08 The Sun
1. Properties of the Sun
A star is a glowing ball of gas held together by its own gravity and powered by nuclear fusion at its center
Our star is a typical one. However, knowledge gathered from the Sun can be applied to other stars easily.
- Radius: ~ 700 000 km
- Mass: ~ 2 E+30 kg
- Escape Speed: ~ 600 km/s
- Period: 25 solar days
- Axial Tilt: 7.25 degree
- Temperature: ~ 6000 K
Period: It is observed from the spots on the surface. However different periods are measured from different locations.
➤ This shows differential rotation like Jupiter and Saturn.
Temperature: Observing the solar spectrum and using radiation laws an effective surface temperature is calculated
➤ Blackbody @ 5800 K
Surface: It has a surface but not a solid one; it is a gas ball. Therefore, surface is taken as the layer where radiation escapes to space
➤ The layer is photosphere which is ~ 500 km thick
It is the total energy radiated by the Sun. It can be calculated from the fraction of that energy that reaches Earth.
- It radiates energy uniformly.
- Radiation collected on a light sensitive area counted per second: m2/s
- This gives the solar constant quantity: 1400 W/m2.
- When it is summed over the sphere at 1 Astronomical Unit (1 AU = distance between Sun and Earth):
- It will give the total energy at 1 AU
- Luminosity = Solar Constant x Area @ 1 AU
- L = 4 × 1026 W
- Equivalent of this energy:
- 1 second = 10 billion 1-megaton nuclear bombs
- 6 second = Evaporates all the oceans
- 3 minutes = It melts Earth's crust
2. Solar Interiors
- Solar interiors cannot be observed directly.
- Therefore, observation of surface and radiation are combined with theoretical models of solar physics and created what is called Standard Solar Models.
- In 1960s, it is discovered that the Sun's surface vibrates :
- How? Internal pressure waves rushing toward to surface reflect off the photosphere
- So, the waves will create surface patterns
- which will allow us to study inner parts: similar to seismology.
- It is called helioseismology.
- The Sun is the only object continously observed.
Using this good data and using the standard solar model Solar density and temperature can be calculated.
3. Energy Transport Mechanism
In or near the core (having high T), the gas is completely ionized.
- with no e– deep solar interior is transparent to radiation
- energy produced by nuclear reactions travels outward towards the surface
- as they move outward T decreases; atoms collides less frequently or less violently
- therefore electrons bounds to their nuclei
- now energy transportation transformed into opaque.
- Therefore at about 200 000 km all photons are absorbed.
So what happens to the energy?
Since we see the Sun therefore energy reaches to the surface. How?
- Hot solar gas moves outward
- Cooler solar gas (above) sinks
➤ Convection cells
Therefore energy transported to upper layers by physical motion of solar gas.
There is a hierarchy in the convective zone
- Deepest ______ larger cells (~ 10 000 km in diameter)
- Shallow (1000 km) ______ smaller cells (~ 1 000 km in diameter)
- Surface ______ granuls
- Photosphere ______ convection stops (it is too thin)
Then, radiation takes over the transport.
4. Solar Atmosphere
In atoms or ions:
- we observe transitions
- they create spectral lines: emission or absorbtion
In normal conditions:
- when radiation from hot background source
- faces with cool foreground gas
they will create absorbtion lines. This is modified for the Sun and we observe:
- bright background lines and dark absorbtion lines
- are formed in roughly the same locations
- the photosphere (photon-sphere: layer of photons)
- lower chromosphere (chromo-sphere: layer of colors)
Spectral analysis can tell us what elements are present. This spectrum has lines from 67 different elements. The most common ones:
Element __ % of Number __ % of Mass
- H __ 91.2 __ 71.0
- He __ 8.7 __ 27.1
- O __ 0.0078 __ 0.97
- C __ 0.043 __ 0.40
- N __ 0.0088 __ 0.096
- Below photosphere:
- the gas is dense
- interaction between photon, e– , ions are common
- therefore, radiation cannot escape directly
- In the solar atmosphere
- the escape will depend on the energy of photon
- if the energy corresponds to an electron transtion ➤ absorbtion
- if not photon is free ➤ radiation
The lines we see on Earth tend to come from higher, cooler levels in the solar atmosphere.
- The dashed lines indicate schematically the levels in the atmosphere where photons corresponding to different parts of the absorption line originate.
- The inset shows a close-up tracing of two of the thousands of solar absorption lines: the "H" and "K" lines of calcium at about 395 nm.
So, except the core, the spectral lines might represent the entire Sun.
- A few thousand kilometers in size
- Layer is cooler and have low density
- Cannot be observed visually (photosphere is too bright)
- During the eclipse a reddish hue is seen (due to H-alpha emission line)
- It is not quiet:
- Storms, jets of hot matter, spicules
- Activity is not evenly distributed
- Speed reaches to ~100 km/s
- The magnetic field is stronger
- The temperature, indicated by the blue line, reaches a minimum of 4500 K in the chromosphere
- Then rises sharply in the transition zone, finally leveling off at around 3 million K in the corona.
- It must have a heat source, probably due to electromagnetic interactions.
- Corona can only be seen during eclipses
- Changes in composition and temperature are observed.
- Therefore spectrum shifts from absorbtion to emission
- Atoms looses several more electrons
- e.g. Iron with 26 e– :
- Corona: It is observed with 13 e–
- Photosphere: It is observed with 1-2 e–
- It contains EM radiation and fast-moving particles (p, e– )
- They escape from the sun all the time.
- Radiation reaches to Earth in 8 minutes.
- Particles are slower (500 km/s) and reach to Earth in few days: ➤ solar wind
- The sun evaporates constantly, throwing mass through the solar wind.
- However its size is small in the Sun's life time:
- ~ 1 million tons of particles / second
- which is ⇶ 0.1 % of Sun in 4.6 billion years
5. Solar Magnetism
- They are known to be the proof of solar magnetism.
- Each spot consists of a cool, dark inner region called the umbra surrounded by a warmer, brighter region called the penumbra.
- The spots appear dark because they are slightly cooler than the surrounding photosphere.
- Sunspot pairs are linked by magnetic field lines.
- The Sun’s magnetic field lines emerge from the surface through one member of a pair and reenter the Sun through the other member.
- The leading members of all sunspot pairs in the solar northern hemisphere have the same polarity (labeled N or S).
- If the magnetic field lines are directed into the Sun in one leading spot, they are inwardly directed in all other leading spots in that hemisphere.
- The same is true in the southern hemisphere, except that the polarities are always opposite those in the north.
- The entire magnetic field pattern reverses itself roughly every 22 years. This cycle is named as solar dynamo cycle.
- The darkest regions have temperatures of about 2 million K (figure b).
Sunspots ⟺ Solar Rotation
- The Sun’s differential rotation wraps and distorts the solar magnetic field.
- Occasionally, the field lines burst out of the surface and loop through the lower atmosphere, thereby creating a sunspot pair.
- The underlying pattern of the solar field lines explains the observed pattern of sunspot polarities.
- If the loop happens to occur on the edge of the Sun and is seen against the blackness of space, we see a phenomenon called a prominence.
Sunspot Cycle (or Solar Cycle)
- Annual number of sunspots throughout the 20th century shows the (roughly) 11-year solar cycle.
- At the time of minimum solar activity, hardly any sunspots are seen.
- About 4 years later, at maximum solar activity, about 100 to 200 spots are observed per year.
- The most recent solar maximum occurred in 2001.
- Sunspots cluster at high latitudes when solar activity is at a minimum.
- They appear at lower and lower latitudes as the number of sunspots peaks. They are again prominent near the Sun’s equator as solar minimum is approached once more.
- The blue lines in the upper plot indicate how the “average” sunspot latitude varies over the course of the cycle.
6. Active Sun
- Areas around sunspots are active; large eruptions may occur in photosphere.
- They are large sheet of ejected gas.
- The filament of hot gas in (b) measures more than 100,000 km in length. Earth could easily fit between its outstretched “arms.”
- Dark regions in the image have temperatures less than 20,000 K; the brightest regions are about 1 million K.
- The ionized gas follows the solar magnetic field lines away from the Sun.
- Most of the gas will subsequently cool and fall back into the photosphere.
- Much more violent than a prominence (Left)
- A solar flare is an explosion on the Sun’s surface that sweeps across an active region in a matter of minutes.
- It accelerates solar material to high speeds and blasting it into space.
Coronal Mass Ejection (CME)
- A few times per week, on average, a giant magnetized “bubble” of solar material detaches itself from the Sun and rapidly escapes into space (Right)
- If a CME encounters Earth with its magnetic field oriented opposite to our own the field lines can join together, allowing high-energy particles to enter and possibly severely disrupt our planet’s magnetosphere.
7. Heart of the Sun
- It is the energy source for the Sun.
- In general, nuclear fusion works like this:
nucleus 1 + nucleus 2 → nucleus 3 + energy
- But where does the energy come from?
- It comes from the mass
- If you add up the masses of the initial nuclei, you will find that it is more than the mass of the final nucleus
- The relationship between mass and energy comes from Einstein’s famous equation:
E = mc2
a small amount of mass is the equivalent of a large amount of energy.
- Nuclear fusion requires that like-charged nuclei get close enough to each other to fuse.
- This can happen only if the temperature is extremely high:
- over 10 million K.
- The first step : 1H + 1H → 2H + positron + neutrino
- The second step : 2H + 1H → 3He + energy
- The third step : 3He + 3He → 4He + 1H + 1H + energy
So, as a summary : 4(1H) → 4He + energy + 2 neutrinos
- The helium stays in the core.
- The energy is in the form of gamma rays, which gradually lose their energy as they travel out from the core, emerging as visible light.
- The neutrinos escape without interacting.
Age of the Sun
- Energy created = E (mass of final particles) - E (mass of initial particles)
- For each interaction this turns out to be 4.3 × 10–12 J.
- 1 kg of H = 6.4 × 1014 J of energy produced.
- The Sun has enough hydrogen left to continue fusion for about another 5 billion years.