The Expanding UniverseChapter 10 – Hawley & Holcomb

Chapter Overview

• Doppler Effect• Scale of Galaxy• Cosmic Distance Ladder• Hubble’s Law• Expansion of the Universe

Redshifting

• Objects moving toward us appear more blue, while objects moving away from us appear more red!

Image Credit: www.cnrt.scsu.edu

Redshifting of Spectra

Image Credit: http://www.sdsu-physics.org

Redshifting of Galaxies

Light from a galaxy moving slowly away from Earth

Light from a galaxy moving faster away from Earth

Image Credit: herschel.jpl.nasa.gov www.cnrt.scsu.edu

Redshifted Spectra

Wavelength (nm)

Image Credit: www.cnrt.scsu.edu

Very Distant Galaxy

Nearby Galaxy

Distant Galaxy

Nearby Star

Redshifted Spectra

Three of the most distant quasars discovered by the Sloan Digital Sky Survey

REDBLUE

Interstellar dust obscures our view at visible wavelengths along lines of sight that lie in the plane of the galactic disk

William Herschel maps out the distribution of stars and gets:

The sun The

“universe”of

Herschel

William Parsons, 3rd Earl of Rosse, builds the “Leviathan of Parsonstown” - draws “spiral nebulae”

What were they?

Stars & planetary systems forming in our own “universe”?

Separate “island universes”?

Henrietta Leavitt & the Cepheid P-L Relationship

Light curve of a Cepheid variable

Large & Small Magellaic Clouds Period versus magnitude of Cepheids in SMC

H. Shapley maps distribution of Globular Star Clusters using “Cepheids”

(“where’s the mass centered?”)

We are NOT at the center.

What happened?

Globular cluster with variable stars

“Dust Happened”At visible wavelengths, the center of our galaxy suffers ~ 30 mag of extinction by dust!! Even with big modern telescopes, we cannot see very far in the plane of our galaxy at visible wavelengths

The Shapley-Curtis Debate (1920)

MWG MWG

ShapleyCurtis

The debate solved nothing!

Questions in science are not resolved by debates, but by observations & experiments

Nature of the Spiral Nebulae and the Great Debate

ShapleyNovae brightnessesincompatible with M31 being as big as MWGRotation of M101

CurtisNovae indicate a smaller MWG than Shapley’sGalaxy proper motions undetectedZones of avoidance in other systems

1923 - Hubble Measures

Distance to M 31 using Cepheid

Variables100-inch Hooker Telescope, Mt. Wilson

Edwin Hubble

Debate OVER!Discovery of

Cepheids in M 31

Star cluster is really HERE

But the extinction makes it fainter, so we would incorrectly think that it is HERE based on brightness measurements

Region with dust absorption: A mags

Ignoring the extinction due to dust will result in deriving a photometric distance that is too large by a factor of 10A/5!

Trumpler - 1929

Shapley’s MWG was too big for a couple of reasons:

Other problems:

S Andromedae, a “nova” in the Andromeda Galaxy, was actually a supernova -with much higher L and hence distance

Proper motions in galaxies “measured” would require speeds greater than light if they were distant - these measurements turned out to be wrong!

Summary: Shapley’s MWG was too big, and his distances to the spiral nebulae too small

Stellar Photometric DistancesFor an apparent (observed) magnitude m, absolute magnitude M, and distance d in parsecs:

Without dust: m = M+5logd-5 and so d = 10(m-M+5)/5 pc

(reminder: m = Md=10pc)

With dust: m = M+5logd-5+A and d = 10(m-M-A+5)/5 pc

where A is the extinction by dust in magnitudes

(Note: sometimes astronomers use the “distance modulus”m-M = 5logd-5 to express the distance to some objects)

How do we know the distances to all these galaxies???

“Extragalactic Distance Ladder”

• Starts with distances to nearest stars…• Ends with distances to furthest galaxies…

We use many different methods to measure distance:

Some only work nearby.Some only work far away.

Parallax works nearbyCan get distances only to the very nearest star clustersin the Milky Way (the Hyades & the Pleiades)Fails when the angular shift is smaller than we

can resolve.

Main Sequence Fittingaka Spectroscopic Parallax

• Make a color-magnitude diagram of individual star clusters

• Groups of stars at different distancesappear shiftedup or down on the HR diagram

Main Sequence Fitting

• Can use to measure distances to anywhere you can resolve large numbers of individual stars.– Star Clusters in the Milky Way– The Large & Small Magellanic Clouds.

which stars are truly luminous, and which stars just look bright?A Trick:Some fraction of very luminous stars “pulsatepulsate”They become brighterbrighterand dimmer in a regular pattern

What about stars that are too far for parallax, but not in clusters?

Pulsating or “Variable” Stars• There is an

“instability strip” in the HR diagram, where stars sizes aren’t stable.

• “Cepheids” are extremely bright!

The “period” (duration) of the pulsation is related to the Cepheid’s luminosity

1.1. Measure Measure periodperiod

2.2. Derive Derive luminosityluminosity

3.3. Measure Measure apparent apparent brightnessbrightness

4.4. Derive Derive distancedistance!!

The luminosity of the observed star is ~1500L !

What about galaxies that are too far to detect Cepheids?

• Use the “Tully-Fisher” Relation:

Luminosity # of stars

rGMV central

rotation=

Rotation speedMass

Measure rotation speed, figure out luminosity

What about galaxies that are too far to measure rotation speeds?

Wait for a supernova to go off!Extremely LuminousLuminous

Can be seen to huge distances

It’s hard to measure a rotation curve if the galaxy just looks like a fuzzy blob…

Works for White Dwarf Supernova (Type 1a)

• All have about the same luminosity, since detonation of 1.4M white dwarf!

• “standard candles”• Measure the apparent

brightness, derive distanceThey have distinctive spectra, so they’re easy to recognize

Lastly, the Hubble Law can be used to estimate distances.

Too hard to use Tully-Fisher for all of them, or to wait for SN Ia’s to explode…

v =H0dInstead, we can use this observed relationship between speed and distance.

Hubble found that more distant galaxies appeared to be moving away from us faster

• Measure the redshift “z”, derive the “recessional velocity”

zcv ×=

z ≡

Δλλ

A “Hubble Diagram”• Recessional

velocity is proportional to distance.

• H0 is the “Hubble Constant”, units are km/s/Mpc

DHv 0=

A galaxy’s recessional velocity lets you estimate its distance.

v =H0d

zcv ×=

1.Measure the redshift z.

2.Derive the velocity v.

3.Use Hubble Law to get the distance

Measure this…

…to derive this.

Example: A galaxy appears to be receding at 7500 km/s…

• H0 ~ 71 km/s/Mpc

The galaxy’s distance is probably closest to

A: 10 MpcB: 50 MpcC: 100 MpcD: 1000 Mpc

Redshift is a “distance indicator”!Astronomers now just measure redshiftsto tell relative distances.

Vr = 2000 km/s Vr = 1000 km/s(A lot easier than Tully-Fisher, SNIa, etc!)

How do we know the distances to all these galaxies?

These have smaller redshifts…

…than these.

Z~0.3 Z~4

Note: The relationship between distance and recessional velocity is not a straight line at high (z>1) redshifts! But, larger redshifts always do indicate larger distances.

By measuring redshifts, we can map the local universe!

Angular distribution of bright galaxies on the sky

Take spectra of all bright galaxies along a “slice”:

Angular distribution of bright galaxies on the sky

Measure redshiftsredshifts (i.e. recessional velocities) for all these galaxies, and

make a 33--D mapD map of the Universe!

Galaxies aren’t smoothly distributed!Structure is made up of Walls and Voids

Same kind of map, over more of the sky. You

are Here

Some “extra”structures that look like lines

extending away from Earth!

These structures are caused by clusters of galaxies, which have their

own extra random velocities…

Cluster velocities can approach ±2000 km/s

These are called“peculiar peculiar velocitiesvelocities”

Peculiar velocities are an extra componenton top of the recessional velocities

discovered by Hubble

All of these galaxies are at the same distance!

VV = = VVclustercluster + + VVHubbleHubble

H0d

>100,000 galaxies!

We can see structure even on very large scales!

At large scales, the Universe does start to look more homogeneous…

Distribution & size of

voids becomes uniform

The Universe starts out as mostly smooth…

…but it has tiny little ripples in it.“Density Fluctuations”

Gravity turns these little ripples into big ones!

Simulations of “Large Scale Structure”formation--all those little points are galaxies!

But why in the world is this true?

• Why is just about every single galaxy in the world moving away from us?

v =H0d

Are we at the center of a big explosion???

• No! The Whole Universe is Expanding!

The Hubble Law implies that the entire Universe is expanding

v =H0d The Hubble Law says that distant galaxies are receding from us

They’re getting further away!

Occurs in every direction!

Why does further=faster imply expansion?

Easier to show that expansion implies

further=faster!

Expa

nds

x2!

It doesn’t matter where you are!

• If everything’s expanding, everyone sees the Hubble Law.

Remember that curved space stuff?• Space is

malleable!• It curves &

stretches!

Every galaxy is becoming more distant from every other galaxy!

• Every point on the surface of an inflating balloon is becoming further away from every other point

But if the universe is expanding, why aren’t I expanding?

• It’s not hard for other forces to be stronger than the push of expansion.

None of these are expanding--They are bound together by electricity and/or gravity!

But if the universe is expanding, why aren’t I expanding?

• You only notice expansion over very large distances, where the force of gravity is very weak in comparison.

Here you notice the expansion

Here you notice the mass of the big ball.

The Cosmological Redshift

• We thought the redshift was due to the Doppler effect (i.e. motion).

• Instead, the redshift is actually due to the wavelength of photons being stretched along with the expansion of the Universe.

The Cosmological Redshift

• As the Universe expands, the wavelength of photons do too wavelengths get REDDERREDDER

The Cosmological Redshift

• Photons that travel for longer (from further away), have experienced more expansion.

Bigger Distance = Bigger RedshiftFurther seems Faster!

What is the Universe

expanding into?

• There’s no “edge”!• If there is something the Universe is

expanding into (which there may not be), it would be into a higher dimension that we cannot perceive.

The Universe had a Beginning:

“The Big Bang”

…The Universe was smaller yesterday.It was even smaller the day before that.

At some point the Universe had to have At some point the Universe had to have been infinitely small!been infinitely small!

So if the Universe is expanding, that means…