chapter 11: the sun - sfsu physics & astronomyfischer/courses/astr420/lectures/ch11.pdfchapter...

26
Chapter 11: The Sun 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/ Chapter 11: The Sun SOHO http://sohowww.nascom.nasa.gov/ SOHO’s orbit around the L1 point.

Upload: others

Post on 29-Dec-2019

7 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

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/

Chapter 11: The Sun

SOHO http://sohowww.nascom.nasa.gov/

SOHO’s orbit around

the L1 point.

Page 2: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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:

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

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-to-

hydrogen ratio.

Constructed with OPAL EOS.

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.

Page 3: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

The solar interior

Time-dependent evolution

of the Sun.

As a result of changes to

internal composition, the

Sun is becoming larger

and more luminous.

Chapter 11: The Sun

The solar interior

Energy generation by different nuclear

fusion rxns as a function of solar age.

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

MT4~ const

Temperature and opacity

change slowly, the increase of

luminosity is compensated by

a decrease in pressure at the

boundary between radiative

and convective equilibrium

Page 4: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

Central values

Tct( )

Rsun

t( )= const

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

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.

Convective zone

Chapter 11: The Sun

The solar interior

The luminosity increases

rapidly to a maximum value.

The luminosity gradient

peaks at the edge of the H-

burning core.

Temperature and Pressure

drop rapidly.

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.

Page 5: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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

Questions

•! Name some groups of pulsating stars?

•! Possible uses of pulsating stars?

•! 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

Page 6: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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!

m !M = 5log10d

10pc

"

# $

%

& '

Period-luminosity relation

Page 7: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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.

Page 8: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

! mechanism

How could the opacity increase with compression?

Kramers law:

compression: !, T increase, opacity

decrease

special circumstances:

partial ionization zones

! "#

T3.5

! 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

! mechanism

•! 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

Internal gravity waves

slight density changes close to the core of

the star ! net force pushes it back to

equilibrium position ! harmonic

oscillation incre

asin

g p

ressu

re

!in>!out

!in=!out

Page 9: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Internal gravity waves

•! 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

Solar-like oscillations

•! 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

•! n = number of nodal lines in radial

direction

•! l = number of nodal lines on surface

•! m = orientation of nodal lines

l=3,m=3 l=3,m=0 l=3,m=1 l=3,m=2

orie

nta

tion

rota

tion

axis

Solar-like oscillations

160 day observations with VIRGO on SOHO

Page 10: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Solar-like Oscillations

!!: large separation ! average density

D0: small separation ! sound speed near the core

!: constant sensitive to surface layers

!n,l

= "!(n +1

2l + #) $ l(l +1)D

0

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)

Page 11: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

! 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

o Coralie data

x Elodie data

De Ridder et al. 2006

! 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!

Page 12: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

! Ophiuchi ! Ophiuchi

2 possible large separations:

-! !! = 4.8 !Hz

-! mass = 1.9 Msun

-! !! = 6.9 !Hz

-! mass = 2.8 Msun

! Ophiuchi

MOST (Canadian microsatelite) observations, 28

consecutive days, !! ~ 5 !Hz

Barban et al. 2006 How to get the modes?

•! Line shape analysis

Page 13: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Moments

<v>: the centroid of a spectral line

<v2>: the width of the spectral line

<v3>: skewness of the spectral line

variations over time in these moments

provides information on oscillations

other diagnostic: line bisector

< vn

>=

vnp(v)dv

!"

+"

#p(v)dv

!"

+"

#

v: total velocity in line of site

p(v): line profile

! Ophiuchi

line bisector

first moment

De Ridder et

al. 2006

Line shape fits Line shape fits

l=0,m=0 l=1,m=0 l=1,m=1

Page 14: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Line shape fits

l=2,m=0 l=2,m=1 l=2,m=2

Line shape fits ! Ophiuchi

!=58.2!Hz !=63.2!Hz

!=67.5!Hz

! 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?

Internal structure

Derive in a quasi

direct way the

internal structure

of a star!

Page 15: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

What is the 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?

What is the typical size and lifetime of

granulation cells?

Chapter 11: The Sun

Solar Neutrino Mystery

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.

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.

4 p!4He + 2e

++ 2" e

Chapter 11: The Sun

Three types of neutrinos

!e

! µ

!"

Electron neutrinos - expected as by products

of the pp chain.

muon neutrinos

Tau neutrinos

No charge, each neutrino has its own anti-neutrino.

Once thought to be massless.

Chapter 11: The Sun

Homestake Neutrino Detector

Raymond Davis built a neutrino detector in the

Homestake Gold Mine in South Dakota.

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.

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:

17

37Cl + !

e"

18

37Ar + e

#

5

8B!

4

8Be + "

e+ e

+

Page 16: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

Homestake Neutrino Detector

Every few months, the accumulated argon was purged from

the detector. The capture rate was measured as:

1 SNU = 10-36 rxns per target atom per second.

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?

Chapter 11: The Sun

The solar neutrino problem

Kamiokande

GALLEX

SAGE

Gallium detectors have a different energy threshold;

measure low energy p-p chain neutrinos (theoretical

predictions better for these neutrinos)

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.

!e

+31

71Ga"

32

71Ga+ e

#

Chapter 11: The Sun

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.

Chapter 11: The Sun

The solar neutrino problem

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.

Page 17: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

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.

Standard solar model vindicated!

Standard model of particle physics had to be revised!

Chapter 11: The Sun

The solar neutrino problem

Flavor Mass Electric Charge

(GeV/c2) (e)

!e electron neutrino <7 x 10-9 0

e- electron 0.000511 -1

!! muon neutrino <0.0003 0

!! muon (mu-minus) 0.106 -1

!! tau neutrino <0.03 0

!! tau (tau-minus) 1.7771 -1

Chapter 11: The Sun

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.

Chapter 11: The Sun

The solar atmosphere

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.

Page 18: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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.

Page 19: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

Chromosphere

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

Solar activity

Chapter 11: The Sun Chapter 11: The Sun

Page 20: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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

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

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

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"r2vdt( )dM

dt= ! 4"r2v = 3#10$14Msun yr

$1

Page 21: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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

d

dr2nkT( ) = !

GMSUNnmp

r2

dn

n= !

GMSunmp

2kT

"

# $

%

& ' dr

r2

ln(n)r0

r= C

1

r!1

r0

(

) *

+

, - = !Cr0 1!

r

r0

(

) *

+

, -

n(r) = n0e!. 1!r0 / r( )

P(r) = P0e!. 1!r0 / r( )

Assume isothermal gas,

collect terms and integrate

Let: !! = Cr0

P0

= 2n0kTSince:

The Parker Wind Model

Chapter 11: The Sun

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.

P(r) = P0e!" 1!r0 / r( )

The Parker Wind Model

Chapter 11: The Sun

The Parker Wind Model: how does the solar corona

produce a solar wind?

dP

dr= !

GMSUN"

r2

" = nmH

µ =1

2

Pg ="kT

µmH

= 2nkT

d

dr2nkT( ) = !

GMSUNnmp

r2

The eqn of ….

Assume gas of

ionized hydrogen

Page 22: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

Replace hydrostatic equations with

hydrodynamic equations

d2r

dt2

=dv

dt=dv

dr

dr

dt= v

dv

dr

!d2r

dt2

= !vdv

dr= "

dP

dr"GM

r!

r2

4#r2!v = const

d !vr2( )dr

= 0

Hydrodynamic equations

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

The outward flux of energy

FE

=1

2!v

w

2vsound

vsound

= "P /!

vsound

="kT

µmH

# T

Hydrodynamic equations

Sound speed: proportional to the

square root of the temperature.

Chapter 11: The Sun

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.

FE

=1

2!v

w

2vsound

vsound

" T

Supersonic flow

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.

8:05

11:23

Calculate the speed of the

particle wave (solar wind).

Each white tick is one solar

radius.

Page 23: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

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.

Magnetohydrodynamics and Alfven waves

Energy is needed to create a magnetic field - that

energy is stored in the field as the magnetic energy density.

If you were to compress the field, the work done:

would be stored in the magnetic field. Therefore,

the magnetic pressure is equal to the magnetic energy density.

µm

=B2

2µ0

Pm

= µm

=B2

2µ0

W = PdV!

Chapter 11: The Sun

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.

Magnetohydrodynamics and Alfven waves

Adiabatic sound speed

vsound =!Pg

"

vAlfven =Pm

"=

B

µ0"

By analogy, the Alfven wave

velocity increases with the

strength of the magnetic field

Chapter 11: 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

Speed of Sound and Alfven waves in the Sun

Sqrt[(5/3)*140./4.9e-6] = 7000 ms-1

vsound =!Pg

"

vAlfven =B

µ0" (0.0002 / sqrt((1.2e-6 * 4.9e-6) ) = 85 ms-1

(negligible)

Chapter 11: The Sun

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.

Parker Spiral

Page 24: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

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 well-

documented 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.

Page 25: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

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

Solar Plages

Chapter 11: The Sun

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 Flares

Chapter 11: The Sun

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.

Solar Prominences

Page 26: Chapter 11: The Sun - SFSU Physics & Astronomyfischer/courses/Astr420/lectures/Ch11.pdfChapter 11: The Sun The solar interior Energy generation by different nuclear fusion rxns as

Chapter 11: The Sun

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.

Coronal Mass Ejections