Lecture 5 Outline

• Einstein’s “Theory of Gravity”• Discussion about Size and Shape of the Milky

Way• Lecture on Size and Shape of the Milky Way

– Curtis’ Method

– Shapley’s Method

– Whom would you believe?

• Providing Feedback

Einstein

Acceleration pulls you down

No Gravity!!

ONLY acceleration

Principle of Equivalence

Need New Theory of Gravity, "General Relativity"

Difference between Newtonian Theory of Gravity and General Theory of Relativity

• Newtonian: The Sun creates a gravitational field that exerts a force upon the Earth, which, in turn, causes it to orbit around the Sun rather than move in a straight line

• General Relativity: The Mass-Energy Distribution of the Sun changes the geometry of space-time. The Earth is in free motion (no forces acting on it!) and travels on a geodesic of space-time. But because space-time is curved around the Sun, the Earth orbits the Sun.

From the Special Theory of Relativity to the General Theory of Relativity

Newtonian Mechanics – 3 space coordinates -- no time coordinate no relation between event 1 and event 1

need the Special Theory of Relativity need frames of reference-- need Lorentz Transformation

However: Galaxy is accelerating due to-- other galaxies around it-- expansion of the Universe

“Acceleration” is due to “forces” Include “forces” into the Theory of Special Relativity General Theory of Relativity

Task of General Relativity

Couple Geometry to the Mass distributions and motions

How does matter affect the Geometry of Space-Time?

How do particles move in this Geometry?

(no forces!)

ijij Tc

GG 2

8

Geometry described by Robertson

Walker Metric

Stress Energy Tensor

A constant

22222

22222 sin

1)( ddr

kr

drtRdtcdS

Test of General RelativityEclipse in 1917

• Curvature strongest in vicinity of dense and massive objects• (black holes are theoretical playgrounds for relativity people)

Einstein Ring

The Castle on the Mall in Washington, D.C., as viewed from the Natural History Museum

Now we place a black hole with the mass of Saturn over the middle of the Mall, and view the Castle through the resulting gravitational lens.

Questions of Antiquity & Today

• What is the Cosmos that we live in?• What is our Position in the Cosmos?• What is the fate of our Cosmos?

_____________________________cos·mos (kŏzʹməs, -mŏs´, -mōs´)

1. The universe regarded as an orderly, harmonious whole.2. An ordered, harmonious whole.3. Harmony and order as distinct from chaos.

Still quite an Art to explain this.

Today’s Lecture again.

And the Saga continues

Last third of course

Cosmologies based on Observations and our Understanding

Flat Earth GeocentricHeliocentricStars = Suns

GalaxyClusters of Galaxies

No Planets – Wondering Star

Also kept changing

More spheres were added

Model was refined

Model & Theory

Applies only to our Solar system

Solar System and other Stars embedded in our Galaxy

All Galaxies, luminous and dark matter as far as we can see

Horizons are Broadened

-or-Human

Understanding increases?

Horizons are Broadened

-or-Size of Universe

increases

next

Broadening Horizons?

Earth?

Solar System?

Galaxies?

Universe?

????

http://antwrp.gsfc.nasa.gov/diamond_jubilee/debate.html

Great Debates in Astronomy

                                                                                                                                                                                                                                                                                                                                                                                                                                                                

The Scale of the Universe (1920); Curtis, Shapley The Distance Scale to Gamma-ray Bursts (1995); Paczynski, Lamb The Scale of the Universe (1996); Tammann, van den Bergh The Nature of the Universe (1998); Peebles, Turner

The Milky Way Galaxy roughly looks like this

Side view of our Galaxy

Top View of our Galaxy

Position of the Earth & Side View of Galaxy

Discussion

• How could you determine the Shape and Size of the Universe?

• Let’s start with the Shape and Size of the Milky Way…

360o Picture of the Milky Way

How can we determine the Size and Shape of our Universe?

Mid 17th Century Thomas Wright:

Two concentric spheres outside the solar system that incorporate all the stars.

Milky Way = band of stars; perpendicular less starsLook around you band of stars puts sun in the middle

Kant – end of 17th Century faint fuzzy nebulae are “Island Universes of stars sort of

like our Solar System” philosophized

--- Parsons 72 inch telescope “nebulae” of stellar systems

How can we determine the Size and Shape of our Universe?

Mid 18th Century

Herschel: Count stars in all directions using telescope

Assume uniform stellar density

more stars imply “larger” in that direction

estimate distances to “edge”

Get better telescopes – more data size of universe Increased slightly

How can we determine the Size and Shape of our Universe?

Turn of CenturyDutch Astronomer Kapteyn used parallax to determine distances to nearest stars. calibrate distances combine with data on star counts more quantitative model (often regarded as the first

real model of the universe)

10 kpc in diameter by 2 kpc in thickness(Or 30,000 by 6,000 lyrs)

Number Counts and the Kaptyn Universe(Sun in the Center)

10 kpc

Curtis – Shapley Debate, ~1920

• How BIG is our Universe?• What is the overall SHAPE of our Universe?• What are the “Spiral Nebulae”?

Opponents were chosen to represent differing views

Curtis

• Look at Nova

Novae – brightening by ~8 mag

sudden onset of H and He burning on the surface of the white dwarf

All Novae have roughly the same Light Curve and

Brightness at Maximum

What is special about Novae?

Get distances to “nebulae”

Can figure out their luminosity at maximum brightness (M)

Measure brightness (m)

Get distance modulus (m-M)

==> Get distance!

5log5 DMm

Apparent magnitude Absolute Magnitude Distance

Curtis – blue stars & novae

Curtis

Claim

• Galaxy Size ~ 10 kpc x 2kpc

(small Galaxy, same as Kapteyn)

use data on star counts & parallaxes

and spectral types and intrinsic

brightness of blue stars

• Sun at the Center of flat lens

Also

• “Spiral Nebulae” are outside our Galaxy

• “Spiral Nebulae” are systems of stars, i.e., other galaxies

• Slipher’s spectroscopic measurements high radial velocities

• Showed photos of spiral nebulae – with absorbing bands

Sun

What are Globular Clusters?

Shapley was leader on studying globular clusters

Detecting the Expansion of the Universe

Method employed by Hubble:

Use Cepheid Variables in Globular Clusters

Method still used today

What are Cepheid Variables?

• "Pulsating Stars“

• A phase in the life of massive stars:– Unstable Stars (not in Hydrostatic

Equilibrium)

– He-burning core, on their way to becoming a giant (supergiant) star the second time around

Distances and Cepheid Variables

What are Cepheid Variables?

• "Pulsating Stars"

• Unstable Stars (not in Hydrostatic Equilibrium)

• He-burning core, on their way to becoming a giant (supergiant) star the second time around

How do you get their Luminosity?

Period Luminosity relationship

Big stars pulsate slowly, Small stars pulsate fast

Measure Period Get LuminosityMeasure m Calculate m-M

Calculate distance…

What is special about these stars?

Can figure out their luminosity (M)

Through Period-Luminosity Relationship

Measure brightness (m)

Get distance modulus (m-M)

==> Get distance!

5log5 DMm

Apparent magnitude Absolute Magnitude Distance

Procedure

• Take picture after picture

• Compare brightness of stars

• Find variable stars

• Re-observe those stars night after night

• Plot magnitude against time of observation

• Get period

• Deduce luminosity

• Determine distance modulus, then distance

==> very tedious

Distributions of Globular Clusters (Bohlin)

Globular Clusters – Shapley

Claim

• Galaxy Size ~ 100 kpc (large)

(10 times larger than Kaptyn)

• Center of Galaxy shifted by 20 kpc

• BIG == The Galaxy is our entire universe!!

Also

• Galaxy contains “Spiral Nebulae”

• Spiral nebulae are “minor objects” of gaseous content

• Galaxy is so large that it contains the entire Universe

Notes on spiral nebulae

• Van Maanen – internal rotational velocities of spiral nebulae

• If outside the Galaxy big fast motion (fraction of speed of light)– Thus spiral nebulae must be closer…

Why is the Curtis-Shapley Debate important?

Irony of the Debate

• Sun moved away from the Center of the Galaxy – Shapley is right• There are other galaxies outside our own – Curtis was right

BUT: Both were wrong too about different aspects of the debate.

• Combines philosophical and scientific thought• Uses scientific Methodology to solve the problem

(Who produces better data; who gives better interpretations?)

• Curtis: Novae mostly in Disk -- Dust causes extinction(stars look dimmer than they really are) under-estimate distances

• Shapley: Cepheids: Wrong Period Luminosity Relation over-estimate distances

Problem of Dust and Extinction

• Novae appear fainter than they really are – Curtis

should really be brighter

light is blocked by dust

distance should be farther

5log5 DMm

Problem with Cepheids variables

• Two types of cepheids –

• Cepheids in globular clusters and in galactic clusters

• Globular clusters are older

• Galactic clusters are younger metal rich Different period luminosity

relationship

5log5 DMm

Absolute Magnitude is really fainter

Distance too large

The Milky Way

Visual Wavelengths

Near IR – Look through the Dust at Old Stars

The Final Picture

Resolution of the Shapley-Curtis Debate 1924 – Hubble: Use Cepheid Variables in M31 distances

Next Big discovery concerning Size of Universe

• 1970’s Quasars

• Universe expanded by a factor of ten overnight…

• 20years later Hubble space telescope HDF

Motion away from us

• All galaxies are moving away from us

• Does this put us at the center of the universe?