* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Deducing Temperatures and Luminosities of Stars
Survey
Document related concepts
Auriga (constellation) wikipedia , lookup
Cassiopeia (constellation) wikipedia , lookup
Corona Australis wikipedia , lookup
International Ultraviolet Explorer wikipedia , lookup
Dyson sphere wikipedia , lookup
Astronomical unit wikipedia , lookup
Cygnus (constellation) wikipedia , lookup
H II region wikipedia , lookup
Perseus (constellation) wikipedia , lookup
Timeline of astronomy wikipedia , lookup
Aquarius (constellation) wikipedia , lookup
Stellar kinematics wikipedia , lookup
Corvus (constellation) wikipedia , lookup
Stellar evolution wikipedia , lookup
Observational astronomy wikipedia , lookup
Transcript
Review: Electromagnetic Radiation Increasing energy ) t ) UV gh (IR t( R Li le d s o a y vi le are a m b R ra si Infr am X Ult Vi s ay Deducing Temperatures and Luminosities of Stars (and other objects…) G 10-15 m 10-9 m 10-6 m 10-4 m M w ro ic es av 10-2 m o di Ra w es av 103 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. Electromagnetic Fields Sinusoidal Fields • BOTH the electric field E and the magnetic field B have “sinusoidal” shape Direction of “Travel” Wavelength λ of Sinusoidal Function Frequency ν of Sinusoidal Wave λ time z Wavelength λ is the distance between any two identical points on a sinusoidal wave. 1 unit of time (e.g., 1 second) z Frequency: the number of wave cycles per unit of time that are registered at a given point in space. (referred to by Greek letter ν [nu]) z ν is inversely proportional to wavelength 1 “Units” of Frequency ⎡ meters ⎤ c⎢ ⎣ second ⎥⎦ = ν ⎡ cycles ⎤ ⎢⎣ second ⎥⎦ ⎡ meters ⎤ λ⎢ ⎥ ⎣ cycle ⎦ ⎡ cycle ⎤ = 1 "Hertz" (Hz) 1⎢ ⎣ second ⎥⎦ Wavelength and Frequency Relation z Wavelength is proportional to the wave velocity v. z Wavelength is inversely proportional to frequency. z e.g., AM radio wave has long wavelength (~200 m), therefore it has “low” frequency (~1000 KHz range). z If EM wave is not in vacuum, the equation becomes ν= where v = v λ c and n is the "refractive index" n Planck’s Radiation Law Light as a Particle: Photons z Photons are little “packets” of energy. z Each photon’s energy is proportional to its frequency. z Specifically, energy of each photon energy is • 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 E = hν Energy = (Planck’s constant) × (frequency of photon) h ≈ 6.625 × 10-34 Joule-seconds = 6.625 × 10-27 Erg-seconds http://scienceworld.wolfram.com/physics/PlanckLaw.html Planck’s Radiation Law • Wavelength of MAXIMUM emission λmax is characteristic of temperature T • Wavelength λmax ↓ as T ↑ Sidebar: The Actual Equation B (T ) = 2hc 2 λ5 1 e hc λ kT −1 • 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 λmax http://scienceworld.wolfram.com/physics/PlanckLaw.html 2 Temperature dependence of blackbody radiation Wien’s Displacement Law • 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 • Can calculate where the peak of the blackbody spectrum will lie for a given temperature from Wien’s Law: λmax [ meters ] = 2.898 × 10−3 T [K] (recall that human vision ranges from 400 to 700 nm, or 0.4 to 0.7 microns) Colors of Stars Colors of Stars • Star “Color” is related to temperature • If T << 5000 K (say, 2000 K), the wavelength of the maximum of the spectrum is: – If star’s temperature is 5000 K, the wavelength of the maximum of the spectrum is: λmax λmax = 2.898 × 10−3 = m 0.579µ m = 579nm 5000 2.898 × 10−3 m 1.45µ m = 1450nm 2000 (in the “near infrared” region of the spectrum) (in the visible region of the spectrum) • The visible light from this star appears “reddish” Why are Cool Stars “Red”? Colors of Stars Less light in blue Star appears “reddish” • If temperature >> 5000-K (say, 15,000-K), wavelength of maximum “brightness” is: λmax = 0.4 0.5 0.6 0.7 0.8 λ (µm) 0.9 1.0 1.1 1.2 2.898 × 10−3 m 0.193µ m = 193nm 15000 1.3 λmax “Ultraviolet” region of the spectrum Star emits more blue light than red ⇒appears “bluish” Visible Region 3 Betelguese and Rigel in Orion Why are Hotter Stars “Blue”? Betelgeuse: 3,000 K (a red supergiant) More light in blue Star appears “bluish” 0.1 0.2 0.3 λmax 0.4 0.5 0.6 0.7 0.8 0.9 1.0 λ (µm) Rigel: 30,000 K (a blue supergiant) Visible Region Blackbody curves for stars at temperatures of Betelgeuse and Rigel Stellar Luminosity • Sum of all light emitted over all wavelengths is the luminosity – brightness per unit surface area – luminosity is proportional to T4: L = σ T4 Joules ⎛ ⎞ −8 , Stefan-Boltzmann constant ⎟ ⎜ σ ≈ 5.67 × 10 m 2 -sec-K 4 ⎝ ⎠ – 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 Stellar Luminosity – Hotter Stars • Hotter stars emit more light per unit area of its surface at 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) Two stars with Same Diameter but Different T • Hotter Star emits MUCH more light per unit area ⇒ much brighter 4 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. 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 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) ⎡ F (10 pc ) ⎤ M = −2.5 × log10 ⎢ ⎥+m ⎢⎣ F ( earth ) ⎥⎦ 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 Sidebar: “Absolute Magnitude” • Recall definition of stellar brightness as “magnitude” m ⎡F⎤ m = −2.5 × log10 ⎢ ⎥ ⎣ F0 ⎦ • F, F0 are the photon numbers received per second from object and reference, respectively. Sidebar: “Absolute Magnitude” Apply “Inverse Square Law” • Measured brightness decreases as square of distance 2 ⎛ 1 ⎞ 2 ⎜ ⎟ F (10 pc ) 10 pc ⎠ ⎛ distance ⎞ = ⎝ = ⎜ ⎟ 2 F ( earth ) ⎛ 1 ⎞ ⎝ 10 pc ⎠ ⎜ ⎟ ⎝ distance ⎠ 5 Simpler Equation for Absolute Magnitude ⎡⎛ distance ⎞ 2 ⎤ M = −2.5 × log10 ⎢⎜ ⎟ ⎥+m ⎢⎣⎝ 10 pc ⎠ ⎥⎦ ⎡ distance ⎤ = −5 × log10 ⎢ ⎥+m ⎣ 10 pc ⎦ Plot Brightness and Temperature on “Hertzsprung-Russell Diagram” 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. α 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 α Cen 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 http://zebu.uoregon.edu/~soper/Stars/hrdiagram.html Hertzsprung-Russell Diagram “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 6 H-R Diagram Hertzsprung-Russell Diagram • Vertical Axis ⇒ luminosity of star – could be measured as power, e.g., watts – or in “absolute magnitude” Lstar – or in units of Sun's luminosity: LSun H-R Diagram “Standard” Astronomical Filter Set • Horizontal Axis ⇒ surface temperature – – – – • 5 “Bessel” Filters with approximately equal “passbands”: ∆λ≈ 100 nm 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 – – – – – – U: “ultraviolet”, λmax ≈ 350 nm B: “blue”, λmax ≈ 450 nm V: “visible” (= “green”), λmax ≈ 550 nm R: “red”, λmax ≈ 650 nm I: “infrared, λmax ≈ 750 nm sometimes “II”, farther infrared, λmax ≈ 850 nm Filter Transmittances Measure of Color 100 R B II I • If image of a star is: – Bright when viewed through blue filter – “Fainter” through “visible” – “Fainter” yet in red V U 50 • Star is BLUISH and hotter 0 L(star) / L(Sun) Transmittance (%) Visible Light 0.3 0.4 0.5 0.6 0.7 0.8 λ (µm) 200 300 400 500 600 700 800 Wavelength (nm) 900 1000 1100 Visible Region 7 Measure of Color How to Measure Color of Star • Measure brightness of stellar images taken through colored filters • If image of a star is: – Faintest when viewed through blue filter – Somewhat brighter through “visible” – Brightest in red L(star) / L(Sun) • Star is REDDISH and cooler – used to be measured from photographic plates – now done “photoelectrically” or from CCD images • Compute “Color Indices” 0.3 0.4 0.5 0.6 λ (µm) 0.7 0.8 – Blue – Visible (B – V) – Ultraviolet – Blue (U – B) – Plot (U – V) vs. (B – V) Visible Region 8