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Colors and Magnitudes

Colors and Magnitudes. PHYS390 (Astrophysics) Professor Lee Carkner Lecture 2. Answers. On the summer solstice, what RA is on the meridian at midnight? Sun’s RA is 6 hr, so when RA 6 is on the other side of the Earth, RA 18 (6+12) is overhead

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Colors and Magnitudes

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  1. Colors and Magnitudes PHYS390 (Astrophysics) Professor Lee Carkner Lecture 2

  2. Answers • On the summer solstice, what RA is on the meridian at midnight? • Sun’s RA is 6 hr, so when RA 6 is on the other side of the Earth, RA 18 (6+12) is overhead • On what date will a star with an RA of 15 hr be on the meridian at midnight? • Want sun to have RA of 15-12 = 3 hr, which is half way between Mar 20 and Jun 21 or ~May 4

  3. Flux and Luminosity • Photometry • Flux • W/m2 • Luminosity • W • From inverse square law F = L/4pr2 • Sometimes use units of Lsun = 3.839 X 1026 W

  4. Magnitude • Eye has semi-log response, so a 1 magnitude difference is a brightness difference of about 2.5 • apparent bolometric magnitude = m • apparent = • bolometric = a • Smaller m, brighter star • Flux = easy, magnitude = hard

  5. Magnitude and Flux • If m1-m2 = 100 then F2/F1 = 100 m1-m2 = -2.5 log (F1/F2) • m (apparent magnitude) • M (absolute magnitude) • M is equal to the apparent magnitude the star would have if it were at 10 pc m-M = -2.5 log [(L/4pd2)/(L/4p102)] m-M = 5 log (d/10pc) • m-M is called the distance modulus • n.b., sometimes distance is “r” and sometimes “d”

  6. Colors • Can’t detect all wavelengths at once • Examples: UBVRI = apparent magnitude in ultraviolet, blue, visible (green), red, and infrared • We write apparent magnitude in a filter band with a capital letter (e.g., V or B)

  7. Bolometric Correction • e.g., B-V, U-V • The smaller the color index, the more important the wavelengths of the first filter are • low U-B: • low B-V: • We can also apply the bolometric correction (BC) to get the bolometric magnitude • Where BC is constant for a specific spectral type • BC tells us what fraction of the total energy distribution V is

  8. Apparent and Absolute • Apparent magnitude • mbol (for bolometric) • Absolute magnitude • Mbol (for bolometric) • Note also that the color index is a the same for apparent or absolute magnitudes • e.g., B-V = MB-MV

  9. Spectral Type Information • Stars are classified by spectral type • Tells us temperature • Absolute magnitudes (MU , MB, MV, MR, MI, Mbol) • Color indices (B-V, U-B)

  10. Color-Color Diagram • The color index tells us something about the shape of a star’s spectral energy distribution • Negative B-V = • Positive B-V = • A star’s color index tells us its temperature B V

  11. Normalizing the Scale • We can also relate the magnitude to the flux integrated over some wavelength range and a constant C • C is a constant chosen to normalize the magnitude scale to standard stars mbol = -2.5 log (∫ Fl dl) + Cbol • Where the integral is now the total flux

  12. Flux Comparisons • Note that our magnitude scale relates two magnitudes to two fluxes m1-m2 = -2.5 log (F1/F2) • e.g., we could input absolute magnitudes and the flux at 10 pc M-Msun = -2.5 log [(L/4p102) / (Lsun/4p102)] M = Msun - 2.5 log (L / Lsun)

  13. Next Time • Read: 3.3-3.5 • Homework: 3.4, 3.5, 3.8, 3.9a-3.9d

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