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horse latitudes

from the loci of the stars in an HR diagram, which is roughly horizontal, at least for some choices of temperature indicator. RR Lyrae variables, one of the common distance indicators, are horizontal branch stars. The corresponding phase for stars of higher metallicity is called the clump phase, while more massive stars pass through the phase without abrupt changes in their locations on the HR diagram. See clump star, CNO cycle, helium burning, HR diagram, metallicity.

horse latitudes The latitudes approximately 30◦N and 30◦S which are regions of calm winds and generally high pressure.

horst An elevated block of crustal material forming a ridge or plateau, bounded by parallel normal or reverse faults. A horst is usually produced by compressional tectonic forces.

hot dark matter See dark matter, hot.

hot spot (1.) A bright, compact component observed in the radio lobes of powerful radio sources, such as radio galaxies and quasars. Hot spots are frequently found in radio source of Fanaroff–Riley class II, which includes the brightest lobe dominated radio source. Hot spots are 1 kpc in size, and they appear unresolved when observed at moderate resolution. Their radio spectrum is described by a powerlaw over the frequency and a spectral index ≈ −0.5, suggesting that radiation is emitted via a synchrotron process. Their location, often at the outer end of the jet, suggests that hot spots are the site of impact between the high speed particles of the jet and the lobes. See Fanaroff– Riley.

(2.) In geophysics, areas of enhanced volcanic activity not directly associated with plate boundary volcanism, either ocean ridges or the volcanic lines behind subduction zones. Hot spots represent areas where magma from the mantle erupts directly onto the surface, creating features associated with fluid lavas such as flood basalts and shield volcanos. The Hawaiian islands show the passage of the Pacific Plate over a hot spot. Iceland is considered to be a hot spot because of its large volcanic flux. Hot spot volcanism is a common process on other plan-

ets, particularly Mars and Venus where many of the large volcanos are the result of this process.

hot towers The cores of large cumulonimbus clouds in the intertropical convergence zone. See intertropical convergence zone.

hour angle The angular distance on the celestial sphere measured westward along the celestial equator from the vernal equinox to the hour circle passing through the celestial object in question. It is equal to 360◦ minus the right ascension.

HR (Hertzsprung–Russell) or color-magni- tude diagram A plot of brightness or luminosity vs. some indicator of effective temperature for observed stars, calculated models of stars, or a comparison between the two. Such diagrams have been a primary tool for displaying and testing ideas of stellar structure and evolution since the early 20th century. Such a plot was first attempted for stars in the Pleiades in 1910 by Hans Rosenberg, following advice from Karl Schwarzschild, while Einar Hertzsprung and Henry Norris Russell soon after considered stars of known distances in the solar neighborhood.

The vertical axis can be luminosity in solar units or absolute magnitude or even apparent magnitude for a cluster of stars known to be all the same distance from us, either over a full range of wavelengths (bolometric luminosity) or over some restricted range of wavelengths (U, B, V ,R, I, etc., UBV colors). The horizontal axis can be effective temperature (especially in the case of models), a color index, or spectral type.

Real stars do not populate such a diagram at random. Ninety percent (in a distance-limited sample) will fall on a diagonal from Hot-Bright (upper left) to Cool-Faint (lower right) called the main sequence. The scattering of stars above the main sequence are called red giants and supergiants; those fainter are sub-dwarfs and white dwarfs. A cluster of stars all with the same age and initial chemical composition has a characteristic HR diagram with signatures for age and metallicity. An HR diagram representing observed stars normally shows individual symbols for each star.

© 2001 by CRC Press LLC

Hubble parameter (Hubble constant)

When calculations are displayed, there can be points for stars of particular masses, compositions, and evolutionary phases, or, more often, continuous trajectories representing the temporal evolution of a particular model (evolutionary track) or the loci of a number of different star masses at the same time (isochrones). Comparisons between theory and observation are made by plotting both real stars and tracks or isochrones. The problem of converting calibration from observers’ quantities (like spectral type and absolute visual magnitude) to theorists’ quantities (bolometric luminosity and effective temperature) remains a serious one.

Major phases of stellar evolution are frequently named for the loci of the stars in an HR diagram, including the main sequence, subgiant branch, Hertzsprung gap, red giant branch, horizontal branch, and asymptotic giant branch. Each of these corresponds to a fairly welldefined nuclear source of stellar energy and to a fairly definite interior structure in temperature, density, and chemical composition vs. radius. Both observations and models show that the primary determinant of what a star will do throughout its life is its initial mass. See absolute magnitude, apparent magnitude, asymptotic giant branch star, bolometric magnitude luminosity, color index, effective temperature, Hertzsprung Gap, horizontal branch star, main sequence star, metallicity, red giant.

Hubble deep field A high galactic latitude sky field (of width ≈ 2 arcmin), intensively observed in four colors with the Wide Field Planetary Camera mounted on board the Hubble Space Telescope in December 1995. Three sets of observations for a total of 35-h exposure time were obtained with broad band filter centered at 450, 606, and 814 nm, and a set of 50 h exposure time with a near UV filter centered at 300 nm. The Hubble deep field was chosen in an area of low HI column density, small far-IR flux, with no radio source brighter than 1 mJy, no bright stars, and no nearby galaxy clusters. These selection criteria were aimed at making possible the identification and morphological study of a large number of faint, field galaxies. The observations allowed counting the number of galaxies in the field down to a magnitude < 29, an unprecedented achievement. See Jansky (Jy).

Hubble diagram A diagram plotting observed redshift of a galaxy on one axis vs. some measure of the distance of the galaxy on the other. Used to verify or to detect deviations from Hubble’s law: v = H0d, where d is the distance to the galaxy.

Hubble parameter (Hubble constant) The proportionality factor H0 in the Hubble law v = H0l, where v is the velocity with which a given galaxy G recedes from our galaxy, a measure of the present expansion rate of the universe, and l is the distance between G and the observer in our galaxy. H0 is traditionally measured in km/(sec · Mpc), so that v comes out in kilometers per second when l is measured in megaparsecs (Mpc). The actual numerical value of H is subject to many random and systematic errors. In the 1930s H0 was believed to be of the order of 500 km/(sec · Mpc). Currently it is believed to be between 50 and 100 km/(sec · Mpc). In determining the Hubble constant, H0, it is the distance determination that introduces uncertainty since the recession is directly measured by the redshift. This uncertainty in the measured value of H is usually taken into account by incorporating the parameter h (called the dimensionless Hubble parameter) into all formulae that depend on H ; by definition h = H/(100 km/s · Mpc) so that h = 1 when H = 100 km/s · Mpc. The value of H determines the age of the universe (i.e., the time since the Big Bang up to now) and the distances between galaxy clusters, so knowing it is of fundamental importance for cosmology. The Hubble parameter is colloquially called “Hubble constant”, but in the currently accepted cosmological models it is a decreasing function of time and “the value of H ” actually means the current value H0. In inhomogeneous models the Hubble law does not apply globally; in them, v is a nonlinear function of l, a different one for every observer. If our universe is inhomogeneous, then the Hubble law applies only as a first approximation to the actual function v(l) in a sufficiently small neighborhood of every observer, and the local value of the Hubble parameter depends on the position of the observer and on the direction of observation. Reference: E.P. Hubble, The Realm of the Nebulae, [republication by] Yale University

© 2001 by CRC Press LLC

Hubble radius

Press 1982; Mon. Not. Roy. Astr. Soc., 113, 658, (1953).

Hubble radius Distance at which the recession velocity of a galaxy will be the speed of light: cHo−1 = 3000 h−1 Mpc. Galaxies located at larger distances will not be in casual contact with us. Hence, it gives the scalelength of the particle horizon. See Hubble parameter.

Hubble–Reynolds law Empirical law describing the brightness profile of an elliptical galaxy, introduced by J.H. Reynolds in 1913. According to Hubble–Reynolds law, the surface brightness depends upon the distance from the galaxy center, r, as (r) = 0/(1 + r/r0), where the scaling parameter r0 is the radius at which the surface brightness falls to one quarter its central value 0. This law, remarkable because of its simplicity, predicts a deficit of light close to the center and more light in the outer envelope of a galaxy with respect to de Vaucouleurs’ law. See de Vaucouleurs’ law.

Hubble sequence A classification scheme of galaxies created by E. Hubble. In the Hubble sequence, galaxies are subdivided into elliptical galaxies, S0 galaxies (galaxies showing evidence of an amorphous disk and a bulge, but no spiral arm, also called lenticular galaxies), spiral galaxies, either barred or non barred, and irregular galaxies. An elliptical galaxy is conventionally indicated with the uppercase letter E and an integer number ranging from 0 to 7, increasing with the apparent flattening, and defined as the integer part of 10 × (1 − (b/a)), where (b/a) is the axial ratio measured on a photograph or digital image. Spiral galaxies are farther subdivided along the sequence in S0, Sa, Sb, Sc according to three criteria: (1) decreasing bulge prominence with respect to disk; (2) spiral arms less tightly wound; (3) appearance of arms more resolved. At the end of the sequence, irregular galaxies (subdivided into Magellanic and amorphous or M82-type) do not show regularly decreasing surface brightness nor spiral arms and are of patchy appearance. Elliptical and S0 galaxies are collectively referred to as “early morphological types”, and Sc and irregulars as “late type” galaxies. Hubble attributed to these terms an evolutionary meaning, i.e., he

thought that a spiral could be an evolved elliptical galaxy. This view is not considered appropriate anymore, since the angular momentum per unit mass, a constant for an isolated galaxy, increases along the sequence from the elliptical to the most flattened galaxies (Sc). Nevertheless, gravitational interaction between galaxies can affect the morphology of spiral galaxies to the point of changing their Hubble type. See elliptical galaxies, spiral galaxy.

Hubble’s law Relation between the recession velocity of a galaxy v and our distance to it d: v = Hod where Ho is called Hubble parameter to honor Edwin Hubble who discovered this relation in 1928. In an expanding universe, this direct proportionality is a consequence of the homogeneity and isotropy (see cosmological principle). The law is only exact on the average. Local irregularities in the matter distribution create small deviations. See peculiar motion.

Hubble space telescope (HST) A spacebased telescope of 2.4 m aperture, launched in 1990 and orbiting in a low terrestrial orbit. Although the optical design of HST is similar to that of a mid-sized ground-based telescope, the absence of atmosphere allows the telescope to operate at a resolution close to the diffraction limit (0.03 arcsec at 3000 Å), and to detect UV light which is absorbed by the terrestrial atmosphere. Currently available instruments on board HST include two imaging cameras, a long-slit spectrograph, and a camera and spectrometer operating in the near infrared. The Wide Field Planetary Camera, which is composed of three CCD detectors in an L-shape configuration plus a single, smaller CCD detector at the center of field, has limiting magnitude of 28 (with 1-h exposure time and S/N ratio 5), and reaches a resolution of 0.053 sec of arc. The highest resolution, 0.042 sec of arc, is achieved with the Faint Object Camera, which has a much smaller field of view, 7×7 square arcsec. (Traditional ground-based optical telescopes have resolution limited by atmospheric seeing to about 1 arcsec, although modern adaptive optics techniques can improve ground-based resolution in some wavelengths to well below 1 arcsec.) The Space Telescope Imaging Spectrometer, which

© 2001 by CRC Press LLC

hydraulic depth

operates between 115 and 1100 nm, offers spectral resolving power ranging from 150 to 100000 and long slit capabilities.

Hubble time Inverse of Hubble constant; Ho−1 = 9.78h−1 × 109 years corresponding to the time it would take the universe to reach its present size expanding at constant rate Ho. Here h = H0 (100 km/sec/Mpc). See Hubble radius.

humic substance High molecular weight organic compounds resulting from plant decay, especially terrestrial plants; water-soluble soil humic substance imparts a yellow color to water. See also colored dissolved organic matter.

hurricane Intense tropical cyclone of the Atlantic Ocean, Caribbean region, and on the northeastern coast of Australia. Similar types of tropical cyclone appearing over the western Pacific are called typhoons. A hurricane is a circulatory strong wind system (180 km/h or so) with low central pressure (below 950 mb), and is confined to a few hundred kilometers. In the northern hemisphere the wind rotation is counterclockwise.

Huygens principle In radiation fields, the phase front at any instant can be thought of as the locus of radiating sources, and the phase front at the next instant is obtained by a phase coherent addition of the radiation from all those sources.

Hyades An open cluster of about 100 stars visible to the naked eye in the constellation of Taurus (45 parsecs from the sun, at right ascension 4h 27m, declination +16◦0 ). The Hyades cluster is about 600 million years old.

hybrid topological defect Different symmetry breaking schemes in quantum field theory allow for the possibility of formation of various kinds of topological defects, like monopoles, cosmic strings, and domain walls, in the early universe. Realistic grand unified models generally involve several phase transitions and therefore one type may become attached to another, and the system will end up, say, with walls bounded by strings or strings connecting monopoles. Such mixed configurations are called hybrid topological defects and are dynam-

ically unstable since no topological constraint can be applied on them. See cosmic phase transition, cosmic topological defect, grand unification, Langacker–Pi mechanism.

hydraulic head (piezometric head) The equivalent height of a fluid required to maintain a pressure hydrostatically. The hydraulic head is of practical meaning only when defined for a uniform fluid density. For a flow field with variable fluid density, a reference head is often defined using a reference density. Given density ρ, the hydraulic head h is defined as

h = p + z ρg

where p is fluid pressure, g is gravitational acceleration, and z is elevation measured from an arbitrary reference point. In groundwater hydrology, the hydraulic head is also called the piezometric head.

hydraulic conductivity (K) The ability of a porous medium to transmit fluid is dependent on both the properties of the fluid and the medium:

ρg

K = κ

µ

where κ is the intrinsic permeability of the porous medium, ρg is the fluid weight, and µ is the viscosity of the fluid. Hydraulic conductivity is generally a tensor because of κ. It has the dimension of velocity. See Darcy’s law. The hydraulic conductivity of natural substances ranges over many orders of magnitude, from 10−21 m s−1 for unfractured crystalline rock to 10−2 m s−1 for karst limestone and gravel. The hydraulic conductivity decreases very rapidly as the medium becomes unsaturated, because the larger pores of the subsurface become airfilled first, causing flow to occur in smaller pores which conduct water at much lower flow rates according to Poiseuille’s law. We therefore write the hydraulic conductivity in unsaturated systems as K(θ), indicating that it is a function of the volumetric moisture content.

hydraulic depth The cross-sectional area of a free-surface flow (such as a river) divided by the top width of the flow.

© 2001 by CRC Press LLC

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