# PHYS 205 Analyzing Starlight PHYS 205 Apparent brightness

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PHYS 205 Analyzing Starlight

PHYS 205 Apparent brightness 2 nd century BC Hipparchus devised 6 categories of brightness. In 1856 Pogson discovered that there is a 1: 100 ratio in brightness between magnitude 1 and 6 mathematical tools are possible. m 1 -m 2 = 2. 5 log (I 2/I 1) m 1 and m 2 are visual magnitudes, I 1 and I 2 are brightness.

PHYS 205 Example Vega is 10 times brighter than a magnitude 1 star I 2/I 1 = 10. m 1 = 1 2. 5 log (I 2/I 1) = 2. 5 1 - m 2 = 2. 5 m 2 = -1. 5 Using the same calculations we can find that Sun : -26. 5 Full Moon : -12. 5 Venus : -4. 0 Mars : -2. 0

PHYS 205 Inverse Square Law Sun is very bright, because it is very near to us, but is the Sun really a “bright” star. The amount of light we receive from a star decreases with distance from the star.

PHYS 205 Absolute Magnitude If two pieces of information is known, we can find the absolute magnitude, M, of a star: 1. Apparent magnitude, m 2. Distance from us. 3. Example: 4. Take the Sun, 1 AU = 1 / 200, 000 parsecs away from us. 5. At 10 parsecs the Sun will be (2, 000)2 times less bright. 6. log(2, 0002) = 31. 5 magnitudes dimmer 7. -26. 5 (apparent) + 31. 5 = 5 (absolute) 8. We define the absolute magnitude as the magnitude of a star as if it were 10 pc away from us.

PHYS 205 Distance modulus m –M : distance modulus Example: We have a table in our hands with distance moduli and we need to find the actual distances to the stars. How do we proceed? ? Distance modulus = 10 means 10(10/2. 5) = 10, 000 times dimmer than the apparent magnitude (10, 000) = 1002 (inverse square law) 10 pc x 1000 pc away

PHYS 205 20 Brightest Stars Common Luminosity Name Distance Spectral Proper Motion R. A. Declination Solar Units LY Type arcsec / year hours min deg min Sirius Canopus Alpha Centauri Arcturus Vega Capella Rigel Procyon Betelgeuse Achernar Beta Centauri 40 1500 2 100 50 200 80, 000 9 100, 000 500 9300 9 98 4 36 26 46 815 11 500 65 300 A 1 V F 01 G 2 V K 2 III A 0 V G 5 III B 8 Ia F 5 IV-V M 2 Iab B 3 V B 1 III 1. 33 0. 02 3. 68 2. 28 0. 34 0. 44 0 1. 25 0. 03 0. 1 0. 04 06 45. 1 06 24. 0 14 39. 6 14 15. 7 18 36. 9 05 16. 7 05 12. 1 07 39. 3 05 55. 2 01 37. 7 14 03. 8 -16 43 -52 42 -60 50 +19 11 +38 47 +46 00 -08 12 +05 13 +07 24 -57 14 -60 22 Altair 10 17 A 7 IV-V 0. 66 19 50. 8 +08 52 Aldeberan 200 20 K 5 III 0. 2 04 35. 9 +16 31 Spica 6000 260 B 1 V 0. 05 13 25. 2 -11 10 Antares 10, 000 390 M 1 Ib 0. 03 16 29. 4 -26 26 Pollux 60 39 K 0 III 0. 62 07 45. 3 +28 02 Fomalhaut 50 23 A 3 V 0. 37 22 57. 6 -29 37 Deneb 80, 000 1400 A 2 Ia 0 20 41. 4 +45 17 Beta Crucis 10, 000 490 B 0. 5 IV 0. 05 12 47. 7 -59 41 Regulus 150 85 B 7 V 0. 25 10 08. 3 +11 58

PHYS 205 Color and Temperature

PHYS 205 Wien’s Law: 1/T The higher the temperature The lower is the wavelengths The “bluer” the star.

PHYS 205 Temperature Dependence Question: Where does the temperature dependence of the spectra come from? Answer: Stars are made up of different elements at different temperatures and each element will have a different strength of absorption spectrum. Take hydrogen; at high temperatures H is ionized, hence no H-lines in the absorption spectrum. At low T, H is not excited enough because there are not enough collisions.

PHYS 205 Color Index To categorize the stars correctly, we pass the light through filters. B is a blue filter, V is a visible filter. Hot stars have a negative B-V color index. Colder stars have a positive B-V color index.

PHYS 205 Spectral Types We now know that we can find the temperature of a star from its color. To categorize the “main sequence” stars we have divided the colors into seven spectral classes: Color Class solar masses solar diameters Temperature -----------------------------------------bluest O 20 – 100 12 - 25 40, 000 bluish B 4 - 12 18, 000 blue-white A 1. 5 - 4 10, 000 white F 1. 05 - 1. 5 1. 1 - 1. 5 7, 000 yellow-white G 0. 8 - 1. 05 0. 85 - 1. 1 5, 500 orange K 0. 5 - 0. 8 0. 6 - 0. 85 4, 000 red M 0. 08 - 0. 5 0. 1 - 0. 6 3, 000 Also each spectral class is divided into 10: Sun G 2

PHYS 205 What do we learn? Temperature and Pressure: ionization of different atoms to different levels. Chemical Composition: Presence and strength of absorption lines of various elements in comparison with the properties of the same elements under laboratory conditions gives us the composition of elements of a star. Radial velocity: We can measure a star’s radial velocity by the shift of the absorption lines using Doppler shift. Rotation speed: Broadens the absorption lines, the broader the lines, the higher the rotation speed. Magnetic field: With strong magnetic fields, the spectral lines are split into two or more components.