THE EARTH S MAGNETIC FIELD; IS IT FADING AWAY AND ARE WE ALL GOING TO DIE? Luis Pedro García Pintos Barcia

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1 THE EARTH S MAGNETIC FIELD; IS IT FADING AWAY AND ARE WE ALL GOING TO DIE? Luis Pedro García Pintos Barcia Space Physics course Umeå University Umeå Sweden 19 th October 2006

2 INTRODUCTION William Gilbert was impressed by the fact that the Earth s rotational and magnetic axis were so close to each other, and was the first one to propose some connection between rotation and magnetic field. He thought that the Earth s magnetic field was the cause for its rotation. P.M. Blackett on the other hand considered the opposite situation: the rotation of the earth is the cause of its magnetic field 1. These are just a couple of theories among many that have failed to explain the origin of the earth s magnetic field. Any theory describing the Earth s magnetic field and its origin must be capable of explaining all of its varied properties. Among some of the hardest things to explain are magnetic flips, magnetic excursions, the asymmetry of the field, and all it s fluctuations in time. There is still today a hot debate in the scientific community over the processes behind the earth s magnetic field. EARTH S MAGNETIC FIELD Its importance is obvious: it is vital for us. Without it the solar wind would hit us directly, damaging life, and slowly blowing away the atmosphere. So it comes as no surprise that there is so much effort to study its past, and to understand its origin. It turns out that the field has some properties that are not easy to explain. The magnetic axis does not coincide with the rotational axis (asymmetry of the magnetic field) and the magnetic axis does not pass through the center of the earth. Moreover, the field is not static at all. There are fluctuations in its intensity (has decreased 15% in 150 years), the poles move as much as 15km every year, and there are reasons to believe that it has even changed polarity in the past. COMPOSITION OF THE EARTH The composition and properties of the Earth are crucial in order to understand any theory explaining the earth s magnetic field. This is of course not a simple thing, given the difficulties involved, but that is the geophysicist job. Through the analysis of seismic data it has been concluded that the Earth s interior core is solid, and the outer core is liquid. Nevertheless, there is still uncertainty on the exact composition of these, and their exact dimensions. Fig 2 Figure 2 shows a diagram of the interior of the Earth. The inner core is composed mostly of solid iron (around 90%), with some lighter element, oxygen or sulfur being the most popular candidates (there is actually quite some controversy over this, and many options have been considered) 2. The outer core is also composed mostly of iron, but in liquid state. There is still discussion over the temperatures in the core and mantle, due to the fact that there is uncertainty in the other components of these. Adding or subtracting a small amount of some elements will vary the physical properties like conductivity, temperature and viscosity, which are important parameters at the time of evaluating any theory.

3 MAGNETIC FLIPS Through the analysis of magnetization in fossil minerals, lava, etc geophysicists have reached the conclusion that the earth s magnetic field has suffered reversals in polarity, or flips. This topic presents many questions. How often does it flip? How does it flip? Does it disappear completely and then appear pointing in the opposite direction? This last question is of particular importance, since a complete disappearance of the field would leave us vulnerable to the solar wind. Nevertheless, information gathered by geophysicists suggests that the magnetic field never disappears completely. Moreover, not only have there been several flips for the past 2 million years (time of humans existence), but also there appears to be no correlation between magnetic flips and the extinction of any species. DYNAMO THEORY DISC DYNAMO The best accepted theory available today to explain the origin of the Earth s magnetic field is the dynamo effect theory. The mathematical details of this theory are quite complicated, and only numerical solutions are now becoming available, but after many approximations and simplifications. I will nevertheless attempt to explain its basics here. I will start with a basic qualitative description of the dynamo theory: the disc dynamo. Fig 1a Fig 1b Fig 1c Figure 1a and 1b illustrate a disc dynamo, concept first introduced by Michael Faraday ( ). It consists of a conducting disc rotating with angular velocity ω, in a magnetic field B. Due to Lorentz s forces on the electrons of the metal, an outward current will be induced in the disc. This electrical current will in turn create a magnetic field. The problem we are interested in is finding solutions such that the resulting magnetic field is also the input field required for generating the current in the disc in the first place 1. Furthermore, another situation (figure 1c) may be thought were we have two discs, and a self sustained system. This configuration will also allow reversals of polarity 2, 3. In the earth s interior the fluid iron interior will be playing the part of the discuses, but the similarity between this model and what actually happens in the Earth s interior cannot be pushed much further. This model just gives a simplified basic idea of the processes that occur (according to

4 the dynamo theory) in the Earth s core. We have to keep in mind that the theory explaining the Earth s magnetic field will have to take into consideration the liquid rotating interior of the earth, and therefore fluid properties will arise, severely complicating the simple idea explained above. DYNAMO THEORY As mentioned before the complete dynamo theory is very complicated. The system of equations that needs to be solved is shown in figure 3. Even after simplifications, a considerable amount of computer power is needed to solve the system. This difficulty adds to the uncertainties in the earth s parameters stated above. Fig 3 SIMULATIONS "No one even dreamed about this," says Glatzmaier. "That's the nice thing about a supercomputer. You can just let it do its thing, solve these equations over and over Glatzmaier and Roberts have managed to simulate the dynamo theory problem, after some approximations. The magnetohydrodynamic equations are solved using a spectral method (spherical harmonic and Chebyshev polynomial expansions) that treats all linear terms implicitly and nonlinear terms explicitly. The simulation is run on parallel supercomputers at the Pittsburgh Supercomputing Center and the Los Alamos National Laboratory, and the simulation now spans more than 300,000 years 4.

5 fig 4a fig 4b fig 4c The simulations have been successful in reproducing the main characteristics of the earth s magnetic field. The most admirable achievement is the fact that a magnetic reversal happened in the simulation, after years of running. Figure 4 shows snapshots of the simulation, where the reversal occurs. The second and third pictures are 500 and 1000 years after figure 4a, respectively. The intensity of the magnetic dipole moment decreased by about a factor of ten during the reversal and recovered immediately after. Another noticeable point is that only one in several attempts of a flip is successful. This means that several times the field suffers the same fluctuations as if during a flip, but then recedes back to the initial state. CRITICS TO THE DYNAMO THEORY The results obtained in the Glatzmaier-Roberts model are impressive, and it is by far the best theory we have to explain the earth s magnetic field, but there are still dark spots in the dynamo theory. The theory can of course be tested with other planets. When applied to Mercury, the theory predicts that it should have no magnetic field, due to the fact that it spins too slowly, and it s supposed to be cool. However, observation tells us that Mercury has indeed a magnetic field. This implies that either there is something wrong with the theory, something wrong with what we believe to know about Mercury, or some other unaccounted effect is taking place. ALTERNATIVE THEORIES The simplest idea to explain the Earth s magnetic field is thinking of a permanently magnetized interior core (somewhat like thinking of the earth as a big magnet). This theory is dismissed on the fact that high temperatures on the core do not allow permanent magnetization, although this is not a conclusive argument 2. Furthermore, it cannot explain magnetic flips, magnetic excursions, etc. Another possibility comes by thinking of thermoelectric effects in the core. A gradient of temperatures in the core will cause a charge separation (electrons on the hotter part have higher kinetic energy, and will therefore travel to the colder end). A rotating sphere with a uniformly distributed charge on its surface will of course generate a magnetic field, given by equations 1 and 2.

6 H r 2 2 Qωa 2cosθ Qωa sinθ = H 3 θ = 3 3 4π r 3 4π r equation 1 equation 2 Of course the earth is neutral, but what will appear with this idea is a separation of charge that will produce a field (seen by just applying the equations above). Nevertheless, calculations will give values far too small for the magnetic field. And, again, as in the last case, this theory does not explain magnetic reversals, etc. There are many other possible theories that have proposed 2, but they have all been discarded for one reason or another. Still, some other process is needed to produce the initial input field needed to start the dynamo effect. CONCLUSION Going back to the question in the title, of course we are all going to die! But in any case, it will not be because of the disappearance of the earth s magnetic field. Even though the decrease in the intensity shown by simulations is considerable (10 times), biologists have found no correlation between extinctions and magnetic flips, and moreover there have been several flips in the past 2 million years, so humans have already survived several flips. REFERENCES The earth s magnetic field - Merrill, McElhinny 3 - A thermally driven disk dynamo - A.Y.K Chui - H.K Moffatt 4- (there is a nice simulation in here)