Astro 13 Galaxies & Cosmology LECTURE 4 Tues 18 Jan 2011 P. Madau. I Cosmological Principles 25m II Why is the Sky Dark? (Olber s

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1 Astro 13 Galaxies & Cosmology LECTURE 4 Tues 18 Jan 2011 P. Madau 20m I Cosmological Principles 25m II Why is the Sky Dark? (Olber s Paradox) 10m III Break 15m IV Expanding Univ. - Hubble Constant 20m V Cosmic Distance Ladder

2 The Cosmological Principle The standard model in cosmology is the nearly homogeneous and isotropic expansion of the Universe, according to the theory of General Relativity, that traces back to a state hot and dense enough to have produced the Cosmic Microwave bckground and the light elements (H, He, D, Li). Einstein s Cosmological Principle: The Universe is homogeneous (same properties everywhere -- e.g. constant pressure and density at any given time) and isotropic (same properties in any direction).

3 NOTE: An isotropic U around every point is homogeneous but a homogeneous U is not necessarily isotropic. Observations show our U to be close to isotropic on large scales, but there are hints of large structures and motions on scales ~100 Mpc. Examples: Isotropic around every point (and thus homogeneous) infinite 3-D flat space Surface of a sphere (not infinite!) Surface of an expanding sphere (not stationary!) Homogeneous & NOT ISOTROPIC: Surface of an infinitely long cylinder with view in direction A not the same as in direction B. B A

4 Perfect Cosmological Principle: Universe is also the same at all TIME. Developed into the continuous creation model called the Steady State Theory. Ruled out by the discovery of the CMB. Anthropic Cosmological Principle: Exact opposite to the Cosmological Principle. It proposes that this Universe is special because of the need for life (observers). Explains what would otherwise be a fine tuning of the cosmological parameters, related to the age of the Universe.

5 Local Group to Homogeneous Universe

6 Why is the Night Sky Dark? Olber s Paradox One of the oldest (5th C Greeks; 17th C Kepler; 18th C Halley; 18th C de Cheseaux; 19th C Olber) and important observations in cosmology. Based on 5 assumptions, each of which are reasonable: 1. On average, the number and brightness of each chunk of space is the same everywhere (Copernican Principle - CP) 2. Also true for all time and the U is infinitely old 3. There are no large scale motions in the U 4. Geometry of space is Euclidian and 3-D 5. Laws of physics are the same everywhere (CP)

7 Olber s Paradox (cont.) The conclusion is that the sky should Blazingly Bright! Since 1. Every sightline will intersect the surface of a bright star; 2. Space will be accumulating infinite energy from infinite stars radiating for an infinite time. What assumptions are possibly wrong? 1 & 5 are based on the Copernican principle - fundamental. 4: Whether space is Euclidian doesn t change the conclusion. 3: Motions may redshift the light (and thus decrease its energy), but this predicts infinite energy towards longer wavelengths, which is not seen. Conclude that 2 is false and that the U is finite in age!

8 Expansion of the Universe and the Hubble Constant One of the most profound discoveries in science has been that the universe is expanding. 1917: Einstein introduced modifications to his theory of gravity via a repulsive force component (cosmological constant) to keep a STATIC UNIVERSE. Meanwhile, V. Slipher publishes a finding that 21 out of 25 galaxies were receding from us (redshifted). This was the first clue that the U was expanding Hubble discovers that the more distant galaxies are more redshifted. The easiest explanation is that the U appears to be expanding.

Recession Speed (Redshift) 0km/s 3,500 7,000 Hubble Law and Expansion Hubble Law seen for 20 Galaxies V = H o d V = Recessional Velocity (km/s) H o Hubble Constant (o=>today) d = distance (Mpc) Mpc =

9 Recession Speed (Redshift) 0km/s 3,500 7,000 Hubble Law and Expansion Hubble Law seen for 20 Galaxies V = H o d V = Recessional Velocity (km/s) H o Hubble Constant (o=>today) d = distance (Mpc) Mpc = 10 6 pc ~ 3x10 6 light years Best Guess (2001): H o = 70 km/s/mpc Distance (Mpc) ===> Every galaxy sees the same Hubble Expansion Recessional velocity is due to EXPANSION of SPACE, which results in light wavelengths being stretched, causing a redshift. NOTE: Galaxies do move with respect to expanding space, but typically only at a few 100 km/s (= a few Mpc of Hubble exp).

10 If Universe is expanding away from us, are we at the center? NO! Note below that each coin (galaxy) experiences the same vision of all other coins moving away from it.

11 And the Copernican Cosmological Principle may still hold, with each galaxy seeing an expansion with the same Hubble constant. 1 sec later 2 sec later 1. Every star sees other stars move away (CP) 2. Isotropy and homogeneity are preserved (CP) 3. Relative speed is greater for the more distant stars so that the blue star is moving away from the black star twice as fast as the red star is moving.

12 Hubble Expansion and Age of the Universe Consequences of an expanding Universe are profound, including limits on the age of the Universe and the existence of the Big Bang. NOTE: Ho expressed as SPEED/DISTANCE so that 1/Ho gives Distance/Speed, i.e. TIME when galaxies were all packed together: 1/Ho = 1/ (70 km/s/mpc) = Mpc/70km/s = 3x10 19 km/70 km/s = 3x10 19 s/70 but since year=3x10 7 s, ===> 3x10 19 s/70x3x10 7 s/yr =10 12 y/70 = 1000 Byr/70 ~ 15 Byr I AGE in Byr(10 9 yr) = 1/Ho = 1000 Byr/ Ho (km/s/mpc) if Ho = 100km/s/Mpc 1/Ho = 1000 Byr/100 = 10 Byr if Ho = 50 km/s/mpc 1/Ho = 1000Byr/50 = 20 Byr

13 Based on distance calibrations of Shapley in 1918, Hubble Derived an Ho = 540 km/s or an age of 1000Byr/540 ~ 2 Billion years. This implied that the Universe is YOUNGER than the earth whose geological age was estimated to be around 4.5 Billion years. These were not reasonable and encouraged the development of the Steady State Theory. Emphasizes a key problem in astronomy -- how to measure Distances. Need to look for STANDARD CANDLES

14 Cosmic Distance Ladder Objects Remote Galax. Remote Clusters Spiral Galaxies METHOD Supernovae Britest Galx. In Cluster Rotation Velocity Useful Distance Light years Light years 10 8 Light years Cepheid Var. Stars Star Clusters Hyades Star Cluster Planets & Stars Nearby Planets Period-Lum. Relat. Color-Mag Rel. Stat. Parallax Moving Cluster Parallax Radar 5x10 7 Light years 10 6 Light years 1000 Light years 120 Light years 100 Light years light minutes

15 Parallax Background Stars Earth Sun A.U. α 2x Parallax (p) in arcsecs A.U. = Astronomical Unit = Earth-Sun Distance = 1.5x10 11 m Parsec = pc = distance when parallax is 1 arcsec ~ 206,000 A.U 3.1x10 16 m 2π radians in circle = 360 deg ==> radian ~ 57 deg ~ 206,000 arcsec 1 deg=60 arcmin 1 arcmin = 60 arcsec

Brightness, Magnitudes, and Distance Modulus Apparent brightness (b): b = W/m 2 where the sun s b(sun) = 1370 W/m 2 Thus e.g. knowing the brightness and luminosity of a star will yield its distance d.

17 Brightness, Magnitudes, and Distance Modulus Apparent brightness (b): b = W/m 2 where the sun s b(sun) = 1370 W/m 2 Thus e.g. knowing the brightness and luminosity of a star will yield its distance d. L L = luminosity in W 4!d 2 d = distance in m Useful to use ratios in comparing stars to each other or especially to the sun: L 1 L 2 = b 1 b 2 ( d 1 d 2 ) 2 Shows surface brightness dropping by distance squared.

18 Magnitudes and Distance Modulus (cont.) Magnitudes are a convenient form to express brightnesses in astronomy, especially since small magnitude differences yield rough fraction of light e.g if 0.1 mag ~ 10% difference m = apparent magnitude= -2.5 log (brightness) + Constant Every INCREASE of 5 mag = 100x FAINTER m ~ 0 Brightest Stars m~6 eye limit m ~ <15, 20, >25 are bright, faint, very faint galaxies M = Absolute magnitude = m when object is 10pc away E.g. m(sun) ~ -26 while M(sun) ~ +5.0 with the sun s luminosity ~ 4x10 26 W (W = watts = Joules/sec = 10 7 ergs/sec) M(luminous stars) ~ -5 M(galaxy) ~ -20 M(Quasar) ~ -27 m-m = Distance Modulus ==> convenient shorthand for distance = 5 log (D(pc)) - 5 with D = distance in parsecs (pc) = 5 log (D(Mpc) +25 with D = distance in Megapc (Mpc or 10 6 pc)

19 Hyades Moving Cluster Method Convergence Point of Extension of Proper Motions µ µ 1) µ = proper motion (arcsec per year) = Vt (km/s) / 4.74xD(pc) Vt= transverse velocity D=distance 2) Velocities in radial direction Vr (km/s) 3) Angle to convergence point α α α µ Vt Vr Tan α = Vt/Vr but Distance(pc) so Direction of Convergence Point V T = 4.74µ = V R (km / s)tan! 4.74µ(arcsec/ yr)

20 Statistical Parallax Method Group of stars Vega 20 km/s SUN Sun travels ~ 4 A.U. per year so after 20 years, the baseline for parallax is ~ 80 A.U. ~ 40x longer than normal parallax. Proper motions (µ) combined with radial velocities (Vr) to get AVERAGE distances of a group of stars.

Astronomy 114. Lecture35:TheBigBang. Martin D. Weinberg. UMass/Astronomy Department

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