Lecture 13Lecture 13

Review: Static Stellar structure Review: Static Stellar structure equationsequations

2r

GM

dr

dP r

24 rdr

dM r

Hm

kTP

Hydrostatic equilibrium:

Mass conservation:

Equation of state:

24 rdr

dLr Energy generation:

3264

3

Tr

L

dr

dT r

2

11

r

GM

k

m

dr

dT rH

Radiation

Convection

PPolytropeor

The Solar modelThe Solar model

• In this way we can build up a model of the interior structure of the Sun

• In general the differential equations are solved numerically

• Instead of assuming a polytrope, choose the temperature gradient depending on the mode of energy transport

•Boundary conditions:in the simplest case, , P and T

=0 at r=RM,L=0 at r=0

Convection zones in the SunConvection zones in the Sun

For the solar model we can plot dlnP/dlnT as a function of radius. Where this is >2.5, radiation is the most effective form of energy transport.

The Solar interiorThe Solar interior

The interior can be divided into three regions:

1. Core: site of nuclear reactions

2. The radiative zone3. The convective zone

Abundance distributionAbundance distribution

•H is depleted in the core, where He is produced• is an intermediate species in the pp chain. It is most

abundant at the top of the H-burning region, where the temperature is lower.

•Abundances are homogeneous within the convective zone, since the plasma is effectively mixed

He32

The solar model: evolutionThe solar model: evolution

• As the abundances in the core change, the nuclear reaction rates change accordingly, and the luminosity, temperature and radius of the star are affected.

Energy productionEnergy production

Although nuclear reaction rates are higher where the temperature is higher, most of the energy is not produced at the centre of the Sun, because:

The amount of mass in a shell at radius r is i.e. there is more mass per unit volume at large radius

(assuming constant density) The mass fraction of hydrogen (X) at the centre has been

depleted due to fusion, and the rate equations depend on X2.

drrdM 24

Recall: Proton-proton chainRecall: Proton-proton chain

The net reactions are:

2224 42

11

eeHeH

eeHeHBe 4

211

74 2

eHeeHHeHe 4

211

42

32 2

PPI

PPII

PPIII

Direct observations of the core: Direct observations of the core: neutrinosneutrinos

• One type of neutrino detector on Earth uses an isotope of chlorine, which will (rarely) interact with a neutrino to produce a radioactive isotope of argon.

eArCl e3718

3717

• This reaction requires the neutrino to have an energy of 0.814 MeV or more, and can only detect neutrinos from the “side-reactions” in the PP chain:

HeHLi

LieBe

BeHeHe

e

42

11

73

73

74

74

42

32

2

HeBe

eBeB

BHBe

e

42

84

84

85

85

11

74

2

PPII PPIII

• The Homestake detector contains ~400,000 L of cleaning fluid

• 2x1030 atoms of Cl isotope• Detect one Argon atom every 2-3 days.

Direct observations of the core: Direct observations of the core: neutrinosneutrinos

• More recently, the GALLEX (also SAGE) experiments uses 30 tons of natural gallium in a 100 ton aqueous gallium chloride solution to detect neutrinos via:

eGeGa e7132

7131

• This is sensitive to lower neutrino energies (0.233 MeV) and can detect neutrinos from the main branch of the PP chain

HHeHeHe

HeHH

eHHH e

11

42

32

32

32

11

21

21

11

11

2

The Solar neutrino problemThe Solar neutrino problem

Both the Homestake and GALLEX experiments detected fewer neutrinos (by a factor 2-3) than were expected from the PP-chain reactions. This problem existed for about 30 years.

The solution to the problem was suggested by results from the Super-Kamiokande detector in Japan

Results showed that electron neutrinos produced in the upper atmosphere can change into tau- or muon-neutrinos

This means neutrinos must have some mass and can therefore oscillate between flavours.

The Solar neutrino problem… solvedThe Solar neutrino problem… solved

• The Sudbury Neutrino Observatory uses heavy water, and was able to directly detect the flux of all types of neutrinos from the Sun.

• The results are now completely consistent with the standard solar model.

BreakBreak

The main sequenceThe main sequence

•The atmospheres of most stars are mostly hydrogen, X=0.7.•The fraction of metals varies from Z~0 to Z~0.03•Because of the relative slow burning of hydrogen, the

structure of the star changes only slowly with time.

In general, the central temperature is higher for more massive stars Thus, low mass stars will

be dominated by the pp-chain

Higher mass stars undergo the CNO cycle

Central density is actually lower for more massive stars. Increasing mass

23.0MTc age

The main sequenceThe main sequence

Assuming hydrogen-burning reactions in the core, we can construct a theoretical relation between L, T and M

• Stars undergoing hydrogen burning lie along the main sequence

• For low-mass stars, <0.08MSun, central temperatures are not high enough to allow nuclear fusion

• At very high masses, M>90 MSun, the stars become unstable: thermal oscillations in the core coupled with extreme temperature sensitivity of the nuclear reactions means an equilibrium is never attained.

Main sequence lifetimesMain sequence lifetimes

At the lower end of the main sequence,

Sun

e

Sun

LL

KT

MM

4

3

1005.5

1074.2

085.0

Such low-mass stars are entirely convective, so all the hydrogen (70% by mass) is available for fusion. What is the lifetime of such a star?

At the upper end of the main sequence,

Sun

e

Sun

LL

KT

MM

6

4

101.1

1027.5

90

Only the central ~10% of the mass is available for hydrogen fusion, because the star is not fully convective. What is the lifetime of such a star?

Stellar lifetimesStellar lifetimes

•From observations of the cosmic microwave background, we know the Big Bang occurred about 13.7 billion years ago

• Galaxies have been observed at a time when the Universe was less than 1 billion years old. Thus stars have been forming for at least ~13 billion years

Main sequence lifetimesMain sequence lifetimes

•Bluer (hotter) stars must be very young, formed within the last 0.01% of the age of the Universe

•On the other hand, some of the reddest (coolest) stars may have been formed shortly after the Big Bang, and would still be around.

•The stars lying off the main sequence are not explained by the hydrogen-burning model: something else must be going on…

00006.0~Universe

star

t

t

900~Universe

star

t

t

The Solar AtmosphereThe Solar Atmosphere

T~106 K

T~25000 K

T~5770 K

• The solar atmosphere extends thousands of km above the photosphere (from which the optical radiation is emitted)

• It is of much lower density and higher temperature than the photosphere

T~107 KCore

The extended solar spectrumThe extended solar spectrum

While the solar radiation is similar to a blackbody prediction at optical wavelengths, there is excess radiation at very short wavelengths. This light is also highly variable.

The chromosphereThe chromosphere

• UV (30.4 nm) images reveal the chromosphere• Can sometimes see large prominences rising high

above the surface of the Sun. •At the north and south poles of the Sun, less EUV

light is emitted - these regions often end up looking dark in the pictures, giving rise to the term coronal holes.

These are low density regions extending above the surface where the solar magnetic field opens up

HeI emission

The X-ray sunThe X-ray sun

•The X-rays we see all come from the corona.

•The corona is a very stormy place, constantly changing and erupting.

Movie from http://www.lmsal.com/SXT/sxt_movie.html

SunspotsSunspots

•Dark (cool) regions of the photosphere•Number of spots changes on a 11 year

cycle

•Concentrations of magnetic field lines

The Sun’s magnetic fieldThe Sun’s magnetic field

•By studying sunspots we can learn about the nature of the Sun’s magnetic field

•Switches polarity every 11 years