HR_Diagrams - Celestial Census Distances d = 1 /...

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Unformatted text preview: Celestial Census Distances d = 1 / p" (pc) d = 206,265 / p" (AU) 1 pc = 3.26 LY Radial Velocity / = v / c = (obs – ) / v = c / Proper Motion & Tangential Velocity T = 4.74 d = 4.74 / p" (km/s) where is in arcsec/year, d is in parsecs, and p" is in arcsec. Space Velocity The total space velocity is V2 = VR2 + VT2 Flux-Distance-Luminosity Brightness = Flux = Luminosity / 4 d2 b = F = L / d2 F1 d12 ---------F2 d22 L1 = ----L2 Apparent Magnitudes F2 / F1 = 100(m1 – m2)/5 log (xn) = n log (x) log (F2 / F1) = (m1 – m2) / 5 log (100) = 2 (m1 – m2) / 5 m1 – m2 = 2.5 log ( F2 / F1 ) Absolute Magnitudes m1 – m2 = 2.5 log ( F2 / F1 ) F = L / 4 d2 F(10) / F(d) = ( d / 10 )2 m – M = 5 log ( d / 10 ) Spectral Types Ionization via Temperature Diameters of Stars L = 4 R2 T4 L R2 T4 Masses of Stars Kepler’s 3rd Law (M1 + M2) P2 = a3 M is in solar masses P is in years, and a is in Astronomical Units (1 AU = mean Earth-Sun distance) Spectroscopic Binaries Conservation of Angular Momentum M1 / M2 = v 2 / v 1 v 2 / v 1 = r 1 / r2 Doppler Shift = v / c Mass-Luminosity Relationship L M 4.0 0.08 solar < M < 50 solar How Can We Visualize It All? E. Hertzsprung (1911) and Norris Russell (1913) independently produced plots to investigate stellar properties. Today, those graphs are called H-R Diagrams. Hertzsprung-Russell Diagram PRS Question 1. The HR Diagram is a statistical plot of which two stellar parameters? a. Luminosity and Surface Temperature b. Radius and Mass c. Mass and Surface Temperature d. Luminosity and Mass e. Radius and Luminosity Hertzsprung-Russell Diagram The most significant feature of the HR diagram is that the stars are not distributed over it at random. Rather they cluster into certain parts of the diagram. Main Sequence Red Giants Supergiants White Dwarfs L R2 T4 Radii Relationships The Brightest Stars Of the 20 brightest, only 6 are within 10 pc of the Sun. The vast majority of nearby stars, those less luminous than the Sun, do not send enough light across interstellar distances to be seen without optical aid. The Nearest Stars Only 3 of the 43 nearest stars (other than the Sun) are among the 20 brightest stars: Sirius, Alpha Centauri, and Procyon. The nearby stars also tend to have large proper motions. Also interesting is that 13 of the 44 stars are really binary- or multiple-star systems. Total of 59 stars within 5 pc. The Nearest Stars The most important datum is that most nearby stars are intrinsically faint. Only 10 of the 50 nearest stars are visible to the unaided eye. Only 3 are as intrinsically luminous as the Sun. 43 have luminosities less than 0.01 solar. If the stars in our immediate stellar neighborhood are representative of the stellar population in general, we must conclude that the most numerous stars are those of low luminosity. In this sample, only about 1 star in 20 is as luminous as the Sun. (90% are main sequence; 10% are white dwarfs) Hipparcos Distances to 20 pc Hipparcos Distances to 50 pc Hipparcos Distances to 100 pc Hipparcos Distances to 200 pc Main Sequence Masses Luminosity, Temp, Radius, & Mass Main Sequence Extremes Most Luminous Least Luminous L = 50,000 solar L = 0.005 solar M = 60 solar M = 0.08 solar R = 400 solar R = 0.1 solar T = 45,000 K T = 3000 K O5 M5 PRS Question 2. Where do we find the most massive stars on the Main Sequence in the HR Diagram? a. Evenly distributed across the Main Sequence b. No correlation of mass on the Main Sequence c. Lower right end d. Upper left end e. Middle Section Further Distances 1. 2. 3. 4. Take the Spectrum of the star. Classify the Spectrum. Use the HR Diagram to assign an Absolute Magnitude (M). Measure the Apparent Magnitude (m). m – M = 5 log ( d / 10 ) Spectroscopic Parallax The White Dwarfs Mass of the Sun but the Size of the Earth = 1.6 x 105 g/cm3 (one spoonful = 50 tons) ...
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