Lecture 5 Outline

1. 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

2. Einstein Principle of Equivalence Acceleration pulls you down  No Gravity!!  ONLY acceleration Need New Theory of Gravity, "General Relativity"

3. 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.

5. 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

6. 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!)

7. Stress Energy Tensor Geometry described by Robertson Walker Metric A constant

8. Test of General RelativityEclipse in 1917 • Curvature strongest in vicinity of dense and massive objects • (black holes are theoretical playgrounds for relativity people)

9. Einstein Ring

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

11. 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.

14. Questions of Antiquity & Today Still quite an Art to explain this. • 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´) • The universe regarded as an orderly, harmonious whole. • An ordered, harmonious whole. • Harmony and order as distinct from chaos. Today’s Lecture again. And the Saga continues Last third of course

15. Cosmologies based on Observations and our Understanding No Planets – Wondering Star Horizons are Broadened -or- Size of Universe increases Flat Earth Geocentric Heliocentric Stars = Suns Galaxy Clusters of Galaxies Also kept changing More spheres were added Model was refined Model & Theory Applies only to our Solar system Horizons are Broadened -or- Human Understanding increases? Solar System and other Stars embedded in our Galaxy All Galaxies, luminous and dark matter as far as we can see next

16. Broadening Horizons? Earth? Solar System? Galaxies? Universe? ????

17. 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

18. The Milky Way Galaxy roughly looks like this

19. Side view of our Galaxy

20. Top View of our Galaxy

21. Position of the Earth & Side View of Galaxy

22. Discussion • How could you determine the Shape and Size of the Universe? • Let’s start with the Shape and Size of the Milky Way…

24. 360o Picture of the Milky Way

25. 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

26. 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

27. 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)

28. Number Counts and the Kaptyn Universe(Sun in the Center) 10 kpc

29. 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

30. Curtis • Look at Nova

31. 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

32. 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

35. Curtis – blue stars & novae

36. 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

37. What are Globular Clusters?Shapley was leader on studying globular clusters

38. 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

39. 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

41. 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…

42. 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

43. 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

44. Distributions of Globular Clusters (Bohlin)

46. 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

47. 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…

48. 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?) • 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 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.

49. 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

50. 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