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Deducing Temperatures and Luminosities of Stars (and other objects…)

Deducing Temperatures and Luminosities of Stars (and other objects…). Ultraviolet (UV). Radio waves. Infrared (IR). Microwaves. Visible Light. Gamma Rays. X Rays. Review: Electromagnetic Radiation. Increasing energy. 10 -15 m. 10 3 m. 10 -9 m. 10 -6 m. 10 -4 m. 10 -2 m.

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Deducing Temperatures and Luminosities of Stars (and other objects…)

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  1. Deducing Temperatures and Luminosities of Stars(and other objects…)

  2. Ultraviolet (UV) Radio waves Infrared (IR) Microwaves Visible Light Gamma Rays X Rays Review: Electromagnetic Radiation Increasing energy 10-15 m 103 m 10-9 m 10-6 m 10-4 m 10-2 m Increasing wavelength • EM radiation is the combination of time- and space- varying electric + magnetic fields that convey energy. • Physicists often speak of the “particle-wave duality” of EM radiation. • Light can be considered as either particles (photons) or as waves, depending on how it is measured • Includes all of the above varieties -- the only distinction between (for example) X-rays and radio waves is the wavelength.

  3. Electromagnetic Fields Direction of “Travel”

  4. Sinusoidal Fields • BOTH the electric field E and the magnetic field B have “sinusoidal” shape

  5. Wavelength  of Sinusoidal Function  • Wavelengthis the distance between any two identical points on a sinusoidal wave.

  6. Frequency n of Sinusoidal Wave time 1 unit of time (e.g., 1 second) • Frequency: the number of wave cycles per unit of time that are registered at a given point in space. (referred to by Greek letter  [nu]) •  is inversely proportional to wavelength

  7. “Units” of Frequency

  8. Wavelength and Frequency Relation • Wavelength is proportional to the wave velocity v. • Wavelength is inversely proportional to frequency. • e.g., AM radio wave has long wavelength (~200 m), therefore it has “low” frequency (~1000 KHz range). • If EM wave is not in vacuum, the equation becomes

  9. Light as a Particle: Photons E = h • Photons are little “packets” of energy. • Each photon’s energy is proportional to its frequency. • Specifically, energy of each photon energy is Energy = (Planck’s constant) × (frequency of photon) h  6.625 × 10-34 Joule-seconds = 6.625 × 10-27 Erg-seconds

  10. Planck’s Radiation Law • Every opaque object at temperature T > 0-K (a human, a planet, a star) radiates a characteristic spectrum of EM radiation • spectrum = intensity of radiation as a function of wavelength • spectrum depends only on temperature of the object • This type of spectrum is called blackbody radiation http://scienceworld.wolfram.com/physics/PlanckLaw.html

  11. http://scienceworld.wolfram.com/physics/PlanckLaw.html Planck’s Radiation Law • Wavelength of MAXIMUM emission max is characteristic of temperature T • Wavelength max  as T  max

  12. Sidebar: The Actual Equation • Complicated!!!! • h = Planck’s constant = 6.63 ×10-34 Joule - seconds • k = Boltzmann’s constant = 1.38 ×10-23 Joules -K-1 • c = velocity of light = 3 ×10+8 meter - seconds-1

  13. Temperature dependence of blackbody radiation • As temperature T of an object increases: • Peak of blackbody spectrum (Planck function) moves to shorter wavelengths (higher energies) • Each unit area of object emits more energy (more photons) at all wavelengths

  14. Sidebar: The Actual Equation • Complicated!!!! • h = Planck’s constant = 6.63 ×10-34 Joule - seconds • k = Boltzmann’s constant = 1.38 ×10-23 Joules -K-1 • c = velocity of light = 3 ×10+8 meter - seconds-1 • T = temperature [K] •  = wavelength [meters]

  15. “Normalized” Planck curve for T = 5700-K Maximum value set to 1 Note that maximum intensity occurs in visible region of spectrum Shape of Planck Curve http://csep10.phys.utk.edu/guidry/java/planck/planck.html

  16. This graph also “normalized” to 1 at maximum Maximum intensity occurs at shorter wavelength  boundary of ultraviolet (UV) and visible Planck Curve for T = 7000-K http://csep10.phys.utk.edu/guidry/java/planck/planck.html

  17. Planck Functions Displayed on Logarithmic Scale • Graphs for T = 5700-K and 7000-K displayed on same logarithmic scale without normalizing • Note that curve for T = 7000-K is “higher” and peaks “to the left” http://csep10.phys.utk.edu/guidry/java/planck/planck.html

  18. Features of Graph of Planck Law T1 < T2(e.g., T1 = 5700-K, T2 = 7000-K) • Maximum of curve for higher temperature occurs at SHORTER wavelength : • max(T = T1) > max(T = T2) if T1 < T2 • Curve for higher temperature is higher at ALL WAVELENGTHS   More light emitted at all  if T is larger • Not apparent from normalized curves, must examine “unnormalized” curves, usually on logarithmic scale

  19. Wavelength of Maximum EmissionWien’s Displacement Law • Obtained by evaluating derivative of Planck Law over T (recall that human vision ranges from 400 to 700 nm, or 0.4 to 0.7 microns)

  20. Wien’s Displacement Law • Can calculate where the peak of the blackbody spectrum will lie for a given temperature from Wien’s Law: (recall that human vision ranges from 400 to 700 nm, or 0.4 to 0.7 microns)

  21. Wavelength of Maximum Emission is: (in the visible region of the spectrum) max for T = 5700-K

  22. Wavelength of Maximum Emission is: (very short blue wavelength, almost ultraviolet) max for T = 7000-K

  23. Wavelength of Maximum Emission for Low Temperatures • If T << 5000-K (say, 2000-K), the wavelength of the maximum of the spectrum is: (in the “near infrared” region of the spectrum) • The visible light from this star appears “reddish”

  24. Why are Cool Stars “Red”? Less light in blue Star appears “reddish” 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 l (mm) lmax Visible Region

  25. Wavelength of Maximum Emission for High Temperatures • T >> 5000-K (say, 15,000-K), wavelength of maximum “brightness” is: “Ultraviolet” region of the spectrum Star emits more blue light than red appears “bluish”

  26. Why are Hotter Stars “Blue”? More light in blue Star appears “bluish” 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 l (mm) lmax Visible Region

  27. Betelguese and Rigel in Orion Betelgeuse: 3,000 K (a red supergiant) Rigel: 30,000 K (a blue supergiant)

  28. Blackbody curves for stars at temperatures of Betelgeuse and Rigel

  29. Stellar Luminosity • Sum of all light emitted over all wavelengths is the luminosity • brightness per unit surface area • luminosity is proportional to T4: L =  T4 • L can be measured in watts • often expressed in units of Sun’s luminosity LSun • L measures star’s “intrinsic” brightness, rather than “apparent” brightness seen from Earth

  30. Stellar Luminosity – Hotter Stars • Hotter stars emit more light per unit area of its surfaceat all wavelengths • T4 -law means that small increase in temperature T produces BIG increase in luminosity L • Slightly hotter stars are much brighter (per unit surface area)

  31. Two stars with Same Diameter but Different T • Hotter Star emits MUCH more light per unit area  much brighter

  32. Stars with Same Temperature and Different Diameters • Area of star increases with radius ( R2, where R is star’s radius) • Measured brightness increases with surface area • If two stars have same T but different luminosities (per unit surface area), then the MORE luminous star must be LARGER.

  33. How do we know that Betelgeuse is much, much bigger than Rigel? • Rigel is about 10 times hotter than Betelgeuse • Measured from its color • Rigel gives off 104 (=10,000) times more energy per unit surface area than Betelgeuse • But the two stars have equal total luminosities •  Betelguese must be about 102 (=100) times larger in radius than Rigel • to ensure that emits same amount of light over entire surface

  34. So far we haven’t considered stellar distances... • Two otherwise identical stars (same radius, same temperature  same luminosity) will still appear vastly different in brightness if their distances from Earth are different • Reason: intensity of light inversely proportional to the square of the distance the light has to travel • Light waves from point sources are surfaces of expanding spheres

  35. Sidebar: “Absolute Magnitude” • Recall definition of stellar brightness as “magnitude” m • F,F0 are the photon numbers received per second from object and reference, respectively.

  36. Sidebar: “Absolute Magnitude” • “Absolute Magnitude” M is the magnitude measured at a “Standard Distance” • Standard Distance is 10 pc  33 light years • Allows luminosities to be directly compared • Absolute magnitude of sun  +5 (pretty faint)

  37. Sidebar: “Absolute Magnitude” Apply “Inverse Square Law” • Measured brightness decreases as square of distance

  38. Simpler Equation for Absolute Magnitude

  39. Stellar Brightness Differences are “Tools”, not “Problems” • If we can determine that 2 stars are identical, then their relative brightness translates to relative distances • Example: Sun vs.  Cen • spectra are very similar  temperatures, radii almost identical (T follows from Planck function, radius R can be deduced by other means) •  luminosities about equal • difference in apparent magnitudes translates to relative distances • Can check using the parallax distance to  Cen

  40. Plot Brightness and Temperature on “Hertzsprung-Russell Diagram” http://zebu.uoregon.edu/~soper/Stars/hrdiagram.html

  41. H-R Diagram • 1911: E. Hertzsprung (Denmark) compared star luminosity with color for several clusters • 1913: Henry Norris Russell (U.S.) did same for stars in solar neighborhood

  42. Hertzsprung-Russell Diagram

  43. “Clusters” on H-R Diagram • n.b., NOT like “open clusters” or • “globular clusters” • Rather are “groupings” of stars • with similar properties • Similar to a “histogram” 90% of stars on Main Sequence 10% are White Dwarfs <1% are Giants http://www.anzwers.org/free/universe/hr.html

  44. H-R Diagram • Vertical Axis  luminosity of star • could be measured as power, e.g., watts • or in “absolute magnitude” • or in units of Sun's luminosity:

  45. Hertzsprung-Russell Diagram

  46. H-R Diagram • Horizontal Axis  surface temperature • Sometimes measured in Kelvins. • T traditionally increases to the LEFT • Normally T given as a ``ratio scale'‘ • Sometimes use “Spectral Class” • OBAFGKM • “Oh, Be A Fine Girl, Kiss Me” • Could also use luminosities measured through color filters

  47. “Standard” Astronomical Filter Set • 5 “Bessel” Filters with approximately equal “passbands”:  100 nm • U: “ultraviolet”, max  350 nm • B: “blue”, max  450 nm • V: “visible” (= “green”), max  550 nm • R: “red”, max  650 nm • I: “infrared, max  750 nm • sometimes “II”, farther infrared, max  850 nm

  48. Filter Transmittances 100 Visible Light II R I V B U Transmittance (%) 50 0 200 300 400 500 600 700 800 900 1000 1100 Wavelength (nm)

  49. L(star) / L(Sun) 0.3 0.4 0.5 0.6 0.7 0.8 l (mm) Visible Region Measure of Color • If image of a star is: • Bright when viewed through blue filter • “Fainter” through “visible” • “Fainter” yet in red • Star is BLUISH and hotter

  50. L(star) / L(Sun) 0.3 0.4 0.5 0.6 0.7 0.8 l (mm) Visible Region Measure of Color • If image of a star is: • Faintest when viewed through blue filter • Somewhat brighter through “visible” • Brightest in red • Star is REDDISH and cooler

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