Today in Astronomy 142 - Astro Pas Rochester

Today in Astronomy 142More on the Sun as a typicalstar:! Radiative transport andoptical depth! The spectrum of thesurface (atmosphere) ofthe Sun! The structure of the sun’souter layers: convection,rotation, magnetism andsunspots! Solar energyMulticolor ultraviolet image of the Sun, showingseveral sunspot-rich active regions (TRACE/NASA).Astronomy 142 1

The solar spectrumBy and large, the spectrum of theSun resembles closely a blackbody.From the total energy flux atEarth (solar constant):we get the Sun’s luminosity:Setting solar luminosity equal to blackbody power givesSun’s effective temperature:Astronomy 142 2

In detail:absorption linesare also seen inthe solarspectrum; theymatch up withmany knowntransitions ofatoms, ions andmolecules. (SeeLab #2.)The solar spectrum (continued)Figure: the ultimate high-resolution spectrum of the Sun (Nigel Sharp, fromdata by Bob Kurucz et al. ( NOAO/NSO/Kitt Peak FTS/AURA/NSF)Astronomy 142 3

Formation of absorption lines in the solaratmosphereFigure: Chaisson andMcMillan, Astronomy TodayAstronomy 142 4

Radiation transportkeeping track of energy in radiationAstronomy 142 5

Radiative transportoptical depth dI = Id⌧dId⌧ =II(⌧) =Ie ⌧light missingintegrateτ is unit lessopticalZdepth⌧ = apple⇢dsκopacity units g -1 cm 2κρ units cm -1amount of light goingmissing per unitlengthAstronomy 142 6

Mean free pathκopacity units g -1 cm 2κρ units cm -1amount of light going missing per unit lengthabsorption per unit lengthκρ = n σn particles per unit volume (cm -3 )σ cross section (cm 2 )l = (n σ) -1 = (κρ) -1 (cm) how far a photon goes before getting absorbedthe mean free pathAstronomy 142 7

Relation between extinction and optical depthAstronomy 142 8

Opacity depends onwavelength because of atomicand molecular transitionsIf the opacity is higher thenwe see only in the top layerswhere it is cooler.When it is cooler the surfacebrightness is lowerAstronomy 142 9

opacity and photosphered⌧ = apple⇢drd⌧dr = apple⇢dPdr = ⇢gdPd⌧ = dPdroptical depth with radiushydrostatic equilibriumdrd⌧ = ⇢g ⇥ 1apple⇢ = g appleat photosphere τ=1P at photosphere =g/κPressure broadening of spectral lines gives ameasurement for gAstronomy 142 10

Solar “granulation:” the tops of convection cellscredit:NOAOFigure: Chaisson and McMillan, Astronomy TodayAstronomy 142 12

Simulations of convectioncredit:FrankRobinsonAstronomy 142 13

Using Adaptive Optics to look at detailVisible images fromThe 1m Swedish SolarTelescope at La Palmashow filaments nearsunspots as well as thegranulation. The darkcored filaments wereunexpected.Astronomy 142 14

More detail on Sun spotsAstronomy 142 15

Further out: the corona and chromosphereCorona: observed tobe well over 1000000K.Theory of corona:heated by acousticnoise from boilingtop of convectionzone; diffuse enoughthat it can’t cool verywell, so it reachesvery hightemperatures.Figure: Chaisson andMcMillan, Astronomy TodayAstronomy 142 16

Solar corona and atmosphere X-ray composite(NASA/SPARTAN)Astronomy 142 17

Sunspots: solar magnetismFigure: Chaisson and McMillan, Astronomy Today! Sunspots appeardark becausethey’re slightlycooler than the restof the solar surface.! Zeeman effectmeasurementsshow that they arealso maxima ofmagnetic field.! Associated withother activity (e.g.prominences)Astronomy 142 18

The multi-wavelength real-time Sun according to SOHOPulled off the SOHOwebsite on Jan24/2003. This iswhat the sun lookedlike in X-rays andUV lines, opticalcontinuum and witha magnetogram.Astronomy 142 19

Sunspot progress, activity during solar cycleFigure:Chaisson andMcMillan,AstronomyTodayAstronomy 142 20

The 11-year sunspot cycleThe first sunspots in a cycle form near ±30° latitude, and thelast near the equator, producing the “butterfly diagram.”David Hathaway, NASA/MSFCAstronomy 142 21

11-year sunspot cycle, for the last 400 yearsFigure: Chaisson and McMillan, Astronomy TodayAstronomy 142 22

Sunspot formation and cycle: interaction ofmagnetism and differential rotationThe Sun rotates, but not as a solid body; this differentialrotation wraps and distorts an initially “poloidal” solarmagnetic field.! Occasionally, the field lines burst out of the surface andloop through the lower atmosphere, thereby creating asunspot pair. The underlying pattern of the solar fieldlines explains the observed pattern of sunspot polarities.! If the loop happens to occur on the limb of the Sun and isseen against dark space, a prominence is visible.! The twisting and wrapping of the field lines eventuallyresults in the production of a poloidal field again, but withnorth and south switched. Then the process repeats.! 22 years between identical field configurations, 11 yearsbetween sunspot-number maxima.Astronomy 142 23

Sunspot formation and cycle: interaction ofmagnetism and differential rotationFigure: Chaisson and McMillan, Astronomy TodayAstronomy 142 24

Energy and the sun! Hydrostatic equilibrium and ideal-gas behavior ensurethat the center of the Sun is very hot, and energy (in theform of light) is radiated from the center.! The high opacity of the Sun to light determines the rate atwhich the energy leaks out. As we have seen, it takes along time for photons to diffuse from center to surface.! This cannot go on forever, without the Sun cooling down,or replacement for the energy that leaks away.! We know that the solar system is about 4.5x10 9 years old(from many radioisotope abundance measurements onmeteorites), and that life has existed here for at least 3x10 9years. Thus the Sun must have had close to its presentluminosity for billions of years.Astronomy 142 25

Cooling timescaleAstronomy 142 26

How long would the Sun’s present heat last?Plasma energy density at center of Sun (energy density of electron gasthere, considered again to be ideal):Energy density of light, which is about to leak away:We showed last lecture that it takes about t = 31000 years for a photon toleak from center to surface, so the heat lastsThus some process must be replacing the energy that leaks away.Astronomy 142 27

Energy sources for the SunChemical energy (burning) doesn’t work.“The Sun is nothing but a burning ember:” Anaxagoras ofClazomenae, ca. 450 BC.Suppose (optimistically) that the Sun were made of anthracitecoal, with enough oxygen to burn it completely to CO 2 :5.5x10 32 gm coal, 1.45x10 33 gm O. Burning 1 gm of anthracitecoal to CO 2 liberates 4.3x10 11 erg. Thus the Sun’s initialenergy reserve would beΔE =4.3x10 11 x 5.5x10 32 erg = 2.4 x 10 44 ergwhich at the Sun’s present luminosity would lastAstronomy 142 28

Energy sources for the Sun (continued)Collapse and liberation of gravitational potential energyalso doesn’t work (Kelvin and Helmholtz, late 19th century):However, mass energy would work, even if only 0.1% of itcould be converted to radiation:Astronomy 142 29

Energy sources for the Sun (continued)How could the Sun convert mass-energy to radiation?! Nuclear fusion: basically the liberation of mass energystored as potential energy of the strong nuclearinteraction.Would this work under the conditions known to prevail atthe center of the Sun?! Yes. Requires such conditions, in fact.To demonstrate these answers we need to talk a bit about thefundamental interactions of matter.Astronomy 142 30

Summary! Phenomenology of the Sun: sunspots, active regions,magnetic activity, solar cycle, solar dynamo.! Solar structure: radiative core and convection zone,photosphere, chromosphere, corona.! Solar energy problem. Only nuclear reactions provide aplausible energy source for the billion year timescale thatthe Sun has been luminous.! Opacity and radiative transportAstronomy 142 31