ELABORACIÓN DEL CORTE DE COMPRAS Y VENTAS

The Sun is a G2V main sequence star of luminosity L = 3.85×1026 W, mass

M = 1.99×1030 kg and radiusR = 6.96×108 m (Prialnik, 2000). It was born from the gravitational collapse of a molecular cloud approximately 4.6×109 _years

ago, is currently in a state of hydrostatic equilibrium (∇P =−ρg), and predicted to enter a red giant phase in another ∼5 billion years before ending its life as a white dwarf (Phillips, 1999). Since we cannot directly observe the interior of the Sun, its structure and evolution are fundamentally realised with the use of the ‘standard solar model’ (SSM; Bahcall, 1989), which is a mathematical treatment of stellar structure described by several differential equations derived from basic physical principles. The SSM is constrained by the well-determined boundary conditions of the Sun’s luminosity, radius, age and composition, and thus provides a basis for understanding the mechanisms of energy transport in the solar interior. It assumes hydrostatic equilibrium, with energy generated by nuclear fusion, although small effects of contraction or expansion are included, and any abundance changes are caused solely by the nuclear reactions. The SSM is the end product of an iterative process that converges on an optimum description of the internal energy generation and transport, and overall evolution of the Sun.

Figure 1.1: Illustration of the structure of the Sun. The core is the source of energy, where fusion heats the plasma to∼15 MK. Energy is transported from the core by radiative processes in the radiation zone. The convection zone is heated from the base at the tachocline, allowing convective currents to flow to the photo- sphere. Locations of strong magnetic fields inhibit convection and appear as dark sunspots on the photosphere. These strong magnetic fields extend into the upper atmosphere of the Sun, responsible for coronal loops, prominences and streamers.

The fundamental energy process driving the Sun is nuclear fusion in the core, through the proton-proton chain at temperatures of∼15 MK:

1 1H + 1 1H → 2 1H + e +_+ν e (1.1) 2 1H + 1 1H → 3 2He +γ (1.2) 3 2He + 3 2He → 4 2He + 2 1 1H (1.3) where 1

1H is a proton, 21H is the deuteron isotope of hydrogen, 32He and 42He are

helium isotopes with 1 and 2 neutrons respectively, e+_{a positron, ν}

e an electron-

neutrino and γ a gamma ray. The resulting energy release for one complete reaction chain is approximately 4.3×10−12 _{J (Phillips, 1995). The core extends}

from the centre out to∼0.25 R, followed by the radiation zone out to∼0.75 R, then the convection zone out to the solar surface at 1 R (Figure 1.1). The temperature across the radiation zone drops to ∼5 MK with radiation being the most efficient method of energy transport. This radiation field is closely approximated by a black body, for which the spectral radiance is described by the Planck equation:

Bλ(T) =

2hc2µ2

λ5_{[exp (hc/λkT)−1]} (1.4)

where Bλ(T) is the intensity of radiation per unit wavelength interval (at tem-

perature T), h is the Plank constant, c is the speed of light, µ is the refrac- tive index of the medium, and k is the Boltzmann constant. By Wien’s law

λmaxT = 2.8979×10−3 m K we determine that the radiation is in the form of

elements move sufficiently rapidly for the energy interchange with their surround- ings to be negligible, i.e., they change adiabatically. A useful measure of when convection is likely to occur is given by the Schwarzschild criterion:

dlogT dlogP star > γ−1 γ (1.5)

where γ = CP/CV is the ratio of specific heats, equal to 5/3 for a perfect

monatomic gas. Essentially convection occurs once the absolute magnitude of the radiative gradient becomes larger than the absolute magnitude of the adi- abatic gradient, so that rising elements of plasma remain buoyant and move towards the surface before they can lose heat to their surroundings. The rising and falling parcels of plasma create the granulation effects observed on the sur- face, with granules ranging in size from hundreds to thousands of kilometres and dissipating over tens of minutes. (Details of the above radiative and convective processes are found in, e.g., Kitchin (1987); Zirin (1998)).

Between the radiation and convection zones is a relatively thin interface called the tachocline, where the solid body rotation of the radiative interior meets the differentially rotating outer convection zone. It thus has a very large shear profile which could account for the formation of large scale magnetic fields in the solar dynamo. The magnetic field of the Sun has an overall dipolar configuration, with opposite polarities dominant at each pole. The differential rotation of the Sun’s convection zone causes a large-scale winding up of the magnetic field, named the

Ω-effect, while the effects of the coriolis force and smaller scale motions of the plasma can give twist and writhe to the field, named the α-effect (Figure 1.2). Buoyancy effects cause the magnetic field to rise up through the convection zone and protrude through the surface of the Sun, observed as sunspots on-disk mark- ing the footpoints of over-arching concentrations of magnetic flux extending up through the solar atmosphere. In a given hemisphere one magnetic polarity leads the sunspot group and the opposite follows, while in the opposite hemisphere the situation is reversed (Hale’s law). The tilt angle between leading and trail- ing sunspots has an average value of 5.6◦ relative to the E-W line (Joy’s law). Furthermore, sunspots are observed to migrate from high latitudes towards the equator over an 11 year cycle due to the continual build-up of field by the αΩ- effect (Sp¨orer’s law). These combined effects lead to an increase of oppositely oriented poloidal field at each of the poles, neutralising the field there and re- sulting in the magnetic dipole flipping every 11 years. This 22 year periodicity is known as the solar cycle, and gives rise to periods of increased and decreased solar activity manifested by the frequency of phenomena such as active regions, flares and transients in the solar atmosphere (Schrijver & Zwaan, 2000).

Figure 1.2: Illustration of theαΩ effect of winding-up magnetic field due to the differential rotation of the Sun, reproduced from Babcock (1961). Sunspots visible on the disk are as a result of protruding field with positivepand negativef polarity as shown.