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Dictionary of Geophysics, Astrophysic, and Astronomy.pdf

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Pandora

domes. Most occur in the lowland plains far from the largest shields, and often near the lowland coronas. “Tick-like” features also show a pattern similar to the pancake domes, both in their spatial distribution and morphological similarities. Thus, it is thought that many ticks are modiﬁed dome features.

Pandora Moon of Saturn, also designated SXVII. It was discovered on Voyager photos in 1980. Its orbit has an eccentricity of 0.004, an inclination of essentially 0, and a semimajor axis of 1.42 × 105 km. Its size is 57 × 42 × 31 km, its mass is 2.2 × 1017 kg, and its density 0.71 g cm−3. It has a geometric albedo of 0.9, and orbits Saturn once every 0.629 Earth days. Pandora is the outer shepherd of Saturn’s F ring.

Pangaea In geophysics, the single supercontinent in which all the continental areas were connected, and which broke up under continental drift about 180 million years ago.

Papapetrou spacetimes (1953) Stationary empty space-times for which the norm and curl scalars of the Killing vector are in a functional relationship. Their asymptotic expansion lacks the mass monopole term, so they are in a sense zero-mass gravitational ﬁelds.

PAR See photosynthetically available radiation.

paraboloid A ﬁgure of revolution based on a parabola. The preferred shape for reﬂecting telescope primaries because it brings all rays parallel to the axis to a focus at the same unique point.

parallax Motion of nearby stars against the more distant background stars, as a result of the different vantage points from the Earth’s orbit at different times of the year. Essentially a baseline of 2 AU (astronomical units) is used to give a perspective on the distance to the star. See astronomical unit, parsec.

parallel electric ﬁeld The component E|| of the electric ﬁeld in a plasma parallel to the magnetic ﬁeld vector. Because charges can easily ﬂow along magnetic ﬁeld lines, in many plasma

conﬁgurations E|| is expected to be virtually zero. However, observations on auroral ﬁeld lines (e.g., that of beams of ions) suggest that a non-zero E|| may exist there, balanced either by the mirror force (see quasi neutral equilibrium) or by turbulent plasma processes. The ambipolar electric ﬁeld, in which a relatively small E|| is balanced by gravity, is another example.

Parker limit A limit on the cosmological ﬂux of magnetic monopoles:

FM ≤ 10−15 cm−2 · sec−1 .

Acceleration of magnetic monopoles in the presence of a magnetic ﬁeld B (like that of a galaxy, for instance), makes the magnetic ﬁeld energy density decrease with time. The characteristic decay time is

τd =	eB
		,
	4πnM vM

where e is the electric charge, nM the magnetic monopole number density, and vM their average velocity. As the time necessary to regenerate the magnetic ﬁeld in a galaxy is comparable to the galactic rotation period τr 108 years, the limit results from the requirement that the decay time τd be larger than τr (so that magnetic monopoles do not affect galactic physics noticeably). The maximum allowed ﬂux is much less than what is expected for monopoles formed at the grand uniﬁed energy scale. See monopole, monopole excess problem.

parsec The distance corresponding to a parallax of one second of arc. A unit of distance deﬁned as the distance at which 1 astronomical

unit (AU) subtends an angle of 1 sec of arc. It is equal to 206264.806 AU = 3.08568×1016 m =

3.26166 light years.

partial derivative For a function f of multiple independent variables xa, the derivative with respect to one variable, say xi, computed by treating the other independent variables xa, a = i constant. Notation:

∂f

∂xi

partial pressure In any mixture of gases, of each component gas, the pressure that the gas

patera

would exert alone, i.e., if all the other gases had been removed. The total pressure equals to the summation of all the partial pressures.

particle acceleration In astrophysics, any process by which ambient particles gain energy. Typically applied to high energy radiation signatures. Planetary atmospheres, the sun, galactic nuclei, and accretion disks are all sites of particle acceleration.

particle horizon The causal horizon determined by the maximum distance from which a particle can receive physical signals. Since no signals can travel faster than light, the particle horizon is given at a ﬁxed time by the past lightcone originating from the space-time position of the particle.

For example, in the Big Bang model of the universe, two particles that emerged from the surface of last scattering (when matter decoupled from radiation) could see each other by now only if enough time has passed such that a beam of light could have traveled the distance that separates the two particles. The proper distance between two particles locally at rest in some spacetime models (e.g., De Sitter and generally inﬂationary models) grows faster than light speed (although no signal is transmitted and causality is not violated), in which case the horizons of the particles actually shrink in time.

pascal (Pa) A unit of pressure, equal to 1 Newton/m2. Atmospheric pressure at sea level is slightly greater than 105 Pa.

Paschen series The series of lines in the spectrum of the hydrogen atom which corresponds to transitions between the state with principal quantum number n = 3 and successive

higher states. The wavelengths are given by 1/λ = RH (1/9 −1/n2), where n = 4, 5, 6, · · ·

and RH is the Rydberg constant. The ﬁrst member of the series (n = 3 ↔ 4), which is often called the Pα line, falls in the infrared at a wavelength of 1.875 µ m. See Rydberg constant.

Pasiphae Moon of Jupiter, also designated JVIII. Discovered by P. Melotte in 1908, its orbit has an eccentricity of 0.378, an inclination of 145◦, and a semimajor axis of 2.35 × 107 km.

Its radius is approximately 25 km, its mass 1.9 × 1017 kg, and its density 2.9 g cm−3. Its geometric albedo has not been well determined, and it orbits Jupiter (retrograde) once every 735 Earth days.

passive continental margin A continental margin that is not a plate boundary. A passive continental margin is the result of a process of continental rift, seaﬂoor spreading, and creation of the oceanic crust.

passive earth force The force exerted (either laterally or vertically) by stationary soil against a surface.

passive margins The boundaries between the oceans and the continents are of two types, active and passive. Passive margins are not plate boundaries and have little or no seismic activity or volcanism. The boundaries of the Atlantic Ocean are almost entirely passive margins.

patchiness and intermittence Oceanic turbulence exhibits strong spatial and temporal variability. Spatially, the turbulence is distributed in layers or “patches” having vertical scales from about 0.5 to 25 m and horizontal scales ranging from several meters to several hundreds of meters. Thinner layers occur more frequently and they are generally less active than thicker layers. Temporally, turbulence is intermittent and occurs in “bursts” caused by local dynamic instabilities in high-gradient regions, such as the breaking of internal waves.

patera A large, low-sloped (< 1◦) volcano found on Mars. Paterae tend to have very highly dissected ﬂanks, indicating they are covered with an easily erodible material such as ash. Most of the Martian paterae have high crater densities, indicating an old age. No terrestrial analogs are known, but many planetary scientists believe patera formed by the interaction of hot magma with surface or near-surface water. When hot magma encounters cold liquid water, a steam explosion causes the creation of ﬁnegrained ash rather than lava ﬂows. It is believed that early in Mars’ history there was much more water on or near the surface than today and that the rates of volcanic activity were also higher,

pathline

which could have led to the formation of the patera.

pathline A line drawn through a region of ﬂuid that indicates the path followed by a particular particle within the ﬂuid.

P-Cygni proﬁle An emission/absorption line proﬁle which is the result of an expanding shell of gas around a star; the star P Cyg is the prototype. Its visible spectrum shows lines that have a wide emission component and an absorption component, with the absorption blue shifted and the emission line approximately at the star’s rest velocity. A simple explanation is that the absorption arises in material in front of the star along our line of sight toward the continuum source. Since this material is expanding directly at us, we see the absorption line blue shifted with respect to the star’s rest frame. The part of the expanding gas that is moving at right angles to our line of sight, on either side of the star, without the stellar continuum in the background, produces emission lines that are roughly centered at the star’s rest velocity. The degree in which the absorption portion is shifted depends on the velocity of the gas that is producing the lines, and thus these lines allow the measurement of wind velocities in astronomical objects. The winds in OB stars and in cataclysmic variables were originally detected through the observation of these line proﬁles in their spectrum.

Peclet number A dimensionless number quantifying the importance of advective heat transfer. It is the ratio of heat ﬂux by advection to heat ﬂux by conduction. For example, if the characteristic ﬂow velocity in the direction of heat conduction is v over a characteristic length L, the Peclet number is deﬁned as P e = vL/κ, where κ is the thermal diffusivity. If P e 1, heat transfer is mainly advective. If P e 1, heat transfer is mainly conductive.

peculiar motion In astronomy, the physical or angular velocity of a source with reference to a ﬁxed frame of interest. For stars, the transverse peculiar motion is typically given in seconds of arc per century. For extragalactic objects, transverse motion is not measurable, but the radial

peculiar motion is measured by means of red shifts, and reported in terms of km/sec.

peculiar velocity

See peculiar motion.

peeling property The Weyl tensor (a form of the curvature tensor) of an asymptotically ﬂat space-time, when expanded in power series of the afﬁne parameter r of outgoing null geodesics, has the form

Cijkl =	Nijkl		+		IIIijkl	+	IIijkl
Cijkl =	r		+		r2	+	r3
	+ r4			+ O r5
		Iijkl				1

where the coefﬁcients Nijkl, IIIijkl, etc. are of the Petrov type indicated by the kernel letter. In particular, gravitational radiation encoded in Nijkl has an amplitude falloff of r−1. See Petrov types.

penetrative convection Sinking plumes in a convectively mixing surface layer (or rising plumes in a convectively mixing bottom layer) impinge with their characteristic velocity scale onto the adjacent stratiﬁed ﬂuid. As the plumes have momentum, they reach a limited penetration of the depth scale before the plumes stop due to entrainment and buoyancy. For instance, substantial, convective motions are present in the upper layer of the sun. At the base of the convection zone there is a gradual transition to the stable, radiative interior, the convective penetration zone. Below it, energy is transported outwards entirely by radiative diffusion. At the penetrative convection depth, the gas becomes suddenly less opaque, becomes unstable, and convective transport becomes dominant.

Penman equation (or combination equation)

Evaporation (E) can be estimated by combining mass-transfer and energy-balance approaches in a theoretically sound and dimensionally homogeneous relation:

E = s (Ta ) (K + L) + γ KE ρwλvua [esat (Ta)] (1 − RH ) ρwλv s (Ta ) + γ

where s(Ta) is the slope of the saturation vapor pressure vs. air temperature (Ta), K is net shortwave radiation, L is net longwave radiation, γ is

perfect ﬂuid space-times

the psychrometric constant, KE is a coefﬁcient that reﬂects the efﬁciency of vertical transport of water vapor by turbulent eddies of the wind, ρw is the density of liquid water, λv is the latent heat of vaporization, ua is the wind speed, esat is the saturation vapor pressure at air temperature Ta, and RH is the relative humidity. The Penman equation assumes no heat exchange with the ground, no water-advected energy, and no change in heat storage, and can be expressed in simpliﬁed form as

E	s (Ta) × net radiation + γ × “mass transfer” .
		s (Ta) + γ
Penman–Monteith		equation	Monteith

showed how the Penman equation can be modiﬁed to represent the evapotranspiration rate (ET ) from a vegetated surface by incorporating canopy conductance

= s (Ta ) (K + L) + γρa ca Cat [esat (Ta )] (1 − RH )

ρwλv s (Ta ) + γ (1 + Cat /Ccan)

where variables from the Penman equation have been supplemented with the density of air ρa, the heat capacity of air ca, the atmospheric conductance Cat , and the canopy conductance Ccan.

Penrose diagram Space-times Min general relativity often have inﬁnite extent, which makes their pictorial representation difﬁcult. However, it is always possible to apply a suitable conformal mapping to the metric,

g (x) = 4(x) g(x) ,

such that M is mapped into a new manifold M which has ﬁnite extension and thus (sections of it) can be drawn on a sheet of paper. This implies certain behavior of the conformal factor 4(x).

The transformation above leaves the causal structure of space-time untouched. Further, it is possible to choose coordinates and representations so that light travel is along 45◦ lines when plotted in M .

Penrose process A process in which energy can be extracted from the rotation of a black hole, by exploding particles in free fall in the ergosphere near the black hole; with correct choice

of the orbits, one of the two fragments reaches inﬁnity with a total energy exceeding the total rest mass-energy of the pieces.

penumbra (1.) The lighter region of a sunspot surrounding the umbra. The penumbra consists of light and dark radial ﬁlaments that are typically 5000 to 7000 km long and 300 to 400 km wide. Individual penumbral ﬁlaments endure 0.5 to 6 hours compared to the days or months for the sunspot as a whole.

(2.) During a solar eclipse, the part of the shadow from which part of the sun is still visible.

percolation The process of a ﬂuid passing through pores in a medium such as soil.

perfect ﬂuid A ﬂuid in which energy transport occurs only by means of matter ﬂow (there is no viscosity or heat ﬂow). A singlecomponent perfect ﬂuid (a ﬂuid composed of atoms or molecules of the same chemical element or compound) is characterized by two functions of state, e.g., pressure and massdensity, from which all other functions (e.g., the temperature and entropy) can be calculated by means of the equation of state and other thermodynamical relations. A multicomponent ﬂuid is not chemically homogeneous and can be perfect only if either there are no chemical reactions or all chemical reactions are reversible (i.e., with no emission of heat). In either case, densities of the chemical components must be speciﬁed separately, and when chemical reactions take place, the chemical potentials are also necessary to describe the state of a ﬂuid. In cosmology, it is often assumed that the matter in the universe behaves like a single-component perfect ﬂuid or a dust; the latter is pressureless and so obeys an even simpler thermodynamic. For stellar interiors, a perfect ﬂuid is only a rather crude ﬁrst approximation to a description of thermodynamical properties.

perfect ﬂuid space-times Space-times containing a perfect ﬂuid with the stress-energy tensor

T ab = (µ + p)uaub + pgab .

Here the functions µ and p are the energy density and the pressure of the ﬂuid. The timelike

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