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Altitude/ km

Figure 1.2 The variation of temperature and density in the Sun's atmosphere with altitude above the base of the photosphere.

The chromosphere is also greatly disturbed in regions where a flare occurs. This is a rapid brightening of a small area of the Sun's upper chromosphere or lower corona, usually in regions of the Sun where there are sunspots. The increase in brightness occurs in a few minutes, followed by a decrease taking up to an hour, and the energy release is spread over a very wide range of wavelengths. Flares, like certain prominences, are associated with bursts of ionised gas that escape from the Sun. Magnetic fields are an essential part of the flare process, and it seems probable that the electromagnetic radiation is from electrons that are accelerated close to the speed of light by changes in the magnetic field configuration. As with so many solar phenomena, the details are unclear.

The corona

Above the chromosphere the density continues to fall steeply across a thin transition region that separates the chromosphere from the corona (Figure 1.2). □ What distinctive feature of the transition region is apparent in Figure 1.2? A distinctive feature is the enormous temperature gradient. This leads into the corona, where the gradient is not so steep. The corona extends for several solar radii (Plate 2), and within it the density continues to fall with altitude, but the temperature continues to rise, reaching 3-4 x 106 K, sometimes higher. Conduction, convection, and radiation from the photosphere cannot explain such temperatures - these mechanisms would not transfer net energy from a body at lower temperature (the photosphere) to a body at higher temperature (the corona). The main heating mechanism seems to be magnetic - magnetic fields become reconfigured throughout the corona, and induce local electric currents that then heat the corona. Waves involving magnetic fields (magnetohydrodynamic waves) also play a role in certain regions.

The corona is highly variable. At times of maximum sunspot number it is irregular, with long streamers in no preferred directions. At times of sunspot minimum, the visible boundary is more symmetrical, with a concentration of streamers extending from the Sun's equator, and short, narrow streamers from the poles. Coronal 'architecture' owes much to solar magnetic field lines. The white colour of the corona is photospheric light scattered by its constituents. Out to two or three solar radii the scattering is mainly from free electrons, ionisation being nearly total at the high temperatures of the corona. Further out, the scattering is dominated by the trace of fine dust in the interplanetary medium.

The solar wind

The solar atmosphere does not really stop at the corona, but extends into interplanetary space in a flow of gas called the solar wind, which deprives the Sun of about one part in 2.5 x 10-14 of its mass per year. Because of the highly ionised state of the corona, and its predominantly hydrogen composition, the wind consists largely of protons and electrons. The temperature of the corona is so high that if the Sun's gravity were the only force it would not be able to contain the corona, and the wind would blow steadily and uniformly in all directions. But the strong magnetic fields in the corona act on the moving charged particles in a manner that reduces the escape rate. Escape is preferential in directions where the confining effect is least strong, and an important type of location of this sort is called a coronal hole. This is a region of exceptionally low density and temperature, where the solar magnetic field lines reach huge distances into interplanetary space. Charged particles travel in helical paths around magnetic field lines, so the outward-directed lines facilitate escape. The escaping particles constitute the fast wind. Elsewhere, where the field lines are confined near the Sun, there is an additional outward flow, though at lower speeds, called the slow wind.

Solar wind particles (somehow) gain speed as they travel outwards, and at the Earth the speeds range from 200 to 900 km s-1. The density is extremely low - typically about 4 protons and 4 electrons per cm3, though with large variations. Particularly large enhancements result from what are called coronal mass ejections, often associated with flares and prominences, and perhaps resulting from the opening of magnetic field lines. If the Earth is in the way of a concentrated jet of solar wind, then various effects are produced, such as the aurorae (the northern and southern lights - Plate 26). The solar wind is the main source of the extremely tenuous gas that pervades interplanetary space.

Solar activity

Solar activity is the collective term for those solar phenomena that vary with a periodicity of about 11 years.

□ What two aspects of solar activity were outlined earlier?

You have already met the sunspot cycle, and it was mentioned that the form of the corona is correlated with it. Prominences (filaments) and flares are further aspects of solar activity, both phenomena being more common at sunspot maximum. The solar luminosity also varies with the sunspot cycle, and on average is about 0.15% higher at sunspot maximum than at sunspot minimum. This might seem curious, with sunspots being cooler and therefore less luminous than the rest of the photosphere. However, when there are more sunspots, a greater area of the photosphere is covered in bright luminous patches called faculae.

All the various forms of solar activity are related to solar magnetic fields that ultimately originate deep in the Sun. The origin of these fields will be considered briefly in the following description of the solar interior.

1.1.3 The Solar Interior

To investigate the solar interior, we would really like to burrow through to the centre of the Sun, observing and measuring things as we go. Alas! This approach is entirely impractical. Therefore, the approach adopted, in its broad features, is the same as that used for all inaccessible interiors. A model is constructed and varied until it matches the major properties that we either can observe, or can obtain fairly directly and reliably from observations. Usually, a range of models can be made to fit, so a model is rarely unique. Many features are, however, common to all models, and such features are believed to be correct. This modelling process will be described in detail in Chapter 4, in relation to planetary interiors. Here, we shall present the outcome of the process as applied to the Sun.

A model of the solar interior

Figure 1.3 shows a typical model of the Sun as it is thought to be today. Hydrogen and helium predominate throughout, as observed in the photosphere. Note the enormous increase of pressure with depth, to 1016 pascals (Pa) at the Sun's centre - about 1011 times atmospheric pressure at sea level on the Earth! The central density is less extreme, 'only' about 14 times that of solid lead as it occurs on the Earth, though the temperatures are so high that the solar interior is everywhere fluid - there are no solids. Another consequence of the high temperatures is that at all but the shallowest depths the atoms are kept fully ionised by the energetic atomic collisions

Fractional radius

Figure 1.3 A model of the solar interior.

Fractional radius

Figure 1.3 A model of the solar interior.

that occur. A highly ionised medium is called a plasma. The central temperatures in the Sun are about 1.4 x 107 K, sufficiently high that nuclear reactions can sustain these temperatures and the solar luminosity, and can have done so for the 4600 million years (Ma) since the Sun formed (an age based on various data to be outlined in Chapter 3, notably data from radiometrically dated meteorites). This copious source of internal energy also sustains the pressure gradient that prevents the Sun from contracting.

Though nuclear reactions sustain the central temperatures today, there must have been some other means by which such temperatures were initially attained in order that the nuclear reactions were triggered. This must have been through the gravitational energy released when the Sun contracted from some more dispersed state. With energy being radiated to space only from its outer regions, it would have become hotter in the centre than at the surface. Nuclear reaction rates rise so rapidly with increasing temperature that when the central regions of the young Sun became hot enough for nuclear reaction rates to be significant, there was a fairly sharp boundary between a central core where reaction rates were high, and the rest of the Sun where reactions rates were negligible. This has remained the case ever since. At present the central core extends to about 0.3 of the solar radius (Figure 1.3). This is a fraction (0.3)3 of the Sun's volume, which is only 2.7%. However, the density increases so rapidly with depth that a far greater fraction of the Sun's mass is contained within its central core.

The Sun was initially of uniform composition, many models giving proportions by mass close to 70.9% hydrogen, 27.5% helium, and 1.6% for the total of all the other elements. In such a mixture, at the core temperatures that the Sun has had since its birth, there is only one group of nuclear reactions that is significant - the pp chains. The name arises because the sequence of reactions starts with the interaction of two protons (symbol p) to form a heavier nucleus (deuterium), a proton being the nucleus of the most abundant isotope of hydrogen (:H). When a heavier nucleus results from the joining of two lighter nuclei, this is called nuclear fusion. The details of the pp chains will not concern us, but their net effect is the conversion of four protons into the nucleus of the most abundant isotope of helium (4He), which consists of two protons and two neutrons.

The onset of hydrogen fusion in the Sun's core marks the start of its main sequence lifetime. A main sequence star is one sustained by core hydrogen fusion, and ends when the core hydrogen has been used up. The main sequence phase occupies most of a star's active lifetime. In the case of the Sun it will be another 6000 Ma or so until it ends, with consequences outlined in Section 11.5.

Various other subatomic particles are involved in the pp cycles, but of central importance are the gamma rays produced - electromagnetic radiation with very short wavelengths. These carry nearly all of the energy liberated by the pp chains' reactions. The gamma rays do not get very far before they interact with the plasma of electrons and nuclei that constitutes the solar core. To understand the interaction, it is necessary to recall that although electromagnetic radiation can be regarded as a wave, it can also be regarded as a stream of particles called photons. The wave picture is useful for understanding how radiation gets from one place to another; the photon picture is useful for understanding the interaction of radiation with matter. The energy e of a photon is related to the frequency f of the wave via where h is Planck's constant. The frequency of a wave is related to its wavelength via where c is the wave speed. For electromagnetic radiation in space c is the speed of light, 3.00 x 105kms-1. Table 1.6 lists values of c, h, and other physical constants of relevance to this book. (For ease of reference, the Chapter 1 tables are located at the end of the chapter.)

On average, after only a centimetre or so, a gamma ray in the core either bounces off an electron or nucleus, in a process called scattering, or is absorbed and re-emitted. This maintains the level of random motion of the plasma: in other words, it maintains its high temperature. The gamma ray photons are not all of the same energy. They have a spectrum shaped like that of an ideal thermal source at the temperature of the local plasma. This is true throughout the Sun, so as the photons move outwards their spectrum moves to longer wavelengths, corresponding to the lower temperatures, until at the photosphere the spectrum is that shown in Figure 1.1 (Section 1.1.1). The number of photons is greater than in the core, but they are of much lower average energy. From the moment a gamma ray is emitted in the core to the moment its descendants emerge from the photosphere, a time of several million years will have elapsed.

a What is the direct travel time?

The direct travel time at the speed of light c across the solar radius of 6.96 x 105km is 6.96 x 105km/3.00 x 105kms-1, i.e. 2.23 seconds!

The transport of energy by radiation is, unsurprisingly, called radiative transfer. This occurs throughout the Sun. Another mechanism of importance in the Sun is convection, the phenomenon familiar in a warmed pan of liquid, where energy is transported by currents of fluid. When the calculations are done for the Sun, then the outcome is as in Figure 1.3. Convection is confined to the outer 29% or so of the solar radius, where it supplements radiative transfer as a means of conveying energy outwards. The tops of the convective cells are seen in the photosphere as transient patterns called granules. These are about 1500 km across, and exist for 5-10 minutes. There are also supergranules, about 10 000 km across and extending about as deep.

Because convection does not extend to the core in which the nuclear reactions are occurring, the core is not being replenished, and so it becomes more and more depleted in hydrogen and correspondingly enriched in helium. The core itself is unmixed, and so with temperature increasing with depth, the nuclear reaction rates increase with depth, and therefore so does the enrichment. This feature is apparent in the solar model in Figure 1.3.

The solar magnetic field

The source of any magnetic field is an electric current. If a body contains an electrically conducting fluid, then the motions of the fluid can become organised in a way that constitute a net circulation of electric current, and a magnetic field results. This is just what we have in the solar interior - the solar plasma is highly conducting, and the convection currents sustain its motion. We shall look more closely at this sort of process in Section 4.2. Detailed studies show that the source of the solar field is concentrated towards the base of the convective zone. The differential rotation of the Sun contorts the field in a manner that goes some way to explaining sunspots and other magnetic phenomena.

The increase of solar luminosity

Evolutionary models of the Sun indicate that the solar luminosity was only about 70% of its present value 4600 Ma ago, that it has gradually increased since, and will continue to increase in the future. This increase is of great importance to planetary atmospheres and surfaces, as you will see in later chapters.

1.1.4 The Solar Neutrino Problem

There is one observed feature of the Sun that solar models had difficulty in explaining. This is the rate at which solar neutrinos are detected on the Earth. Solar neutrinos are so unreactive that most of them escape from the Sun and so provide one of the few direct indicators of conditions deep in the solar interior. A neutrino is an elusive particle that comes in three kinds, called flavours. The electron neutrino is produced in the pp chains of nuclear reactions that occur in the solar interior. The rates at which electron neutrinos from the Sun are detected by various installations on the Earth are significantly below the calculated rate. Are the calculated pp reaction rates in the Sun too low?

No, they are not. It is now known that neutrinos oscillate between the three flavours. If, in their 8 minute journey at the speed of light from the solar core to the terrestrial detectors, they settle into this oscillation, then at any instant only some of the neutrinos arriving here are of the electron type. The earlier neutrino detectors could only detect the electron type. Now, all three can and have been detected coming from the Sun, giving a greater flux. This accounts for most of the discrepancy. The rest of it has been accounted for by improvements in solar models that have modified the predictions of the solar neutrino flux.

Question 1.1

The Sun's photospheric temperature, as well as its luminosity, has also increased since its birth. What is the combined effect on the solar spectrum in Figure 1.1?

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