Chapter 11: The 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

Chapter 11: The Sun Chapter 11: The Sun

SOHO http://sohowww.nascom.nasa.gov/ 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 into ... At an age of about 4.5 Gyr, about half of the 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:

Temperature 1.57 x 107 K 2.34 x 1016 N m-2 1.527 x 105 kg m-3 X 0.34 Y 0.64

Chapter 11: The Sun Chapter 11: The Sun

The solar interior The solar interior

Over the past 40 , solar models have been refined, tested by observations of (measuring pressure-mode oscillations In 1982, the solar model consisted of 27 radial shells, with ten and velocity fields as a function of radius and depth of the convective variables for each shell: mass, radius, , density, zone) and flux. hydrogen fraction, helium fraction, , and source density of p-p, 7Be, and 8B . The (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 , as well as the heavy-element-to- Current models have 875 shells, with additonal variables: hydrogen ratio. pressure, number density, mass fractions of 3He, 7Be, 12 14 16 Constructed with OPAL EOS. C, N, O, and source for all eight of the most important fluxes. Chapter 11: The Sun Chapter 11: The Sun

The solar interior The solar interior

Time-dependent evolution Energy generation by different nuclear of the Sun. 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 Chapter 11: The Sun

Convective Zone Convective Zone Boundary

The depth of the CZ is increasing with time (black curve) but is roughly proportional to the The base of the CZ is stellar radius at all times (red curve). defined by the Schwarzchild criterion; Time is limited to 6.5Gyr because of the onset the density of an of semiconvection (triggered by element adiabatic cell decreases diffusion). As metals accumulate under the as it rises relative to the CZ, the opacity increases and the former surrounding gas: radiative zone becomes convective. Metals mix into the CZ, and the boundary recedes as !PL the opacity decreases. ~ const MT 4

The mass of the CZ is decreasing with time Temperature and opacity (black curve) but is roughly proportional to the change slowly, the increase of square of the stellar radius at all times (red luminosity is compensated by curve). After 6.8Gyr, the CZ mass begins to a decrease in pressure at the increase. boundary between radiative and convective equilibrium Chapter 11: The Sun Chapter 11: The Sun

Central values The solar interior Convective zone

Tc (t) = const Rsun (t) Radial composition of the Sun today. 3He is normally destroyed rapidly, but it has a longer lifetime is derived from at the top of the H-burning region H-fusion, and X decreases by c where the are a factor of 2 from ZAMS to cooler than in the core. present time.

Chapter 11: The Sun Chapter 11: The Sun

The solar interior Energy transport

Schwarzchild condition for Temperature and Pressure convection plotted vs radius. drop rapidly. At the center of the Sun, the pressure gradient approaches that for convective instability. For where the CNO cycle takes place (more The luminosity increases massive stars) the cores are rapidly to a maximum value. unstable to convection. The luminosity gradient peaks at the edge of the H- burning core. Questions

Stellar Pulsations •! Name some groups of pulsating stars? Saskia Hekker (See Ch 14 in the textbook) •! Possible uses of pulsating stars?

Paper 1: Line Profine Analysis of the Pulsating Red Giant Eps Ophiuchi Paper 2: Pulsations detected in the line profile variations of red giants •! Types of pulsations?

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 Discoveries

•! 1784 John Goodricke observed ! Cephei –!variation less than 1 magnitude –!period 5 minutes, 8 hours, 48 minutes

Cepheids Period-luminosity relation

•! 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$ ' # 10pc&

Stellar oscillations occur in almost all phases of . 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 ! mechanism

•! p-modes: acoustic waves, restoring •! suggested by Eddington: if a layer of a force is pressure star becomes more opaque upon –!driven by ! mechanism compression it could hold the energy –!driven by turbulent convection flowing towards to the surface and push •! g-modes: restoring force is gravity the surface layers upward. The –!driven by density fluctuations close to the expanded layer would become more core transparent, the trapped heat could escape and the layer would fall back. ! mechanism ! mechanism

How could the opacity increase with •! Hydrogen partial zone: compression? 4 # H I !H II, He I!He II @ 1.5 x 10 K Kramers law: ! " T 3.5 •! He II partial ionization zone: He II!He III @ 4 X 104 K compression: !, T increase, opacity •! also partially ionized can cause the decrease pulsation special circumstances: partial ionization zones

! mechanism Internal gravity waves

•! hot star Teff = 7500 K: ionization zone close slight density changes close to the core of to the surface ! density to low to drive the star ! net force pushes it back to pulsations ! blue edge instability strip equilibrium position ! harmonic

oscillation increasing pressure •! cool star Teff = 5500 K: ionization zone deep

enough to drive pulsations, BUT pulsations !in>!out damped in outer layers due to convection ! red edge instability strip !in=!out Internal gravity waves Solar-like oscillations

•! rapid fluctuations close to the core •! driven by turbulent convection in stellar •! damp towards the outer parts of the star atmosphere •! not known to reach the surface of stars •! timescales shorter than fundamental with a convective outer layer 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 160 day observations with VIRGO on SOHO direction •! l = number of nodal lines on surface •! m = orientation of nodal lines rotation axis orientation

l=3,m=3 l=3,m=2 l=3,m=1 l=3,m=0 Solar-like Oscillations Solar-like oscillations 1 ! n,l = "!(n + l + #) $ l(l +1)D0 2 •! amplitudes ! Luminosity / Mass !!: large separation ! average density ! m/s amplitudes in red giants D0: small separation ! sound speed near the core !: constant sensitive to surface layers •! 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 •! Red giants: observing time short enough not to -! ! Ophiuchi (G9.5III) average over a large fraction of the -! ! Serpentis (K0III) oscillation period. -! ! Hydrae (G7III) •! slow rotating narrow spectral lines ! -! ! Eridani (K0IV) •! no companions or spots (confirmed solar-like • low multi site campaign ! ! oscillators) ! Ophiuchi ! Ophiuchi

•! G 9.5 giant (De Ridder et al. 2006) 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 o Coralie data •! ~ 900 observations over 3 month with CORALIE and ELODIE x Elodie data

! Ophiuchi 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 How to get the modes? Barban et al. 2006

•! Line shape analysis

MOST (Canadian microsatelite) observations, 28 consecutive days, !! ~ 5 !Hz Moments ! Ophiuchi

+" n v p(v)dv v: total velocity in line of site n #!" < v >= +" p(v)dv p(v): line profile #!" line bisector : the centroid of a spectral line : the width of the spectral line : 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 Line shape fits ! Ophiuchi

l=2,m=0 l=2,m=1 l=2,m=2 !=58.2!Hz !=63.2!Hz !=67.5!Hz

! Ophiuchi Internal structure

Evidence for non-radial modes in red giants: Derive in a quasi •! Not predicted so far by theory: only non-radial direct way the modes should be observable internal structure •! Important to derive the internal structure of the stars. Why? of a star! Chapter 11: The Sun Chapter 11: The Sun

What is the solar neutrino mystery? Solar Neutrino Mystery How was it resolved? Two neutrinos produced in the p-p chain. In a spectral line, is the core of the line formed 4 + 4 p! He + 2e + 2" e If 700 billion tons of H are fused every deeper or higher up in the than the second, where are the neutrinos? continuum? Should be 100 billion neutrinos passing through your thumbnail every second. What is the typical size and lifetime of However they are practically massless granulation cells? and weakly interacting. Only 1 out of every 100 billion neutrinos that pass through the is expected to interact with material in the Earth. Neutrinos escape easily from the solar interior.

Chapter 11: The Sun Chapter 11: The Sun

Three types of neutrinos Homestake

Electron neutrinos - expected as by products Raymond Davis built a neutrino detector in the ! e of the pp chain. Homestake Gold Mine in South Dakota.

! muon neutrinos The detector consisted of a tank filled with 100,000 gal of µ 37 C2Cl4. Electron neutrinos interact with the isotope Cl, which undergoes radioactive decay to form 37Ar. !" Tau neutrinos 37 37 # 17Cl + ! e"18 Ar + e No charge, each neutrino has its own anti-neutrino. Once thought to be massless. 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 :

8 8 + 5 B!4 Be + " e + e

Chapter 11: The Sun Chapter 11: The Sun

Homestake Neutrino Detector The Kamiokande Every few months, the accumulated was purged from GALLEX detectors have a different energy threshold; the detector. The capture rate was measured as: measure low energy p-p chain neutrinos (theoretical predictions better for these neutrinos) 1 SNU = 10-36 rxns per target atom per second. SAGE Only 1/3 of the expected neutrinos were detected => the 71 71 # ! e + 31Ga"32 Ga + e “Solar Neutrino Problem.” •!Wrong rate of production? Super-Kamiokande: Inner volume of 32,000 tons •!Incorrect estimate of interaction in detector of water surrounded by 11,000 PMT’s surrounded to form 37Ar? Experimental design error? by 18,000 tons of water. The PMT’s detect pale •!New neutrino physics? blue Cherenkov light emitted when neutrinos scatter , 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 Combining the total number of neutrinos from all experiments measurements fit theoretical interior velocities to 0.1% accuracy, (electron, muon, tau) gives the number of neutrinos expected from suggesting that the theoretical reaction rates were correct. the , but electron neutrinos only constituted about 1/3 of all these neutrinos. Mikheyev-Smirnov-Wolfstein (MSW) effect proposed: neutrinos Solar neutrino observatory (SNO): change form.

contained 1000 tons of D2O, surrounded The standard model from only predicted electron by a steel structure containing 10000 neutrinos - the standard model was wrong. PMTs. Observation mode that was sensitive to electron neutrinos only detected 1/3 the number predicted by the standard model. Chapter 11: The Sun Chapter 11: The Sun

The solar neutrino problem The solar neutrino problem

Flavor Mass Electric Charge The SNO data showed that solar neutrinos are not missing. (GeV/c2) (e) 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 !e <7 x 10-9 0 reach Earth. In order for neutrinos to undergo oscillations, they must e- electron 0.000511 -1 muon neutrino <0.0003 0 have mass (standard model assumed that they were massless). The !! ! simplest model now suggest neutrino masses that are 108 times ! muon (mu-minus) 0.106 -1 ! tau neutrino <0.03 0 smaller than the mass of an electron. ! !! tau (tau-minus) 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

Recall: Spectral lines Sun appears to have an edge, but the atmosphere changes fromopticaly thin formed at different depths ot optically thick over about 600 km in the photosphere.

(0.1% RSUN). Spectral lines start forming at the same Temperature in the photosphere varies depth as the continuum, from ~9400K at -100km (! ~ 23.6) to ~4400K at the top of the photosphere. however the line cores are formed higher in the Temperature reversal occurs going atmosphere where the higher into the . gas is cooler and opacity T = 5777K at !!= 2/3 is therefore greater. Continuum opacity: H- even though only 1 in 107 H atoms forms H-, neutral H is transparent. Chapter 11: The Sun Chapter 11: The Sun

The solar atmosphere 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 Chapter 11: The Sun

Solar rotation Differential rotation

From helioseismology, know that rotation changes with depth. The 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. Rotation rate at the solar equator is about 25 days. At the poles it is about 36 days. Chapter 11: The Sun Chapter 11: The Sun

Chromosphere 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 Chapter 11: The Sun

Corona Coronal Holes and the

X-ray image of the sun shows bright Temperature rises through the regions that appear/disappear on transition zone. Since the density is timescales of hours. Closed magnetic -10 low (10 times the density of air at field lines trap charged particles - the sea level), the gas is not in LTE and higher density of charged accelerating there is not a well defined particles create bright spots at X-ray temerpature. Thermal motion, wavelengths. ionization levels and radio emissions give consistent results. The Dark coronal holes are tied to the global presence of FeXIV indicates magetic field of the Sun. These holes are temperatures greater than 1 x 106 K 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 Chapter 11: The Sun

Solar Wind 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 30 Fast solar wind (longer solid red rate from the Sun? (MSUN = 1.99 x 10 kg) lines): continuous stream of charged particles moving at speeds of about 750 km/s. 2 Gusty, slow, dense, solar wind dM = !dV = !(4"r vdt) (short, dashed red arrows): dM produced by streamers in the 2 $14 $1 = ! 4"r v = 3#10 Msun yr corona associated with magnetic dt fields. Travels at about half the speed of the fast solar wind.

Chapter 11: The Sun Chapter 11: The Sun

The Parker Wind Model For the past few days, the Earth has been passing through a stream of solar d GM nm (2nkT) = ! SUN p Assume isothermal gas, wind that is flowing out of this dr r2 collect terms and integrate (seen here on March 12-14, 2007). Since " GM m % coronal holes are 'open' dn Sun p dr = ! $ ' 2 magnetically, strong solar n # 2kT & r wind gusts can escape from them and carry solar ( + ( + particles out to our r 1 1 r ln(n) = C ! = !Cr0 1! Let: !! = Cr r0 * - * - 0 magnetosphere and beyond. ) r r0 , ) r0 , Solar wind streams take several days to travel from n(r) = n e!.(1!r0 / r) the Sun to Earth. 0

The magnetic field lines in a !.(1!r0 / r) Since: P0 = 2n0kT P(r) = P0e 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 Chapter 11: The Sun

The Parker Wind Model The Parker Wind Model: how does the solar corona produce a solar wind? But the pressure does not go !"(1!r0 / r) dP GM " P(r) = P0e to zero as r approaches SUN The eqn of …. = ! 2 infinity. So, why does this dr r derivation fail?

" = nmH One of our assumptions must be wrong. The isothermal 1 Assume gas of µ = ionized hydrogen assumption is not too bad - measuring the temperature of 2 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 that is incorrect. "kT Pg = = 2nkT Since P(infinity) exceeds the pressure in the ISM, material µmH must be expanding outward from the Sun, implying the d GM nm existence of a solar wind. (2nkT) = ! SUN p dr r2

Chapter 11: The Sun Chapter 11: The Sun

Hydrodynamic equations Hydrodynamic equations 2 d r dv dv dr dv Replace hydrostatic equations with 2 = = = v hydrodynamic equations 1 2 dt dt dr dt dr F = !v v The outward flux of energy E 2 w sound

2 d r dv dP GMr! ! 2 = !v = " " 2 dt dr dr r vsound = "P /!

2 4#r !v = const "kT Conservation of mass flow across a boundary: v = # T Sound speed: proportional to the at the top of the CZ, the motion of hot rising gas sound µm square root of the temperature. and the return flow of cool gas sets up H d !vr2 longitudinal waves (pressure waves) that ( ) = 0 propagate outward through the photosphere dr and into the chromosphere.

Chapter 11: The Sun 8:05 Calculate the speed of the Supersonic flow particle wave (solar wind). Each white tick is one . 1 F v 2 v The velocity amplitude of particles in the solar E = ! w sound wind, v , starts out less than the sound speed. 2 w But, the density of gas decreases by 4 orders of magnitude over 1000km through the transition zone. The sound speed changes by vsound " T sqrt(2) because the temperature change is only a factor of 2. 11:23

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. Chapter 11: The Sun Chapter 11: The Sun

Magnetohydrodynamics and Alfven waves Magnetohydrodynamics and Alfven waves

The temperature gradient through the corona is also tied to When the magnetic field line is displaced, a magnetic the presence of a magnetic field, coupled with dynamo pressure gradient is established that tends to push back in motion in the CZ. MHD is the study of the interactions the opposite direction to restore the original field line position. between magnetic fields and plasmas.

2 B Energy is needed to create a magnetic field - that !Pg µ = vsound = Adiabatic sound speed m 2µ energy is stored in the field as the magnetic " 0 energy density.

P B v = m = By analogy, the Alfven wave 2 Alfven B If you were to compress the field, the work done: " µ0" P = µ = velocity increases with the m m W = PdV 2µ0 ! strength of the magnetic field 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 Parker Spiral

The gas pressure at the top of the photosphere is about 140 N m-2, The rotation of the Sun with a density of 4.9 x 10-6 kg m-3. The surface magnetic field strength drags the magnetic field is about 2 x 10-4 T. Assuming an ideal monatomic gas, calculate the lines, transferring angular sound speed and Alfven speeds momentum away from the Sun. The Parker Spiral is the !P v = g Sqrt[(5/3)*140./4.9e-6] = 7000 ms-1 shape of the Sun’s extended sound " magnetic field. Results in a change in the shape of the magnetic field beyond 10 - 20 AU from poloidal to B toroidal. The Parker Spiral v = -1 Alfven (0.0002 / sqrt((1.2e-6 * 4.9e-6) ) = 85 ms may be responsible for the µ0" (negligible) differential rotation observed in the Sun.

Chapter 11: The Sun Chapter 11: The Sun

Solar constant? Solar constant?

Solar minimum now - what is the impact on global climate change?

Chapter 11: The Sun Chapter 11: The Sun Butterfly diagram One of the most well- documented connection between solar activity and climate change is the Maunder Minimum. This was a 40- period when extreme cold weather prevailed in Europe. It also coincided with astronomers watching the sun and not seeing many ! 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 Bright H-alpha emission temperature in the central in the chromosphere, spots may be as low as around sunspots. Plages 3900K compared to are particularly visible 5770K for the effective when photographed temperature of the Sun through filters passing the spectral light of hydrogen or calcium. The adjacent image shows plages near a (the white cloud-like feature) as imaged by the Big Bear

Chapter 11: The Sun Chapter 11: The Sun

Solar Flares Solar Prominences

Release 1017- 1025 J of energy in time intervals of Solar prominences are cooler minutes to hours. clouds of gas that float above the solar surface. Magnetic field lines are associated with creation Prominences are not very stable of a sheet of current in and quite often they do break away the highly conducting from the Sun when the magnetic , heats forces that hold it in place become temperatures to 107K. disrupted. Neither the previous image taken just six hours before Surface nuclear this or the one taken six hours later reactions, spallation, show any sign of a filament. break down heavier elements into lighter At about the time prominence this ones. This is the one way appeared, another instrument on for to be created. 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.