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AY202a Galaxies & Dynamics Lecture 2: Basic Cosmology, Galaxy Morphology 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 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 o origin: Tcmb = 2.725 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. 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 Principles: Relativistic Cosmological Principle: The Laws of Physics are the same everywhere and everywhen (!!!) absolutely necessary (!!!) And we constantly check these Mathematical Cosmology The simplest questions are Geometric. How is Space measured? Standard 3-Space Metric: 2 2 2 2 ds = dx + dy + dz 2 2 2 2 2 2 = dr +r d + r sin df In Cartesian or Spherical coordinates in Euclidean Space. Now make our space Non-Static, but “homogeneous” & “isotropic” 2 2 2 2 2 ds = R (t)(dx + dy + dz ) And then allow transformation to a more general geometry (i.e. allow nonEuclidean geometry) but keep isotropic and homogeneous: 2 2 -2 ds = (1+1/4kr ) 2 2 2 2 2 2 (dx +dy +dz )R (t) 2 2 where r = x + y + z , and k is a measure of space curvature. Note the Special Relativistic Minkowski Metric 2 2 2 2 2 2 ds = c dt – (dx +dy + dz ) So, if we take our general metric and add the 4th (time) dimension, we have: 2 2 2 2 ds = c dt – R (t)(dx2 +dy2 + dz2)/(1+kr2/4) or in spherical coordinates and simplifying, 2 2 2 2 2 2 ds = c dt – R (t)[dr /(1-kr ) + r (dq +sin q df )] 2 2 2 2 which is the (Friedman)-Robertson-Walker Metric, a.k.a. FRW • 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 Rasin Bread Analogy K = +1 Spherical c < pr K = -1 Hyperbolic c > pr K=0 Flat c = pr 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 Gmu = 8pTmn + Lgmu Gmu = Rmn - 1/2 gmu R and 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 The vector/scalar terms of the Tensor Equation give Einstein’s Equations: (dR/dt) /R + kc /R = 8pGe/3c +Lc /3 2 2 2 2 2 2 energy density 2 2 2 2 CC 2 2(d R/dt )/R + (dR/dt) /R + kc /R = -8pGP/c +Lc 2 3 pressure term CC And Friedman’s Equations: (dR/dt) = 2GM/R + Lc R /3 – kc 2 2 2 2 So the curvature of space can be found as 2 kc = 2 2 Ro [(8pG/3)ro – Ho ] if L = 0 (no Cosmological Constant) or (dR/dt) /R - 8pGro /3 =Lc /3 – kc 2 2 2 which is known as Friedman’s Equation 2 /R 2 Critical Density Given 2 2 kc = Ro [(8pG/3)ro – Ho2] With no cosmological constant, k = 0 if 2 (8pG/3)ro = Ho So we can define the “critical density” as ρcrit = 3H02/ 8πG = 9.4 x 10-30 g/cm3 for H=70 km/s/Mpc COSMOLOGICAL FRAMEWORK: The Friedmann-Robertson-Walker Metric + the Cosmic Microwave Background = THE HOT BIG BANG Λ 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. 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). 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? 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!) 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 Supergalactic Coordinates 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 Galaxy Morphology “Simple” observable properties Classification 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. 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) • 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 Luminosity Classes (S vdB + S&T Cal) Real scatter much(!) larger • 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 PostEruptive Galaxies (1971) Surface Brightness Effects Arp (1965) WYSIWYG Normal galaxies lie in a restricted Range of SB (aka the Lampost Syndrome) 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 Mix of types in any sample depends on selection by color, surface brightness, and even density. Note tiny fraction of Irregulars 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 De Vaucouleurs R ¼ Law (a.k.a. Sersic profile with N=4) -7.67 ((r/re) ¼ -1) I(r) = Ie e 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 ] 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 ]2 And many others, e.g.: Oemler truncated Hubble Law Hernquist Profile NFW (Navarro, Frenk & White) Profile generally dynamically inspired King profiles Rt/Rc Typical numbers I0 ~ 15-19 in B <I0> ~ 17 Giant E r0 ~ 1 kpc re ~ 10 kpc Sersic profiles Small N, less centrally concentrated and steeper at large R 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 ? 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 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. 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 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 Calibration of brightest stars ---future use as distance indicators Masses via rotation, Opik’s 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