Download Lecture5 - Tufts Institute of Cosmology

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
Principle of Equivalence
Acceleration pulls you down
 No Gravity!!
 ONLY acceleration
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!)
8G
Gij  2  Tij
c
Stress Energy
Tensor
Geometry
described by
Robertson
Walker Metric
A constant
 dr 2
2
2
2
2 
dS  c dt  R (t )  
 r d  sin  d 
 1  kr2

2
2
2
2


Test of General Relativity
Eclipse 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?
Still quite
an Art to
explain this.
Today’s
Lecture again.
Last third
of course
_____________________________
cos·mos (kŏzʹməs, -mŏs´, -mōs´)
1.
2.
3.
The universe regarded as an orderly, harmonious whole.
An ordered, harmonious whole.
Harmony and order as distinct from chaos.
And the Saga
continues
Cosmologies based on Observations and our Understanding
No Planets – Wondering Star
Flat Earth
Geocentric
Heliocentric
Stars = Suns
Galaxy
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
Clusters of Galaxies
All Galaxies, luminous and dark
matter as far as we can see
next
Horizons are
Broadened
-orSize of Universe
increases
Horizons are
Broadened
-orHuman
Understanding
increases?
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 stars
Look 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 Century
Dutch 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!
m  M  5 log D  5
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
Sun
• “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
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 Luminosity
Measure 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!
m  M  5 log D  5
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?
• Combines philosophical and scientific thought
• Uses scientific Methodology to solve the problem
(Who produces better data; who gives better interpretations?)
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.
•
•
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
m  M  5 log D  5
should really be brighter
light is blocked by dust
distance should be farther
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
m  M  5 log D  5
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?