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lecture_4 - T h e S u n E x a m p l e o f R a d i a t i o n...

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Unformatted text preview: T h e S u n : E x a m p l e o f R a d i a t i o n L a w s • L circledot = 4 · 10 33 erg/s • Yellow color means that the peak wavelength of the Sun’s spectrum is λ max similarequal 5 · 10- 5 cm • Use Wien’s Law to find the surface temperature of the Sun: T circledot = 0 . 29 cm /λ max similarequal 6000 K • Invert the blackbody luminosity formula to derive the solar radius: R circledot = radicalbigg L circledot 4 πσ T 4 circledot = 7 · 10 10 cm General Properties of Stars • Masses: from 0.1 M circledot to 100 M circledot • Luminosities: from 0.0001 L circledot to 10 6 L circledot • Radii: from 0.1 R circledot to 1400 R circledot • Surface Temperatures: from 2000 K (infrared) to 40,000 K (ultraviolet) • However, properties of white dwarfs and neutron stars can be more extreme. Lattimer, AST 248, Lecture 4 – p. 1/1 7 P r o p e r t i e s a n d T y p e s o f S t a r s • The main physical properties of stars are their luminosity L , surface temperature T , radius R and mass M . E. Hertzsprung and H. Russel discovered that plotting L vs. T was a useful way to discriminate types of stars. www.daviddarling.info/encyclopedia/H/HRdiag.html Lattimer, AST 248, Lecture 4 – p. 2/1 7 • Most stars are Main Sequence stars, which burn H into He in their cores. • Other groups are red giants, which have exhausted H fuel and “burn” He into C and O, supergiants which are burning even heavier elements, and white dwarfs (dead low-mass stars). • Main Sequence stars can be divided into spectral types O, B, A, F, G, K and M based on surface temperature or color • Note that there are straight lines of constant radius contours www.daviddarling.info/encyclopedia/H/HRdiag.html Lattimer, AST 248, Lecture 4 – p. 3/1 7 S p e c t r a l T y p e s Initial M-S M-S Surface M-S M-S Number Spectral Mass Luminosity Temperature Lifetime Radius in Galaxy Type (M circledot ) L circledot ◦ K (years) (R circledot ) O 60 800,000 50,000 1 · 10 6 12 5 . 5 · 10 4 B 6 800 15,000 1 · 10 8 3.9 3 . 6 · 10 8 A 2 14 8000 2 · 10 9 1.7 2 . 4 · 10 9 F 1.3 3.2 6500 6 · 10 9 1.3 1 . 2 · 10 10 G 0.9 0.8 5500 1 . 3 · 10 10 0.92 2 . 8 · 10 10 K 0.7 0.2 4000 4 · 10 10 0.72 6 · 10 10 M 0.2 0.01 3000 2 . 5 · 10 11 0.3 3 · 10 11 • A star’s physical properties on the Main Sequence (M-S) are related: T int ∝ M/R ; R ∝ M 1 / 2 • These, taken with the relations L ∝ R 2 T 4 and T int ∝ T , imply L ∝ M 3 • The volume of a star’s habitable zone is approximately proportional to M 4 ∼ L 4 / 3 . • A star’s Main Sequence lifetime can be estimated by considering the amount of fuel and dividing by the rate at which the fuel is burned: τ ∝ M L ∝ M M 3 = 1 M 2 ; τ = τ circledot M L • So, massive stars burn out too quickly for life to ever form on planets orbiting them....
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