ay202a galaxies & dynamics lecture 2: basic cosmology, galaxy morphology
TRANSCRIPT
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AY202a Galaxies & Dynamics
Lecture 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:
Einstein’s General Relativity
The Copernican Principle
Fundamental Observations & Principles
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Fundamental Observations: The Sky is Dark at Night (Olber’s 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 CosmologyThe simplest questions are Geometric.
How is Space measured?
Standard 3-Space Metric:
ds2 = dx2 + dy2 + dz2
= dr2 +r2dθ2 + r2sin2θd2
In Cartesian or Spherical coordinates in
Euclidean Space.
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Now make our space Non-Static, but
“homogeneous” & “isotropic”
ds2 = R
2(t)(dx
2 + dy2 + dz
2)
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 = (1+1/4kr2) -2 (dx2+dy2+dz2)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)/(1+kr2/4)
or in spherical coordinates and simplifying,
ds2 = c2dt2 – R2(t)[dr
2/(1-kr
2) + rdθsinθd
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 infiniteinfinite
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Rasin Bread Analogy
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K = +1
Spherical
c < r
K = -1
Hyperbolic
c > r
K = 0
Flat
c = r
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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 Einstein’s (tensor) Field Equations
Gg and
GRgR
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Where
is the Stress Energy tensor
R is the Ricci tensor
g is the metric tensor
G is the Einstein tensor
and R is the scalar curvature
RgR = g
is the Einstein Equation
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The vector/scalar terms of the Tensor Equation
give Einstein’s Equations:
(dR/dt)2/R
2 + kc
2/R
2 = 8Gc2+c
2/3
energy density CC
2(d2R/dt
2)/R + (dR/dt)
2/R + kc
2/R
2
= -8GPc3+c2
pressure term CC
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And Friedman’s Equations:
(dR/dt)2
= 2GM/R + c2R
2/3 – kc
2
So the curvature of space can be found as kc
2 = Ro2[(8G/3)o – Ho
2]
if = 0 (no Cosmological Constant)
or
(dR/dt)2/R2 - 8Go /3 =c
2/3 – kc
2/R2
which is known as Friedman’s Equation
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Critical DensityGiven
kc2 = Ro
2 [(8G/3)o – Ho2]
With no cosmological constant, k = 0 if
(8G/3)o = Ho2
So we can define the “critical density” as
ρcrit = 3H02/ 8πG = 9.4 x 10-30 g/cm3
for H=70 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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Λ
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Cosmology is now the search for three numbers + the geometry:
1. The Expansion Rate = Hubble’s Constant H0
2. The Mean Matter Density = Ω (matter) = ΩM
3. The Cosmological Constant = Ω (lambda)= ΩΛ
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.
(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 & Megaparsecshttp://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 Systems2-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 l=123o b=+27.4o
J2000 (Julian year)
NGP at 12h51m26.28s +27o07’42.01” NCP at l=122.932o b=27.128o
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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, b=+6.32o
J2000 ~18.9h +15.7o
SGB=0, SGL=0 at l = 137.37o b = 0o
Lahav et al 2000, MNRAS 312, 166L
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Galaxy Morphology“Simple” observable propertiesClassification goal is to relate form to physics.First major scheme was Hubble’s “Tuning Fork
Diagram” (1) Hubble’s original scheme lacked the missing link
S0 galaxies, even as late as 1936 (2) Ellipticity defined as e = 10(a-b)/a ≤ 7 observationally (3) Hubble believe that his sequence was an
evolutionary sequence.(4) 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.
(1) Irr Im (Magellanic Irregulars)
+ I0 (Peculiar galaxies)
(2) Sub classes have been added, S0/a, Sa, Sab, Sb …
(3) S0 class well established (DV L+, L0 and L-)
(4) Rings, mixed types and peculiarities added
(e.g. SAbc(r)p = open Sbc with inner ring and peculiarities)
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•
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S. van den Bergh introduced two additional
schema:
(1) Luminosity Classes --- a galaxy’s appearance is related to its intrinsic L.
(2) 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 + S&T 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”
Zwicky’s Catalogue of Compact and Post-Eruptive Galaxies (1971)
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Surface Brightness Effects
Arp (1965)
WYSIWYGNormal galaxieslie in a restrictedRange of SB(aka the Lampost Syndrome)
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By the numbers
In a Blue selected, z=0, 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 π ∫ I(r) r dr diverges
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De Vaucouleurs R ¼ Law (a.k.a. Sersic profile with N=4)
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 + rt
2/rc2)-1/2 ]2
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
<I0> ~ 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 Zwicky’s “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 Zwicky’s comments and Hernquist’s 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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E’s “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 M~12.5
Luminosity-diameter relation
Edge on Spirals fainter
Apparent vs actual Ellipticity -- inclination
Absolute mags for small # with D’s
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Calibration of brightest stars ---future use as distance indicators
Masses via rotation, Opik’s methodLog 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