2. PHYS 205 Analyzing Starlight

3. 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.

4. 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

5. 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.

6. 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. 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(2,000,000 2 ) = 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.

7. 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) = 100 2 (inverse square law)  10 pc x 100  1000 pc away

8. PHYS 205 20 Brightest Stars CommonLuminosityDistanceSpectralProper MotionR. A.Declination NameSolar UnitsLYTypearcsec / yearhours mindeg min Sirius409A1V 1.3306 45.1-16 43 Canopus150098F01 0.0206 24.0-52 42 Alpha Centauri24G2V 3.6814 39.6-60 50 Arcturus10036K2III 2.2814 15.7+19 11 Vega5026A0V 0.3418 36.9+38 47 Capella20046G5III 0.4405 16.7+46 00 Rigel80,000815B8Ia 005 12.1-08 12 Procyon911F5IV-V 1.2507 39.3+05 13 Betelgeuse100,000500M2Iab 0.0305 55.2+07 24 Achernar50065B3V 0.101 37.7-57 14 Beta Centauri9300300B1III 0.0414 03.8-60 22 Altair1017A7IV-V 0.6619 50.8+08 52 Aldeberan20020K5III 0.204 35.9+16 31 Spica6000260B1V 0.0513 25.2-11 10 Antares10,000390M1Ib 0.0316 29.4-26 26 Pollux6039K0III 0.6207 45.3 +28 02 Fomalhaut5023A3V 0.3722 57.6-29 37 Deneb80,0001400A2Ia 020 41.4+45 17 Beta Crucis10,000490B0.5IV 0.0512 47.7-59 41 Regulus15085B7V 0.2510 08.3+11 58

9. PHYS 205 Color and Temperature

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

11. 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.

12. 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.

13. 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: ColorClasssolar massessolar diametersTemperature ---------------------------------------------------------------------------------- bluestO20 – 10012 - 2540,000 bluishB4 - 124 - 1218,000 blue-whiteA1.5 - 41.5 - 410,000 whiteF1.05 - 1.51.1 - 1.57,000 yellow-whiteG0.8 - 1.050.85 - 1.15,500 orangeK0.5 - 0.80.6 - 0.854,000 redM0.08 - 0.50.1 - 0.63,000 Also each spectral class is divided into 10: Sun  G2

14. 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.