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Analyzing Starlight

Analyzing Starlight. 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 )

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Analyzing Starlight

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  1. Analyzing Starlight

  2. Apparent brightness 2nd 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. m1-m2 = 2.5 log (I2/I1) m1 and m2 are visual magnitudes, I1 and I2 are brightness.

  3. Example Vega is 10 times brighter than a magnitude 1 star  I2/I1 = 10. m1 = 1 2.5 log (I2/I1) = 2.5  1 - m2 = 2.5  m2 = -1.5 Using the same calculations we can find that Sun : -26.5 Full Moon : -12.5 Venus : -4.0 Mars : -2.0

  4. 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.

  5. Absolute Magnitude • If two pieces of information is known, we can find the absolute magnitude, M, of a star: • Apparent magnitude, m • Distance from us. • Example: • Take the Sun, 1AU = 1 / 200,000 parsecs away from us. • At 10 parsecs the Sun will be (2,000,000)2 times less bright. • log(2,000,0002) = 31.5 magnitudes dimmer  • -26.5 (apparent) + 31.5 = 5 (absolute) • We define the absolute magnitude as the magnitude of a star as if it were 10pc away from us.

  6. 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 100  1000 pc away

  7. 20 Brightest Stars Common Luminosity Distance Spectral Proper Motion R. A. Declination Name Solar Units LY Type arcsec / year hours min deg min Sirius 40 9 A1V 1.33 06 45.1 -16 43 Canopus 1500 98 F01 0.02 06 24.0 -52 42 Alpha Centauri 2 4 G2V 3.68 14 39.6 -60 50 Arcturus 100 36 K2III 2.28 14 15.7 +19 11 Vega 50 26 A0V 0.34 18 36.9 +38 47 Capella 200 46 G5III 0.44 05 16.7 +46 00 Rigel 80,000 815 B8Ia 0 05 12.1 -08 12 Procyon 9 11 F5IV-V 1.25 07 39.3 +05 13 Betelgeuse 100,000 500 M2Iab 0.03 05 55.2 +07 24 Achernar 500 65 B3V 0.1 01 37.7 -57 14 Beta Centauri 9300 300 B1III 0.04 14 03.8 -60 22 Altair 10 17 A7IV-V 0.66 19 50.8 +08 52 Aldeberan 200 20 K5III 0.2 04 35.9 +16 31 Spica 6000 260 B1V 0.05 13 25.2 -11 10 Antares 10,000 390 M1Ib 0.03 16 29.4 -26 26 Pollux 60 39 K0III 0.62 07 45.3 +28 02 Fomalhaut 50 23 A3V 0.37 22 57.6 -29 37 Deneb 80,000 1400 A2Ia 0 20 41.4 +45 17 Beta Crucis 10,000 490 B0.5IV 0.05 12 47.7 -59 41 Regulus 150 85 B7V 0.25 10 08.3 +11 58

  8. Color and Temperature

  9. Wien’s Law Wien’s Law:   1/T  The higher the temperature  The lower is the wavelengths  The “bluer” the star.

  10. 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.

  11. 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.

  12. 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 4 - 12 18,000 blue-white A 1.5 - 4 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  G2

  13. 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.

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