February 14, 2006 Astronomy Chapter 18: Celestial Distances A Galaxy 150 Million Light Years From Earth

February 14, 2006Astronomy 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 light year (LY): distance light travels in one year 1 LY = 9.46 x km 1 LY = 9.46 x km Rigel 775 LY, Betelgeuse 1,400 LY Rigel 775 LY, Betelgeuse 1,400 LY Proxima Centauri 4.2 LY nearest Proxima Centauri 4.2 LY nearest parsec: 1 pc = 3.26 LY 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

February 14, 2006Astronomy 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. 1.Precise determination of the meter. 2.Radar measurements of distances to planets to determine the astronomical unit (AU). 3.Parallax measurements of nearby stars 4.Variable stars 5.H-R diagram 6.Red shift and supernovae (later chapters)

February 14, 2006Astronomy   wavy motion: parallax effect   period of 1 year   distance to star is 6.0LY   type M   straight line is the star's proper motion Parallax Effect

February 14, 2006Astronomy 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

February 14, 2006Astronomy 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

February 14, 2006Astronomy 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

February 14, 2006Astronomy Parallax  Distance  measure angular shift p  know baseline distance (1 AU)  trigonometry  star distance d

February 14, 2006Astronomy 20109Parsecs  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.

February 14, 2006Astronomy Trigonometry  Use basic trigonometric relations.  Used by modern surveyors to measure great distances (also called surveyor's method). d : distance b : baseline p : angle d b p

February 14, 2006Astronomy 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.

February 14, 2006Astronomy 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

February 14, 2006Astronomy 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.

February 14, 2006Astronomy 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  L Sun

February 14, 2006Astronomy luminosity time Cepheid Variable Stars  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

February 14, 2006Astronomy Why Cepheid Variables Vary 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 cloud pressure from hot gas weight from gravity

February 14, 2006Astronomy 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 observing the Moon from Earth  found: brighter Cepheids have longer periods Calibrate distance scale: nearby Cepheid Variables within parallax distance

February 14, 2006Astronomy Million Light Years away

February 14, 2006Astronomy

February 14, 2006Astronomy 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 spectral lines  broad classes supergiants supergiants bright giants bright giants giants giants subgiants subgiants main sequence main sequence HR diagram  luminosity HR diagram  luminosity luminosity  distance luminosity  distance

February 14, 2006Astronomy 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.

February 14, 2006Astronomy 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.

February 14, 2006Astronomy Discussion Question  How would you explain how far away even the nearest star is to your Mother/Father/Sister/Brother?