AY202a Galaxies

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AY202a Galaxies DynamicsLecture 2 Basic
Cosmology, Galaxy Morphology

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• COSMOLOGY is a modern subject
• The basic framework for our current
• view of the Universe rests on ideas and
• discoveries (mostly) from the early 20th
• century.
• Basics
• Einsteins General Relativity
• The Copernican Principle
• Fundamental Observations Principles

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• Fundamental Observations
• The Sky is Dark at Night (Olbers P.)
• The Universe is Homogeneous on
• large scales (c.f. the CMB)
• The Universe is generally Expanding
• The Universe has Stuff in it, and the
• stuff is consistent with a hot
  
• origin Tcmb 2.725o

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Basic Principles

• Cosmological Principle (aka the Copernican
  principle). There is no preferred place in space
  --- the Universe should look the same from
  anywhere The Universe is
  HOMOGENEOUS and ISOTROPIC.

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Principles

• Perfect Cosmological Principle The Universe is
  also the same in time. The STEADY
  STATE Model (XXX)
• 
  Anthropic Cosmological Principle
• We see the Universe in a preferred state(time
  etc.) --- when Humans can exist

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Principles

• Relativistic Cosmological Principle The Laws of
  Physics are the same everywhere and everywhen
• (!!!) absolutely necessary (!!!)
• And we constantly check these

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Mathematical Cosmology

• The simplest questions are Geometric.
• How is Space measured?
• Standard 3-Space Metric
• ds2 dx2 dy2 dz2
• dr2 r2d?2 r2sin2? df2
• In Cartesian or Spherical coordinates in
• Euclidean Space.

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• Now make our space Non-Static, but homogeneous
  isotropic ?
• ds2 R2(t)(dx2 dy2 dz2)
• And then allow transformation to a more general
  geometry (i.e. allow non-Euclidean geometry) but
  keep isotropic and homogeneous

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• ds2 (11/4kr2) -2 (dx2dy2dz2)R2(t)
• where r2 x2 y2 z2, and k is a
• measure of space curvature.
• Note the Special Relativistic
• Minkowski Metric
• ds2 c2dt2 (dx2 dy2 dz2)

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• So, if we take our general metric and add the 4th
  (time) dimension, we have
• ds2 c2dt2 R2(t)(dx2 dy2 dz2)/(1kr2/4)
• or in spherical coordinates and simplifying,
• ds2 c2dt2 R2(t)dr2/(1-kr2) r2(dq2sin2q
  df2)
• which is the (Friedman)-Robertson-Walker
  Metric, a.k.a. FRW

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• The FRW metric is the most general,
• non-static, homogeneous and isotropic
• metric. It was derived 1930 by Robertson
  and Walker and perhaps a little earlier by
  Friedman.
• R(t), the Scale Factor, is an unspecified
  function of time (which is usually assumed to be
  continuous)
• and k 1, 0, or -1 the Curvature Constant
• For k -1 or 0, space is infinite

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Rasin Bread Analogy
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K 1 Spherical c lt pr K -1
Hyperbolic c gt pr K 0 Flat c pr
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What about the scale factor R(t)?

• R(t) is specified by Physics
• we can use Newtonian Physics (the
  Newtonian approximation) but now General
  Relativity holds.
• Start with Einsteins (tensor) Field Equations
• Gmu 8pTmn Lgmu and
• Gmu Rmn - 1/2 gmu R

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• Where
• Tmn is the Stress Energy tensor
• Rmn is the Ricci tensor
• gmu is the metric tensor
• Gmu is the Einstein tensor
• and R is the scalar curvature
• ? Rmn - 1/2 gmu R 8pTmn Lgmu
• is the Einstein Equation

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• The vector/scalar terms of the Tensor Equation
• give Einsteins Equations
• (dR/dt)2/R2 kc2/R2 8pGe/3c2Lc2/3
• energy
  density CC
• 2(d2R/dt2)/R (dR/dt)2/R kc2/R2
• 
  -8pGP/c3Lc2
• 
  pressure term CC

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• And Friedmans Equations
• (dR/dt)2 2GM/R Lc2R2/3 kc2
• So the curvature of space can be found as
• ? kc2 Ro2(8pG/3)ro Ho2
• if L 0 (no
  Cosmological Constant)
• or
• (dR/dt)2/R2 - 8pGro /3 Lc2/3 kc2/R2
• which is known as Friedmans Equation

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Critical Density

• Given
• kc2 Ro2 (8pG/3)ro Ho2
• With no cosmological constant, k 0 if
• (8pG/3)ro Ho2
• So we can define the critical density as
• ?crit 3H02/ 8pG 9.4 x 10-30 g/cm3
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  for H70 km/s/Mpc

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• COSMOLOGICAL FRAMEWORK
• The Friedmann-Robertson-Walker
• Metric
  the Cosmic Microwave Background
• THE HOT BIG BANG

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?
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Cosmology is now the search for three numbers
the geometry

• 1. The Expansion Rate Hubbles Constant H0
• 2. The Mean Matter Density O (matter) OM
• 3. The Cosmological Constant O (lambda) O?
• 4. The Geometric Constant k -1, 0, 1
• Nota Bene H0 (dR/dt)/R
• Taken together, these numbers describe the
  geometry of space-time and its evolution. They
  also give you the Age of the Universe.

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• The best routes to the first two are in the
  Nearby Universe
• H0 is determined by measuring distances
  and redshifts to galaxies. It changes with time
  in real FRW models so by definition it must be
  measured locally.
• W(matter) is determined locally by
  (1) a census, (2) topography, or (3) gravity
  versus the velocity field (how things move in the
  presence of lumps).

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Other Basics

• Units and Constants
• Magnitudes Megaparsecs
• http//www.cfa.harvard.edu/huchra/ay145/constants
  .html
• http//www.cfa.harvard.edu/huchra/ay145/mags.html
  
• For magnitudes, always remember to think about
  central wavelength, band-pass and zero point.
  E.g. Vega vs AB.
• Surface brightness (magnitudes per square
  arcsecond), like magnitudes, is logarithmic and
  does not add.
• Why are magnitudes still the unit of choice?

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Coordinate Systems

• 2-D Celestial Equatorial (B1950, J2000)
• (precession, fundamental
  grid)
• Ecliptic
• Alt-Az (observers only)
• Galactic (l b)
• Supergalactic (SGL SGB)
• 3-D Heliocentric, LSR
• Galactocentric, Local Group
• CMB Reference Frame (bad!)

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Galactic Coordinates

• Tied to MW.
• B1950 (Besselian year)
• NGP at 12h49m 27.4o
• NCP at l123o b27.4o
• J2000 (Julian year)
• NGP at 12h51m26.28s
• 27o0742.01
• NCP at l122.932o
• b27.128o

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Supergalactic Coordinates
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Supergalactic Coordinates

• Equator along supergalactic plane
• Zero point of SGL at one intersection with the
  Galactic Plane
• NSGP at l 47.37o, b6.32o
• J2000 18.9h 15.7o
• SGB0, SGL0 at l 137.37o b 0o
• Lahav et al 2000, MNRAS 312, 166L

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Galaxy Morphology

• Simple observable properties
• Classification goal is to relate form to physics.
• First major scheme was Hubbles Tuning Fork
  Diagram
• Hubbles original scheme lacked the missing link
  S0 galaxies, even as late as 1936
• Ellipticity defined as
• e 10(a-b)/a 7
  observationally
• Hubble believe that his sequence was an
  evolutionary sequence.
• Hubble also thought there were very few Irr gals.
  

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• Hubble types now not considered evolutionary
  although there are connnections between
  morphology and evolution.
• Hubble types have been considerably embellished
  by Sandage, deVaucouleurs and van den Bergh,
  etc.
• Irr ? Im (Magellanic Irregulars)
• I0 (Peculiar galaxies)
• Sub classes have been added, S0/a, Sa, Sab, Sb
• S0 class well established (DV ? L, L0 and L-)
• Rings, mixed types and peculiarities added
• (e.g. SAbc(r)p open Sbc with inner ring
  and peculiarities)

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• S. van den Bergh introduced two additional
  schema
• Luminosity Classes --- a galaxys appearance is
  related to its intrinsic L.
• Anemic Spirals --- very low surface brightness
  disks that probably result from the stripping of
  gas
• (c.f. Nature versus Nurture debate)
• Morgan also introduced spectral typing of
  galaxies as in stars a, af, f, fg, g, gk, k

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Luminosity Classes (S vdB ST Cal)

Real scatter much(!) larger
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• Other embellishments of note
• Morgan et al. during the search for radio
  galaxies introduced N, D, cD
• Arp (1966) Atlas of Peculiar Galaxies
• Some 30 of all NGC Galaxies are in the Arp
  or Vorontsov-Velyaminov atlases
• Arp and the Lampost Syndrome
• Zwickys Catalogue of Compact and Post-Eruptive
  Galaxies (1971)

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Surface Brightness Effects

• Arp (1965)
• WYSIWYG
• Normal galaxies
• lie in a restricted
• Range of SB
• (aka the Lampost
• Syndrome)

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By the numbers

• In a Blue selected, z0, magnitude limited
  sample
• 1/3 E (20) S0 (15)
• 2/3 S (60) I (5)
• Per unit volume will be different.
• also for spirals, very approximately
• 1/3 A 1/3 X 1/3 B

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• Mix of types in any sample depends on selection
  by color, surface brightness, and even density.

Note tiny fraction of Irregulars
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Quantitative Morphology

• Elliptical galaxy SB Profiles
• Hubble Law (one of four)
• I(r) I0 (1 r/r0)-2
• I0 Central Surface Brightness
• r0 Core Radius
• Problem 4 p ? I(r) r dr diverges

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• De Vaucouleurs R ¼ Law
• (a.k.a. Sersic profile with N4)
• I(r) Ie e -7.67 ((r/re) ¼ -1)
• re effective or ½ light radius
• I e surface brightness at re
• I0 e 7.67 Ie 103.33 Ie 2100 Ie
• re 11 r0
• and this is integrable
• Sersic ln I(R) ln I0 kR1/n

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• King profile (based on isothermal spheres fit to
  Globular Clusters) adds tidal cutoff term
• re r0 rt tidal radius
• I(r) IK (1 r2/rc2)-1/2 (1 rt2/rc2)-1/2
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• And many others, e.g.
• Oemler truncated Hubble Law
• Hernquist Profile
• NFW (Navarro, Frenk White) Profile
• generally dynamically inspired

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King profiles

Rt/Rc
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• Typical numbers
• I0 15-19 in B
• ltI0gt 17
• Giant E
• r0 1 kpc
• re 10 kpc

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• Sersic profiles
• Small N, less centrally concentrated and steeper
  at large R

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Spiral Galaxies

• Characterized by bulges exponential disks
• I(r) IS e r/rS
• Freeman (1970) IS 21.65 mB / sq arcsec
• rS 1-5 kpc, f(L)
• If Spirals have DV Law bulges and exponential
  disks, can you calculate the Disk/Bulge ratio for
  given rS, re, IS Ie ?

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NB on Galaxy Magnitudes

• There are MANY definitions for galaxy
  magnitudes, each with its s and s
• Isophotal (to a defined limit in mag/sq arcsec)
• Metric (to a defined radius in kpc)
• Petrosian
• Integrated Total etc.
• Also remember COLOR

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Reading Assignment

• For next Wednesday
• The preface to Zwickys Catalogue of Compact and
  Post-Eruptive Galaxies
• and NFW The Structure of Cold Dark Matter
  Halos, 1996, ApJ...463..563
• Read, Outline, be prepared to discuss Zwickys
  comments and Hernquists profile.

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Hubble,1926

• Investigated 400 extragalactic nebula in what he
  though was a fairly complete sample.
• Cook astrograph 6 refractor (!) 60
  100
• Numbers increased with magnitude
• Presented classification scheme (note no S0)
• 97 regular
• Sprials closest to E have large bulges
• Some spirals are barred

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• Es more stellar with decreasing luminosity
• mT C - K log d
• 23 E 59 SA 15 SB 3 Irr II
• (no mixed types)
• Plots of characteristics. Fall off at M12.5
• Luminosity-diameter relation
• Edge on Spirals fainter
• Apparent vs actual Ellipticity -- inclination
• Absolute mags for small with Ds

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• Calibration of brightest stars ---future use as
  distance indicators
• Masses via rotation, Opiks method
• Log N - M or Log N log S
• Space Density 9 x 10-18 Neb /pc3
• 1.5 x 10-31 g/cc
• Universe Size 2.7 x 1010 pc 30000 Mpc
• Volume 3.5 x 1032 pc3
• Mass 1.8 x 10 57 g 9
  x1022 M_sun