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Chapter 11: The Sun Chapter 11: The Sun SOHO http://sohowww.nascom.nasa.gov/ Week 8 The Solar Interior Bahcall, Pinnsonneault, Basu 2001 (linked from class syllabus) will expand upon Chapter 11 in our book. http://www.physics.sfsu.edu/~fischer/courses/Astr420/hmwk/Bahcall_Pinsonneault_Basu.pdf Additional reading: http://www.physics.sfsu.edu/~fischer/courses/Astr420/hmwk/missing_neutrinos.pdf Solar atmosphere Solar Cycle Chapter 11: The Sun SOHO http://sohowww.nascom.nasa.gov/ Chapter 11: The Sun SOHO http://sohowww.nascom.nasa.gov/ SOHO’s orbit around the L1 point. Chapter 11: The Sun Chapter 11: The Sun The solar interior Is the Sun getting brighter or dimmer? Every second, the Sun turns 700 billion tons of protons into helium... At an age of about 4.5 Gyr, about half of the hydrogen in the core of the Sun has been fused into He. Current surface composition: X = 0.74, Y = 0.24, Z = 0.02. Current Central Conditions: Chapter 11: The Sun The solar interior Over the past 40 years, solar models have been refined, tested by observations of helioseismology (measuring pressure-mode oscillations and velocity fields as a function of radius and depth of the convective zone) and neutrino flux. The standard solar model (revised continuously) is a model constructed with the best physics and input data. Fits the observed luminosity and radiu of the sun at the present epoch, as well as the heavy-element-tohydrogen ratio. Constructed with OPAL EOS. Temperature 1.57 x 107 K Pressure 2.34 x 1016 N m-2 Density 1.527 x 105 kg m-3 X 0.34 Y 0.64 Chapter 11: The Sun The solar interior In 1982, the solar model consisted of 27 radial shells, with ten variables for each shell: mass, radius, temperature, density, hydrogen fraction, helium fraction, luminosity, and source density of p-p, 7Be, and 8B neutrinos. Current models have 875 shells, with additonal variables: pressure, electron number density, mass fractions of 3He, 7Be, 12C, 14N, 16O, and source densities for all eight of the most important solar neutrino fluxes. Chapter 11: The Sun The solar interior Time-dependent evolution of the Sun. Chapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as a function of solar age. As a result of changes to internal composition, the Sun is becoming larger and more luminous. At 1Gyr, red-circled p-p chain dominates. The situation changes as the Sun heats up - by 8Gyr, the CNO cycle becomes important. Chapter 11: The Sun Convective Zone The depth of the CZ is increasing with time (black curve) but is roughly proportional to the stellar radius at all times (red curve). Time is limited to 6.5Gyr because of the onset of semiconvection (triggered by element diffusion). As metals accumulate under the CZ, the opacity increases and the former radiative zone becomes convective. Metals mix into the CZ, and the boundary recedes as the opacity decreases. The mass of the CZ is decreasing with time (black curve) but is roughly proportional to the square of the stellar radius at all times (red curve). After 6.8Gyr, the CZ mass begins to increase. Chapter 11: The Sun Convective Zone Boundary The base of the CZ is defined by the Schwarzchild criterion; the density of an adiabatic cell decreases as it rises relative to the surrounding gas: !PL ~ const MT 4 Temperature and opacity change slowly, the increase of luminosity is compensated by a decrease in pressure at the boundary between radiative and convective equilibrium Chapter 11: The Sun Central values Tc ( t ) = const Rsun ( t ) Solar luminosity is derived from H-fusion, and Xc decreases by a factor of 2 from ZAMS to present time. Chapter 11: The Sun The solar interior Temperature and Pressure drop rapidly. The luminosity increases rapidly to a maximum value. The luminosity gradient peaks at the edge of the Hburning core. Chapter 11: The Sun The solar interior Radial composition of the Sun today. 3He is normally destroyed rapidly, but it has a longer lifetime at the top of the H-burning region where the temperatures are cooler than in the core. Chapter 11: The Sun Energy transport Schwarzchild condition for convection plotted vs radius. At the center of the Sun, the pressure gradient approaches that for convective instability. For stars where the CNO cycle takes place (more massive stars) the cores are unstable to convection. Convective zone Questions Stellar Pulsations Saskia Hekker (See Ch 14 in the textbook) Paper 1: Line Profine Analysis of the Pulsating Red Giant Star Eps Ophiuchi Paper 2: Pulsations detected in the line profile variations of red giants Discoveries •! 1595 David Fabricius observed o Ceti –! star vanished from the sky and re-appears month later ! Mira –! 11 month period variation of 7 magnitudes •! Name some groups of pulsating stars? •! Possible uses of pulsating stars? •! Types of pulsations? Discoveries •! 1784 John Goodricke observed ! Cephei –! variation less than 1 magnitude –! period 5 minutes, 8 hours, 48 minutes Cepheids •! late 1800s and start 1900s Henrietta Swan Leavitt discovered 2400 classical Cepheids in the SMC ! same distance •! More luminous Cepheids take longer to go through their pulsation cycle! " d % m ! M = 5log10 $ ' #10 pc & Period-luminosity relation Stellar oscillations occur in almost all phases of stellar evolution. However there exist a particular region in the HR diagram in which the density of pulsating stars is more outspoken than elsewhere: the classical instability strip Pulsation modes •! p-modes: acoustic waves, restoring force is pressure –! driven by ! mechanism –! driven by turbulent convection •! g-modes: restoring force is gravity –! driven by density fluctuations close to the core ! mechanism •! suggested by Eddington: if a layer of a star becomes more opaque upon compression it could hold the energy flowing towards to the surface and push the surface layers upward. The expanded layer would become more transparent, the trapped heat could escape and the layer would fall back. ! mechanism How could the opacity increase with compression? # ! " 3.5 Kramers law: T compression: !, T increase, opacity decrease special circumstances: partial ionization zones ! mechanism •! Hydrogen partial ionization zone: H I !H II, He I!He II @ 1.5 x 104 K •! He II partial ionization zone: He II!He III @ 4 X 104 K •! also partially ionized iron can cause the pulsation Internal gravity waves slight density changes close to the core of the star ! net force pushes it back to equilibrium position ! harmonic oscillation !in>!out !in=!out increasing pressure •! hot star Teff = 7500 K: ionization zone close to the surface ! density to low to drive pulsations ! blue edge instability strip •! cool star Teff = 5500 K: ionization zone deep enough to drive pulsations, BUT pulsations damped in outer layers due to convection ! red edge instability strip ! mechanism Internal gravity waves Solar-like oscillations •! rapid fluctuations close to the core •! damp towards the outer parts of the star •! not known to reach the surface of stars with a convective outer layer •! driven by turbulent convection in stellar atmosphere •! timescales shorter than fundamental radial period •! expected to be present in all stars with convective outer layers •! parameters: –! frequency –! number and orientation nodal lines Solar-like oscillations Solar-like oscillations •! n = number of nodal lines in radial direction •! l = number of nodal lines on surface •! m = orientation of nodal lines l=3,m=2 l=3,m=1 l=3,m=0 orientation rotation axis l=3,m=3 160 day observations with VIRGO on SOHO Solar-like Oscillations ! n,l 1 = "! (n + l + #) $ l(l + 1)D0 2 !!: large separation ! average density D0: small separation ! sound speed near the core !: constant sensitive to surface layers Solar-like oscillations •! amplitudes ! Luminosity / Mass ! m/s amplitudes in red giants •! frequency peak ! Mass / (Radius2 * !Teff) decreases from dwarfs to giants ! periods of a few hours in red giants Target Selection (spectroscopy) •! bright ! high signal to noise ratio observing time short enough not to average over a large fraction of the oscillation period. •! slow rotating ! narrow spectral lines •! no companions or spots •! low declination ! multi site campaign •! Red giants: -! ! Ophiuchi (G9.5III) -! ! Serpentis (K0III) -! ! Hydrae (G7III) -! ! Eridani (K0IV) (confirmed solar-like oscillators) ! Ophiuchi •! •! •! •! •! •! •! •! •! G 9.5 giant (De Ridder et al. 2006) mv = 3.24 ± 0.02 mag Mv = 0.65 ± 0.06 mag B - V = 0.96 ± 0.01 mag d = 33.0 ± 0.9 pc Teff = 4900 ± 100 K vsini = 3.4 ± 0.5 km/s dec = -04 41 33.0 ~ 900 observations over 3 month with CORALIE and ELODIE ! Ophiuchi ! Ophiuchi De Ridder et al. 2006 o Coralie data x Elodie data Period Analysis Fourier analysis: one tries to define a function of test frequencies in such a way that it reaches an extreme for the test frequency that is close to the true frequency present in the data. Observations show 1 day aliasing! ! Ophiuchi ! Ophiuchi 2 possible large separations: -! !! = 4.8 !Hz -! mass = 1.9 Msun -! !! = 6.9 !Hz -! mass = 2.8 Msun ! Ophiuchi Barban et al. 2006 How to get the modes? •! Line shape analysis MOST (Canadian microsatelite) observations, 28 consecutive days, !! ~ 5 !Hz Moments < v >= n # +" v n p(v)dv !" +" # !" p(v)dv ! Ophiuchi v: total velocity in line of site p(v): line profile line bisector <v>: the centroid of a spectral line <v2>: the width of the spectral line <v3>: skewness of the spectral line first moment variations over time in these moments provides information on oscillations other diagnostic: line bisector De Ridder et al. 2006 Line shape fits Line shape fits l=0,m=0 l=1,m=0 l=1,m=1 Line shape fits l=2,m=0 l=2,m=1 Line shape fits ! Ophiuchi l=2,m=2 ! Ophiuchi Evidence for non-radial modes in red giants: •! Not predicted so far by theory: only non-radial modes should be observable •! Important to derive the internal structure of the stars. Why? !=58.2!Hz !=67.5!Hz !=63.2!Hz Internal structure Derive in a quasi direct way the internal structure of a star! Chapter 11: The Sun What is the solar neutrino mystery? Chapter 11: The Sun Solar Neutrino Mystery How was it resolved? In a spectral line, is the core of the line formed deeper or higher up in the photosphere than the continuum? 4 p!4 He + 2e + + 2" e Two neutrinos produced in the p-p chain. If 700 billion tons of H are fused every second, where are the neutrinos? Should be 100 billion neutrinos passing through your thumbnail every second. However they are practically massless and weakly interacting. What is the typical size and lifetime of granulation cells? Only 1 out of every 100 billion neutrinos that pass through the Earth is expected to interact with material in the Earth. Neutrinos escape easily from the solar interior. Chapter 11: The Sun Three types of neutrinos !e !µ !" Chapter 11: The Sun Homestake Neutrino Detector Electron neutrinos - expected as by products of the pp chain. Raymond Davis built a neutrino detector in the Homestake Gold Mine in South Dakota. muon neutrinos The detector consisted of a tank filled with 100,000 gal of C2Cl4. Electron neutrinos interact with the isotope 37Cl, which undergoes radioactive decay to form 37Ar. Tau neutrinos No charge, each neutrino has its own anti-neutrino. Once thought to be massless. 37 17 37 Cl + ! e "18 Ar + e# The goal: to confirm hydrogen fusion as the energy source for the Sun. The threshold energy for this rxn is 0.814 eV, less than the neutrino energies produced in every step of the p-p chain except the first one. So, the detector was only sensitive to neutrinos coming from the decay of Boron: 8 5 B!48 Be + " e + e + Chapter 11: The Sun Chapter 11: The Sun Homestake Neutrino Detector The solar neutrino problem Kamiokande Every few months, the accumulated argon was purged from the detector. The capture rate was measured as: GALLEX 1 SNU = 10-36 rxns per target atom per second. SAGE Gallium detectors have a different energy threshold; measure low energy p-p chain neutrinos (theoretical predictions better for these neutrinos) 71 ! e + 31 Ga"3271Ga + e# Only 1/3 of the expected neutrinos were detected => the “Solar Neutrino Problem.” •!Wrong rate of production? •!Incorrect estimate of interaction in Chlorine detector to form 37Ar? Experimental design error? •!New neutrino physics? Super-Kamiokande: Inner volume of 32,000 tons of water surrounded by 11,000 PMT’s surrounded by 18,000 tons of water. The PMT’s detect pale blue Cherenkov light emitted when neutrinos scatter electrons, causing them to move faster than the speed of light in water. Confirmed the deficit of neutrinos: only 1/2 the expected number were detected. Chapter 11: The Sun Chapter 11: The Sun The solar neutrino problem The solar neutrino problem Meanwhile, the standard solar model was re-examined. Helioseismology measurements fit theoretical interior velocities to 0.1% accuracy, suggesting that the theoretical reaction rates were correct. Solar neutrino observatory (SNO): contained 1000 tons of D2O, surrounded by a steel structure containing 10000 PMTs. Observation mode that was sensitive to electron neutrinos only detected 1/3 the number predicted by the standard model. Combining the total number of neutrinos from all experiments (electron, muon, tau) gives the number of neutrinos expected from the standard model, but electron neutrinos only constituted about 1/3 of all these neutrinos. Mikheyev-Smirnov-Wolfstein (MSW) effect proposed: neutrinos change form. The standard model from particle physics only predicted electron neutrinos - the standard model was wrong. Chapter 11: The Sun Chapter 11: The Sun The solar neutrino problem The solar neutrino problem The SNO data showed that solar neutrinos are not missing. Most of the neutrinos that form in the core of the Sun undergo oscillations and change into muon and tau neutrinos by the time they reach Earth. In order for neutrinos to undergo oscillations, they must have mass (standard model assumed that they were massless). The simplest model now suggest neutrino masses that are 108 times smaller than the mass of an electron. Flavor Mass (GeV/c2) !e electron neutrino e- electron !! muon neutrino !! muon (mu-minus) !! tau neutrino !! tau (tau-minus) <7 x 10-9 0.000511 Electric Charge (e) 0 -1 0 <0.0003 0.106 <0.03 -1 0 1.7771 -1 Standard solar model vindicated! Standard model of particle physics had to be revised! Chapter 11: The Sun Chapter 11: The Sun The solar atmosphere The solar atmosphere Sun appears to have an edge, but the atmosphere changes fromopticaly thin ot optically thick over about 600 km (0.1% RSUN). Temperature in the photosphere varies from ~9400K at -100km (! ~ 23.6) to ~4400K at the top of the photosphere. Temperature reversal occurs going higher into the chromosphere. T = 5777K at !!= 2/3 Continuum opacity: H- even though only 1 in 107 H atoms forms H-, neutral H is transparent. Recall: Spectral lines formed at different depths in the photosphere. Spectral lines start forming at the same depth as the continuum, however the line cores are formed higher in the atmosphere where the gas is cooler and opacity is therefore greater. Chapter 11: The Sun The solar atmosphere Chapter 11: The Sun The solar atmosphere Typical cell size is 700 km Characteristic lifetime is 5 - 10 minutes Typical radial velocities of the cells: ~500 m/s Rotational speed varies with latitude and depth Chapter 11: The Sun Solar rotation From helioseismology, know that rotation changes with depth. The tachocline is the boundary between the core and convective zone (CZ). Strong shear in this region results in electric currents that likely generate the Sun’s magnetic field. Chapter 11: The Sun Differential rotation Rotation rate at the solar equator is about 25 days. At the poles it is about 36 days. Chapter 11: The Sun Chromosphere Chapter 11: The Sun Solar activity Lower densities, higher temperatures than the photosphere. Boltzmann-Saha equation shows that lines not formed in the photosphere can form in the chromosphere. HeII, FeII, SiII, CrII, CaII (H & K lines) Chapter 11: The Sun Chapter 11: The Sun Chapter 11: The Sun Corona Temperature rises through the transition zone. Since the density is low (10-10 times the density of air at sea level), the gas is not in LTE and there is not a well defined temerpature. Thermal motion, ionization levels and radio emissions give consistent results. The presence of FeXIV indicates temperatures greater than 1 x 106 K Chapter 11: The Sun Solar Wind Fast solar wind (longer solid red lines): continuous stream of charged particles moving at speeds of about 750 km/s. Gusty, slow, dense, solar wind (short, dashed red arrows): produced by streamers in the corona associated with magnetic fields. Travels at about half the speed of the fast solar wind. Chapter 11: The Sun Coronal Holes and the Solar Wind X-ray image of the sun shows bright regions that appear/disappear on timescales of hours. Closed magnetic field lines trap charged particles - the higher density of charged accelerating particles create bright spots at X-ray wavelengths. Dark coronal holes are tied to the global magetic field of the Sun. These holes are associated with regions where the magnetic field lines are open. Charged particles can flow out along the open field lines, creating a solar wind. Chapter 11: The Sun Corona If the velocity of solar wind particles above the Earth’s atmosphere (r = 1.5 x 108 km) is 500 km/s, and the density of the particles is 7 x 106 protons m-3, what is the mass loss rate from the Sun? (MSUN = 1.99 x 1030 kg) dM = !dV = ! ( 4 "r 2vdt ) dM = ! 4 "r 2v = 3 #10$14 M sun yr$1 dt Chapter 11: The Sun Chapter 11: The Sun For the past few days, the Earth has been passing through a stream of solar wind that is flowing out of this coronal hole (seen here on March 12-14, 2007). Since coronal holes are 'open' magnetically, strong solar wind gusts can escape from them and carry solar particles out to our magnetosphere and beyond. Solar wind streams take several days to travel from the Sun to Earth. The magnetic field lines in a coronal hole open out into the solar wind rather than connecting to a nearby part of the Sun's surface. Coronal Chapter 11: The Sun GM nm d (2nkT ) = ! SUN2 p dr r dn =! n Assume isothermal gas, collect terms and integrate " GM Sun m p % dr $ ' 2 # 2kT & r (1 1 + ( r+ r ln(n) r = C* ! - = !Cr0 *1! 0 ) r r0 , ) r0 , Let: !! = Cr0 n(r) = n 0e! .(1!r0 / r) Since: P0 = 2n 0 kT P(r) = P0e! .(1!r0 / r) Chapter 11: The Sun The Parker Wind Model P(r) = P0e! "(1!r0 / r) The Parker Wind Model The Parker Wind Model: how does the solar corona produce a solar wind? But the pressure does not go to zero as r approaches infinity. So, why does this derivation fail? One of our assumptions must be wrong. The isothermal assumption is not too bad - measuring the temperature of particles near the Earth ( r ~ 215 RSUN ), the wind has a temperature of about 105 K, similar to the corona. It is the assumption of hydrostatic equilibrium that is incorrect. Since P(infinity) exceeds the pressure in the ISM, material must be expanding outward from the Sun, implying the existence of a solar wind. dP GM SUN " =! dr r2 " = nm H 1 µ= 2 The eqn of …. Assume gas of ionized hydrogen "kT = 2nkT µm H GM nm d (2nkT ) = ! SUN2 p dr r Pg = Chapter 11: The Sun Chapter 11: The Sun Hydrodynamic equations 2 Hydrodynamic equations d r dv dv dr dv = = =v 2 dt dt dr dt dr ! Replace hydrostatic equations with hydrodynamic equations d 2r dv dP GM r ! = !v =" " 2 dt dr dr r2 4 #r 2 !v = const d ( !vr 2 ) dr =0 Conservation of mass flow across a boundary: at the top of the CZ, the motion of hot rising gas and the return flow of cool gas sets up longitudinal waves (pressure waves) that propagate outward through the photosphere and into the chromosphere. Chapter 11: The Sun 1 FE = !v w2 v sound 2 v sound = "P / ! v sound = 8:05 Supersonic flow 1 FE = !v w2 v sound 2 v sound " T The outward flux of energy "kT # T µm H Sound speed: proportional to the square root of the temperature. Calculate the speed of the particle wave (solar wind). Each white tick is one solar radius. The velocity amplitude of particles in the solar wind, vw, starts out less than the sound speed. But, the density of gas decreases by 4 orders of magnitude over 1000km through the transition zone. The sound speed changes by sqrt(2) because the temperature change is only a factor of 2. As a result, the wave speed quickly becomes supersonic (Vw > Vs). The pressure wave develops into a shock wave. As a shock moves through gas, it produces heating through collisional, turbulent motion and the gas behind the shock is highly ionized. The shock quickly dissipates. Thus, gas in the chromosphere and above is effectively heated by mass motions in the CZ. 11:23 Chapter 11: The Sun Chapter 11: The Sun Magnetohydrodynamics and Alfven waves The temperature gradient through the corona is also tied to the presence of a magnetic field, coupled with dynamo motion in the CZ. MHD is the study of the interactions between magnetic fields and plasmas. B2 2µ0 Energy is needed to create a magnetic field - that energy is stored in the field as the magnetic energy density. B2 Pm = µm = 2µ0 If you were to compress the field, the work done: W = ! PdV µm = Magnetohydrodynamics and Alfven waves When the magnetic field line is displaced, a magnetic pressure gradient is established that tends to push back in the opposite direction to restore the original field line position. v sound = !Pg " v Alfven = Pm B = " µ0 " would be stored in the magnetic field. Therefore, the magnetic pressure is equal to the magnetic energy density. Chapter 11: The Sun Chapter 11: The Sun Speed of Sound and Alfven waves in the Sun The gas pressure at the top of the photosphere is about 140 N m-2, with a density of 4.9 x 10-6 kg m-3. The surface magnetic field strength is about 2 x 10-4 T. Assuming an ideal monatomic gas, calculate the sound speed and Alfven speeds v sound = !Pg " v Alfven = B µ0 " Sqrt[(5/3)*140./4.9e-6] = 7000 ms-1 (0.0002 / sqrt((1.2e-6 * 4.9e-6) ) = 85 ms-1 (negligible) Parker Spiral The rotation of the Sun drags the magnetic field lines, transferring angular momentum away from the Sun. The Parker Spiral is the shape of the Sun’s extended magnetic field. Results in a change in the shape of the Suns magnetic field beyond 10 - 20 AU from poloidal to toroidal. The Parker Spiral may be responsible for the differential rotation observed in the Sun. Adiabatic sound speed By analogy, the Alfven wave velocity increases with the strength of the magnetic field Chapter 11: The Sun Solar constant? Chapter 11: The Sun Solar constant? Solar minimum now what is the impact on global climate change? Chapter 11: The Sun Butterfly diagram Chapter 11: The Sun Maunder Minimum One of the most welldocumented connection between solar activity and climate change is the Maunder Minimum. This was a 40-year period when extreme cold weather prevailed in Europe. It also coincided with astronomers watching the sun and not seeing many sunspots! Eddy pointed this out in the 1970's, and since then many other sun-climate connections have been looked for and in some cases uncovered. Chapter 11: The Sun Chapter 11: The Sun Solar Plages At optical wavelengths, the darkness of spots is caused by cooler temperatures. The temperature in the central spots may be as low as 3900K compared to 5770K for the effective temperature of the Sun Chapter 11: The Sun Bright H-alpha emission in the chromosphere, around sunspots. Plages are particularly visible when photographed through filters passing the spectral light of hydrogen or calcium. The adjacent image shows plages near a sunspot (the white cloud-like feature) as imaged by the Big Bear Solar Observatory Chapter 11: The Sun Solar Flares Solar Prominences Release 1017- 1025 J of energy in time intervals of minutes to hours. Magnetic field lines are associated with creation of a sheet of current in the highly conducting plasma, heats temperatures to 107K. Surface nuclear reactions, spallation, break down heavier elements into lighter ones. This is the one way for lithium to be created. Solar prominences are cooler clouds of gas that float above the solar surface. Prominences are not very stable and quite often they do break away from the Sun when the magnetic forces that hold it in place become disrupted. Neither the previous image taken just six hours before this or the one taken six hours later show any sign of a filament. At about the time prominence this appeared, another instrument on SOHO observed a solar outburst called a "streamer" eruption near the same general area of this prominence. Chapter 11: The Sun Coronal Mass Ejections More spectacular, CME’s average to about 1 per day. When sunspot activity is stronger, there may be 3-4 per day. During sunspot minima, there will only be one CME every few days. Generally associated with solar prominences. Up to 1013 kg material may be ejected at speeds exceeding 1000 km/s.