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 = 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 : Full Moon : 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. 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  (apparent) = 5 (absolute) We define the absolute magnitude as the magnitude of a star as if it were 10pc 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) = (inverse square law)  10 pc x 100  1000 pc away

PHYS Brightest Stars CommonLuminosityDistanceSpectralProper MotionR. A.Declination NameSolar UnitsLYTypearcsec / yearhours mindeg min Sirius409A1V Canopus150098F Alpha Centauri24G2V Arcturus10036K2III Vega5026A0V Capella20046G5III Rigel80,000815B8Ia Procyon911F5IV-V Betelgeuse100,000500M2Iab Achernar50065B3V Beta Centauri B1III Altair1017A7IV-V Aldeberan20020K5III Spica B1V Antares10,000390M1Ib Pollux6039K0III Fomalhaut5023A3V Deneb80, A2Ia Beta Crucis10,000490B0.5IV Regulus15085B7V

PHYS 205 Color and Temperature

PHYS 205 Wien’s Law 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: ColorClasssolar massessolar diametersTemperature bluestO20 – ,000 bluishB ,000 blue-whiteA ,000 whiteF ,000 yellow-whiteG ,500 orangeK ,000 redM ,000 Also each spectral class is divided into 10: Sun  G2

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.