January 18, 11 AY13

Astro 13 Galaxies & CosmologyLECTURE 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

January 18, 11 AY13

The Cosmological Principle

Einstein’s Cosmological Principle:– The Universe is homogeneous (same properties

everywhere -- e.g. constant pressure and densityat any given time) and isotropic (sameproperties in any direction).

The standard model in cosmology is the nearly homogeneous andisotropic expansion of the Universe, according to the theory ofGeneral Relativity, that traces back to a state hot and denseenough to have produced the Cosmic Microwave bckground andthe light elements (H, He, D, Li).

January 18, 11 AY13

NOTE: An isotropic U around every point is homogeneous but ahomogeneous U is not necessarily isotropic. Observations show ourU to be close to isotropic on large scales, but there are hints oflarge 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 longcylinder with view in direction A not the same as in direction B.

A

B

January 18, 11 AY13

Perfect Cosmological Principle: Universe isalso the same at all TIME. Developed into thecontinuous creation model called the SteadyState Theory. Ruled out by the discovery of theCMB.

Anthropic Cosmological Principle: Exactopposite to the Cosmological Principle. Itproposes that this Universe is special because ofthe need for life (observers). Explains whatwould otherwise be a fine tuning of thecosmological parameters, related to the age ofthe Universe.

January 18, 11 AY13

Local Group to Homogeneous Universe

January 18, 11 AY13

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 observationsin cosmology.Based on 5 assumptions, each of which are reasonable:1. On average, the number and brightness of each chunk ofspace is the same everywhere (Copernican Principle - CP)2. Also true for all time and the U is infinitely old3. There are no large scale motions in the U4. Geometry of space is Euclidian and 3-D5. Laws of physics are the same everywhere (CP)

January 18, 11 AY13

Olber’s Paradox (cont.)The conclusion is that the sky should Blazingly Bright! Since1. Every sightline will intersect the surface of a bright star;2. Space will be accumulating infinite energy from infinite starsradiating 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!

January 18, 11 AY13

Expansion of the Universe and the Hubble ConstantOne of the most profound discoveries in science has beenthat the universe is expanding.

1917: Einstein introduced modifications to his theory ofgravity via a repulsive force component (cosmologicalconstant) to keep a STATIC UNIVERSE. Meanwhile,V. Slipher publishes a finding that 21 out of 25 galaxieswere receding from us (redshifted). This was the firstclue that the U was expanding.

1929 Hubble discovers that the more distant galaxies aremore redshifted. The easiest explanation is that the Uappears to be expanding.

January 18, 11 AY13

Hubble Law seen for 20 GalaxiesR

eces

sion

Spe

ed (R

edsh

ift)

0km

/s

3,

500

7

,000

0 50 100Distance (Mpc) ===>

V = Ho d

V = Recessional Velocity (km/s)Ho ≡ Hubble Constant (o=>today)d = distance (Mpc) Mpc = 106 pc ~ 3x106 light years

Best Guess (2001): Ho = 70 km/s/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, buttypically only at a few 100 km/s (= a few Mpc of Hubble exp)….

Hubble Law and Expansion

January 18, 11 AY13

If Universe is expanding away from us, are we at the center?

NO! Note below that each coin (galaxy) experiences thesame vision of all other coins moving away from it.

January 18, 11 AY13

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 starsmove away (CP)

2. Isotropy and homogeneity arepreserved (CP)

3. Relative speed is greater forthe more distant stars so that theblue star is moving away from theblack star twice as fast as the redstar is moving.

January 18, 11 AY13

Hubble Expansion and Age of the Universe

Consequences of an expanding Universe are profound, includinglimits on the age of the Universe and the existence of the BigBang.

NOTE: Ho expressed as SPEED/DISTANCE so that 1/Hogives Distance/Speed, i.e. TIME when galaxies were allpacked together:1/Ho = 1/ (70 km/s/Mpc) = Mpc/70km/s = 3x1019km/70 km/s= 3x1019 s/70 but since year=3x107s, ===> 3x1019s/70x3x107s/yr=1012 y/70 = 1000 Byr/70 ~ 15 Byr IAGE in Byr(109yr) = 1/Ho = 1000 Byr/ Ho (km/s/Mpc)if Ho = 100km/s/Mpc 1/Ho = 1000 Byr/100 = 10 Byrif Ho = 50 km/s/Mpc 1/Ho = 1000Byr/50 = 20 Byr

January 18, 11 AY13

Based on distance calibrations of Shapley in 1918, HubbleDerived 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 developmentof the Steady State Theory.

Emphasizes a key problem in astronomy -- how to measureDistances …. Need to look for STANDARD CANDLES

January 18, 11 AY13

Cosmic Distance Ladder

Radar

METHOD

Supernovae

Britest Galx. In Cluster

Rotation Velocity

Period-Lum. Relat. Color-Mag Rel.

Stat. Parallax

Moving Cluster Parallax

Objects

Remote Galax.

Remote Clusters Spiral Galaxies

Cepheid Var. Stars Star Clusters Hyades Star Cluster Planets & Stars Nearby Planets

Useful Distance

1010 Light years

1010 Light years 108 Light years

5x107 Light years 106 Light years 1000 Light years 120 Light years 100 Light years light minutes

January 18, 11 AY13

Parallax

A.U.

Earth

Sun α

2x Parallax (p) in arcsecs

BackgroundStars

A.U. = Astronomical Unit = Earth-Sun Distance = 1.5x1011mParsec = pc = distance when parallax is 1 arcsec ~ 206,000 A.U3.1x1016m

2π radians in circle = 360 deg ==> radian ~ 57 deg ~ 206,000 arcsec1 deg=60 arcmin 1 arcmin = 60 arcsec

January 18, 11 AY13

January 18, 11 AY13

Brightness, Magnitudes, and Distance Modulus

Apparent brightness (b): W/m2 where the sun’s b(sun) = 1370 W/m2

b =L

4!d2

L = luminosity in Wd = distance in m

Thus e.g. knowing the brightness and luminosity of a star will yield its distance d.

Useful to use ratios in comparing stars to each other or especially to the sun:

L1

L2

=b1

b2

(d1

d2

)2

Shows surface brightness dropping by distance squared.

January 18, 11 AY13

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) + ConstantEvery INCREASE of 5 mag = 100x FAINTERm ~ 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 awayE.g. m(sun) ~ -26 while M(sun) ~ +5.0 with the sun’s luminosity ~ 4x1026 W (W = watts = Joules/sec = 107 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 106 pc)

January 18, 11 AY13

Hyades Moving Cluster MethodConvergence 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

Directio

n of Converg

ence Point

µVt

Vrα

α

Tan α = Vt/Vr but

Distance(pc) so

=VT

4.74µ

=VR(km / s)Tan!

4.74µ(arcsec/ yr)

January 18, 11 AY13

Statistical Parallax Method

Sun travels ~ 4 A.U. per year so after20 years, the baseline for parallax is~ 80 A.U. ~ 40x longer than normal parallax.

Proper motions (µ) combined withradial velocities (Vr) to get AVERAGE distances of a group of stars.

Vega 20 km/s SUN

Group of stars