1. Astrophysics of Life : Stars

2. 2 Wave Characteristics: Wavelength - Distance between successive wave peaks Period – Time between passing wave peaks Frequency – Number of wave peaks passing per unit time (1/Period) Wave Speed – wavelength x frequency (follow a crest ) Light Speed is 3x10 8 m/s

3. 3 Visible light ranges in wavelength from ~400 to ~700 nanometers. 400nm 500nm 600nm 700nm Wavelength = COLORCOLOR

4. 4 Electromagnetic Spectrum communication heat detected by our eyes sunburn most energetic penetrate tissue Microwav es, cooking

5. 5 Blackbodies with different temperatures look like this: Hotter blackbodies are brighter and “bluer.”

6. 6 Wien’s Law  “Hotter bodies radiate more strongly at shorter wavelengths (i.e. they’re bluer).” max = 0.29 cm T (K) We can measure a star’s temperature from its spectrum!

7. 7 (Flux) max = 0.29 cm T (K) Wien math fun

8. 8 Stefan’s Law  “Hotter blackbodies are brighter overall (at every wavelength).” where: F = total radiative flux  = constant F =  T 4

9. 9 Emission Line Spectra Each element produces its own unique pattern of lines

10. 10 Absorption Line Spectra Spectrum of the Sun Spectrum of the Sun:

11. Luminosity and Apparent Brightness Star B is more luminous, but they have the same brightness as seen from Earth.

12. Apparent Brightness and Inverse Square Law  Light appears fainter with increasing distance.  If we increase our distance from the light source by 2, the light energy is spread out over four times the area. (area of sphere = 4  d 2 ) Luminosity 4  d 2 Flux = To know a star’s luminosity we must measure its apparent brightness (flux) and know its distance. Then, Luminosity = Flux *4  d 2

13. The Magnitude Scale 2 nd century BC, Hipparchus ranked all visible stars – brightest = magnitude 1 faintest = magnitude 6. To our eyes, a change of one magnitude = a factor of 2.5 in flux. The magnitudes scale is logarithmic. A change of 5 magnitudes means the flux 100 x greater! Hence Brightest Faintest

14. Apparent Magnitude - Apparent Magnitude - star’s apparent brightness when seen from its actual distance Absolute Magnitude Absolute Magnitude - apparent magnitude of a star as measured from a distance of 10 pc. Sun’s apparent magnitude (if seen from a distance of 10 pc) is 4.8. This is then the absolute magnitude of the Sun.

15. Enhanced color picture of the sky Notice the color differences among the stars

16. Starlight: Who Cares? We do! Primary source of “life energy” on Earth Many living things convert sunlight to energy Most other living things eat them (or eat things that eat them, or …) Also, heat/temperature Living things want liquid phase (remember) Need the right star/distance combination for this Also, want STABLE temperatures for long time (i.e. millions, or better yet, BILLIONS of years)

17. Stellar Temperature: Color You don’t have to get the entire spectrum of a star to determine its temperature. Measure flux at blue (B) and yellow (“visual”=V) wavelengths. Get temperature by comparing B -V color to theoretical blackbody curve.

18. Stellar Temperature: Spectra 7 stars with same chemical composition Temperature affects strength of absorption lines Example: Hydrogen lines are relatively weak in the hottest star because it is mostly ionized. Conversely, hotter temperatures are needed to excite and ionize Helium so these lines are strongest in the hottest star.

19. Spectral Classification: Before astronomers knew much about stars, they classified them based on the strength of observed absorption lines. Annie Jump Cannon Classification by line strength started as A, B, C, D, …., but became: O, B, A, F, G, K, M, (L) A temperature sequence! Cannon’s system officially adopted in 1910.

20. Spectral Classification “Oh Be A Fine Girl/Guy Kiss Me” “Oh Brother, Astronomers Frequently Give Killer Midterms”

21. Stellar Sizes Almost all stars are so small they appear only as a point of light in the largest telescopes A small number are big and close enough to determine their sizes directly through geometry

22. Stellar Sizes : Indirect measurement Stefan’s Law F =  T 4 Luminosity is the Flux multiplied by entire spherical surface Area of sphere A = 4  R 2 Giants - more than 10 solar radii Dwarfs - less than 1 solar radii L  R 2  T 4 Luminosity = 4  R 2  T 4 -or-

23. Understanding Stefan’s Law: Radius L  R 2  T 4

24. Understanding Stefan’s Law: Temperature L  R 2  T 4

25. Hertzsprung-Russell (HR) Diagram About 90% of all stars (including the Sun) lie on the Main Sequence. …where stars reside during their core Hydrogen-burning phase. HR diagrams plot stars as a function of their Luminosity & Temperature

26. L = 4  R 2  T 4 From Stefan’s law…...  More luminous stars at the same T must be bigger!  Cooler stars at the same L must be bigger!

27. The HR Diagram: 100 Brightest Stars  Most of these luminous stars are somewhat rare – they lie beyond 5pc.  We see almost no red dwarfs (even though they are very abundant in the universe) because they are too faint.  Several non-Main Sequence stars are seen in the Red Giant region

28. Using The HR Diagram to Determine Distance: Spectroscopic “Parallax” Main Sequence 1) Determine Temperature from color 2) Determine Luminosity based on Main Sequence position 3) Compare Luminosity with Flux (apparent brightness) 4) Use inverse square law to determine distance Example: Luminosity 4  d 2 Flux =

29. What if the star doesn’t happen to lie on the Main Sequence - maybe it is a red giant or white dwarf??? We determine the star’s Luminosity Class based on its spectral line widths: These lines get broader when the stellar gas is at higher densities – indicating a smaller star. A star Supergiant A star Giant A star Dwarf (Main Sequence) Wavelength  The HR Diagram: Luminosity & Spectroscopic Parallax

30. The HR Diagram: Luminosity Class Bright Supergiants Supergiants Bright Giants Giants Sub-giants Main-Sequence (Dwarfs)

31.  We get distances to nearby planets from radar ranging.  That sets the scale for the whole solar system (1 AU).  Given 1 AU plus stellar parallax, we find distances to “nearby” stars.  Use these nearby stars, with known Distances, Fluxes and Luminosities, to calibrate Luminosity classes in HR diagram.  Then spectral class + Flux yields Luminosity + Distance for farther stars (Spectroscopic Parallax). The Distance Ladder

32. With Newton’s modifications to Kepler’s laws, the period and size of the orbits yield the sum of the masses, while the relative distance of each star from the center of mass yields the ratio of the masses. The ratio and sum provide each mass individually. Stellar Masses: Visual Binary Stars

33. Stellar Masses: Spectroscopic Binary Stars In this example, only the yellow (brighter) star is visible… Many binaries are too far away to be resolved, but they can be discovered from periodic spectral line shifts.

34. Stellar Masses: Eclipsing Binary Stars How do we identify eclipsing binaries? The system must be observed “edge on”. Also tells us something about the stellar radii.

35. The HR Diagram: Stellar Masses Why is mass so important? Together with the initial composition, mass defines the entire life cycle and all other properties of the star! Luminosity, Radius, Surface Temperature, Lifetime, Evolutionary phases, end result….

36. Example: On the Main Sequence: Luminosity  Mass 3 Why? More mass means more gravity, more pressure on core, higher core temperatures, faster nuclear reaction rates, higher Luminosities!

37. Lifetime  Fuel available / How fast fuel is burned Lifetime  Mass / Mass 3 = 1 / Mass 2 Lifetime  Mass / Luminosity So for a star Or, since Luminosity  Mass 3 For main sequence stars How long a star lives is directly related to the mass! Big stars live shorter lives, burn their fuel faster…. How does Mass effect how long a star will live