Light from Stars cont.... Motion of stars

Three types of spectra: Blackbody – all solids, liquids and gases radiate EM waves at all wavelengths with a distribution of energy over the wavelengths that depends on temperature T 2) Absorption spectrum: result of light comprising a continuous spectrum passing through a cool, low density gas 3) Emission spectrum: result of a low density gas excited to emit light. The Light is emitted at specific wavelengths

Three types of spectra: Blackbody – all solids, liquids and gases radiate EM waves at all wavelengths with a distribution of energy over the wavelengths that depends on temperature T 2) Absorption spectrum: result of light comprising a continuous spectrum passing through a cool, low density gas 3) Emission spectrum: result of a low density gas excited to emit light. The Light is emitted at specific wavelengths

How do we define ‘Brightness’? Flux: the total light Energy emitted by one square meter of an object every second F (J/m2/s) 1m 1m

How do we define ‘Brightness’? Luminosity: the total light Energy emitted by the whole surface area of an object every second L = Area × F (J/s) Note: 1 J/s is 1 Watt (W) e.g. Luminosity of Sun = 4πR2 × Flux R

How do we define ‘Brightness’? e.g. 100W light bulb has a surface area of about 0.01 m2 Flux = Luminosity/Area = 100 / 0.01 = 10,000 J/ m2/s

Stefan-Boltzmann law: Flux from a Black Body F = σT4 e.g. If a star were twice as hot as our Sun, it would radiate 24 = 16 times as much energy from every square meter of the surface Luminosity from a star’s surface L = 4πR2σT4 σ = 5.67 × 10-8 J/m2/s/degree4

Wien’s law: wavelength at which the star radiates most of its energy is given by λmax = 3,000,000/T so long λmax as is measured in nanometers (nm) (1nm = 10-9m = 0.000000001m) Given λmax we can calculate T from T = 3,000,000/ λmax e.g. λmax = 1000nm gives T = 3,000,000/1000 = 3,000 K

The Photosphere

Hydrogen Spectral Lines

The Chromosphere

Corona/Upper Chromosphere Spectrum

Hydrogen Spectral Lines

Corona/Upper Chromosphere Spectrum

Hydrogen Spectral Lines

The Sun: G2

Million Dollar Question: Are two stars which look to have the same brightness: Actually the brightness and therefore same distance from our solar system? Different brightnesses, with the more bright star farther from our solar system than the less bright star?

Brightness at a distance: the inverse square law

Brightness at a distance: the inverse square law Increase the size of a sphere from radius d to radius 2d: Area increases from 4πd2 to 4π(2d)2 = 16 πd2 i.e. by a factor of 22 = 4. Therefore flux (light energy per second per unit area) decreases by a factor of 22 = 4. Fobserver = F/ d2

Apparent Magnitude mv (How bright stars appear) First encountered written down in Ptolemy’s Almagest (150 AD) Thought to originate with Hipparchus (120 BC) Stars classified by giving a number 1 - 6 Brightest stars are class 1 Dimmest stars visible to naked eye are class 6 Class 1 is twice as bright as class 2, class 2 is twice as bright as class 3, and so on. So class 1 is 26 = 64 times as bright as class 6

Apparent Magnitude mv (How bright stars appear) Refined in the 19th Century when instruments became precise enough to accurately measure brightness Modern scale is defined so that 6th magnitude stars are exactly 100 times brighter than 1st magnitude stars This means stars that differ in magnitude by 1 differ by a factor of 2.512 (e.g. a 3rd magnitude star is 2.512 times brighter than a 2nd magnitude star).

Absolute Magnitude Mv – How bright stars would appear If they were all the same distance away

Absolute Magnitude and Luminosity M1 – M2 = -2.5 log10(L1/L2) Magnitudes and the Distance Modulus mv – Mv = -5 + 5 log10(d) d in parsecs Distance Modulus mv – Mv 1 2 3 4 5 6 7 8 9 10 15 20 d (pc) 10 16 25 40 63 100 160 250 400 630 1000 10,000 100,000

Apparent Absolute 30 Moon 31.5 Venus 30.14 20 Barnard’s Star 13.24 10 Sun 4.83 Polaris 2.5 Alpha Centauri 4.38 Betelgeuse 0.8 Sirius 1.4 Alpha Centauri -1.1 Polaris -3.63 Sirius -1.1 Venus -4.4 Betelgeuse -5.6 -10 Moon -12.5 -20 Sun -26.5 -30

Motions of the Stars

Space Velocity can be decomposed into two perpendicular components vt vr

Proper Motion vt = μ d d

The Doppler Effect

The Doppler Effect