The Sun
142-150
Few simple pleasures can compete with basking in the warm Canadian Sun! The Sun is a "garden variety" star and yet it rightfully commands our attention and fascination. Not only is it the closest star to us and sustainer of all life on Earth, it also serves as our template for many of the activities and properties of other stars. In this unit you will encounter the Sun and learn some of its secrets.
Basic Solar Facts:
A surprising amount can be learned about the sun. As you saw in an earlier chapter, the Greeks knew that the Sun was much more distant from Earth than the Moon. With Newton's physics humanity acquired the ability to better understand the mass, size and distance to the Sun. By the middle of the 19th century the new science of spectroscopy was telling us the temperature and hinting at the composition of the sun. In the early part of the 20th century came our understanding that the sun was made mostly of hydrogen and helium and by the middle of the last century we discovered the means by which the Sun is able to shine eon after eon. We now classify our Sun as a G2 V (main sequence) star. |
Distance | 1.49 x 1011 m | |
| Mass | 1.989 X 1030 kg | ||
| Radius | 6.96 X 105 km | ||
| Period of Rotation | 25 days (equatorial) | ||
| Average density | 1.409 g/cm3 | ||
| Central density | 160 g/cm3 | ||
| Luminosity | 3.826 X 1026 W | ||
| Surface Temp | 5800 K | ||
| Central Temp | 14 X 106 K | ||
| Spectral Type | G2 V | ||
| Table 7.1 Basic facts about the Sun. | |||
Table 7.1 summarizes the basic facts about our sun.
The Solar Profile:
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| Figure 7.1 The solar profile (Image in public domain - courtesy NASA) |
Figure 7.1 presents a schematic view of the Sun. The core (roughly the inner 10%) is extremely hot (> 14 million K) and relatively. As you will see in the next section it is here that the enormous energy output from the Sun originates. The temperature drops from 14 million K to about 5800 K in the span of 6.96 X 108m. The rate at which the temperature drops is called the temperature gradient (in the case of the Sun the average gradient is (14 million K)/(6.96 X 108m) or about 0.02 K/m. This is an important idea because the temperature gradient controls how energy will be transported from the core to the surface. We can summarize this in the following way:
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Figure 7.2 shows a video clip of convection in action on the Sun's surface. Clearly seen in this clip are granulation cells - bright regions of hot gas about 1000 km across and "bubbling" up to the solar surface. Darker regions have delivered their thermal energy and are now sinking back into the Sun. Doppler shift measurements tell us that these cells are moving up and down with speeds on the order of a few hundred meters per second (average about 400 m/s). As you van see in the video clip (look at the "clock" in the lower left hand corner) granules have lifetimes on the order 20 minutes or so. Larger masses of granulation cells are also present and organized into "super-granules". A typical supergranule will consist of several hundred granules and exist for several days as a gently up and down motion on the surface of the sun. |
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Figure 7.2  Video clip showing granulation cells convecting in the Sun's atmosphere. (Video courtesy NASA) |
What if the Sun Went Out?
This rather startling question has an even more startling answer. If the energy production in the core of the sun was to suddenly stop it would take about 1 million years before you would see a change!! How can this be?
Example 7.1 How long would it take for a photon to travel a distance equal to the distance from the centre of the Sun to its outer edge?
Solution: Another way to say this is to ask how long it takes light to travel a distance equal to the radius of the Sun (6.96 X 105 km). Since light travels with a speed 'c' = 300 000 km/s the travel time should be 
. It takes light a little over 2 seconds to travel this distance.
| So - what gives here? The resolution of this riddle comes when you consider how a photon interacts with matter as it travels outward. The photon is constantly be absorbed and scattered (re-emitted) by electrons and ions in the solar interior. The re-emission can occur in any direction so the photon has almost as good a chance of being scattered back toward the centre than outward. Although this only takes a tiny fraction of time there are so many scattering collisions that the photons will take a very long time to emerge from the sun. The applet RandomWalk (Figure 7.3) illustrates this for you. Press go and watch the random walk of the photon. | |
Figure 7.3  Random Walk |
While in the core the photon can travel only a tiny distance between absorptions and re-emissions. However, as it proceeds to higher layers in the Sun and as the density drops the mean-free-path of the photon increases. Eventually it gets to the surface and is able to escape.
The Solar Atmosphere
The Photosphere
This is what we see when we look at the sun or other stars. A flood of energy wells up from below, heats the photosphere on one side. The photosphere leaks this energy away. We can define the base of the photosphere as the region in the Sun where a photon has a higher probability of escaping into space than being scattered back into the interior. At the base the photosphere has a temperature of about 6400 K while at the top of the photosphere the temperature is approximately 4400 K. The average temperature of the photosphere is about 5800 K and when we speak about surface temperatures of stars we are referring to the average photospheric temperature for the star.
Although the photosphere is a hot gas and approximates a black body its spectrum is criss-crossed by numerous spectral lines. You can use the techniques discussed in Unit 2 to determine the temperature at some locations in the photosphere. Another method and one that actually tells us more about temperature profile of the photosphere is to observe the phenomenon of limb darkening. Evidence of this temperature structure can be seen when you look at the sun in a small telescope. Towards the limb the sun's brightness drops noticeably. When you look at the limb of the sun then you are seeing photons that emerged higher up in the photosphere where it is cooler (hence the limb appears a bit darker). Figure 7.4 illustrates this effect.
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| Figure 7.4 Image of sun illustrating limb darkening.(Image courtesy The King's University Observatory) | Figure 7.5 Close-up of a sunspot with granulation cells visible. (Image courtesy NASA) |
The photosphere is also the region in which sunspots form. As you will see in section 7.3, sunspots are regions of enhanced magnetic activity on the sun which are slightly cooler (about 4200 K) than the surrounding gases in the photosphere.
The total extent of the photosphere is only about 500 km or 0.07% of the solar radius. We don't see much of the sun!
The Chromosphere
At the top of the photosphere the temperature drops to about 4500 K and then the temperature begins to climb again. This marks the transition into the chromosphere. The chromosphere is the region directly above the photosphere and extends approximately 2000 km above the photosphere. The density in the chromosphere is becoming very low and rather than absorbing photons to produce absorption spectral lines the chromosphere glows a pinkish-red colour and shows many emission lines. However, the low density of the chromosphere implies that light emitted by the chromosphere is very faint - about 1/1000 the brightness of the photosphere. This makes the chromosphere very difficult to observe. Nature does provide us with a way however. During a total solar eclipse, for a brief few seconds, the photosphere is blocked from view which enables us to see the chromosphere. Figure 7.6 shows a low resolution spectrum of the chromosphere. This is referred to as the "Flash Spectrum" since it coincides with the sudden appearance of the chromosphere during a total eclipse of the Sun.
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If you look carefully at pictures of the Sun during total eclipse (or if you have seen one for yourself) you will notice a thin pink-red band along the limb of the sun. This is the chromosphere and the pink colour is largely due to the Hydrogen alpha line emitting at 656 nm. |
| Figure 7.6 The "Flash Spectrum" of the chromosphere seen during a total solar eclipse. |
Another way to observe the chromosphere is to look at it through filters that pass only the light produced in a very narrow part of the spectrum around 656 nm. This wavelength corresponds to the Hydrogen-alpha line produced by hydrogen atoms in the chromosphere. Images taken through such filters are referred to as filtergrams and this technique is commonly used to provide images of the upper layers of the sun. Figure 7.8 illustrates this.
The top of the chromosphere reaches a temperature of approximate 20 000 K and is very jagged with numerous little "tongues" of chromospheric gas darting up into the transition region between the chromosphere and the coronal region. These are shown in Figures 7.7 and 7.8. The spicules represent jets of gas spurting up from the photosphere below.
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| Figure 7.7 The transition from the photosphere into the chromosphere with chromospheric spicules present. | Figure 7.8 Filtergram of chromosphere and spicules as imaged in the Hydrogen-aplha line. (video courtesy of Big Bear Solar Observatory) |
The Corona
Above the chromosphere is the tenuous and beautiful shell of gases that represents the outermost part of the solar atmosphere. X-ray emission from the corona tells us that it reaches temperatures as high as 3.5 million K. The corona is the dramatic and complex ghostly light that shines during mid eclipse. Figure 7.8 shows the corona as it appeared in the August 2008 eclipse. The corona's structure is highly variable and changes markedly from eclipse to eclipse. Since the Sun is composed primarily of hydrogen it follows that the corona consists mostly of hydrogen ions or protons with a smattering of heavier ions. X-ray emissions from the corona reveal traces of calcium, iron and other heavier elements.
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| Figure 7.8 The corona as visible during the August 2017 total solar eclipse. (Image courtesy The Kings University Observatory) |
Example 7.2 How big is the corona? Use Figure 7.2 to help estimate the size of the corona. Do you think your estimate is an over-estimate, under-estimate or "just right"?
Solution: In Figure 7.8, the corona extends in some areas nearly a full solar diameter out from the Sun's surface. From this you could conclude that the corona must be larger than 3 solar radii or about 2 million km in radius. This is a gross under-estimate however. If you could block out the glare of the sun and over-expose the inner part of the corona you will discover that the solar corona extends out an incredible 20 solar radii of about 12 million km!
What explains the curious behaviour of the solar temperature? At the top of the photosphere the temperature is 4400 K but the temperature of the outer parts of the corona is well over 3 million K!
| Astronomers know believe that they have solved the puzzle. Spicules point the way. It has been known for a century that the Sun is an active, magnetic environment. Loops of magnetic field lines from the photosphere "poke" through and into the more rarefied chromosphere and corona. The low density gas in these regions is constrained to move along these loops as shown in Figure 7.9. The turbulent churning of the photosphere below means that these loops of material are constantly jostling back and forth and colliding with each other. This causes heating in the gas and is a mechanism for transferring some of the energy of the turbulent gas in the photosphere to the highly rarefied gas in the corona. |  |
| Figure 7.9 Loops of gas trapped by the Sun's magnetic field contribute to chromospheric and coronal heating. |
The Solar Wind
As you saw in an earlier unit the concept of temperature ties directly to the speed of particles in a gas. At temperatures of more than 3 million K the protons that make up the corona are moving very fast with average speeds of 300 km/s which is approaching the escape velocity from the Sun. THe churning motion of the photosphere and the magnetic coupling in the chromosphere and corona produces gusts of over 1000 km/s. This means that there is a steady stream of high energy particles (mostly protons) blowing out into the solar system. This is called the solar wind and we will discus this in greater detail in sections 7.3 and 7.4.
The Oscillating Sun - GONG (Global Oscillation Network Group)
Our sun quakes and quivers with an amazing diversity of vibrational patterns or modes. The constant churning in the convective zone below the photosphere creates wave disturbances that ripple through the photosphere and travel around the Sun. This was first discovered in the 1960's when it was noticed that spectral lines produced on the surface of the sun were "wiggly" in a very specific way. Figure 7.10 shows an example of the "wiggly line" spectrum. Solar astronomers soon realized that this was being produced by a highly organized pattern of rising and falling regions on the Sun's surface vibrating with a period of about 5 minutes. This was the first vibrational mode discovered on the Sun and today we can recognize literally millions of different modes of vibration in the sun. This has even ushered in a new branch of astronomy called Helioseismology which is the solar counterpart of the seismological studies carried out daily by geophysicists and prospectors . In effect, helioseismology enables us to peer into the central regions of the sun. We do this by measuring the many different frequencies with which the sun vibrates. Each frequency carries with it some information about the interior of the sun including knowledge about pressure, density and temperature. The applet Helio shown in Figure 7.11 illustrates some of the many patterns with which the sun can "jiggle". This amazing beach-ball pattern is actually a very subtle effect and is grossly exaggerated in the applet.
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| Figure 7.10 The "Wiggly Line" spectrum (image courtesy W.Mattig -Kiepenheuer-Institut für Sonnenphysik) | Figure 7.11 Helio demonstrates some of the vibrational modes detected in the Sun and other stars. |
The red and blue regions in Figure 7.11 represent regions on the solar surface that are pulsating in and out with periods from 3 to 20 minutes. The red regions would be sinking downward (red-shifted) and blue regions rising upward. Typical amplitudes for these vibrations are about 10 km. Figure 7.12 shows a video clip of what a vibrational mode might look like. Next to the clip in Table 7.1 are two sound clips that represent low vibrational modes in the Sun. For these to be "audible" the frequency was increased by a factor of 42 000 times! Note - these are rendered as sound clips to help you visualize the vibration on the sun - you would not "hear" this in space!
| This is the sound of a low vibrational mode (period 5.67 minutes but sped up by a factor of 42000!) |  |
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| This is sound of 3 vibrational modes blended together. Now you can detect frequencies beating against each other. | |
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| Figure 7.12 Simulation of a vibrational mode in the Sun. |
Table 7.1 Sound clips of low vibrational modes in the Sun. | |
Helioseismology has revolutionized the study of the Sun. Today the Sun is monitored 24 hours a day by a global network of solar telescopes. This is called the Global Oscillation Network Group or GONG and it is instrumental in refining our understanding of what occurs deep within the Sun.
Example 7.3 Explain why turbulent motion on the surface of the Sun would be expected to produce the "wiggly line" spectrum seen in Figure 7.10.
| Solution: Since we can see detail on the surface of the Sun the light from different parts of a region on the sun would be Doppler shifted to the red or blue depending on whether the region producing the light was moving away from us or toward us. The wiggly line spectrum is produced when a spectral line from a particular region is shifted to the red or blue part of the spectrum. A region directly above or below may be moving in the opposite direction and hence the line shifts the other way. When combined by taking the spectrum of a vertical slice from the solar surface you will see the characteristic wiggly line spectrum. This is illustrated in the sketch on the right. |  |
Practice
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| (image courtesy of Institute for Solar Physics of the Royal Swedish Academy of Sciences, Sweden) |
To understand the basic characteristics of the Sun and to understand the Sun as a star
Chp 8.1
