Efectos de la apertura de la liquidación judicial

Very few sunspot-related phenomena are well understood. It is only superficially known how the large-scale plasma circulation and the decay and dispersion of sunspot magnetic fields are connected to the reversal of the global magnetic field. Above the photosphere, the magnetic field strength and structure can only be roughly estimated, and below the photophere neither is known to any certainty. Additionally, predicting the strength of the next solar cycle, the frequency of sunspot emergence, and the occurrence of flares with the accuracy required by the operational community is not possible.

The aim of this thesis is to better understand the evolution of individual sunspot groups and the global magnetic field. The study aims to address three questions in a series of studies:

1.10 Thesis Aims

• What are the conditions in sunspot groups that result in solar flares? The re- lationship between flaring and sunspot group property dynamics is investigated. Property distributions associated with different flare magnitudes are compared. The properties of sunspot groups over the solar cycle are compared to global flare productivity.

• What mechanisms determine the configuration of the global magnetic field and how does this relate to the solar dynamo? The distribution of magnetic features affects the global magnetic field of the Sun. A comparison between the properties of sunspot groups and the global field configuration over solar cycle 23 is presented.

• What mechanisms govern the evolution and decay of sunspot groups? A mech- anism for the decay of sunsot groups is investigated by comparing a large-scale observation of magnetic field dispersion to a simulation.

To allow a large-scale study of the solar magnetic field, a combination of image process- ing techniques is used to automatically detect, characterise, and track sunspot groups over time.

The remainder of this thesis is organised as follows. The theory describing magnetic fields in a plasma is presented in Chapter 2. The magnetic field observations and other data used in the investigations are described (see Chapter 3). The methods for automatically detecting and characterising sunspot groups are described in 4. Three scientific studies of the solar magnetic field follow in Chapters 5, 6, and 7. Finally, the main results and conclusions of the studies, including prospects for future work, are summarised in Chapter 8.

2

Theory of Magnetic Fields in a

Plasma

In this chapter, theories explaining the dynamics and energetics of magnetised plasmas are discussed. Electrodynamic, fluid, and plasma equations leading to magnetohydro- dynamics are described. Also, magnetic fields in the solar atmosphere, the magnetic energy release in flares, and the quantification of surface fields are explained. This chapter summarises the background theory of ideas presented throughout this thesis.

2.1

Plasma Physics

The material composing the Sun can be described as a plasma, which is defined as a gas in which a significant fraction of atoms are ionised. This ionisation is due to the enormous temperatures and pressures in the Sun. The fraction of ionisation varies with

location and is described by the Saha equation, ni+1 ni = 2Zi+1 neZi (2πmekBT)3/2 h3 e (−χi/kBT)_{, (2.1)}

where,niandni+1are the number of ions in the ionisation stateiandi+1, respectively.

The partition function of each state is given byZ (Zi ≈2 andZi+1≈1), andχi is the

ionisation energy for a given state. For hydrogen this reduces to,

(n+/n)2 1−(n+_/n) = 4×10−9 ρ T 3/2_e(−1.6×105_/T) , (2.2)

wheren+is the number density of ions andnis the summed number density of neutrals

and ions, assuming macroscopic charge neutrality. This can also be written in terms of pressure, (n+/n)2 1−(n+_/n) = 4×10−9 ρ5/2 P µmH kB 3/2 e(−1.6×105ρkB/µmHP), (2.3) Hydrogen transitions from nearly neutral to almost completely ionised over a narrow transition region in temperature centered at ∼10 000 K. This temperature occurs at outer layers of the solar convection zone. The Saha equation can not be applied in most of the solar atmosphere where local thermodynamic equilibrium does not hold. Also, in the core of the Sun, the pressure is so immense and the density so large that adjacent hydrogen atoms are close enough to affect each other’s ionisation energies. Thus, in the core, the ionisation fraction approaches unity due to the added effect of “pressure ionisation”.

The average random kinetic (thermal) energy for a plasma is given by,

⟨E⟩= (3/2)kBT. (2.4)

The charged particles of a plasma are in constant motion, striving to cancel charge imbalance locally. The electron plasma oscillation frequency due to this motion is

2.1 Plasma Physics given by, ω= √ ne2 meϵ0 , (2.5)

where e is the charge of an electron, me is the mass of an electron, and ϵ0 is the

permittivity of free space. In cgs this can be written,

fp =

ωp

2π = 9 000

√

ne, (2.6)

where the result is in Hz.

The Debye length is given by,

λD = √ ϵ0kBTe e2_n e (2.7)

This is the distance over which an electron’s charge is “felt” by other charged particles. An electron’s electric potential falls off exponentially outside of its Debye sphere. The plasma parameter is,

Λ = 4πnλ3_D, (2.8)

and indicates the number of particles within a Debye sphere. If Λ>>1, the plasma is

strongly coupled (regarding collective effects), or weakly coupled if Λ<<1. Generally,

strongly coupled plasmas are “cold” and dense (as in white dwarf and neutron star atmospheres), while weakly coupled plasmas are diffuse and hot (as in solar and space plasmas). In a “collisional plasma”1, the mean free path of electrons within the plasma is small compared to the observational length scale2. The dominant electron collision process depends on which region of the Sun is considered, as mentioned in Section 1.3.

1

Collisional plasmas include those in collisional equilibrium, such as the solar corona.

The electron mean free path is given by,

λmf p=

1

n₋σcs

, (2.9)

wheren₋is the number of negatively charged particles, andσcsis the electron collisional

cross-section. For charged particles σcs is much larger than for neutrals due to the

Coulomb force.

F = 1 4πϵ0

q1q2

r2 , (2.10)

where q1 and q2 are the charges of each particle, and r is the distance between the

particles. The electron collision frequency is,

ν ≈ √ 2ω_p4 64πne ( kBT me )₋3/2 ln Λ , (2.11)

whereneis the electron number density. Since the mass of an electron is∼1/1000 that

of a proton, collisions result in a much higher velocity for electrons and so the electron collision frequency is much higher as well. Thus, proton collisions may be neglected. In the absence of magnetic fields, disturbances in the plasma travel at the sound speed,

vs=

√

γp

ρ , (2.12)

where γ is the ratio of specific heat at constant pressure (CP) to that at constant

volume (CV).

Magnetic and electric fields are ubiquitous on the Sun. In general, these fields are governed by Maxwell’s equations, the equations of electrodynamics,

∇ ·E= 1

ϵ0

ρe (Gauss’s law), (2.13)