SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond

1. SPU-22: The Unity of Science from the Big Bang to the Brontosaurus and Beyond Lecture 6 14 February 2014  Science Center Lecture Hall A

2. Outline of Lecture 6 The Cosmic Distance Ladder (CDL), bottom to top: - Radar (done) - Parallax - Period-Luminosity Relation (PLR) - Redshift-Distance Relation (RDR) (including Doppler shift) - Supernovae (maybe reach) - Three truths (doubtful reach)

3. Reaching For The Stars Next rung of CDL goes to stars: How measure? Use parallax (see demo & next slide) Choose brightest stars as targets; choose far dimmer stars nearby on sky as references. Why? Serious attempts to measure parallax of stars spread over more than two centuries, before Bessel success in 1838. What was original interest?

4. Parallax: Definition of Parsec(Drawing NOT to Scale)

5. Reaching For The Stars (Concluded) Parallax rung of CDL reliable: Based on geometry. Limited in distance by accuracy at which changes in angle can be determined: Ground-based optical telescopes ≈100 pc; accuracy to few milliarcseconds Space-based (GAIA): ≈10 kpc; accuracy up to ≈20 microarcseconds 1 pc = 3.26 ltyr

6. The Serendipity Rung How measure distances further out than parallax allows? Enter Henrietta Leavitt at Harvard College Observatory (HCO), start 20th century Was computer (see next 2 slides). Assignment: study brightness variations of stars, especially those located in Magellanic clouds (what are they?) She made discovery; profound effect on astronomy; still used today

7. Henrietta Leavitt (1868-1921)

8. Computers c. 1900

9. The Serendipity Rung (Concluded) Leavitt’s discovery: linear (straight line) relation between logarithm (what’s that? see next slide) of period of variation of brightness of class of stars, Cepheid variables, and logarithm of their maximum or minimum brightness (see next slide plus one). Named “Period-Luminosity Relation” (see next slide plus two) So what? Measure maximum and/or minimum brightness and period of variation; infer distance: B = B0 (r0/r)2 ; r = r0 (B0/B)1/2 Measuring brightness of Cepheid variable, and period of variation of brightness, one infers its distance by using inverse square law to “match” brightness measured against brightness and known distance of reference Cepheid of same period of brightness variation. Calibration was Big Issue: How to determine reliably distance to single Cepheid to allow this technique to work. (Situation similar to use of one radar measurement to set distance scale for whole solar system, with period of brightness variation here playing, roughly, role of Kepler’s 3rd law.) First calibration via “nearby” Cepheid variable in Milky Way by EjnarHertzsprung (1913) (save for tenfold “slip”) Calibration still limiting factor today! GAIA to rescue

10. Definition of Logarithm Logarithm (“log”) of number is useful concept. You will not be required to master it, but should at least be exposed to its definition: Ordinary, or common, logarithm of number is another number such that 10 raised to power equal to this second number equals first number. For example, if m = 10n, then logarithm of m is n. (These numbers are not generally integers.)

11. Typical Brightness Variation For Cepheid

12. Original Leavitt Data for PLR(Log of Max. and Min. Brightnesses, called “magnitudes,” vs. Log of Period In Days, Plotted Below)

13. Basic Assumption UnderpinningPeriod-Luminosity Relation Leavitt developed relation on assumption variable stars observed all at same distance. Why good assumption? Because all in direction of compact group on sky (see next slide); hence probably not more than small (<10%) fractional spread in distance compared to average distance of all from us

14. Small Magellanic Cloud

15. Does Period-Luminosity Relation Constitute Top Rung of CDL? Many astronomers then thought Milky Way (MW) galaxy was whole universe. Shape seemed pancake like, size unclear, location of sun relative to center unclear Disturbing aspects: Newly discovered (via more powerful ‘scopes) “nebulae” were, to some, collections of gas within MW; to others “island universes,” i.e., other collections of stars and gas distinct from MW. Also, sun not obviously at center of MW Thus perhaps premature to stop climbing CDL

16. Hubble’s Resolution Of Conflict With world’s then most powerful (100”) telescope, he observed Cepheid variables in nebula, M31. Found distance: over one million light years, hence way outside MW. Case closed. New case opened: How determine distances to further out island universes (hereafter, “galaxies”), in which Cepheids cannot be individually resolved? Ladder needs another rung. Hubble obliged.

17. Back At 100” Telescope… Hubble kept observing galaxies and found another relation - most profound - between distances of galaxies (determined via Cepheid rung of CDL) and their redshifts, so-called “redshift-distance relation” (RDR) Clearly, another digression in order: What is “redshift”? To answer, we give primer on aspect of light (and sound) behavior

18. Introduction For Redshift-Distance Relation Development of new tool - Doppler shift - and how to use it for fun and profit Doppler shift discovered in 1840s by Christian Doppler when observing double stars (see demonstration and next slide)) Keep in mind my promise to try to tell you why we believe what we believe, not just what we believe; hence this (somewhat long) digression

19. Doppler Shift Explored Demonstration showed: pitch or frequency of sound you hear depends on motion of source. Christian Doppler observed: color of light from stars in binary (mutually orbiting, two-star) system seemed to depend on whether star moving towards or away from him. Specifically, light appeared (slightly) redder when star moving away and (slightly) bluer when star moving towards him Violation of Einstein’s postulate on speed of light?

20. Doppler-Shift Exploration (Concluded) Answer: No! When frequency, or color, changes, so does wavelength, with speed unchanged How does frequency change depend on speed? f = f0[1 – v/c]; v<<c, where f is observed frequency of light (or sound); f0 is frequency transmitted by source; and v is velocity (actually, speed) between source of light and observer, measured along straight line connecting them. Sign of v is positive for source and observer moving apart, and negative when source and observer are coming together.

21. Redshift-Distance Relation Redshift for galaxy (nearly) directly proportional to its distance: perfection not expected; perfection not observed. In addition to other effects, there were “peculiar” velocities Aside from such (relatively small) problems, redshifts were good proxies for distances reaching far out in space to rather distant galaxies, thus forming the next rung of our CDL: the Redshift-Distance Relation (RDR). What about calibration? Use Period-Luminosity Relation (PLR) for nearby galaxies, as Hubble initially did (see next slide; note “sloppiness” of y-axis label) Is ladder now fully in place?

22. Hubble’s Redshift-Distance Relation

23. What Next On CDL? At “really” great distances, was hard to get reliable galaxy velocities/speeds: Another rung on ladder needed Supernovae to the rescue (next slide)

24. Supernovae: Standard Candles What are supernovae? Basically exploding stars; they become extraordinarily bright, often brighter than their host galaxy (but not for long, often of order month). Because so bright, looked for possible use as standard candles. What are standard candles? See next slide

25. Concept Of Standard Candle(Appear 1/n2 as bright; always are n times as far away)

26. Can Supernovae Serve AsStandard Candles? Many kinds supernovae. (How know? Observe light curves and spectra: See next two slides) One kind does serve: So-called Type 1a; need to observe in many color bands to account for dimming due to dust on line of sight Highly developed standard candle; provides last rung of our CDL. We’ll see its fundamental importance soon

27. Typical Supernovae Light Curves

28. Typical Supernovae Spectra

29. Irresistible Aside: Two Profound And Unforgettable Truths Speed of light implies: When looking out in space, one is looking back in time – the further out the further back Origin of atoms in your body: Aside from hydrogen (product of Big Bang, we believe), vast majority came from supernovae! (See next slide for evidence)

30. X-ray Image Of Supernova Remnant(Exhibits Different Types Of Atoms In False Colors)

31. Third Truth (Not So Profound, But Interesting) Relative to their sizes, stars are extremely far apart (distance between sun and nearest star, in scaled example in which sun is basketball, places nearest star somewhat further from here than Beijing) By contrast, relative to their sizes, galaxies are very close to one another (small numbers, e.g., order ten, can usually express ratio of distances of neighboring galaxies to galaxy sizes)