The Sun

Astro 129: Chapter 1a


The Solar Constant

What is the Solar flux arriving at Earth?Use relation between luminosity and fluxL = 3.9×1026 W, 1AU = 150×106 km

What is the source of the Sun’s energy?


The Source of the Suns Energy1. Kelvin-Helmholz contraction doesn’t work

2. Chemical reactions don’t work. To produce the observed solar flux from chemical reactions the sun would have burned out in about 10,000 years. (a chemical reaction releases roughly 1x10-19 Joules per atom)

We need a process that can liberate more energy per unit mass than what can be achieved by chemical reactions. Albert Einstein discovered such a process.

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E = mc 2

m = quantity of mass, in kg

c = speed of light = 3 ×108m/sE = amount of energy into which the mass can be converted, in joules


The Source of the Suns Energy

There are two avenues by which fusion of hydrogen proceeds in stars.

T ≈ T(T = 16 million K) proton – proton chain (example: 4 1H → 4He + neutrinos + gamma-ray photons)

T >> T CNO cycle (a carbon nucleus absorbs protons and finally emits a helium nucleus)


The Source of the Suns EnergyProton-Proton Chain


The Proton-Proton ChainProton-Proton Chain

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3He + 3He = 4He + 1H + 1H

The proton-proton chain has four branches PP1, PPII, PPIII, and PPIV. The PPI and PPII branches produce about 86% and 13.9%, respectively, of the Sun’s energy.

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3He + 4He = 7Be + γ7Be + e -=7Li + ν7Li + 1H = 24 He

PPI Branch

PPII Branch

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1H + 1H = 2H + e+ + ν e

1H + 2H = 3He + γ


The Proton-Proton ChainProton-Proton Chain

We can summarize the thermonuclear fusion of hydrogen as follows:

4 1H 4He + neutrinos + gamma-ray photons

Mass of 1H proton = mp = 1.672×10-27 kgMass of 4He = mHe = 6.645×10-27 kg

Dm = 4mp – mHe = 0.0435×10-27 kg

How much energy is released for every PPI reaction? Hint use E = mc2


Theoretical Model of the SunProton-Proton Chain

We expect fusion to occur mostly near the center of the sun where the temperature is high enough for fusion reactions to occur (T > 10 million K)

We need to address the issue of the propagation of energy produced in the center to its surface.

To learn about the interior of the sun scientist have followed the following approach: Create a model of the sun which contains as much of the physics as we know and fit this model to the observations.



Model Assumption:1. Hydrostatic Equilibrium (A balance

between the weight of a layer in a star and the force from pressure that supports it.

2. Thermal Equilibrium (A balance between the input and outflow of heat in a system). As a consequence while the temperature in the solar interior is different at different depths, the temperature at each depth remains constant in time.

3. Energy Transport via radiative diffusion and convection)

(FP = P/A, where P is pressure, A is area and FP is the force from this pressure)


Convection is the movement of molecules within fluids (i.e. liquids, gases). In the suns convection zone hotter gas rises outward and cooler gas descends inwards thus facilitating the bulk transfer of energy outward.

Radiative Diffusion is the process by which the gamma rays released in fusion reactions are absorbed in only a few millimeters of solar plasma and then re-emitted again in random direction and at slightly lower energy.

It takes a long time for radiation to reach the Sun's surface. Estimates of the photon travel time range between 10,000 and 170,000 years.


Fitting Models of the Sun to ObservationsProton-Proton Chain

Observations:1. Surface Temperature (T = 5,800 K)2. Solar Luminosity (L = 3.9×1026 W)3. Gas pressure and density at the Sun’s surface are almost

zero.

The result is a model of how, T,L, pressure, mass and density vary as a function of distance from the Sun’s center.


The Sun’s OscillationsProton-Proton Chain

The sun vibrates (oscillates) at certain frequencies. We can learn about the interior of the sun by studying oscillations on the surface of the sun.

The science studying wave oscillations in the Sun is called helioseismology.

The solar oscillations are thought to be produced by the motion of fluid(turbulence) in the convection zone.

A simulated sound wave resonating in the Sun. The regions that are moving outward are colored blue, those moving inward, red. As the cutaway shows, these oscillations are thought to extend into the Sun’s radiative zone.



Waves in the sun are divided into three different types: 1. Acoustic or pressure (p)

modes, driven by internal pressure fluctuations within the sun; their dynamics being determined by the local speed of sound.

2. Gravity (g) modes, driven by buoyancy,

3. Surface gravity (f) modes, akin to ocean waves along the stellar surface.

Different oscillation modes penetrate to different depths inside a star.



Discoveries made by helioseismology

1. Set limits on the amount of helium in the Sun’s core and convective zone.

2. constrained the thickness of the transition region between the radiative zone and convective zone.

3. The convective zone and the radiative zone rotate at different speeds, which is thought to generate the main magnetic field of the Sun by a dynamo effect.

A simulated sound wave resonating in the Sun. The regions that are moving outward are colored blue, those moving inward, red. As the cutaway shows, these oscillations are thought to extend into the Sun’s radiative zone.

Photon Transport from Sun’s Core

Proton-Proton Chain

Energy radiated by photons from the surface of the sun originates from the suns core. To get to the surface, however, energy is transported via various mechanisms thus making it difficult to tell how it was actually produced in the core.

Photon transport from the core to the surface:1. Photons created in the Suns core from hydrogen fusion

diffuse towards the Suns surface (~ 170,000 years to get out).2. Beyond the radiative zone energy is transported to the

surface through convection (bulk transfer of plasma).3. At the surface photons are mostly radiated out through

blackbody radiation.

How do we obtain direct evidence of hydrogen fusion in the Suns core?

Solar Neutrinos

Proton-Proton Chain

A direct method of proving that hydrogen fusion is occurring in the Suns core relies on detecting neutrinos that are released during nuclear fusion.

4 1H 4He + n + g

A neutrino is a subatomic particle with no charge and very little mass. It can travel through ordinary matter almost undisturbed. More than 50 trillion solar electron neutrinos pass through the human body every second. The Sudbury Neutrino

Observatory

Solar Neutrino Detections

Proton-Proton Chain

On a rare occasion a neutrino will strike a neutron and convert it to a proton. Using this process Raymond Davis designed and built a neutrino detector that used 100,000 gallons of perchloroethylene (C2Cl4).

Detection Method: Occasionally a neutrino will strike the nucleus of one of the chlorine atoms (37Cl) in the cleaning fluid (C2Cl4) and convert one of its neutrons into a proton, creating a radioactive atom of argon (37Ar).

Atomic number of Cl = 17. Atomic number of Ar = ?

Solar Neutrino Detections

Proton-Proton Chain

John Bahcall calculated the expected detection rate of neutrinos but Davis's experiment turned up only one third of this figure. The experiment was the first to successfully detect and count solar neutrinos, and the discrepancy in results essentially created the solar neutrino problem.

The Davis Experiment

Solving the Solar Neutrino Problem

Proton-Proton Chain

Where were the neutrinos detected in the Davis experiment coming from?

The Kamiokande experiment in Japan led by physicist Masatoshi Koshiba measured the direction of the incoming neutrinos and confirmed that they emanated from the Sun.

Kamiokande Observatory

Solving the Solar Neutrino Problem

Proton-Proton Chain

The Kamiokande experiment consisted of a large underground tank containing 3000 tons of water surrounded by 1100 light detectors. A solar neutrino would from time to time interact with an electron in the water molecule.

The electron recoils in roughly the direction that the neutrino was travelling, so the electrons "point back" to the sun.

About half of the predicted neutrinos were detected in the Kamiokande experiment.

Kamiokande Observatory

Solution to the Solar Neutrino ProblemProton-Proton Chain

There are actually three types of neutrinos (ne, nm, nt) but only ne is produced in the sun.

The Davis and Kamiokande experiments could only detect ne.

It turns out that the ne can change into nm,n t during its flight from the Sun to the Earth. The change between neutrinos is called neutrino oscillations. The Sudbury Neutrino

Observatory

Solution to the Solar Neutrino ProblemProton-Proton Chain

The solution to the solar neutrino problem came from the Sudbury Neutrino Observatory (SNO) in Canada. SNO could measure all three types of neutrinos.

Instead of regular water SNO used heavy water. In heavy water each of the hydrogen nuclei contain a proton and a neutron.

Process: neutrinos may knock a neutron out of one of the 2H nuclei of the heavy water molecule. When the neutron is recaptured by another nucleus it creates a flash of light that is recorded.

The Sudbury Neutrino Observatory

The Sun’s StructureProton-Proton Chain

1. Core2. Radiative zone3. Convective zone4. Photosphere5. Chromosphere6. Corona7. Sunspot8. Granules9. Prominence

PhotosphereProton-Proton Chain

The photosphere is the layer in the solar atmosphere from which the Sun’s visible light is emitted.

The Sun is gaseous throughout its volume.

Below the photosphere the Sun is opaque to visible light.

The photosphere is heated from below by energy streaming outward from the solar interior.


Question: Why is the “thin” photosphere opaque?

The photosphere is made primarily of hydrogen and helium, and has a density of about 10-4 kg/m3.

Despite its low density the photosphere is opaque and we can only see through ~400 km of gas in the photosphere.

The main reason for the photosphere being very opaque is the presence of negative H ions which are H atoms with an additionally bound electron.

Answer: Negative H ions in the photosphere are efficient light absorbers.


The edge or limb of the Sun looks darker because we are seeing the upper photosphere which is cooler. This effect is called limb darkening.

The high-altitude gas we observe at the Sun’s limb is not as hot (about 4,000 K) and thus does not glow as brightly as the deeper, hotter gas (5,800 K) seen near the disk center.

The Sun’s spectrum is close to a blackbody with a temperature of 5,800 K. Superimposed on this spectrum are absorption lines produced by the cooler gas (4,000 K) in the outer photosphere.


The Photosphere has a blotchy pattern called granulation. A granule is about 1,000 km wide. Granulation is caused by convection currents. Where gas rises it is hotter and looks brighter and when gas sinks into the photosphere it is cooler and looks darker.

PhotosphereProton-Proton ChainSuperimposed on the pattern

of granulation are even larger convection cells called supergranules.

A supergranule is about 35,000 km wide.

Gases rise upward in the middle of a supergranule, move horizontally outward toward its edge, and descend back into the Sun. Supergranules detected in

a Doppler image.

ChromosphereProton-Proton Chain

The chromosphere is a thin layer of the Sun's atmosphere above the photosphere, ~ 2,000 km deep.

The chromosphere’s spectrum is dominated by the red Ha emission line at 656 nm and also contains emission lines of highly ionized He, Ca, and ionized metals.

Tphotosphere: 6,000K(bottom) – 4,000K(top), over 400 km

Tchromosphere : 4,000K(bottom) – 25,000K(top), over 2000 km

During a total solar eclipse, the Sun’s glowing chromosphere can be seen around the edge of the Moon. The expanded area above shows spicules, jets of chromospheric gas.

SpiculesProton-Proton Chain

Spicules are jets of gas that rise from the top of the chromosphere and are located near the edges of the supergranules.

Each spicule lasts for about 15 min and together all spicules cover about 1% of the sun's surface.

A spicule rising from the chromosphere.

CoronaProton-Proton Chain

The corona is the outermost region of the Sun's atmosphere and extends from the chromosphere to several million kilometers.

The corona is very faint compared to the photosphere but can be viewed during a solar eclipse.

An image of the corona taken during an eclipse shows a number of streamers extending millions of km above the sun.


Properties of the solar corona:

Temperature ≈ 1 − 2×106 K

Spectrum: emission-line spectrum of highly ionized gases (G corona).

The corona is 10−12 times as dense as the photosphere.

Example: One of the prominent lines found in the sun is at 530 nm produced by Fe XIV (has lost 13 e− of its 26 e−).

Because there are so few atoms in the corona, despite its high temperature, the total amount of energy in these moving atoms of the corona is rather low.


Because of the large temperature of the corona many ions and electrons escape the suns gravitational pull and form the solar wind.

The corona’s high temperature results in intense UV and X-ray emission.

One of the major surprises was the discovery that the temperature of the chromosphere and corona increase with increasing distance from the sun.

UV observations of the corona made by SOHO show coronal holes that emit much less UV and have lower temperature and density than their surrounding areas. The solar wind is stronger near these coronal holes.

SunspotsProton-Proton Chain

(a) An isolated sunspot, (b) a group of sunspots Sunspots are temporary cool regions in the solar photosphere. Because of their relatively low temperature they appear dark.They have typical sizes of ~ 10,000 km across and have a lifetime of hours to years. TUmbra ~ 4,300 K and TPenumbra ~ 5,000 K.

Estimate the ratio of the flux from the umbra to that from the photosphere assuming a similar emitting area.

Proton-Proton Chain

The sun's rotation can be tracked by observing the rotation of sunspots.

Observations show that a sunspot near the equator takes ~ 25 days to go around once whereas sunspots at larger latitudes take longer.

The sun does not rotate as a rigid body. Different parts of the sun rotate at different velocities. This is referred to as differential rotation.

Sunspotting

Sunspot Cycle Proton-Proton Chain

The average number of sunspots varies with a period of ~ 11 years. The periodic change in the number of sunspots is called the sunspot cycle.

Sunspot Latitudes Proton-Proton Chain

At the beginning of each sunspot cycle, most sunspots are found near latitudes 30° north or south. As the cycle goes on, sunspots typically form closer to the equator.

Zeeman EffectProton-Proton Chain

When an atom is placed in a magnetic field, the interaction between the field and the electron current shifts the atom’s energy.

According to the principles of quantum mechanics, only certain orientations are allowed.

An energy level is split into different energy levels, corresponding to the different orientations of a particular electron orbit.

Zeeman showed that a spectral line splits when the atoms are subjected to an intense magnetic field. The more intense the magnetic field, the wider the separation of the split lines.

Sunspots have strong magnetic fields Proton-Proton Chain

When Hale focused a spectroscope on sunlight coming from a sunspot, he found that many spectral lines appear to be split into several closely spaced lines. Hale’s discovery showed that sunspots are places in the photosphere that have strong magnetic fields.

Magnetograms Proton-Proton Chain

A magnetogram is an image of the sun showing variations in strength of a magnetic field. It is based on the Zeeman effect.

Hale also discovered that the Sun’s polarity pattern completely reverses itself every 11 years. The Sun’s magnetic pattern repeats itself only after two sunspot cycles, which is why astronomers speak of a 22-year solar cycle.

Preceding and Following Members of Sunspot Groups

Proton-Proton Chain

As a given sunspot group moves with the Sun’s rotation, the sunspots in front are called the “preceding members” of the group. The spots that follow behind are referred to as the “following members.” Preceding members in one solar hemisphere all have the same magnetic polarity, while the preceding members in the other hemisphere have the opposite polarity.

The Magnetic-Dynamo Model Proton-Proton Chain

Magnetic field lines tend to move along with the plasma in the Sun’s outer layers. Because the Sun rotates faster at the equator than near the poles, a field line that starts off running from the Sun’s north magnetic pole (N) to its south magnetic pole (S) ends up wrapped around the Sun. Sunspots appear where the magnetic field protrudes through the photosphere.

The Magnetic-Dynamo Model Proton-Proton Chain

Preceding members of sunspots move towards the equatorand following members of sunspots move towards the poles.When preceding members from the two hemispheres meet at the equator they cancel and when following members of sunspots reach the pole they initially cancel and then reverse the polarity of the pole. This explains the magnetic field reversal.

Rotation of the Solar InteriorProton-Proton Chain

The solar rotation period (shown by different colors) varies with depth and latitude.

The surface and the convective zone have differential rotation.

Deeper within the Sun, the radiative zone seems to rotate like a rigid sphere.

Rotation of the Solar interior

Magnetic ReconnectionProton-Proton Chain

Plasma can easily flow along magnetic field lines but takes more time to diffuse across field lines. Occasionally the magnetic field lines protrude through the suns surface (near the edges of supergranules) forming giant coronal loops. Plasma flows along these loops. Whenever magnetic field lines reconnect a large amount of energy is released that heats up the surrounding plasma to high temperatures.

Plages and Prominences

Proton-Proton Chain

Plages are areas of the chromosphere that are much brighter (especially in Ha) than their surroundings.

Plages tend to form just before sunspots appear and are thought to be produced by magnetic fields that protrude from the sunspot regions below. These magnetic fields may compress and heat the gas in the chromosphere.

Prominences are columns of gas from the chromosphere that follow magnetic field lines anchored at sunspots. They can extend tens of thousands of meters above the photosphere.

Solar Flares

Proton-Proton Chain

Solar flares are eruptions on the sun that occur near sunspot groups.They can release near 1026 joules of energy within a few hours.They heat nearby regions of the suns atmosphere to temperatures of up to tens of millions of K. Energy released in a flare is thought to come from magnetic energy stored near the group of sunspots.

Coronal Mass Ejection

Proton-Proton Chain

In a coronal mass ejection, more than 1012 kilograms of high-temperature coronal gas is blasted into space at speeds of hundreds of kilometers per second. A typical coronal mass ejection lasts a few hours.

The Sun

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