Solar Energy Transport & Luminosity

Transcription

1 Solar Energy ranort & Luminosity Energy transer rom core to solar surace by radiative tranort mode ollowed by convective energy tranort! Luminosity in erg/s: L r r 2 r (r) is energy lux in erg s - cm -2 at radius r M core 0.M With: L = erg/s = erg s - cm -2 or R = cm

2 Black Body Radiation o the Sun Black bodies have 00% absorption o photons and zero relectivity! he sun, stars and all stellar objects are treated as black bodies! Energy lux or black bodies is described by Stean Boltzmann law: = erg s - cm -2 K - = W m -2 K - (Stean s constant) Planck unction describes the ectral distribution o a black body o temperature B ( ) 3 2h 2 c h k e Planck constant: h= J s Boltzmann constant: k= J K - c k c k hc E h : requency : wavelength k: wavenumber hc k 8 W MW 0 erg K sun 2 2 m K m cm 2 s

3 emperature dependence o solar lux he solar lux or the luminosity depends very sensitively on the temperature ( )! Emission rom cooler areas is reduced! Wien s law: the peak o the lux distribution depends on the temperature! 2897 m max

4 Homework 2 Calculate the Planck unction B () and the wavelength max or maximum radiation emission or earth assuming an average surace temperature o 280K.

5 Solar constant 0 = (R /R orbit ) 2 R = km = AU R orbit = km = AU 0 = (R /R orbit ) 2 = erg s - cm -2 (R /R orbit ) 2 = = erg s - cm -2 lux=solar Constant: 0 = W/m 2, R earth = 637 km Solar power incident on earth: S 0 = R earth2 0 = W

6 Variations o solar constant lux Irridiance Measurements o solar constant over last 30 years indicate variation o 0.03% Model based reconstruction o long term irradiance suggests slight increase by 0.0%. A regular oscillation o 0.0% is observed in an eleven year cycle!

7 Sun ots Sun ots are correlated to strong magnetic ields breaking through the photohere o our sun! Granule 5800 K Penumbra 5500 K Umbra 500 K Outlow o material along magnetic ield lines rom inner to outer penumbra sunots are associated with increased cosmic ray intensity (highly ionized particles) Magnetic ield at center is vertical, at outer penumbra it becomes horizontal Magnetic ield strength B drops rom G towards boundary strong magnetic ields quench convective motion reduce energy tranort opacity changes with temperature, through sunots one can see deeper

8 Sunot cycles years Maunder minimum

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10 Solar cycle and cosmic ray lux # o sunots n N(n,p) C rel. C concentration years Decline o C equilibrium content in Atmohere. Why? year C concentration in Georgian wine during the 0 year period o 908 to 952 shows direct correlation with sunot activity, similar observations with old whisky!

11 Quick and dirty example he average sunot has a diameter o 500 km (large ones can reach the size o earth diameter) and a temperature o = 500 K. he anular solar surace has an average temperature o = 5800 K. he solar energy lux and solar power reaching earth at a time o low sunot activity is W/m 2 compared to a lux o W/m 2 at a time o maximum sunot activity? Estimate the raction o the sun covered by sunots! quiet active quiet active quiet active quiet active 0.%

12 km km km km n R r n A A n sun sun A /2 =7.7 0 km 2

13 he uture o the Sun or the ultimate climate change in ~ 6-8 Billion years According to solar model simulations the hydrogen content in our sun has declined to about 50% o the initial value, we run low in uel! Hydrogen burning zone expands outward, orcing the sun to expand! he solar here ows slowly enguling the inner planets, causing the ultimate global warming on earth!

14 he movie to the book he inal global warming scene!

15 he ectra o the stars depend on composition, density, and temperature o the stellar atmohere. Atoms in the atmohere absorb light emitted at lower layers and produce the dark vertical lines or bands in the ectrum. Solar ectrum