4. What are Cepheid Variables Cepheids are unstable (on human time scales) stars with cycles of 1  50 days. And the longer the period the intrinsically more luminous they are =>

5. Fun animation on how standard candle works

6. Basic Concept: Measure the period know the intrinsic brightness infer the distance using: F = L/4  d 2 ; where F = the apparent brightness L = the intrinsic brightness luminosity d= distance

7. What is Cepheid Variable A Cepheid is a star that has a core which generates so much pressure, the envelope expands and “over shoots the point where the internal heat (and light) pressure will hold up the envelope. The result is that the envelope then comes falling down, Over shoots inward Then starts over

8. Simplistically, the envelope acts like a “brick wall” (in physics terms it’s optically thick and radiates as black body), so...

9. The more expansion, the larger the surface area and the higher [or larger] the intrinsic brightness. But more expansion takes longer => Longer periods go with higher brightness.

10. Time scale OK for Human endevor

11. But be careful, life is complex: Complications: Two types of Cepheids: type I (also called “classical Cepheids”) and type II; Type I’s are about 4 times brighter for the same period and are found in young star groups called open clusters. Type II’s are also called WW Virginis stars are found in old star clusters called Globular clusters

12. La vie n’est pas facile, cont. DUST can make the stars appear dimmer than otherwise. Edwin Hubble over corrected for dust Was looking at II’s when thought looking at I’s And used objects too close He ended up deriving H 0 = 500 km/sec-Mpc!

13. Hubble’s Original Diagram From Ned Wright Notice top distance, => amazing he saw anything at all =>

14. It’s better to be lucky than good. or maybe

15. Generate an overlap with Cepheids and go out. Method is to cross check/overlap as far as we can to calibrate other methods. Requirements for methods: Bright enough to measure far beyond 15 Mpc (distance to Virgo z = about 0.003, v = about 1000 km/sec) Numerous or frequent enough to get 30-100 data points ( to define a “Hubble relation” => v = H 0 D)

16. BTW, before we go too far Pun intended How far out can we go and still use the simple Hubble relation v = H 0 D Answer is z < 0.1

17. And, how close is too close? Certainly z must be > about 0.003 (the distance to Virgo where we still feel a “tug.” (More on the “Great Attractor” later). And ideal is to start with z = 0.02 Also for the record 1+z = ob / em ; works even for blueshift, just doesn’t correspond to R 0 /R then. 1+z = for v/c << 1

18. Or what is commonly used is: z = v/c or v = zc v > 0 means recession; v = < 0 means coming towards us. We usually don’t quote a z value for approaching objects, just a velocity.

19. Some “classic” distance measures (1) Tully-Fisher/Jackson-Faber Relation... (2) Brighter standard candles A. Supernovae B. Red giants, globular clusters, brightest galaxy in a cluster Must cross calibrate all of these with Cepheids

20. If Supernovae are so good, why bother? Supernovae are not frequent => not frequent enough if we want to measure the distance to some objects directly. Indirect = Hubble relationship (or a fancier form for z > 0.1) and measure a redshift. Indirect doesn’t work if it’s too close = closer than about 20Mpc (z= about 0.003) When the objects become faint and the necessary large (10 meter) telescope time is not available

21. What is Tully-Fisher? Relationship between the absolute (visible or infra-red) brightness of a spiral galaxy versus the width of the 21 cm line. 21 cm line is intrinsically narrow which helps a lot

22. Physics of line width: relational quantities and the Heisenberg Uncertainty Principle: Time and Energy => Line is made from a very very slow transition ( about 10 7 years*!) and  t x  E > h => High  t => Very low  E => line is well defined or line width is small h is called Planck’s constant *http://tesla.phys.unm.edu/phy537/8/node3.htmlhttp://tesla.phys.unm.edu/phy537/8/node3.html

23. Did you know? Famous colleague of Planck’s was Max Born who had a famous grand daughter Also a famous X-ray optics design called Kirkpatrick … was named after who has a famous daughter Olivia Newton-John; cf http://www.onlyolivia.com/onj.htmlonlyolivia Joan Baez http://imagine.gsfc.nasa.gov/ docs/science/how_l2/ xtelescopes_systems.htmlxtelescopes_systems.html and http://baez.woz.org/jbchron.html

24. What is Tully-Fisher, cont. A spiral galaxy is one that has a spiral shape, and these enough atomic hydrogen in them to allow a detection of the 21 cm line. This image of NGC 628 (M-74) was obtained by the 8.1-meter Gemini North Telescope on Mauna Kea Hawaii using the newly commissioned Gemini Multi-Object Spectrograph. To make the color image, three images were combined to make this red, green and blue composite. 18 kpc

25. Need to look edge-on, or no motion relative to us Need spiral galaxy to get regular circular motion (more on that later) And to have enough atomic hydrogen to be detectable

26. The 21 cm line is very special, cont. Also, 21 line is in the radio = 1420 MHz (Mega Herz) on your radio dial (FM is about 100) Also 21 cm can be observed during day and through clouds. => Dutch astronomers got good at this.

27. From J. Schombert