1. Distance Ladder

2. Pre-class Problem You stand are looking at “famous local landmark” from two positions on either side of the “other famous local place”. You see that it moves relative to more distant landmarks. The angle it moves through is X degrees. Work out the distance between the two landmarks.

3. Unit Learning Goals Understand 3 different ways astronomers measure distances in the Universe - parallax - variable stars - Type Ia supernovae Understand some of the techniques used by astronomers to study the accelerating Universe and Dark Energy

4. Lecture 1 Understand “astronomical triangulation” – the parallax method Calculate a parsec – an important quantity for astronomers Understand Cepheid variables Know the methods and limits of both methods Homework: problems plus research on RRLyrae stars

5. Pre-class Problem You stand are looking at “famous local landmark” from two positions on either side of the “other famous local place”. You see that it moves relative to more distant landmarks. The angle it moves through is X degrees. Work out the distance between the two landmarks.

6. Parallax Method Eyes Finger Distant Objects

7. Parallax Method 1.Star appears at B 2.Star appears at A Observation 6 months apart on opposite sides of the Sun shows a nearby star moving relative to the more distant stars

8. Parallax Method From trig we know: For small angles using radians Therefore we can measure the distance to the star if we know the angle 1AU

9. Aside on Angles x

10. Question Quick question: what would you see at 1 and 2? What would you see at position 3? A B 1 2 3 Distant Stars C D

11. Parsec Distance for which the parallax angle is 1 arcsecond What is the angular change on the sky? Calculate a parsec in: meters, AU, lightyears Input into Google Doc http://tinyurl.com/cu569uj Earth – Sun distance = 1.5x10 11 m 1ly = 3x10 8 m/s x 60 x 60 x 24 x 365.25

14. Homework Question: Distance to nearest stars 1. Barnard’s star is 1.83pc away, what is its parallax angle? What is the change in position on the sky? Its apparent magnitude in V is 9.54, what is its absolute magnitude? What does that tell you about the star? Where is it on an HR diagram? 2. What does the parallax method assume about the motions of stars in our Galaxy relative to the Sun? What is proper motion? Remember to draw diagrams, label quantities you use and show all the steps in your workings

15. Homework Question: Hipparcos (1989) and Gaia (2013) are 2 satellites for measuring distances using parallax. Why are astronomers going into space for these measurements? Using the information below, explain why Gaia will be a great improvement on the Hipparcos catalogue For giant stars (M=0), Sun-type stars (M=4.8) and red dwarfs (M=11) what is the maximum distance in pc that Hipparcos and Gaia will provide?. The Milky Way is 16 kpc in size; what does this tell you about the mission? Why will Gaia help in the study of binary stars? Limiting magPosition accuracy Hipparcos12.40.002 arcsec Gaia20200 micro-arcsec

16. Variable Stars We can see these in external galaxies RRLyrae stars on homework Cepheid variables in class

17. Cepheid Variables Luminous variable star Period relates to luminosity You have all seen a Cepheid variable star!

18. Which has the brightest absolute magnitude? Which has the dimmest absolute magnitude? What do we know about their apparent magnitudes? ABCDABCD

19. Homework Question: Sketch an HR diagram with a main sequence. Show the region where you’d find Cepheids. Hubble measured Cepheids in external galaxies. This is one of his graphs. Measure the periods and get luminosities for the stars

20. Homework Question Research RR Lyrae stars. Summarize: what type of star they are; the relationship that allows them to be used as distance indicators; including a lightcurve sketch; what luminosity/distance range they can be used for; how their use compares to Cepheids. Add them to your HR diagram along with the Cepheids.

21. Class Summary Described the parallax method For nearby stars we can measure their positions 6 months apart and use that to get their distances Use Cepheid variables to measure distances to external galaxies Evolved stars Relationship between the period of their brightness change and luminosity

22. Lecture 1 Recap Measuring distances in the Universe is difficult Parallax method for nearby stars Cepheid and RR Lyra star variables are visible in external galaxies Can only get to nearby galaxies

23. Lecture 2 Understand Type Ia supernovae which are a probe for the most distant universe Study of SNe Ia lead to the discovery of dark energy Homework: group project to summarise other techniques to characterise dark energy

24. Type Ia Supernovae Can shine brighter than a galaxy for a couple of months See them across vast distances: most distant z=1.9. One of the most powerful tools in cosmology

25. What are SNe Ia? Still an active area of research White dwarf star reaches about 1.4M  and explodes Two competing theories: one, the other, or both?

26. How Do We Do Cosmology? Same mass = same energy Same energy = same absolute magnitude We can use their apparent magnitude to measure their distance modulus which is related to distance d tells us about the content of the universe – matter, radiation etc

27. Questions 1. I observe a Type Ia supernova at magnitude 18. Its absolute magnitude is -19.3. What distance away is it? A 29 Mpc B 290 kpc C 290Mpc D 2900 Mpc` 2. A Typa Ia supernova goes off in the LMC (50 kpc) away. Will it be observable with the naked eye? A Yes B No

28. Supernova Cosmology Not all supernovae have exactly the same brightness. Mark Phillips in 1993 found a way round this. Make a correction to the peak magnitude based on the width of the lightcurve

29. Supernova Cosmology d depends on the matter/energy content of the universe Too much energy and it expands forever. Not enough and it collapses in on itself. Use observations of the SNe to “weigh” the universe

30. Discovery of Dark Energy In 1990s, 2 groups were using supernovae to populate these diagrams They were really surprised that supernovae were fainter than they should have been in the distance universe This means the universe must have been expanding faster in recent cosmic times than in the past Velocity Distance Where the SN should have been

31. Where are we now? Many more supernovae to measure the distances in the universe Much more precise understanding of what the universe is made of.

32. Limits for SN Cosmology We need to understand more about the SN explosions Limited by our understanding of simple things like a galaxy calibration star, or the spectrum of our filters Getting to 1% precision on measurements is going to be a bit challenge new surveys in the local universe Does dark energy vary with time? More distant supernovae will tell us. How do we get the data?

33. Future Projects WFIRST – NASA IR space mission Will find distant supernovae for cosmology LSST – 8m survey telescope Will find thousands of transients per night

34. Group Homework Get into groups of 4 Read the article http://onlinelibrary.wiley.com/doi/10.1111/j.1468- 4004.2006.47420.x/abstracthttp://onlinelibrary.wiley.com/doi/10.1111/j.1468- 4004.2006.47420.x/abstract Each person makes notes for the rest of the group on one of the topics: ISW, weak lensing, baryon acoustic oscillations, cluster counts Theory behind the technique, measurements made, current and future projects etc… Next week you will compare notes and EVERY PERSON will submit THEIR OWN summary article of the tools to measure dark energy plus whatever notes they provided the rest of the group You will submit a brief report on the contributions of other members of your group as well as self-assessment