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Mach’s principle

the medium:

M = v/vp ,

where vp is the propagation speed.

Mach’s principle The idea that the local inertial rest frame (non-accelerating, non-rotating) is determined by the inﬂuence of all the matter in the universe. Einstein’s general relativity includes some of the features of Mach’s principle. See general relativity.

Maclaurin Spheroid A uniform density ellipsoid used to describe self-gravitating rotating objects. Maclaurin Spheroids are secularly unstable when the rotational kinetic energy of the object exceeds roughly 14% of its potential energy and, given sufﬁcient time, will evolve into Jacobi or Dedekind ellipsoids. If the rotational kinetic energy exceeds 27% of the potential energy, the object is dynamically unstable and this evolution process will occur on a dynamical timescale.

macroscopic description (cosmic string)

See equation of state (cosmic string).

Madden–Julian oscillation (MJO) A dominant mode of variability in the tropical troposphere with typical time scales of 30 to 60 days, thus also called intraseasonal oscillation. It was ﬁrst discovered by R.A. Madden and P.R. Julian in 1972. Its signals are observed in pressure, temperature, and wind velocity, predominantly in the zonal wavenumber = 1 component. It is generally believed to arise from interaction of deep convection and large-scale ﬂow ﬁeld. The associated variability in precipitation is largest in the Indian and western Paciﬁc Oceans, where the sea surface temperatures are among the highest in the world ocean. A typical MJO starts with enhanced convective activity in the Indian Ocean, and then moves eastward through the maritime continents into the western equatorial Paciﬁc. This is accompanied by eastward shifts in the rising branch of the Walker circulation on intraseasonal time scales.

Magellanic Clouds Satellite galaxies of the Milky Way galaxy that are visible to the naked

eye in the southern hemisphere. The Large Magellanic Cloud (LMC) is at a distance of about 50 kpc, and subtends about 8◦ centered at RA

=5.3 h and Dec = − 68.5◦. The Small Mag-

ellanic Cloud (SMC) is at a distance of about 58 kpc, and subtends about 4◦ centered at RA

=0.8 h and Dec = − 72.5◦. Both the LMC and SMC were originally classiﬁed as irregular galaxies, though they exhibit a bar-like spiral structure that also supports SB(s)m classiﬁcation.

Magellan Mission The ﬁrst planetary spacecraft to be launched by a space shuttle (the shuttle Atlantis). On May 4, 1989, Atlantis took Magellan into low Earth orbit, where it was released from the shuttle’s cargo bay, and then a transfer engine took it to Venusian orbit.

Magellan used an imaging radar (in order to image through Venus’ dense atmosphere) to make a highly detailed map of 98% of the Venusian surface during its four years in orbit between 1990 to 1994. Each orbital cycle lasted eight months.

In Magellan’s fourth orbital cycle (September 1992 to May 1993), the spacecraft collected data on the planet’s gravity ﬁeld by transmitting a constant radio signal to Earth. At the end of this cycle ﬂight controllers lowered the spacecraft’s orbit using a then-untried technique called aerobraking. This maneuver produced a new, more circularized orbit that allowed Magellan to collect better gravity data in the higher northern and southern latitudes near Venus’ poles. Gravity data was obtained for 95% of the planet’s surface.

On October 11, 1994, Magellan’s orbit was lowered a ﬁnal time to plunge the spacecraft to the surface by catching it in the atmosphere. Although much of the spacecraft would have vaporized, some sections will have hit the planet’s surface intact.

magma Term given to molten rock when it is still underground. Once the magma has been erupted onto the surface of a body by volcanism, it is usually called lava.

magma chamber Beneath many active volcanos there is a magma chamber at a depth of 2

magnetic ﬁeld

or more km where the magma resides before an eruption occurs and it ascends to the surface.

magmatic water Water that forms in phase separation from magma. This water carries large amounts of dissolved minerals which it deposits in veins as it travels to the surface of the Earth. Also called juvenile water.

magnetic anomaly The local deviation of the geomagnetic ﬁeld from the global ﬁeld generated by the dynamo in the core and the external ﬁeld, due to the magnetization of nearby crust. This is usually obtained by measuring the local magnetic ﬁeld and then subtracting the prediction of a global ﬁeld model such as an IGRF. Crustal rock may be magnetized in situ after a heating event by cooling down through its Curie temperature in the ambient magnetic ﬁeld of the Earth, or else magnetized particles may be oriented on or after deposition in a sedimentary environment by the Earth’s ﬁeld so that the rock is left with net magnetization. Magnetic anomalies in oceanic plate show reversals in magnetization as one travels perpendicular to the mid-ocean ridge that produced them, due to the occasional reversal of the Earth’s magnetic ﬁeld so that rock that cools at different times may have oppositely oriented magnetization. This provided evidence for the hypothesis of sea ﬂoor spreading. Continental anomalies may be associated with geological structures such as subduction or collision zones or volcanos, where the crust has been heated. Many anomalies, including one at Bangui in Africa, are large enough to be detected through satellite magnetic measurements.

magnetic bay A dip in the trace of a highlatitude magnetogram, resembling a bay in a shoreline. Magnetic bays observed this way in the 1950s and earlier were later identiﬁed as magnetic substorms.

magnetic carpet The distribution of magnetic ﬁeld in small scales over the quiet sun which is observed to be recycled over a period of 40 h. A discovery of the Michelson Doppler Imager on the SOHO spacecraft.

magnetic cloud The interplanetary counterparts of coronal mass ejections (CMEs) that exhibit the topology of helical magnetic ﬂux ropes. Magnetic clouds make up about one third of all solar wind streams that are identiﬁed as interplanetary consequences of CMEs.

magnetic crochet Accompanying a solar ﬂare, dayside magnetic ﬁelds may show a sharp change, called a crochet, starting with the ﬂare, but shorter-lived, due to electric currents set up in the lower ionosphere as a result of the ﬂare induced ionization and conductivity changes. See short wave fadeout.

magnetic declination The azimuth, measured from geographic north, of the geomagnetic ﬁeld vector at a given location.

magnetic diffusivity A measure of the ability of a magnetic ﬁeld to diffuse out of a volume of plasma. A perfectly conducting plasma has zero magnetic diffusivity. The solar atmosphere has a magnetic diffusivity comparable to that of copper wire. However, because of the large scales involved on the sun, compared to the typical length of a copper wire, the diffusion times are extremely long.

magnetic dipole The simplest source of a magnetic ﬁeld envisaged to consist of two magnetic poles of equal strengths but opposite signs a small distance apart. The ﬁrst-order geomagnetic ﬁeld is a dipole ﬁeld.

magnetic ﬁeld In general, the conceptualization due to Faraday, and rigorized by Maxwell of the laws relating the magnetic forces between current loops (or ﬁctitious magnetic monopoles) as embodied in a space-ﬁlling collection of vectors (a ﬁeld) which collectively deﬁne magnetic ﬂux tubes. In geophysics, the magnetic of the Earth or of other planets. On Earth, the ﬁeld is closely approximated by that of a dipole. The north and south magnetic poles are relatively close to the geographic poles. The magnetic ﬁeld is generated by dynamo processes in the Earth’s liquid, iron-rich core. The rotation of the Earth plays an important role in the generation of the magnetic ﬁeld and this is the reason for the close proximity of the magnetic and ge-

magnetic ﬁeld spiral

ographic poles. The Earth’s magnetic ﬁeld is subject to near random reversals on time scales of hundreds of thousands of years.

In solar physics, the sun’s magnetic ﬁeld is presumably also generated by a dynamo process, but the resulting ﬁeld is much more complex than that of a simple dipole, with alternating polarities in small regions on the solar surface. Magnetic ﬁelds capture energetic charged particles into radiation belts, like the Earth’s Van Allen belts. These magnetic ﬁelds thus help to protect a planet’s atmosphere and/or surface from the bombardment and erosion caused by these charged particles. As charged particles spiral in towards the magnetic poles, they can interact with molecules in the planet’s atmosphere, creating vivid aurora displays.

magnetic ﬁeld spiral	See Archimedian spi-
ral.

magnetic helicity One of the quadratic invariants occurring in the theory of hydromagnetic turbulence. The cross helicity within a volume V is deﬁned as

HM = A·Bd3x ,

where A is the magnetic vector potential, B = curl A is the magnetic ﬁeld, and the integral is taken over V. In an incompressible dissipationfree ﬂuid, for suitable boundary conditions, HM is conserved and is gauge invariant. In fully developed three-dimensional dissipative hydromagnetic turbulence, the magnetic helicity exhibits self-organization in the sense that it cascades from small eddies up to large-scale eddies. This inverse cascade process may be contrasted to the direct cascade and small-eddy decay exhibited by the energy. See cross helicity, helicity, hydromagnetic turbulence.

magnetic inclination The angle of the geomagnetic ﬁeld vector with the horizontal at a given location. It is deﬁned to be positive when the ﬁeld vector dips downward.

magnetic latitude The latitude of a point on Earth in a system of spherical coordinates centered on the magnetic poles deﬁned by the

dipole component of the main magnetic ﬁeld of the Earth.

magnetic local time (MLT) The magnetic longitude (converted to hours) in a system whose zero meridian is shifted to local midnight. Thus MLT = 0 is the magnetic meridian through midnight, MLT = 12 is the one through noon, and MLT = (6,18) are the ones at dawn and dusk, respectively.

magnetic longitude The longitude of a point on Earth in a system of spherical coordinates centered on the magnetic poles deﬁned by the dipole component of the main magnetic ﬁeld of the Earth. Zero magnetic longitude marks the magnetic meridian which overlaps the geographic meridian on which the north magnetic pole (off northern Canada) is located.

magnetic mirror Charged particles spiral around magnetic ﬁeld lines. Since the magnetic ﬁeld can do no work on the particle, the kinetic energy of the motion is conserved. As a particle moves toward a stronger magnetic ﬁeld, the orbiting kinetic energy increases, slowing the translational motion, and eventually reversing the drift. The location of this reversal, which depends on the strength and gradient of the magnetic ﬁeld, and on the kinetic energy of the particle, is a magnetic mirror.

magnetic pole Loosely speaking, if the Earth’s ﬁeld is approximated by a dipole, the two points on the surface of the Earth corresponding to the poles of that dipole.

Several more precise deﬁnitions exist, and should be carefully distinguished. The magnetic poles of the main dipole are the ones obtained by neglecting all non-dipole terms of the harmonic model of the geomagnetic potential: the positions of the resulting poles on the surface have north-south symmetry. The poles of the eccentric dipole are similarly based on the eccentric dipole model but are not symmetric. The dip poles (favored by early explorers) are the surface points where the magnetic dip angle is 90◦.

magnetic pressure Basic concept in magnetohydrodynamics. Graphically, magnetic pressure can be described as the tendency of neigh-

magnetism

boring magnetic ﬁeld lines to repulse each other. Thus, an inhomogeneity in the magnetic ﬁeld B gives rise to a force density f pushing ﬁeld lines back from regions of high magnetic density into low density areas:

f = 1 ( × B) × B .

4π

In contrast to the gas-dynamic pressure, the magnetic pressure is not isotropic but always perpendicular to the magnetic ﬁeld and can be deﬁned as pM = B2/(8π).

magnetic reconnection The dissipation of magnetic energy via magnetic diffusion between closely separated regions of oppositely directed magnetic ﬁeld. The result of the dissipation is that the oppositely directed ﬁeld lines form a continuous connection pattern across the diffusion region resulting in a change in the magnetic conﬁguration.

magnetic regime (cosmic string)	See elec-
tric regime (cosmic string).

magnetic reversal In geophysics, the Earth’s magnetic ﬁeld is subject to near random reversals on time scales of hundreds of thousands of years. These reversals are attributed to the chaotic behavior of the Earth’s dynamo. In solar physics, similar but much more rapid and local effects occur.

magnetic Reynolds number In ordinary hydrodynamics, the Reynolds number gives the ratio between inertial and viscous forces. If in a ﬂow the Reynolds number exceeds a critical value, the ﬂow becomes turbulent. A similar deﬁnition can be used in magnetohydrodynamics, only here the viscous forces do not depend on the viscosity of the ﬂuid but on the conductivity of the plasma:

RM =	UL	=	4πσ UL
	η		c2

with U being the bulk speed, L the length scale, σ the conductivity, and η = c2/(4πσ ) the magnetic viscosity. The coupling between the particles therefore does not arise from collisions as in ordinary ﬂuids but due to the combined effects of ﬁelds and particle motion.

magnetic secular variation Time variations of the Earth’s magnetic ﬁeld, usually taken to imply the time variation of the part of the ﬁeld generated by the dynamo in the Earth’s core. This generally includes most variation in the magnetic ﬁeld on periods of decades or longer: external variations in the ﬁeld, and their associated induced internal counterparts, tend to be on diurnal timescales, although some time averaging of the ﬁeld may cause measurements to exhibit power on longer timescales such as that of the solar cycle. On the other hand, the highest frequency on which the core ﬁeld varies is not well known: geomagnetic jerks, for example, appear to have timescales of around a year or two.

magnetic shear The degree to which the direction of a magnetic ﬁeld deviates from the normal to the magnetic neutral line, deﬁned by the loci of points on which the longitudinal ﬁeld component is zero. A sheared magnetic ﬁeld indicates the presence of currents since ×B = 0.

magnetic tension Basic concept in magnetohydrodynamics. Graphically, magnetic tension can be interpreted as a tendency of magnetic ﬁeld lines to shorten: if a magnetic ﬁeld line is distorted, for instance by a velocity ﬁeld in the plasma, a restoring force, the magnetic tension, acts parallel but in opposite direction to the distorting ﬂow. Thus, magnetic tension can be interpreted as a restoring force like the tension in a string. This concept can be used, for instance, to derive Alfvén waves in a simple way.

magnetism Magnetic ﬁelds and interactions. In solar system physics, solar and planetary magnetic ﬁelds are usually produced by moving electric currents in an interior conducting layer. In the sun, this is internal motion of the ionized gas. In the case of the Earth, the conducting layer is the liquid iron outer core. In the case of Jupiter and Saturn, the magnetic ﬁelds are produced by motions within a metallic hydrogen layer, and for Uranus and Neptune an interior slushy-ice layer is thought to give rise to the magnetic ﬁelds. Mercury’s magnetic ﬁeld is produced by its very large iron core, but debate continues as to whether this is an active (i.e., currently produced by interior currents)