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!)

Geometry described by Robertson Walker Metric Stress Energy Tensor A constant

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? _____________________________ cos·mos (kŏz ʹ məs, -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 Geocentric Heliocentric Stars = Suns Galaxy Clusters 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? ????

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

360 o Picture of the Milky Way

How can we determine the Size and Shape of our Universe? Mid 17 th 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 17 th 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 18 th 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! 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 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! 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

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 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?