Photometry - Photometry Hipparchus [160 - 127 BC]...

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Unformatted text preview: Photometry Hipparchus [160 - 127 BC] Hipparchus compiled a catalog of about a thousand stars in the second century, BC. He classified them into six categories of brightness, now called magnitudes. bi h ll d Magnitudes Recognizing that (a) the response of the human eye is basically logarithmic and (b) the average flux difference between first and sixth magnitudes stars is about 100, Norman Robert Pogson (1856) proposed that: 5 magnitudes exactly corresponds to a ratio of 100 : 1, or 1 magnitude corresponds to a flux ratio of 2.512 : 1. ( 2.512 )5 = 100.0 Note that numerically smaller numbers correspond to brighter stars. 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 Δm = m1 – m2 = 2.5 log ( F2 / F1 ) Apparent Magnitudes Δm = m1 – m2 = 2.5 log ( F2 / F1 ) 25 Δm 0.0 00 0.5 1.0 2.0 2.5 3.0 4.0 5.0 10.0 10 0 Flux Ratio 1.0 10 :1 1.6 : 1 2.5 : 1 6.3 : 1 10 : 1 16 : 1 40 : 1 100 : 1 10,000 10 000 : 1 Example m1 – m2 = 2.5 log ( F2 / F1 ) Let m1 = 4.2m and F2 / F1 = 27 4.2 – m2 = 2.5 log ( 27 ) 4.2 – m2 = 3.6 m2 = 4.2 – 3.6 m2 = 0.6m PRS Question 1. If Star A has a magnitude of 15, and Star B is 10,000X brighter, then the magnitude of Star B is a. 25 d. 10 b. 20 e. 5 c. 15 The Pleiades Magnitude Scale Object Sun Full Moon Venus Jupiter Sirius Naked-eye limit Binoculars 4-m telescope Hubble m -26.7 -12.6 -4.4 -2.0 -1.4 6.5 10 26 30 Full Range Δm = m1 – m2 = 2.5 log ( F2 / F1 ) Δm = 30 – (-26.7) = 56.7 ( ) 56.7 = 2.5 log ( F2 / F1 ) log ( F2 / F1 ) = 56.7 / 2.5 = 22.7 ≅ 23 F2 / F1 = 1023 100,000,000,000,000,000,000,000 : 1 Luminosity and Flux Luminosity (power) is the rate at which electromagnetic energy is radiated into space by an astronomical object. Lsun = 3.826 x 1026 J/s “Brightness” of a star is radiant flux F – The total amount of light energy of all wavelengths that crosses a unit area perpendicular to the direction of the light’s travel in unit time. The flux is the number of joules per second at 1 cm2 of a detector aimed at the star. F = L / (4 π d2) Propagation of Light Apparent Brightness Flux Fl = Luminosity / 4 π d2 L i it Inverse Square L I S Law Flux1 4 π d22 d22 --------- = ----------- = -----Flux2 4 π d12 d12 Flux-Distance-Luminosity Brightness = Flux = Luminosity / 4 π d2 b = F = L / d2 F1 d12 ---------F2 d22 L1 = ----L2 The Pleiades How to Compare Magnitudes The way to compare the intrinsic brightness is to compare the magnitudes for a given distance, which is 10 pc. Example: E ample: m = 7.5 mag d = 100 pc Change d to 10 pc Distance has been reduced by 10X, so the Brightness has increased by (10)2 = 100X or 100X, the Magnitude must decrease by 5.0 mag Therefore, M = 7.5 – 5.0 = 2.5 mag , g Absolute Magnitudes m1 – m2 = 2.5 log ( F2 / F1 ) F = L / 4 π d2 F(10) / F(d) = ( d / 10 )2 m – M = 5 l ( d / 10 ) log Example m – M = 5 log ( d / 10 ) Let m = 6.3m and d = 38 pc 6.3 – M = 5 log ( 38 / 10 ) 6.3 – M = 2.9 M = 6.3 – 2.9 M = 3 m 3.4 PRS Question 2. What is the distance to Star C if its m = +20 mag and its M = -5 mag? a. 106 pc d. 103 pc b. b 105 pc e. e 102 pc c. 104 pc The Sun’s Absolute Magnitude m – M = 5 log ( d / 10 ) Let m = -26.7m and d = 1/206265 pc -26.7 – M = 5 log (1/206265 / 10 ) -26.7 – M = -31.5 M = -26.7 + 31.5 M = 4.8m 8 Color and Temperature UBV Filter Bandpasses Color Indices Filters U B V Ultraviolet Blue Visual ( U – B ) and ( B – V ) are color indices B – V = MB – MV Ultraviolet, blue, and visual magnitude scales are adjusted to be equal to , , g j q one another, so that they give a color index of 0 to a star with a temperature of about 10,000 K. The (B – V) index ranges from about -0.4 (bluest, hottest stars) to more than +2.0 (redder, coolest stars). Color and Temperature Bolometric Magnitudes Occasionally, astronomers do discuss the magnitudes of stars based on their entire luminosity. In other words, no filter is used. The Bolometric Magnitude covers the entire electromagnetic spectrum. Instead of using Flux, one uses the Luminosity of the Sun: Lsun = 3.826 x 1026 J/s The corresponding magnitude is Mbol = 4.75 mag . Table of Colors ...
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