from light profile
  they match the observed rotation curves !
    dark matter not required; bulge + disk with normal M/L suffices

• Fortunately, HI extends well beyond the optical disk [image]
  while H goes to 2-3 R_d (~0.75 R₂₅),   HI often goes to > 5 R_d

• V_rot rarely declines; still flat or rising well beyond the disk [image]
  It is necessary to invoke an invisible halo
  
  Since = _d + _h and V_c² = r d/dr, then:
  V_c² = V_d² + V_h²
  Use the observed rotation, V_c, and the (predicted) disk rotation, V_d, to
  infer the halo contribution, V_h, and its potential.

• Typically, bulge + disk accounts for inner rotation curve with reasonable M/L_B ~ 3 - 5
  If this is forced to fit the inner rotation, it is a called "maximum disk" model
  Dark matter halo needed at larger radii, giving total M/L_B ~ 30
    ~5 times more dark matter than normal matter in stars + gas
  This is a lower limit since V_rot still constant/rising!

• Historically important paper: van Albada et al (1985) analysis of NGC 3198 : [image]

• It is now generally accepted that galaxies reside within large halos of dark matter. [image]

• At largest measured radii V_rot is ~flat, so (r)   ~   r^-2 in this region
  Unknown beyond this, but must drop faster to keep total mass finite.

• Difficult to constrain the inner parts
  Bulge + "maximum disk" fits yield plausible M/L (~ 3-5), suggesting DM not important here
  Halo contribution clearly drops at small radii, but functional form not well constrained.

• N-body codes which follow hierarchical assembly of DM halos yield a particular form:
  The Navarro-Frenk-White (NFW) 2-parameter broken power-law profile:

  (5.8)

  This has (r) ~ r^-1 in the center and (r) ~ r^-3 at r >> a.

  Or a slightly better 3-parameter fit is the "Einasto Profile": [image]

  (5.9)

  In this case, d_n 3n - 1/3 + 0.0079/n, ensures that r_e contains half the total mass.
  n ~ 7 4, decreasing systematically with halo mass (cluster galaxy halos).
  [See Merritt et al (2006 o-link) for a detailed discussion of halo fitting functions]

  Both these give rotation curves that rise to a peak and slowly decline [image]
  They are approximately flat in the regions measured by optical or HI rotation curves.

There is an intriguing property of these rotation curves:
• After a rapid rise, most rotation curves are ~flat at all radii :
    in regions where V_c is determined by disk matter, and
    in regions where V_c is determined by dark matter
• How do these two different regions know they should have the same rotation amplitude ??
• This is not currently understood, but indicates something important about galaxy formation

• Notice that a related puzzle also underlies the Tully-Fisher relation
  
  V_max is set by the halo, while
  M_I is set by the luminous matter
• Indeed, the theoretical origin of the TF relation is not yet fully understood.

(7) Spiral and Bar Structures

(i) Spiral Classes

• recall, two types (extremes) of spiral structure [image]
  • Grand Design (AC 12), two strong arms (~10%)
  • Flocculent (AC 1), more chaotic (~90%)
  • Multiple Arm (intermediate), strong inner arms, outer ratty

  (ii) Arm Prominence

• Arm / Inter-arm contrast is useful [image]
  • for contrast m magnitudes (typically 1-2 in B), define A = dex(0.4 m)

• A depends on color:
  • Grand Design : A_B   ~   A_I   ~   large (1.5 - 8)
  • Flocculent : A_B   >>   A_I   ~   1.0
      a plot of A_B / A_I   vs   A_I separates the classes well. [image]

• Clearly:
  • spiral arms are bluer than the underlying (red) disk
  • sprial arms are younger than the disk
  • the old disk in Grand design has spiral pattern
  • the old disk in flocculents is uniform

• Interpretation:
  • Grand design is a density wave:   it involves a spiral in the underlying mass distribution
    global coherence implies global process generates structure

  • Flocculent spirals are not density waves
    lack of coherence implies local process generates structure

  (iii) Leading or Trailing ?

• Consider orientation of spiral w.r.t. direction of disk rotation: [image]
  • arm ends point forward     leading spiral
  • arm ends point backwards     trailing spiral

• To decide: need to know which side is nearest:
  • Difficult, but try to identify the least obscured by dust (near side)
      arms are almost always trailing

• Many arms have dust lanes & HII regions on inside (concave) edge
    gas runs into arms on concave side; compressed; star formation
    HI and CO distribution is narrow and focussed on inner edge [image]

  (iv) Pitch Angle

• Defined as the angle between the tangents of arm and circle [image]
  e.g. tight spiral has small
  clearly:   tan = dr / r d   (where is azimuth)

• Most spirals have ~ const throughout disk
    logarithmic spiral : r()   =   r_o exp[( - _o) tan]
  with r = r_o at _o

• This is, in fact, predicted by density wave theory.

  (v) The Winding Problem

• If arms were "fixed" w.r.t. the disk (e.g. like leaves on water)
  With flat rotation (V ~ const), inner parts rotate many times compared to outer parts
  E.g. for one rotation at R, two rotations at R/2, four at R/4, 8 at R/8.
  This leads to very tightly wound arms.

  More precisely: with = V_c / R and V_c = constant we find [image]

  tan   =   R / V t   =   1 / t   =   1 /
  so after 1 rotation: tan = 1 / 2 or = 9°; after 2 rotations: ~ 4.5°.
  This quickly becomes a very tight spiral in which decreases with radius

• In reality:   for Sa: < > ~ 5° ;   for Sc: < > ~ 10°-30°
  This suggests we might have two types of condition

• Long lived spiral arms are not material features in the disk
  they are a pattern, through which stars and gas move
  these might be the grand design spirals

• Short lived spiral arms can arise from temporary patches pulled out by differential rotation
  the patches might arise from local disk instabilities, leading to star formation
  these might be the flocculent spirals

• Barred galaxies are common (~50%): [image]

• Isophotes not fit by ellipses; more rectangular
  Probably flat in disk plane
  K (2.2µm) images can show bars within bars (inner bar ~independent)

• Bars are straight, and stars stay in the bar rigid rotation of pattern with well defined _b
  Bars are not density waves:
  Stars move along the bar on closed orbits in frame rotating at _b
  Such orbits only occur for _b < _stars   bars occur inside co-rotation (CR)
  
  Bars can drive a density wave in disk helps maintain spiral structure.

• Gas motions important and interesting :
  Observations:
  Star formation occurs at bar ends
  Dust lanes seen down leading edge of bar
  Velocity fields suggest strong non-circular motion, including radial inflow.
  Simulations :
  Orbits mildly self-intersecting weak shocks compression where dust lanes seen
  Inner gas loses angular momentum and moves inwards
  May collect in disk/ring near ILR, or continue to fuel AGN & build black hole mass.
  Outer gas stored in ring near bar ends (CR)
  Gas beyond the bar can be stored in an outer ring at OLR
  may explain inner and outer rings seen in many barred galaxies [image]