PY4A01 - Solar System Science Lecture 17 - The solar surface and atmosphere oTopics to be covered: oPhotosphere oChromosphere oTransition region oCorona

PY4A01 - Solar System Science The solar atmosphere oPhotosphere oT ~ 5,800 K od ~ 100 km oChromosphere oT ~ 10 5 K od <2000 km. oTransition Region oT ~ K od ~2500 km oCorona oT >10 6 K od >10,000 km

PY4A01 - Solar System Science The photosphere oT ~ 5,800 K or ~ R Sun oPhotosphere is the visible surface of the Sun. oAt the photosphere, the density drops off abruptly, and gas becomes less opaque. oEnergy can again be transported via radiation. Photons can escape from Sun. oPhotosphere contains many features: oSunspots oGranules  >>1 in photosphere

PY4A01 - Solar System Science The photosphere (cont.) oSunspots are dark areas in the photosphere. oFormed by the concentration of large magnetic fields (B>1000 G). oSunspots appear dark because they are cooler (~4,300 K). oGranulation is a small scale pattern of convective cells oResults from temperature gradients close to the solar surface.

PY4A01 - Solar System Science Photospheric granulation oAssume mass element in photosphere moves slowly and adiabatically (no energy exchange) oAmbient density and pressure decrease:    a oMass element expands and    i and T  T i oIf  i >  a => cell falls back (stable) oIf  i cell rises (unstable) oNow replace internal parameters with adiabatic:  i   ad, T i  T ad and  a   rad , T  i, T i  a, T a , T xx

PY4A01 - Solar System Science Photospheric granulation oNow, pressure inside cell must balance with outside pressure: P rad = P ad =>  rad T rad =  ad T ad oStable if |  ad | < |  rad | or over  x if or equivalently if oFrom equation of hydrostatic equilibrium (dP/dx =-  g) and the ideal gas law: oTherefore, stable if , T  i, T i  a, T a , T xx Schwartzchild criterion

PY4A01 - Solar System Science Determining the photospheric temperature. oThe Sun emits a blackbody spectrum with peak ~ 5100 Å oUsing Wein’s Law: and K peak

PY4A01 - Solar System Science The solar constant oWe know from Stephan-Boltzman Law that L = A  T 4 W oA is area of Sun’s surface, T is temperature, and  is Stephan-Boltzman constant (5.67  W m -2 K -4 ). oThe flux reaching the Earth is therefore: F = L / 4πd 2 = 4πR 2  T 4 / 4πd 2 Wm -2 [d = 1AU, R = solar radius] =  T 4 (R/d) 2 = 1396 W m -2 oThis is relatively close to the measured value of 1366 W m -2.

PY4A01 - Solar System Science The solar constant oThe “solar constant” actually has a tiny variation (<1%) with the solar cycle. oRepresents the driver for Earth and planet climate modelling.

PY4A01 - Solar System Science The chromosphere oAbove the photosphere is a layer of less dense but higher temperature gases called the chromosphere. oFirst observed at the edge of the Moon during solar eclipses. oCharacterised by “spicules”, “plage”, “filaments”, etc. oSpicules extend upward from the photosphere into the chromosphere.

PY4A01 - Solar System Science The chromosphere (cont.) oProminence and filaments are cool volumes of gas suspended above the chromosphere by magnetic fields. oPlage is hot plasma (relative to the chromosphere), usually located near sunspots.

PY4A01 - Solar System Science Model solar atmosphere

PY4A01 - Solar System Science The corona oHot (T >1MK), low density plasma (i.e. an ionized gas). oThere are currently two coronal heating theories: oMagnetic waves (AC). oMagnetic reconnection (DC). oCoronal dynamics and properties are dominated by the solar magnetic field. Yohkoh X-ray image

PY4A01 - Solar System Science Static model of the corona oAssuming hydrostatic equilibrium: where the plasma density is  =n (m e +m p ) ≈ nm p (m p = proton mass) and both electrons and protons contribute to pressure: P = 2 nkT = 2  kT/m p oSubstituting into Eqn.3, and integrating => where  0 is the density at r ~ R. oOK in low coronae of Sun and solar-type stars (and planetary atmospheres). Eqn. 3

PY4A01 - Solar System Science Static model of the corona oChapman (1957) attempted to model a static corona with thermal conduction. oCoronal heat flux is q =   T where thermal conductivity is  =  0 T 5/2, oIn absence of heat sources/sinks,  q = 0 =>  (  0 T 5/2  T) = 0 oIn spherical polar coordinates, Eqn. 1

PY4A01 - Solar System Science Static model of the corona oEqn. 1 => oSeparating variables and integrating: oTo ensure T = T 0 at r = r 0 and T ~ 0 as r  ∞ set oFor T = 2 x 10 6 K at base of corona, r o = 1.05 R => T ~ 4 x 10 5 K at Earth (1AU = 214R). Close to measured value. Eqn. 2

PY4A01 - Solar System Science Static model of the corona oSubing for T from Eqn. 2, and inserting for P into Eqn. 3 (i.e., including conduction), oUsing multiplication rule, Eqn. 4

PY4A01 - Solar System Science Static model of the corona oBoth electrons and protons contribute to pressure: P = 2 nkT = 2  kT/m p oSubstituting into Eqn. 4 => Eqn. 5 o As r  ∞, Eqn.4 =>   ∞ and Eqn. 5 => P  const >> P ISM. o P ISM ~ P 0. Eqn. 5 => P ~ P 0 => There must be something wrong with the static model.