The Sun as a Star

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.

Key Properties:

• Radius : ~ 700 000 km

• Mass :  ~ 2 × 1030  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

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.

So what happens to the energy?

Since we see the Sun therefore energy reaches to the surface. How?

➤ Convection

• 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 : smaller cells (~ 1 000 km in diameter)

• Surface : granuls

• Photosphere : convection stops (it is too thin)

Then, radiation takes over the transport.

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:

• 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 Number(%) 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.

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).

Sunspot Cycle (or Solar Cycle)

Annual number of sunspots throughout the 20th century shows the (roughly) 11-year solar cycle. The most recent solar maximum occurred in 2024 (Cycle 25).

• 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.

Sunspots cluster at high latitudes when solar activity is at a minimum. The blue lines in the upper plot indicate how the “average” sunspot latitude varies over the course of the cycle.

• 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.

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.