PHYSICS OF THE SPACE ENVIRONMENT

 

PHYS/EATS 3280

 

 

Part 1 - The Sun and Its Influence on Earth’s Upper Atmosphere and Ionosphere

 

1. Basic Solar Physics

 

1.1 Formation of the Sun and our Solar System

 

1.1.1 Origin of the Sun

 

The history of our star the Sun goes back to the origins of the universe itself.  The conventional view is that the history of ‘our’ universe began about 15 billion years ago with the ‘Big Bang’.  Age estimate is based on present distance to the most remote objects combined with the speed at which they appear to be moving away from us as the universe continues to expand (or not?).

 

Expansion velocities are based on Doppler shifts.  Distance is linearly related to the velocity through the Hubble constant; namely 60 km s^-1 Mpc^-1 where 1 pc = 3 x 10¹³ km = 2 x 10⁵ AU with 1 AU = 150 million km.

 

Just after the big bang (<<1ms), the universe was dominated by gamma rays and neutrinos at extremely high temperatures. As things cooled (T = 7x10¹² K) protons and neutrons first formed and then the temperatures dropped below the threshold for muons (T = 8x10¹¹ K), and then for electrons (T = 10⁹ K). The age of the universe to the muon threshold was about 10 ms, and for electrons about 10 s.

 

Protons and neutrons can form deuterium via p + n ® D⁺ + g ; below 10⁹ K the photons have insufficient energy to re-dissociate the deuterium nuclei.

 

Two deuterium fuse to give ³He²⁺ + n, or  ³H⁺ + p and finally, ³He²⁺ +  ³He²⁺  ® ⁴He²⁺ + 2p + g.

 

⁴He²⁺ was the largest nucleus formed during the Big Bang.  The heavier nuclei we see today, including in our bodies, must have been formed by some other process (stars!)

 

After about 10 million years things had cooled enough  (10⁴ K) to allow electrons to attach to the ions to form neutral at­oms; at this time the universe consisted of 28% ⁴He (by mass) and 72% H.

 

 

1.1.2  Star Formation

 

Something drastic had to happen to make the universe more interesting, and more habit­able!

A relatively dense gas cloud will collapse if its own gravitational potential energy is greater than its internal thermal energy - known as the (Sir James) Jean’s criterion and a primitive star will be born:

GM/r_c  ³  (3/2)mkT   ; where m is the number of particles per unit mass.

 

The mean density over the whole observable universe (a sphere with a radius of ~5 Gpc) is about 10^-27 kg m^-3 corresponding to about 1 H atom per cubic meter. Within our galaxy, the Milky Way, the density is 10⁶ times larger.

 

Stars are classified according to the Hertzsprung-Russell (H-R) diagram, shown in Figure 1.1, involving the temperature (corresponding to the spectral class), the luminosity (in solar lumi­nosity units) and the absolute magnitude, m_a. Vega has an apparent magnitude of +1, and about the weakest star we can observe by eye is +4 (fourth magnitude). One magnitude is a factor of 2.51…( ⁵Ö100) in luminosity. The Sun has an apparent magnitude of -26.7. The absolute magnitude is the apparent magnitude the star would have if placed at a distance of 10 pc.

 

Most stars lie on the main sequence, with white dwarfs, giants and supergiants lying off the main sequence. Both mass and radius increase as we move upward on the diagram.

 

The very hot O and B stars are emitting at a very rapid rate so evolve very rapidly, and on

average must be younger in absolute age than other stars on the main sequence.

                        

                           Figure 1.1 The Hertzsprung-Russel Diagram

 

1.1.3 Stellar Evolution

 

If the star is sufficiently massive and the temperature at the core becomes high enough, the helium can begin to burn, moving it off the main sequence to the giant class as shown in Figure 1.2, where the star builds a up a core of carbon and heavier elements. The star expands, but when its fuel is exhausted, becomes a white dwarf.

 

The evolutionary track as shown in Figure 1.2 is as follows.  A nebular phase lasting 10⁵- 10⁶ years collapses to form a T-Tauri protostar, which after 10⁷ years settles on the main sequence, where it burns H for 10¹⁰ years. Ignition of helium burning then moves it off the main sequence for 10⁸ years as a red giant until it runs out of fuel and collapses to a white dwarf usually shedding a planetary nebula.

 

A star of 5 L_S spends 10⁹ years on the main sequence, whereas a 100 L_S star spends only 5 x 10⁷ years there. Thus a 100 L_S star must be less than 5 x 10⁷ years old. Since stars as luminous as 10⁴ L_S exist, they were created within the lifetime of the human species. A red dwarf can live as long as 10¹² years. Stars are observed with ages of 10 Gyr, or even 14 Gyr, close to the Hubble estimated age of the uni­verse, 15 Gyr. 

 

 

       

                  

Figure 1.2  Stellar evolution from T-Tauri protostars to white dwarfs.  There is only a supernova (rather than just shedding of a planetary nebula) if the star is large enough.

 

The key to the formation of heavy elements appears to lie in violent events. One possibility is the interiors of highly evolved red giant stars with high core temperatures. The reactions here have passed through hydrogen, helium and carbon burning, and the inner core is mostly iron-group elements. Temperatures are so high that photon-photon interactions can create electron-positron pairs, with associated neutrino production. Neutrinos are 100% efficient at removing energy from the star because they are not absorbed. The core suddenly cools and collapses, and the process runs away. The star then collapses inward in free fall, because of the cessation of core pressure. The col­lapse process creates an almost instantaneous heat pulse, as gravitational energy is converted into compressional heating. Since the reaction rates of some nuclear reactions goes as the 20th power of the temperature, the nuclear reactions immediately run away, causing catastrophic changes in the composition of the star in about 1 second, with the release of vast amounts of energy.

 

Such an explosion, which ejects a significant percentage of the mass of a highly evolved star into the interstellar medium at high speeds is called a supernova, which can briefly have a lu­minosity that is greater than that of an entire galaxy

1.2 Solar Structure

 

1.2.1 The Sun’s interior

 

Best estimates are that the Sun formed from the gravitational collapse of an medium sized interstellar cloud about 4.5 Gyr ago and it seems that the planets formed at about the same time.

 

Today our Sun is a very average main sequence star, and is 'burning' hydrogen deep within its interior with 4 protons effectively being converted to one ⁴He nucleus. A proton has a mass of 1.0078 amu; while ⁴He has a mass of 4.003 amu, a defect of 0.028 amu or 0.7% of the hydrogen mass consumed. From Einstein’s equation, one kilo of mass is equivalent to 9 x 10¹⁶ J, giving an energy conversion rate of 6.3 x 10¹⁴ J per kg of hydrogen consumed.  The solar mass is 2 x 10³⁰ kg, and energy is produced at a rate of 2 x 10^-4 W per kg of total solar mass.

 

The Sun contains about 2x10⁵⁷ particles so the number of particles per unit mass is

 

m = 1x10²⁷ kg^-1

 

 It has a visible radius of ~7x10⁵ km and a ‘surface’ blackbody temperature of 5700-5900 K.

 

The total solar irradiance at the top of Earth’s atmosphere is 1370 W m^-2 and is called the Solar Constant.  Given Earth’s distance from the Sun of 1 AU, or 150,000,000 km, this gives a total solar output of ~3.9 x 10²⁶ W.

 

Since the radius of the Sun is 700,000 km, the solar surface irradiance (exitance) is 6.3 x 10⁷ W m^-2.

 

From the Stefan-Boltzmann law L(W m^-2) = sT⁴ and a Stefan-Boltzmann contant of s = 5.7x10^-8 W m^-2 K^-4, surface irradiance implies a surface temperature of 5770 K which is consistent with the Sun's apparent colour temperature.

 

Like other main sequence stars, the Sun ‘burns’ H to He in the ‘proton-proton chain’. To sustain its output it consumes 620 million tonnes of hydrogen per second but since it has about 2 x 10³⁰ kg of hydrogen to consume it could go on for about 1x10¹¹ years at its present rate.

 

However, we know that it will move off the main sequence well before that in about 1x10¹⁰ years.

 

Although the Sun’s 'surface’ temperature is about 5800 K we know that its core must be about 10,000,000 K in order to sustain hydrogen fusion.  But how do we know what is going on below the surface?  Well, without direct observations we can only make rough guesses based on model calculations.

 

We know, for example, that the mean temperature of the Sun must be higher than 5800 K otherwise it would be forced to collapse more under the Jean’s criterion.  Indeed we can use the Jean's criterion to predict what the mean temperature is.

 

Since the Sun is in steady state, or equilibrium, and neither collapsing or expanding very fast, it must just be at the Jean' equality.

 

GM/r  =  (3/2)mkT   ; where m is the number of particles per kg

 

Since GM/r =2x10¹¹ N m kg^-1, then (3/2)mkT  = 2x10¹¹ J kg^-1, and substituting for m = 1x10²⁷ kg^-1 yields T = 9.7x10⁶ K or approximately 10⁷ K as expected.

 

Until recently model calculations and theory provided the only means to hypothesize about the interior of the Sun, but some new observational methods are now being applied. The first of these new methods uses observations of short term (~5 min) oscillations in the Sun's luminosity.  These observations allow us to perform seismological analyses of the Sun's interior.

 

Similar methods based on the measurement of movement of the solar surface using Doppler shifts, and even measurements of relatively small variations in the di­ameter of the Sun, are also now being applied.

 

As already mentioned, we can’t actually observe directly the deadly energetic emissions from the Sun's core since they don’t reach us. The only particles escaping the core are neutrinos. Most solar neutrinos come from the photon-photon reaction with an energy of 0.5 MeV; neutrinos with these energies are impossible to detect.  However, ⁸B within the Sun decays into two ⁴He nuclei plus an electron and a neutrino with an energy of 14 MeV, this more energetic neutrino is more easily detected. Measurements of this solar neutrino flux at SNO, the Sudbury Neutrino Observatory,  are now providing a great deal of information about the Sun’s interior.

 

1.2.2 The Photosphere, Chromosphere and Corona

 

As already stated, the solar visible radiation flux is very stable, and is referred to as the Solar Constant, at about 1370 W m^-2 at the Earth’s surface. And as we saw from the Stefan-Boltzmann law and the Sun-Earth distance, etc., this corresponds to a black body temperature of about 5800 K. This temperature is characteristic of the Sun's photosphere, from which most of the radiation is emitted. Wavelengths near 300 nm deviate from this, corresponding to temperatures nearer 4500 K, the temperature near the base of the chromosphere. It is in this cooler chromosphere that the solar absorption lines are formed. Figure 1.3 shows the solar spectrum, indicating from which regions the different wavelengths originate. The outermost region is the corona, where the temperatures reach millions of degrees, and highly ionized species are formed.

 

In the Sun’s core, radiation is the primary means of transporting energy because absorp­tion is small, since everything is ionized, and absorption is limited to free-free transitions. Nearer the surface the gas suddenly becomes highly absorbing, causing a steep temperature gradient and con­vection takes over. Hot gas is ionized at the bottom, moves up and releases its ion­ization energy at the top. The photosphere is the level from which radiation escapes.  

Figure 1.3 The solar spectrum over a wide wavelength range. The visible region is shaded, and the extent of variability at the shorter wavelengths is shown.

 

The photosphere is the bright surface that we see; under magnification one sees a granular structure, with cells roughly 1000 km in size, having lifetimes of about 20 minutes. They appear to be rising convective cells of hot gas. The pressure at the base of the photosphere is only 0.1 bar, i.e 1/10 of Earth’s surface pressure, and its opacity is explained as broadband absorption by H^- ions. The chromosphere immediately above is initially somewhat cooler and this is where the Fraunhofer lines occur.  Also, CO has absorption lines in the IR, indicating a temperature as low as 4000 K. As altitude increases in the chromosphere the temperature rises, owing to the deposition of energy of various types transported upwards. One source can be wave motions in the photosphere.  At first, the enhanced deposited energy causes increases excitation, and thus in­creased radiation that tends to balance the absorbed energy - this maintains a somewhat constant temperature (thermostat). But at higher altitudes, as the density falls and T increases. Each absorbing species acts as a "thermostat" at its own level, Ly-a at 20,000 K for example. Eventually, the temperature begins to rise rapidly, as we enter the corona.  The tempera­ture profile for the chromosphere is shown in Figure 1.4.  The corona has a temperature of about 2 x 10⁶ K. The corona is visible owing to photospheric light scattering from two components (Figure 1.5).  The first is free electrons, which extend about 2 solar radii out; these have very high velocities so that the Doppler shifts wash out the Fraunhofer lines - they are not evident. This is called the K corona.

 

The second component is the F corona (for Fraunhofer), which results from scattering from interplanetary dust, which exists in a disk around the Sun, more or less in the ecliptic plane. This

 

             

 

Figure 1.4 Temperature profile in the chromosphere. The heights over which the Ha , Ly-a, Ca II  and the Mg II lines originate are indicated.

 

                 

 

Figure 1.5 The luminosity of the corona as a function of distance from the Sun.

 

extends so far from the Sun that it can be seen from the earth after dark, the zodiacal light. It can also be seen as scattering from a point exactly opposite to the Sun, called the gegenschein. The corona is characterized by highly ionized states, e.g. Fe XIV. The corona itself can be observed in the visible only during an eclipse. The corona also emits x-rays via bremmstrahlung radiation, and radio emission with l > 0.1 m. Coronal "holes" are seen in soft x-ray images, these are regions with strong outflows of solar wind, as discussed later. Other coronal features are loops from magnetic bipolar regions, and prominences. The question of what heats the corona is a difficult one; the most likely source appears to be heating by MHD waves.