Chapter 18: Celestial Distances

1. Chapter 18:Celestial Distances A Galaxy 150 Million Light Years From Earth Astronomy 2010

2. Distance and Motion of Stars • To infer luminosity, mass, and size from observations we need to know the distance to a star. • Distance units for stars: • light year (LY): distance light travels in one year • 1 LY = 9.46 x 1012 km • Rigel 775 LY, Betelgeuse 1,400 LY • Proxima Centauri 4.2 LY nearest • parsec: 1 pc = 3.26 LY • Motion of the star relative to the Sun (Ch. 16): • radial motion: star moves along line of sight • proper motion: star moves across celestial sphere Astronomy 2010

3. Stellar Distances • How can we measure such great distances? • We use several techniques, useful at different scales, with each scale connecting to the next, like the steps of a ladder. • Precise determination of the meter. • Radar measurements of distances to planets to determine the astronomical unit (AU). • Parallax measurements of nearby stars • Variable stars • H-R diagram • Red shift and supernovae (later chapters) Astronomy 2010

4. Parallax Effect • wavy motion: parallax effect • period of 1 year • distance to star is 6.0LY • type M • straight line is the star's proper motion Astronomy 2010

5. What is Parallax? • nearby star appears to move back and forth compared to more distant stars • Barnard's star: 6.0 LY • parallax depends on distance  use it to measure distance Astronomy 2010

6. Parallax on the Earth • View object from 2 vantage points • Determine distance using trigonometry • Object appears to shift positions compared to the far off background • Angular shift, called the parallax: angle of a triangle and the distance between the two vantage points is one side of the triangle • how far away is the tree? • measure baseline distance B with a meter stick • measure parallax angle p • use trigonometry to derive distance Astronomy 2010

7. Parallax for Stars • Need Earth Sun distance • why we need AU • View Sun and Venus • measure Venus-Earth distance using radar • measure angular distance between Sun and Venus in 1st quarter phase • use trigonometry to derive Earth-Sun distance • Now you know how far Earth travels in year – baseline distance Astronomy 2010

8. Parallax  Distance • measure angular shift p • know baseline distance (1 AU) • trigonometry  star distance d Astronomy 2010

9. Parsecs • Distances to the stars in units of astronomical units are huge, a more convenient unit of distance called a parsec is used • abbreviated “pc”. • parsec = distance of a star that has a parallax of one arc second using a baseline of 1 astronomical unit. • 1 parsec = 206,265 AU = 3.26LY. • Nearest star is ~1.3 parsecs from the Sun. Astronomy 2010

10. Trigonometry • Use basic trigonometric relations. • Used by modern surveyors to measure great distances (also called surveyor's method). d : distance b : baseline p : angle b p d Astronomy 2010

11. Parallax at Large Distances (but not too large) • For Earth-based measurements one can write: d = (1AU) / tan(p), • Where angle p is the parallax measured in arc seconds • And d is the distance in parsecs. • The farther away the object is, the less it appears to shift. • Since the shifts of the stars are so small, arc seconds are used as the unit of the parallax angle. • 3,600 arc seconds in just one degree. • The ball in the tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second. Astronomy 2010

12. More parsecs • Conversion of parsecs to LY • 1 parsec = 3.26 light years. • Which unit to use to specify distances: a light year or a parsec? • Both are fine and are used by astronomers. • Using a parsec for the distance unit and an arc second for the angle, we can express the relation between distance and parallax in the simple form: p = 1/d and d=1/p Astronomy 2010

13. What about more distant stars? • parallax fails for stars > 1000 LY away • baseline of 1 AU is too small • Variable Stars: Cepheids and RR Lyrae • The luminosity of these stars can be determined by measuring the time it takes them to vary in brightness. • Apparent brightness and luminosity tell us the distance. • Outline • What are Cepheid Variable Stars? • Why do they vary? • How is their variation related to luminosity. Astronomy 2010

14. Cepheid Variables • large yellow pulsating stars • first: Delta Cephei • Discovered by John Goodricke in 1784 • magnitude changes over 5.4 day cycle • hundreds known • periods range from 3 to 50 days • average luminosities are 1,000 to 10,000 LSun Astronomy 2010

15. Cepheid Variable Stars luminosity time • Polaris, the North Star, is a Cepheid Variable • variation of 10% of magnitude (10% of luminosity) • period of 4 days • pulsation decreases over time • Cepheid variable stars are in a flickering phase of life Astronomy 2010

16. Why Cepheid Variables Vary pressure from hot gas cloud weight from gravity pulsations: • changes in color and spectral class  temperature varies • doppler shift of spectra  size varies • luminosity changes when temperature and area change • normal stars: balance of pressure and gravity • variable stars: pressure and gravity out of synch Astronomy 2010

17. Period – Luminosity Relationship Henrietta Levitt (1908): systematic search found many Cepheid variables including hundreds in the Magellanic Clouds • The Magellanic Clouds are nearby “dwarf” galaxies • All stars in the Magellanic Clouds are roughly same distance away -- like observingthe Moon from Earth • found: brighter Cepheids havelonger periods Calibrate distance scale: nearby Cepheid Variables within parallax distance Astronomy 2010

18. 150 Million Light Years away Astronomy 2010

19. Astronomy 2010

20. Distance from Spectral Types • close star (within our galaxy) – parallax • variable star – if you find one • alternative: spectral class + HR diagram • spectrum  temperature • spectral lines  broad classes • supergiants • bright giants • giants • subgiants • main sequence • HR diagram  luminosity • luminosity  distance Astronomy 2010

21. Summary • Determine the meter • Use the meter to determine the astronomical unit (AU) • Use the AU and stellar parallax to measure stars out to about 300 LY with satellite measurements, like Hipparcos • Use the period-luminosity relationship for variable stars to measure distances out to 100million LY. Calibrate with nearby variables. Often the distance measured is to a cluster of stars or another galaxy. Astronomy 2010

22. Summary (cont’d) • For distant stars that are not variable and don’t have a nearby variable star, use the temperature - luminosity relation of the H-R diagram. Does require some work to determine if the star is main sequence, dwarf, or giant. • Later we will see the use of red shift and supernovae to measure the largest distances. Astronomy 2010

23. Discussion Question • How would you explain how far away even the nearest star is to your Mother/Father/Sister/Brother? Astronomy 2010