Celestial Distances A Galaxy 150 Million Light Years

Celestial Distances A Galaxy 150 Million Light Years From Earth 6/4/2021 Astronomy 2010 1

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 6/4/2021 Astronomy 2010 2

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) 6/4/2021 Astronomy 2010 3

Parallax Effect § wavy motion: § § parallax effect period of 1 year distance to star is 6. 0 LY type M straight line is the star's proper motion 6/4/2021 Astronomy 2010 4

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 6/4/2021 Astronomy 2010 5

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 6/4/2021 Astronomy 2010 6

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 1 st quarter phase § use trigonometry to derive Earth-Sun distance § Now you know how far Earth travels in year – baseline distance 6/4/2021 Astronomy 2010 7

Parallax Distance § measure angular shift p § know baseline distance (1 AU) § trigonometry star distance d 6/4/2021 Astronomy 2010 8

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. 26 LY. § Nearest star is ~1. 3 parsecs from the Sun. 6/4/2021 Astronomy 2010 9

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 6/4/2021 Astronomy 2010 10

Parallax at Large Distances (but not too large) § For Earth-based measurements one can write: d = (1 AU) / 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. 6/4/2021 Astronomy 2010 11

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 6/4/2021 Astronomy 2010 12

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 § § § 6/4/2021 What are Cepheid Variable Stars? Why do they vary? How is their variation related to luminosity. Astronomy 2010 13

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 6/4/2021 Astronomy 2010 14

luminosity Cepheid Variable Stars 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 6/4/2021 Astronomy 2010 15

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 pressure from hot gas cloud weight from gravity 6/4/2021 § normal stars: balance of pressure and gravity § variable stars: pressure and gravity out of synch Astronomy 2010 16

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 6/4/2021 Astronomy 2010 17

150 Million Light Years away 6/4/2021 Astronomy 2010 18

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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 subgiants main sequence • HR diagram luminosity • luminosity distance 6/4/2021 Astronomy 2010 20

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 100 million LY. Calibrate with nearby variables. Often the distance measured is to a cluster of stars or another galaxy. 6/4/2021 Astronomy 2010 21

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. 6/4/2021 Astronomy 2010 22

Discussion Question § How would you explain how far away even the nearest star is to your Mother/Father/Sister/Brother? § Source: http: //hep. physics. wayne. edu/~harr/courses/20 10/w 06/Slides/ 6/4/2021 Astronomy 2010 23