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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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Miles–Phillips–Hasselmann theory

do not directly cause global warming or cooling. Such astronomical cycles occur for other planets as well, particularly Mars.

Miles–Phillips–Hasselmann theory A theory for description of the growth of wind wave energy in the sea.

Milky Way The band of light in the night sky resulting from the stars in the galactic plane. The term is also used to denote the galaxy in which the sun is located. See galaxy.

millibar A measure of pressure. One onethousandth of a bar. One bar is equivalent to 750 mm (29.53 in.) of mercury, or 105 Pascals (Pa), and represents 98.7% of normal atmospheric pressure.

Mimas Moon of Saturn, also designated SI. Discovered by Herschel in 1789. Its surface is dominated by the crater Herschel which has a radius of 65 km, nearly 1/3 the radius of the entire moon. This is probably the largest crater the body could have sustained without disruption. Its orbit has an eccentricity of 0.02, an inclination of 1.53◦, a precession of 365◦ yr−1, and a semimajor axis of 1.86 × 105 km. Its radius is 196 km, its mass 3.80 × 1019 kg, and its density 1.17 g cm−3. It has a geometric albedo of 0.5, and orbits Saturn once every 0.942 Earth days.

minimal coupling The expression of the behavior of some ﬁeld φ, which may be a scalar, spinor, vector, or tensor in a second ﬁeld, written by simply replacing the partial derivatives in the description of the free motion of φ, by covariant derivatives involving the connection from the second ﬁeld. An example is the equation for a scalar wave φ in a gravitational background, where the equation of motion is

gαβ α β φ = 0 ,

where α is the covariant derivative along α. If there is no gravitational ﬁeld (ﬂat space), then in rectangular coordinates gαβ is the simple form diag(−1, 1, 1, 1), and is the ordinary partial derivative, but in a general spacetime additional terms in the equation arise beyond second partial derivatives. Nonetheless, this is in a geometrical sense the simplest way to express an inﬂuence

of the gravitational ﬁeld or φ. See afﬁne connection.

minimum-B surface Another name for the equatorial surface of the magnetosphere. Because of the weak ﬁeld of the cusps, this surface splits into two sheets on the dayside of the Earth, in the region near the magnetopause. The sheets that lead to the cusps are associated with butterﬂy distributions.

minisuperspace In general relativity, the space of geometries obtained by restricting the form of the spatial metric in superspace so as to have a ﬁnite number of degrees of freedom (functions of time only). For such choices of the metric tensor, Einstein’s equations greatly simplify, and it is possible, for instance, to carry out quantization of the gravitational ﬁeld, a problem which has no known unambiguous solution in the general case. See geometrodynamics, superspace, Robertson–Walker cosmological models.

minor axis In an ellipse, the distance corresponding to the minimum length measured along one of the two symmetry axes, or this axis itself.

Mira Refers to a class of cool variable stars called long period variables, or LPV. The star Mira (o Ceti) is the proto-type, ﬁrst observed in 1596. Mira is a red giant classiﬁed as spectral type M5e – M9e and luminosity class III. Mira variables typically have long, regular periods of variation, usually 300 days or longer. The light curve is typically asymmetric with the rise from minimum to maximum light being faster than the decline. The deﬁning characteristic of Mira variables is the large change in brightness from minimum to maximum light, being at least 2.5 visible magnitudes and often as much as 10 magnitudes for some Miras. LPV stars (see also semi-regular, irregular variables) are thought to be past the He core-burning red giant stage and in a very brief end stage of evolution called the asymptotic giant branch, where the inert C, O core is surrounded by concentric shells of Heburning and H-burning material. About 90% of LPVs are oxygen-rich and 10% are carbon-rich (known as carbon stars).

mixing ratio

mirage Appearance of the image of some object, usually in distorted form, arising from refraction in air with strong index of refraction variations, caused by temperature variations. The refraction generically bends light rays toward air with greater density (lower temperature). Hence, mirages near the hot sand surface in a desert produce a false pond (the light paths are concave upward, so objects above the ground appear to be reﬂected in a surface near the ground); and those at sea over cold ocean produce looming (the light paths curve downward and follow the curve of the Earth, allowing far distant objects to be seen, and stretched out in the vertical direction).

Miranda Moon of Uranus, also designated UV. It was discovered by Kuiper in 1948. Its orbit has an eccentricity of 0.0027, an inclination of 4.7◦, a semimajor axis of 1.30 × 105 km, and a precession of 19.8◦ yr−1. Its radius is 236 km, its mass is 6.3×1019 kg, and its density is 1.14 g cm−3. Its geometric albedo is 0.27, and it orbits Uranus once every 1.413 Earth days. Miranda is known for its highly irregular terrain.

mirror instability Instability of a thermally anisotropic collisionless plasma, usually associated with an excess of pressure transverse to the magnetic ﬁeld. The general instability criterion is complicated; it takes a simple form for a biMaxwellian hydrogen plasma with equal proton and electron anisotropy:

8π	P − P	>	P
B2			P

where B is the mean magnetic ﬁeld strength, and P and P are, respectively, the pressures transverse and parallel to the mean magnetic ﬁeld.

mixed layer In atmospheric physics, over land, a layer of 1 to 2 km thick where the vertical transport of sensible heat, moisture, and momentum is so efﬁcient that potential temperature, mixing ratio, and wind show relatively little change with height. Also called planetary boundary layer. In oceanography near-surface waters subject to mixing by wind and waves; there is little variation in salinity or temperature within the mixed layer. Typically a layer of 100 m or less thick, it is separated from the

colder waters of the deep ocean by the thermocline.

mixing efﬁciency Parameter commonly used in oceanic turbulence studies, which relates the buoyancy production of turbulent kinetic energy B to the dissipation rate G: γ = B/G. The mixing efﬁciency is related to the ﬂux Richardson number Rif by

=Rif

γ.

1 − Rif

Most estimates for shear-induced turbulence in natural stratiﬁed water fall within the range of γmix = 0.15 ± 0.05 (Ivey and Imberger, 1991), but oceanic observations of γ range from 0.05, obtained from measurements at open ocean locations, to 0.7 in highly energetic ﬂows in tidal channels. See also Richardson number.

mixing length In the theory of the turbulent ﬂow of ﬂuid, the average distance through which each turbulent cell moves by turbulent motion before meeting other turbulent cells. Symbol is l . Deﬁned by Planck, who assumed that moving within the mixing length, the properties of turbulent cell will not change. In the parameterization of turbulent shear stress, the mixing length is expressed as

−ρ < u w >= p < l 2 >		∂ <∂z			∂z
			V >	∂ < u >



where l	is mixing length, V and u are horizontal

wind speed and its component on the x direction, < > means average value, and u and w are turbulent ﬂuctuating velocity. A turbulent coefﬁcient Km can be deﬁned as

Km =< l 2 >	∂ <∂z		.
		V >

Different effective mixing lengths may be observed for different ﬂuid properties. Thus, usually the turbulent coefﬁcient Km is used instead of using mixing length l . However, mixing length theory is still widely used in astrophysics.

mixing ratio The ratio of the mass of vapor to the mass of dry air.

Mixmaster universe

Mixmaster universe A dynamically anisotropic but homogeneous theoretical cosmology (Misner, 1966) which expands from a Big Bang to a maximum size and recollapses to a ﬁnal “big crunch”. The constant-time 3-spaces are distorted 3-spheres. A nonlinear oscillation occurs because the spatial curvature generates a “force term” in the motion of the anisotropy, bounding the anistropy by an amount which is ﬁnite at any one time, though the bound itself diverges at the Big Bang and big crunch. The universe behaves like an expanding, then contracting, ball that shrinks to a ﬂattened spindle and then puffs out ﬁrst in one direction and then in another, changing into a pancake conﬁguration, and so on. Any shape can eventually arise. Further, cosmological horizons can be eliminated in some situations, allowing mixing of matter and providing, in principle, a homogenization (though this has been shown to be of very small probability); thus the name, which also stems from the analogy with a particular kitchen appliance.

MJD See Modiﬁed Julian Date.
MK system of stellar classiﬁcation	In the

1890s Harvard Observatory began to classify stars according to hydrogen features, such as the strength of Balmer lines. In the 1920s this system of classiﬁcation based on temperature was revised and compiled by E.C. Pickering, A.J. Cannon, and others, leaving us with O, B, A, F, G, K, M. The types were divided up into 10 subtypes, from 0 to 9, and special types R, N, and S were added for carbon-rich stars. However, often stars of the same temperature type differed greatly in luminosity, and so several luminosity classiﬁcation schemes were used. In the 1930s W.W. Morgan and P.C. Keenan of Yerkes Observatory documented a luminosity classiﬁcation in combination with a temperature type that is still used today. The system used Roman numerals along with the subdivided temperature classiﬁcation. Class V stars are on the main sequence, class Ia, b are the supergiants, class II are the bright giants, class III are the normal giants, class IV are the sub-giants, class VI are the dwarfs, and class VII are the white dwarfs. Each of these luminosity classes occupy distinct positions on the Hertzprung–Russell diagram. Stars

with the same temperature yet different luminosity must differ in surface area (see effective temperature). This difference produces measurable effects in some spectral features, such as pressure broadening, and can thus be measured. Later, Keenan developed, along with others, a dual type of classiﬁcation for the difﬁcult latetype carbon-rich stars, the carbon stars. Types N and R have been replaced by a C classiﬁcation followed by two numbers, one indicating the temperature and the other the strength of the carbon abundance.

M magnitude Stellar magnitude derived from observations in the infrared at a wavelength of 5 µm.

model atmosphere A computationally constructed atmosphere model, created according to physics laws and representing the atmospheric status by discrete values on horizontal grid mesh and vertical levels. By inputting initial atmospheric state conditions, numerical atmospheric models can start time integration to simulate the real atmospheric processes approximately. Their accuracy depends on the model’s resolution, the number and quality of contained physics processes, and parameterization packages to describe the sub-grid processes in the models. By simulating real atmospheric processes, numerical atmospheric models can provide products for weather forecasts, research on different atmospheric science issues, and on climate status in ancient times.

mode water An ocean water mass characterized by small vertical gradient in temperature and density. For this, it is also called thermostad or pycnostad. Occupying a great depth range, this water mass stands out as a distinct mode in a volumetric census taken against temperature or density. Subtropical mode waters, found in northwestern parts of the North Paciﬁc and North Atlantic subtropical gyres, are the most famous ones, with a characteristic temperature centered on 18◦C, they are sometimes called 18◦-waters. They form in the deep mixed layer under intense cooling in winter and are advected southwestward by the wind-driven subtropical gyres. Other mode waters with different tem-

Mohr’s circle

perature characteristics are found in other parts of the oceans.

Modiﬁed Julian Date (MJD) The Julian date minus 2400000.5 days. MJD is used in atomic time work.

modulation of galactic cosmic rays The intensity of galactic cosmic rays (GCRs) in the inner heliosphere varies in anticoincidence with the 11-year cycle of solar activity: during times of high solar activity, the intensity of GCRs is diminished while it is maximal during times of low solar activity. This temporal variation is called modulation; it is most pronounced at energies between about 100 MeV/nucl, decreases to about 15 to 20% at energies around 4 GeV/nucl, and vanishes at energies higher than about 10 GeV/nucl.

Modulation of GCRs results from the variation of the structure of the heliosphere during the solar cycle, allowing cosmic rays to propagate faster and/or in larger numbers from the outer borders of the heliosphere (such as the termination shock) into the inner heliosphere during solar minimum, when the heliospheric structure is rather simple with a small tilt angle and only very few transient disturbances such as magnetic clouds and interplanetary shocks. Since different effects inﬂuence the propagation of energetic particles in the interplanetary magnetic ﬁeld, modulation is determined by these processes as well. Of all the processes inﬂuencing interplanetary propagation (see interplanetary propagation) for modulation only those processes that vary during the solar cycle are important:

1. Drift in the heliospheric current sheet. The heliospheric current sheet separates magnetic ﬁeld lines of opposite polarity. Thus, gradient drift allows particles to propagate along this neutral line from the outer skirts of the heliosphere toward the orbit of Earth. During solar minimum conditions, when the tilt angle is small, the heliospheric current sheet is rather ﬂat. During maximum conditions, however, the tilt angle becomes much larger, leading to a wavier heliospheric current sheet and consequently a much longer drift path for particles traveling into the heliosphere, thus diminishing intensities of galactic cosmic rays at times of solar maximum conditions.

2.Drift from polar to equatorial regions and vice versa. This drift should lead to a charge separation of electrons and positively charged particles and therefore in the equatorial plane different intensity-time proﬁles for both species should be observed depending on the polarity of the solar magnetic ﬁeld. The inﬂuence of this effect is still debated because observations are inconclusive.

3.Transient disturbances. In contrast to the drift, transient disturbances cause step-like intensity decreases, called Forbush decreases (see Forbush decrease). These transient disturbances are shocks and magnetic clouds; thus, their number increases with increasing solar activity. Therefore, part of the decrease in cosmic ray intensity during solar maximum can be understood as a fast sequence of decreases related to transient disturbances.

4.Merged and grand merged interaction regions (MIRs and GMIRS). Not only traveling shocks but also shocks at corotating interaction regions cause a reduction in cosmic ray intensity. This reduction becomes even more pronounced when at larger radial distances corotating interaction regions and transient disturbances merge, eventually forming a closed torus around the inner heliosphere. Galactic cosmic radiation then can be blocked efﬁciently and globally by this torus.

Mohoroviciˇc´ discontinuity A discontinuity in the speed of seisimic waves which marks the transition from the Earth’s crust to its mantle. Also called the moho for short, it is found at depths of between 25 and 40 km under continents, and about 5 km under the ocean ﬂoor. Its location is relatively easily determined because seismic waves reﬂect off of it.

Mohr’s circle A circle whose diameter is the difference between maximum and minimum principal stresses which are on an axis of normal stress as the abscissa, and an axis of shear stress as the ordinate. Using Mohr’s circle, we can obtain the relation between normal stress and shear stress exerted on a plane with arbitrary direction within a plane containing the axes of the two principal stresses. All the Mohr’s circles at the time of fracture drawn at a variety of state of stresses are tangent to a straight line represented

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