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# Measuring the Stars

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1. Measuring the Stars

2. Distances

3. Stellar Parallax • Parallax is an object's apparent shift relative to some more distant background as the observer's point of view changes

4. Stellar Parallax • As the distance to the object increases, the parallax becomes smaller and therefore harder to measure.

5. Stellar Parallax • Astronomers measure parallax in arc seconds rather than in degrees. • At what distance must a star lie in order for its observed parallax to be exactly 1 arc-sec? • We get an answer of 206,265 A.U.

6. Stellar Parallax • Astronomers call this distance 1 parsec (1 pc), from "parallax in arc seconds."

7. Stellar Parallax • Calculating Parallax: • Sirius displays a large known stellar parallax, 0.377”. Calculate its distance in parsecs and in light years d = 1/p d = 1/0.377 d = 2.65 pc away • 1 pc = 3.26 light years, so d = 8.65 light years

8. Standard Candle • Astronomers measure the apparent brightness • This is compared to the star’s luminosity (actual brightness) • Distance is calculated by comparing the two values

9. Other Methods • Distances to galaxies can be measured via: • Redshift • Brightness of supernovae

10. Color & Temperature

11. Color & Temperature Temperature • The color of a star indicates its relative temperature – blue stars are hotter than red stars • More precisely, a star’s surface temperature is given by Wien’s law 3x106 λm T = star’s surface temperature in Kelvin λm = strongest wavelength in nanometers (nm) T =

12. Luminosity & apparent brightness

13. Definitions Luminosity • The amount of energy a star emits each second is its luminosity (usually abbreviated as L) • A typical unit of measurement for luminosity is the watt • Compare a 100-watt bulb to the Sun’s luminosity, 4x1026 watts

14. Definitions Luminosity • Luminosity is a measure of a star’s energy production (or hydrogen fuel consumption) • Luminosity is determined by diameter and temperature

15. Inverse Square Law • The inverse–square law relates an object’s luminosity to its distance (apparent brightness) • As the distance to a star increases, the apparent brightness decrease with the SQUARE of the distance

16. Inverse Square Law

17. THE MAGNITUDE SCALE • About 150 B.C., the Greek astronomer Hipparchus measured apparent brightness of stars using units calledmagnitudes • Brightest stars had magnitude 1 and dimmest had magnitude 6 • A star’s apparent magnitude depends on the star’s luminosity and distance.

18. MAGNITUDE SCALE NOW Magnitude differences equate to brightness ratios: • A difference of 5 magnitudes = a brightness ratio of 100 • 1 magnitude difference = brightness ratio of 1001/5=2.512

19. MAGNITUDE SCALE NOW “Absolute magnitude” is a measure a star’s luminosity • The absolute magnitude of a star is the apparent magnitude that same star would have at 10 parsecs • An absolute magnitude of 0 approximately equates to a luminosity of 100L¤

20. Spectral Types

21. Spectra of Stars Introduction • A star’s spectrum typically depicts the energy it emits at each wavelength • A spectrum also can reveal a star’s composition, temperature, luminosity, velocity in space, rotation speed, and it may reveal mass and radius

22. Spectra of Stars Measuring a Star’s Composition • A star’s spectrum = absorption spectrum • Every atom creates its own unique set of absorption lines • Match a star’s absorption lines with known spectra to determine surface composition

23. Classification of Stellar Spectra • Historically, stars were first classified into four groups based on color (white, yellow, red, and deep red), then into classes using the letters A through N • Annie Jump Cannon: classes were more orderly if arranged by temperature – Her new sequence became O, B, A, F, G, K, M (O being the hottest and M the coolest) and are today known as spectral classes

24. Spectral Types

25. Spectral Types

26. Measuring aStar’s Motion • A star’s radial motion is determined from the Doppler shift of its spectral lines • The amount of shift depends on the star’s radial velocity • Δλ = the shift in wavelength of an absorption line • λ = resting wavelength, the radial speed v is given by: V = Δλ/ λ • c where c is the speed of light

27. H-R Diagrams • Surface temperature and luminosity can be plotted to make the single most important graph for the study of stars, the Hertzsprung-Russell Diagram • Luminosity (y-axis) increases upwards, and temperature (x-axis) increases to the left

28. H-R Diagrams • The majority of stars lie along a band (not a sharp line) from top left to bottom right called the main sequence. • On the main sequence, hot stars are the most luminous, (top left) and cool stars are the least luminous (bottom right).

29. H-R Diagrams • We now know that the main sequence comprises all the stars that are converting hydrogen to helium in their cores. • Stars that are not on the main sequence are doing something else

30. H-R Diagrams • The Mass-Luminosity Relation • Main-sequence stars obey a mass-luminosity relation, approximately given by: L = M3 where L and M are measured in solar units • Consequence: Stars at top of main-sequence are more massive than stars lower down

31. Sizes of Stars Another look

32. Sizes of Stars • Dwarf stars are comparable in size (or smaller) to the Sun • Giants range from 10 to 100 times the radius of the Sun • Supergiants range from 100 to 1000 solar radii

33. Sizes of Stars • The range in sizes of Main Sequence stars is about 0.1 to 100 solar radii. • Supergiants can be enormous. Betelgeuse would reach out to the orbit of Mars. • White dwarfs stars are around the size of the Earth

34. Measuring Mass: Binaries • Visual binaries • actually see the stars moving around each other • Spectroscopic binaries • make use of the Doppler shift of the spectral lines of the stars • Eclipsing binaries • binaries may be orbiting in such a way that one star moves in front of the other as in an eclipse

35. Visual Binary Eclipsing Binary

36. Star Clusters: Open (Galactic) Clusters • Shape: Irregular, no specific shape • Where: Galactic disk • Types of Stars: Population I • Age of Stars: Young!

37. Star Clusters: Open (Galactic) Clusters

38. Star Clusters: Globular Clusters • Shape: Spherical • Where found: Galactic Halo • Types of Stars: Population II • Age of Stars: Old

39. Star Clusters: Globular Clusters http://www.astrographics.com/GalleryPrints/Display/GP0046.jpg http://images.astronet.ru/pubd/2008/05/07/0001227653/OmegaCen_spitzer_c800.jpg

40. Stellar Motion • Stellar motion has two components: • The transverse component measures a star's motion perpendicular to our line of sight—in other words, its motion across the sky. • The radial component measures a star's movement along our line of sight—toward us or away from us.

41. Stellar Motion • The annual movement of a star across the sky, as seen from Earth (and corrected for parallax), is called proper motion. • It describes the transverse component of a star's velocity

42. Stellar Motion