The Tully-Fisher Relation A relation between the rotation speed of a spiral galaxy and its luminosity The more mass a galaxy has  the brighter it is  the faster it rotates  the wider the spectral lines are Measuring rotation speed allows us to estimate luminosity; comparing to observed (apparent) brightness then tells us the distance

Beyond the Galactic Scale – Clusters of Galaxies The Local GroupThe Virgo Cluster

Superclusters

Beyond Superclusters Strings, filaments, voids Reflect structure of the universe close to the Big Bang Largest known structure: the Great Wall (70 Mpc  200 Mpc!)

Cosmology The part of astronomy (and astrophysics) that deals with the greatest structures in the universe – and the evolution of the universe itself!

Cosmologically relevant Questions –What is in the universe? –How do these things interact? –How does the universe change in time? Is there a beginning? Is there an end?

What’s in the Universe? Answers come from observations  Let’s observe:

What’s in the Universe? THE UNIVERSE clusters and superclusters voids galaxies like the Milky Way quasars Stars nebulae molecular clouds star clusters Solar System black holes pulsars Sun planets moons comets meteors asteroids dust terrestrial jovian Big ……………………………………..small

So, why is the night sky dark? (Olbers’ Paradox) Conclusion: either –Universe is not infinite or –Universe changes in time

Everything is moving away from us! Measure spectrum of galaxies and compare to laboratory measurement lines are shifted towards red This is the Doppler effect: Red-shifted objects are moving away from us

Hubble’s Law The final rung on the cosmic distance ladder Hubble’s observations (1920’s): –Light from distant galaxies is red- shifted –The more distant the galaxy, the greater the red-shift Interpretation: –Galaxies are moving away from us –More distant galaxies are moving faster The universe is expanding, carrying the galaxies with it!

Hubble, 1929 Doppler Shifts of Galaxies

Hubble’s Law H 0 = (65 ± 15) km/sec/Mpc is Hubble’s constant Compare to distance = velocity  time Appears the universe “exploded” from a single point in the past – the Big Bang Age of the universe is 1/H 0 or about 14 billion years Velocity = H 0  Distance Distance = Velocity /H 0

The Expanding Universe Except for a few nearby galaxies (like Andromeda), all the galaxies are seen to be moving away from us Generally, the recession speed of a galaxy is proportional to its distance from us; that is, a galaxy that’s twice as far away is moving twice as fast (aside from local motions within galaxy clusters)

The Expanding Universe This expansion pattern (speed proportional to distance) actually implies that galaxies are all moving away from each other Expansion Milky Way

The Expanding Universe This expansion pattern (speed proportional to distance) actually implies that galaxies are all moving away from each other Expansion Milky Way Twice as far away, so moves twice as fast

The Expanding Universe This expansion pattern (speed proportional to distance) actually implies that galaxies are all moving away from each other A while later: d Start: d 2d2d

The Expanding Universe Each galaxy sees the others moving away with the same pattern (further → faster) As though the galaxies ride on a rubber band that is being stretched! A while later: Start:

The Expanding Universe In three dimensions, imagine the galaxies are raisins in an expanding loaf of bread

Appears the universe “exploded” from a state in which matter was extremely dense and hot – the Big Bang Where did the expansion begin? Everywhere! Every galaxy sees the others receding from it – there is no special point (center) The Expanding Universe

Cosmological Red-Shift Not really a Doppler effect Space itself is being stretched between galaxies

Conclusions from our Observations The Universe has a finite age, so light from very distant galaxies has not had time to reach us, therefore the night sky is dark. The universe e x p a n d s now, so looking back in time it actually s h r i n k s until…?  Big Bang model: The universe is born out of a hot dense medium 13.7 billion years ago.

Big Bang The “start” of the universe, a primordial fireball  the early universe was very hot and dense  intimate connection between cosmology and nuclear/particle physics  “To understand the very big we have to understand the very small”

How does the expansion work? Like an explosion (hot, dense matter in the beginning), but space itself expands! Slowed down by gravitational attraction Attraction is the stronger, the more mass there is in the universe Scientifically described by Einstein’s General theory of Relativity (1915)

More General General Relativity is more general in the sense that we drop the restriction that an observer not be accelerated The claim is that you cannot decide whether you are in a gravitational field, or just an accelerated observer The Einstein field equations describe the geometric properties of spacetimeEinstein field equations

The Idea behind General Relativity –We view space and time as a whole, we call it four- dimensional space-time. It has an unusual geometry, as we have seen –Space-time is warped by the presence of masses like the sun, so “Mass tells space how to bend” –Objects (like planets) travel in “straight” lines through this curved space (we see this as orbits), so “ Space tells matter how to move ”

Effects of General Relativity Bending of starlight by the Sun's gravitational field (and other gravitational lensing effects)

Assumption: Cosmological Principle The Cosmological Principle: on very large scales (1000 Mpc and up) the universe is homogeneous and isotropic Reasonably well-supported by observation Means the universe has no edge and no center – the ultimate Copernican principle!

What General Relativity tells us The more mass there is in the universe, the more “braking” of expansion there is So the game is: Mass vs. Expansion And we can even calculate who wins!

The Fate of the Universe – determined by a single number! Critical density is the density required to just barely stop the expansion We’ll use  0 = actual density/critical density: –  0 = 1 means it’s a tie –  0 > 1 means the universe will recollapse (Big Crunch)  Mass wins! –  0 < 1 means gravity not strong enough to halt the expansion  Expansion wins! And the number is:  0 < 1 (probably…)

The “size” of the Universe – depends on time! Expansion wins! It’s a tie! Mass wins! Time

The Shape of the Universe In the basic scenario there is a simple relation between the density and the shape of space-time: Density Curvature 2-D example Universe Time & Space  0 >1 positive sphere closed, bound finite  0 =1 zero (flat) planeopen, marginal infinite  0 <1 negative saddleopen, unbound infinite