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Chemical symbol for hydrogen. The most abundant chemical in the universe. H2 is the symbol for the molecular hydrogen molecule which is abundant in giant clouds in our galaxy and can be detected by its infrared spectrum. The symbols HI and HII are used to indicate neutral and ionized hydrogen respectively. HII regions are usually associated with star formation, e.g. the Orion Nebula, and are detected by their emission lines such as H-alpha at 656.3 nm. Radio emission at 21 cm wavelength can be detected from neutral hydrogen. [McL97]


The quantity h (Planck's constant) divided by 2pi: hbar = 1.054 x 10-27 erg seconds. [H76]


Hubble's constant in units of 100 km s-1 Mpc-1. [H76]


An Mg II resonance line at 2803 Å. [H76]

H and K Emission Line Stars

Late objects (F4 to M), which exhibit emission features in their H and K lines of Ca II. [JJ95]

H and K lines

The two closely spaced lines of singly ionized calcium at 3968 and 3934 Å, respectively. [H76]

H- ion

An H ion with an extra electron in its shell. It is an important source of stellar opacity in stars whose spectral types are later than about A5. [H76]


The magnitude derived from infrared observations at 1.6 microns. [H76]


Neutral hydrogen gas. It emits radio waves that are 21 centimeters long. [C95]

H I Region

Region of neutral (atomic) hydrogen in interstellar space. The temperature is about 125 K (the spin temperature of neutral hydrogen - far too low for electrons to emit radiation in the optical part of the spectrum (see 21-cm radiation). At least 95 percent of interstellar H is H I. (Density is about 10 atoms per cm3, about the same as in H I regions.) [H76]


Ionized hydrogen - that is, hydrogen with its electron missing. [C95]

H II Condensation

A high-density H II region. [H76]

H II Region

(a) An area of ionized hydrogen. Most H II regions are red and arise from hot blue O and B stars, whose ultraviolet light can ionize all the hydrogen for dozens or even hundreds of light-years in every direction. The most famous H II region is the Orion Nebula. [C95]
(b) Region of ionized hydrogen in interstellar space. H II regions occur near stars with high luminosities and high surface temperatures. The kinetic temperature of H II regions is about 10,000-20,000 K, and the density is about 10 atoms per cm3. Ionized hydrogen, of course, having no electron, does not produce spectral lines; however, occasionally a free electron will be captured by a free proton and the resulting radiation can be studied optically (see also radio recombination lines). [H76]

H-R Diagram

Hertzsprung-Russell diagram. A diagram of stars arranged according to their luminosity (measured on the y axis) and temperature (on the x axis). In the early part of the twentieth century, the Danish astronomer E. Hertzsprung and the American astronomer H. Russell plotted known stars in such a diagram and found a definite correlation between luminosity and temperature. (See main sequence.) [LB90]


Hydrogenated Amorphous Carbon


An unofficial name for Jupiter IX, the outermost satellite of Jupiter (P = 758 days retrograde, i = 156°, e = 0.28). Discovered by Nicholson in 1914. [H76]


(a) The generic name for any particle which experiences the strong nuclear force. [CD99]
(b) The word applied to an object made of quarks and/or antiquarks. Thus protons, neutrons, antiprotons, antineutrons and pions are examples of hadrons. Since quarks have `color' they experience the strong QCD forces and so therefore do hadrons. Examples of particles which are not hadrons are leptons (electrons, neutrinos, muons, etc.) and photons and W and Z particles. [D89]
(c) Elementary particles that are influenced by the strong nuclear force. There are two sorts of hadrons - mesons, which have zero spin, and baryons, which have spin 1/2 or 3/2. [F88]
(d) Strongly interacting elementary particles. The hadrons all tend to have high masses. [P88]
(e) The properties of the color force and the rules of quantum theory allow certain combinations of quarks (and antiquarks) and gluons to bind together to make a composite particle; all such particles are called hadrons. When mainly three quarks bind, the resulting hadron is called a baryon. When quark and antiquark combine, the result is called a meson, and when gluons combine, it is called a glueball. Hadrons have diameters of about 10-13 cm. The proton and neutron are the most familiar baryons. Pions are the lightest mesons, so they are produced frequently in collisions. Kaons are the next lightest hadrons; their properties make them useful in many studies. [K2000]

Hadron Barrier

The interval (t approx 10-43 [10-23] s after the big bang, when rho = 1093 [1052] g cm-3) during which quantum and general-relativistic effects are expected to modify each other in an unknown way. The quantities in brackets are for a different equation of state. [H76]

Hadron Era

The interval (t approx 10-5 s after the big bang) when the Universe was matter-dominated and when kT approx mpi. It was followed by the lepton era (q.v.). [H76]

Hadronic Era

The interval lasting until some 10-4 seconds after the Big Bang when the universe was matter-dominated, containing many hadrons in equilibrium with the radiation field. The Hadronic Era ended when the characteristic photon energy fell below the rest mass of a pion or pi-meson (270 electron masses), and very few hadrons remained (about one hadron for every 108 photons). [Silk90]


A transition metal found in zirconium ores. Hafnium is difficult to work and can burn in air. It is used in control rods for nuclear reactors and in certain specialized alloys and ceramics.
Symbol: Hf; m.p. 2230°C; b.p. 5197°C; r.d. 13.31 (20°C); p.n. 72; r.a.m. 178.49. [DC99]

Hagedorn Equation of State

An equation of state for extremely degenerate matter (density greater than about 1015 g cm-3). [H76]


The formation of a halo around bright star images by light reflected from the back of the photographic plate or emulsion. [H76]


(a) The time it takes for half of a given quantity of radioactive material to decay. [F88]
(b) For any radioactive substance, the length of time required for half the atoms to disintegrate (cf. mean life). [H76]

Half-Power Beamwidth

(HPBW) The angle across the main lobe of an antenna pattern between the two directions where the sensitivity of the antenna is half the value at the center of the lobe. This is the nominal resolving power of the antenna system. [H76]

Hall Effect

When an electric current is passed through a conductor and a magnetic field is applied at right angles, a potential difference is produced between two opposite surfaces of the conductor. The direction of the potential gradient is perpendicular to both the current direction and the field direction. It is caused by deflection of the moving charge carriers in the magnetic field. The size and direction of the potential difference gives information on the number and type of charge carriers. [DC99]

Halley's Comet

Probably the best known of all comets. Its orbit was computed by Edmund Halley in 1704, at which time he predicted that the bright comet of 1682 would return in 1758 (Halley died in 1742, before he could see his prediction verified). Records of Halley's comet (a = 17.8 AU, e = 0.967, i = 162°.3, P = 76.2 yr perihelion distance 0.587 AU) have been traced back to 240 B.C. Last appearance 1910, next appearance 1986. [H76]


(a) Nebulous quality round a celestial body (particularly round a red giant); the galactic halo, however, describes the spherical collection of stars forming a surrounding "shell" for our otherwise compact, discoid Galaxy. [A84]
(b) The somewhat round population of old, metal-poor stars in the Milky Way. Also, the huge entity that surrounds the disk and contains most of the Galaxy's dark matter. To distinguish between the two, astronomers call the former the stellar halo and the latter the dark halo. Most of the stellar halo lies closer to the Galactic center than the Sun, while most of the dark halo lies farther from the Galactic center than the Sun. [C95]

Halo Population

Old stars typical of those found in the halo of the Galaxy; also called Population II. [H76]

Halo Stars

Stars that have high spatial velocity and low metallicity. This is not an observational definition. [JJ95]

Hamiltonian Function (H)

The quantity in classical mechanics corresponding to the total energy of a system, expressed in terms of momenta and positional coordinates. [H76]

Hamiltonian Operator (H)

The dynamical operator in quantum mechanics that corresponds to the Hamiltonian function in classical mechanics. [H76]

Hamiltonian Theory

A theory for calculating the trajectory of a particle under an applied force. Hamiltonian theory, developed in the nineteenth century, is equivalent to Newton's laws of mechanics but is reformulated in a mathematically elegant way to allow easier solutions to some problems. [LB90]

Hanning Method

A method of smoothing out the noise in radio data. For each data point, one-half the value of that point is taken, plus one-quarter the value of the point on each side. The result is usually a smoother curve. [H76]

Hardness Ratio

In high-energy (x-ray and gamma-ray) astronomy the hardness ratio is defined as the number of counts in a high-energy band minus those in a lower-energy band, normalized by the sum of the counts in both bands. For X-ray sources the hardness ratio can provide a rough indication of the source temperature, spectral index, or associated column density. Terms such as "hard", "soft" and "supersoft" are often used in the literature to qualitatively characterize the hardness ratio. [BFM2004]

Harkins's Rule

The rule that atoms of even atomic number are more abundant than those of odd atomic number. [H76]

Harman-Seaton Sequence

An evolutionary sequence of hot subdwarfs and nuclei of planetary nebulae. [H76]

Harmonic Law

See Kepler's third law. [H76]

Harmonic Motion A motion that repeats itself in equal intervals of time. (also called periodic motion) [H76]
Harmonic Oscillator

Any oscillating particle in harmonic motion. [H76]

Harmonic Overtone

Any integral multiple of the fundamental frequency (q.v.). [H76]

Haro Galaxies

Blue objects whose spectra show sharp emission lines.

Hartle-Hawking Proposal

See no-boundary proposal. [LB90]

Harvard Classification

See Henry Draper system.


A transactinide element formed artificially.
Symbol: Hs; p.n. 108; most stable isotope 265Hs (half-life 2 × 10-3s). [DC99]

Hawking Radiation

the radiation produced by a black hole when quantum effects are taken into account. It can be viewed as a type of virtual pair production in which one of the particles falls through the event horizon of the black hole and hence cannot escape to rejoin its partner. [D89]

Hawking's Theorem

(1) A stationary black hole must be either static (i.e., nonrotating) or axisymmetric. (2) In interactions involving black holes, the surface area of the event horizon can never decrease. [H76]

Hayashi Track

A nearly vertical track of stellar evolution toward the main sequence during phases when the star is largely or completely in convective equilibrium. The luminosity, originally very high, decreases rapidly with contraction, but the surface temperature remains almost constant. [H76]

HB or Horizontal Branch Stars

Globular cluster stars defined by their position in the color-magnitude diagram. They are located on both sides of the RR Lyr gap and one speaks therefore of blue or red HB stars. [JJ95]


High energy peaked BL Lac object


Henry Draper Catalogue, which lists over 200,000 stars. It was published in nine volumes between 1918 and 1924. [C95]

head (of comet)

See coma. [H76]

Head-Tail Galaxies

A class of relatively weak radio sources associated with clusters of galaxies and characterized by a high-brightness "head" close to the optical galaxy and a long low-brightness "tail". [H76]


High-Energy Astronomical Observatory. [LLM96]


High Energy Astrophysics Science Archive Research Center

Heat of Formation

Energy which would be required to form a molecule from dissociated atoms. If positive, the structure will not be formed spontaneously. Lower heats of formation indicate more stable molecules, which are formed preferentially. [SEF01]

Heavy-Fermion Systems

a class of recently discovered materials, usually rare-earth or actinide compounds, in which the `effective mass of the electrons appears to be hundreds or thousands of times the real electron mass. [D89]

Heaviside Layer

See E layer. [H76]

Heavy-Metal Stars

A class of peculiar giants that includes the Ba II stars and the S stars. [H76]


Elevation above ground or distance upwards from a given level (especially sea level) to a fixed point. (See altitude.) [S92]

Heisenberg Model

A model of magnetic systems in which each magnetic atom has a spin which is free to point in any direction in space. Neighboring atoms are coupled by a force which tends to align the spins in parallel (for a ferromagnet) or opposite (for an antiferromagnet) directions. [D89]

Heisenberg Uncertainty Principle

(a) States that the position and momentum of a particle can only be known to a certain level of precision. The more precisely one quantity is known, the less certain the precision of the other. A similarly linked pair of quantities is the time and energy content in a volume of space. [C97]
(b) The uncertainty in the measurement of the position of an elementary particle varies inversely as the uncertainty in measuring its momentum. Thus, it is impossible to make a measurement of an atomic or nuclear process of arbitrary accuracy; the process will be disturbed by the act of measurement. [Silk90]
(c) In quantum mechanics, the position, x, and the momentum, p, of a particle do not have well-defined values simultaneously. The uncertainty, or statistical spread, in their measured values satisfies the relation Deltax Deltap geq hbar/2. Similar inequalities apply to other pairs of dynamical variables. [D89]


Asteroid 624, the largest (about 100 km long) of the Trojans. Its shape is apparently as elongated as that of Eros. Rotation period 6.9225 hours. Its visual mean opposition magnitude is near +14.5, which makes it the brightest of the Trojans. Assumed albedo 0.28. It has a large obliquity. [H76]


A process of joining two metals using an electric arc in an atmosphere of a noble gas. [McL97]


(a) The projection of a particle's spin along its direction of motion. The helicity of a particle is described as being either left-handed or right-handed depending on whether its spin projection is in the direction of motion or against it. [CD99]
(b) This could be thought of as the "spin" of a massless object such as a twistor, null line, or photon of light. [P88]


Having the Sun at the center. [A84]

Heliocentric Cosmology

School of models in which the sun was portrayed as standing at the center of the universe. [F88]


Device for recording the positions of SUNSPOTS. [A84]


Instrument to measure the apparent diameter of the Sun at different seasons, also used to measure angular distances between stars. [A84]


(a) Element which, after hydrogen, is the second lightest and second most abundant in the Universe. Its atom comprises two protons, two neutrons and two electrons; its nucleus is sometimes called an alpha particle. Helium is the product of the nuclear fusion of hydrogen in most stars, but this does not explain the overall helium abundance. [A84]
(b) The second lightest (atomic number two) and second most common element in the universe. Most of it was produced by the big bang, with main-sequence stars making an additional contribution. It has two stable isotopes, helium-3 (two protons and one neutron) and helium-4 (two protons and two neutrons). The latter isotope is by far the more common; it is also the most stable and tightly bound of the light nuclei. [C95]
(c) A colorless monatomic gas; the first member of the rare gases (group 18 of the periodic table). Helium has the electronic configuration 1s2 and consists of a nucleus of two protons and two neutrons (equivalent to an alpha-particle) with two extra-nuclear electrons. It has an extremely high ionization potential and is completely resistant to chemical attack of any sort. The gas accounts for only 5.2 × 10-4% of the atmosphere; up to 7% occurs in some natural gas deposits. Helium is the second most abundant element in the universe, the primary process on the Sun being nuclear fusion of hydrogen to give helium. Helium is recovered commercially from natural gas in both the USA and countries of the former USSR and it also forms part of ammonia plant tail gas if natural gas is used as a feedstock. Its applications are in fields in which inertness is required and where the cheaper alternatives, such as nitrogen, are too reactive; for example, high-temperature metallurgy, powder technology, and as a coolant in nuclear reactors. Helium is also used for balloons (it is less dense than air) and for low-temperature physics research.
Helium is unusual in that it is the only known substance for which there is no triple point (i.e., no combination of pressure and temperature at which all three phases can co-exist). This is because the interatomic forces, which normally participate in the formation of solids, are so weak that they are of the same order as the zero-point energy. At 2.2 K helium undergoes a transition from liquid helium I to liquid Helium II, the latter being a true liquid but exhibiting superconductivity and an immeasurably low viscosity (superfluidity). The low viscosity allows the liquid to spread in layers a few atoms thick, described by some as `flowing uphill'.
Helium also has an isotope. 3He is formed in nuclear reactions and by decay of tritium. This also undergoes a phase change at temperatures close to absolute zero.
Symbol: He; m.p. 0.95 K (pressure); b.p. 4.216 K; d. 0.1785 kg m-3 (0°C); p.n. 2; r.a.m. 4.002602. [DC99]

Helium Abundance

(a) Presence - and dominance - of helium atoms in the Universe. The fact that about 8% of all atoms are helium can be traced, through the alpha-beta-gamma theory, to the primordial big bang. [A84]
(b) As the universe cooled after the Big Bang, it eventually reached a stage (about a minute after the beginning) when protons and neutrons formed, and then nuclei. Nuclei up to helium formed, but collisions were too soft for heavier nuclei to form. The theory of the Big Bang predicts the fraction of nuclei that are helium. That fraction has been measured, and the observed amount agrees very well with the predicted amount. This is one of the main reasons why it is generally believed that the universe began in a hot Big Bang. [K2000]

Helium Burning

The stage when a star fuses helium into carbon and oxygen. All stars born with more than half a solar mass eventually burn helium. [C95]

Helium Flash

The onset of runaway helium burning under degenerate conditions. The helium flash occurs in the hydrogen-exhausted core of a star in the red-giant phase of evolution. When gravitational pressure has brought the degenerate core to a temperature of about 108 K, the helium nuclei can start to undergo thermonuclear reactions. Once the helium burning has started, the temperature builds up rapidly (without a cooling, stabilizing expansion), and the extreme sensitivity of the nuclear reaction rate to temperature causes the helium-burning process to accelerate. This in turn raises the temperature, which further accelerates the helium burning, until a point is reached where the thermal pressure expands the core and thus removes the degeneracy and limits the flash. The helium flash can only occur when the helium core is less than the 1.4 Msmsun Chandrasekhar mass limit and thus it is restricted to low-mass stars. [H76]

Helium Problem

Poses the question: what physical process caused the current abundance of helium in the Universe? [C97]

Helium Shell Flash

It has been shown that helium shell burning outside a degenerate core is unstable; the helium-burning shell does not generate energy at a constant rate but instead produces energy primarily during short flashes. During a flash, the region just outside the helium-burning shell becomes unstable to convection. The resultant mixing probably leads to the s-process as well as to the upward movement of carbon produced by helium burning. [H76]

Helium-Strong Stars

B-type stars in which the helium lines are stronger than in normal stars. One distinguishes usually the extreme helium stars (also called hydrogen-deficient stars), in which no trace of hydrogen is seen, and the intermediate helium-rich stars, in which the hydrogen lines are still visible, but weaker than in normal stars. Related to these objects are the hydrogen deficient C stars. [JJ95]

Helium-Weak Stars

B-type stars in which the helium lines are weaker than in normal stars. Also called Bp helium-weak stars. [JJ95]

Helium Variable Stars

Bp stars in which the strength of the helium lines varies periodically. At the extreme phases the objects appear as helium-rich, whereas at other phases He can be very weak or absent. [JJ95]

Helix Nebula

A planetary nebula about 140 pc distant in Aquarius with the largest known angular diameter of any planetary. (NGC 7293) [H76]

Helmholtz Contraction

See Kelvin-Helmholtz contraction. [H76]

Henry Draper system

A classification of stellar spectra into the sequence O, B, A, F, G, K, M, in order of decreasing temperature. [H76]

Henyey Track

An almost horizontal track of stellar evolution between the Hayashi track and the main sequence. [H76]


Unofficial name for Jupiter VII. P = 259.65 days, e = 0.21, i = 28°. Discovered by Perrine in 1905. [H76]

Herbig Ae, Be Stars

Be or Ae stars associated with nebulosity. [JJ95]

Herbig-Haro Object

An object with many of the characteristics of a T Tauri star (e.g., its spectrum shows a weak continuum with strong emission lines), believed to be a star in the very early stages of evolution. All known Herbig-Haro objects have been found within the boundaries of dark clouds. They are strong infrared sources and are characterized by mass loss. [H76]

Hercules Cluster

An unsymmetrical cluster of about 75 bright galaxies (z = 0.036) of which about half are spiral or irregular and about half elliptical or 50. It contains a rather large number of disturbed and peculiar galaxies. The "missing mass", if present, must constitute more than 95% of the total. (3U 1551 + 15) [H76]

Hercules X-1

An X-ray pulsar probably about 5 kpc distant, a member of an occulting binary system with an orbital period of 1.7 days. The visible component has been identified as the blue variable HZ Herculis, whose spectrum varies from late A or early F to B. Her X- l has a pulsation period of 1.2378 seconds, presumably its rotation period, and exhibits a 35-day quasi-periodicity in the X-ray region (but not in the optical). It is probably a rotating neutron star in a circular orbit (e < 0.1) with a mass of about 0.7 Msmsun, which is accreting matter from HZ Her. The orbital period is stable, but the pulsation period is speeding up at a rate of about 1 part in 105 per year. The X-ray eclipse lasts 0.24 days. (3U 1653+35) [H76]

DQ Herculis

A slow nova. It is an eclipsing binary with an orbital period of only 4h39m. It also has a regular flickering period of 71 seconds, the shortest period of regular variations known, except for pulsars and compact X-ray objects. It is probably composed of an M dwarf and a white dwarf with an accretion disk. (Nova Herculis 1934) [H76]


Of or relating to Hermes Trismegistus, a mythical philosopher beloved of the Neoplatonists and usually identified with ancient Egypt. [F88]

Hermitian Matrix

A matrix which remains unchanged if each element is replaced by its complex conjugate and the rows and columns are interchanged. In quantum mechanics all matrices corresponding to observables have this property. [H76]


(Hz) A unit of frequency equal to one cycle (or wave) per second. [F88]

Hertzsprung Gap

A gap (from about A0 to F5) in the horizontal branch of the H-R diagram (see instability strip). The few stars that populate this gap are RR Lyrae and other variable stars. It is regarded as a region through which a star moves rapidly in its evolutionary track away from the main sequence. [H76]

Hertzsprung-Russell Diagram

(a) A plot of stellar color, temperature, or spectral type versus stellar luminosity. The H-R diagram segregates three principal types of stars: the main sequence, which forms a diagonal band from bright blue stars to faint red ones; red giants and supergiants, which appear in the upper right of the diagram; and white dwarfs, which lie below the main sequence. [C95]
(b) In present usage, a plot of bolometric absolute magnitude against effective temperature for a group of stars. Related plots are the color-magnitude plot (absolute or apparent visual magnitude against color index) and the spectrum-magnitude plot (visual magnitude versus spectral type)the original form of the H-R diagram. [H76]
(c) A plot of luminosity against temperature for stars. Stars are only found in certain well-defined regions of this diagram. There are various different ways in which the diagram can be plotted. The most convenient presentation for the observer is to plot the colors of stars against their magnitudes; this is then known as a color-magnitude diagram. This diagram has to be related to the theoretician's luminosity-temperature diagram through suitable models for stellar atmospheres which enable the relation between the temperature of the surface layers of the star and its observed color to be determined. [D89]

Hess Diagram

(a) A diagram showing the frequencies with which stars occur at various positions in an H-R diagram. [H76]
(b) Within the confines of the HR diagram and/or the corresponding Color-Magnitude diagram it is also possible to give representation to the number density of stars at any particular luminosity and color/spectral-type by the use of contours or grey scale plotting. Such a representation is referred to as a Hess Diagram after R. Hess (Die Verteilungsfunktion der absol. Helligkeiten etc. Seeliger Festschrift, Springer, Berlin 1924 p. 265.) Later, Lonnquist gave similar results in Meddel. Astron. Obs. Upsala, No. 25, (1927); his contour plot is shown in this figure. [BFM]


Unofficial name for Jupiter VI. Discovered by Perrine in 1904. P = 250 days, e = 0.16, i = 29°. [H76]


A detection method used extensively in radio astronomy in which the wave nature of light is used. The method usually involves combining the measured wave with a local oscillator or reference wave and looking for the signal at the difference frequency. [McL97]

Heterotic E-String Theory

Heterotic E8 × E8 string theory One of the five superstring theories; involves closed strings whose right-moving vibrations resemble those of the Type II string and whose left-moving vibrations involve those of the bosonic string. Differs in important but subtle ways from the Heterotic-O string theory. [G99]

Heterotic String

Gross's version of string theory in which space-times of different dimensions are associated with the same closed loop. [P88]

Heterotic O-String Theory

heterotic O(32) String Theory One of the five superstring theories; involves closed strings whose right-moving vibrations resemble those of the Type II string and whose left-moving vibrations involve those of the bosonic string. Differs in important but subtle ways from the Heterotic-E string theory. [G99]


Asteroid 944, perhaps 20 km in diameter, with the largest known orbit (a = 5.8 AU), second highest inclination to the ecliptic (42°.5), and second highest eccentricity (e = 0.66) of any known minor planet. Period 13.7 years. Discovered by Baade in 1920. [H76]

Hidden Mass

Matter whose presence is inferred from dynamical measurements but which has no optical counterpart. The luminous regions of galaxies have mass-luminosity ratios of about 10. However, the mass-uminosity ratio in the outer halos of many spiral galaxies is 100 or more; one sees the brightness fall off with distance from the center of the galaxy but considerable mass is present. A similar situation prevails in galaxy clusters, where nonluminous matter must provide most of the self-gravitational attraction that holds the clusters together. The missing mass is not really missing; it is present but invisible (at least to current detectors). It is generally believed to consist either of the remnants of massive stars or of planetary-sized objects comparable in mass to Jupiter. [Silk90]

Hidden Variables Theory

one of a class of physical theories which deny that the quantum state of a physical system is a complete specification. The hidden variables are those components of the hypothetical complete state which are not contained in the quantum state. [D89]

Hierarchical Clustering

The process by which a system of self-gravitating particles will gradually aggregate into larger and larger gravitationally bound groups and clusters. Small clusters merge into larger clusters, which retain little trace of the subunits from which they formed. Elliptical galaxies may have formed in this way from mergers of globular-cluster-sized star clusters; clusters of galaxies may have formed by a similar process. [Silk90]

Hierarchical Clustering Model

A model of galaxy clustering in which different patterns appear at different scales of distance and in which the "average" density of matter depends on the size of the volume over which the average is performed. In a homogeneous model, on the other hand, the average density is independent of the size of the volume over which the average is performed. (See pancake model.) [LB90]

Hierarchical Cosmology

A cosmology characterized by a system of clusters within clusters within clusters. [H76]

Hierarchy Problem

In the context of grand unified theories, the hierarchy problem is our inability to understand theoretically why the energy scale at which the unification becomes apparent, about 1016 GeV (billion electron volts), is so much higher than other energy scales of relevance to particle physics, such as the mass/energy of a proton, which is only 1 GeV. [G97]

Higgs Boson

(a) A hypothetical, spinless particle that plays an important role in the Glashow-Weinberg-Salam electroweak theory (and in other theories involving spontaneous symmetry breaking, e.g. GUTs). [CD99]
(b) The Higgs boson is the quantum of the Higgs field. If the theory implying the existence of Higgs bosons is correct, it will be possible to produce and detect Higgs bosons at the CERN LEP collider if they are light enough, and almost certainly at the Fermilab collider sometime between 2002 and 2006, depending on the mass of the Higgs boson and on how well the collider and detectors operate. The CERN LHC that is expected to begin operation in 2005 will be a Higgs boson factory. See also Higgs Field, Higgs Mechanism, and Higgs Physics. [K2000]

Higgs Field

(a) Mechanism operating in symmetry-breaking events; in electroweak theory, the Higgs field is said to have imparted mass to the W and Z particles. [F88]
(b) An energy field predicted by certain new theories of elementary particles and forces, particularly the grand unified theories. The energy stored in a false vacuum is the energy of a Higgs field. (See false vacuum; field theory; grand unified theories.) [LB90]
(c) Higgs fields are part of the standard model of particle physics, and analogous fields, also called Higgs fields, are part of grand unified theories. In both cases, the Higgs fields have nonzero values in the vacuum, and they serve to create distinctions between particles that would otherwise be identical. The standard model contains four Higgs fields. There are many combinations of nonzero values of the four fields that equally well minimize the energy density, so the combination of nonzero values in the vacuum is chosen randomly as the universe cools. Since the other fields of the theory interact with the Higgs fields, their behavior is affected by this random choice. In the standard model, it is the interactions with the Higgs fields that are responsible for the difference between electrons and neutrinos. In grand unified theories, Higgs fields are responsible for all the differences between electrons, neutrinos, and quarks. [G97]
(d) Higgs fields constitute a set of fundamental fields, named after P.W. Higgs, which induce spontaneous symmetry breaking, e.g. in the Glashow-Weinberg-Salam model and in grand unified theories; a Higgs particle is associated with a Higgs field in the same way that a photon is associated with the electromagnetic field, The Glashow-Weinberg-Salam theory predicts a neutral Higgs particle with a mass-energy in the vicinity of 100 GeV (billion electron-volts); grand unified theories typically predict Higgs particles with mass energies of order 1014 GeV (see spontaneous symmetry breaking.) [D89]
(e) In the Standard Model, particles (bosons and fermions) are thought to get mass by interacting with the Higgs field. The Higgs field and the way the particles interact with it must have very special properties for the masses to be included in the theory in a consistent way. The other fields we know of arise from particles that carry charges, but we do not yet understand the origin of the Higgs field. That is why physicists are very nervous about the Higgs physics and do not yet agree about whether Higgs bosons exist, even though there is good indirect evidence for the Higgs bosons. Many extensions of the Standard Model imply the existence of a Higgs field. See also Higgs Mechanism. [K2000]

Higgs Mechanism

(a) A mechanism by which gauge bosons acquire mass through spontaneous symmetry breaking. In the Glashow-Weinberg-Salam electroweak model, for example, Higgs fields are introduced into the theory in a gauge-invariant way. However, the state of minimum energy breaks the local gauge symmetry, generating masses for the W± and Z0 bosons, and giving rise to a real, observable Higgs boson, phi'. [CD99]
(b) The Higgs mechanism is a special set of circumstances that must hold if bosons and fermions are to get masses from interacting with a Higgs field, given that the Higgs field exists. In the Standard Model these circumstances can be imposed, and in the supersymmetric Standard Model they can be derived. [K2000]

Higgs Particle

The particle or particles associated with the bundles of energy in the Higgs field. Such particles are analogous to the photons that are associated with the electromagnetic field. The standard model of particle physics predicts one electrically neutral Higgs particle which has not yet been found, but which will be sought in upcoming particle accelerator experiments. The grand unified theories predict many Higgs particles, but they are too massive to be accessible at existing or foreseeable accelerators. [G97]

Higgs Physics

This is the combined physics that explains the origin of the Higgs field, the reason the Higgs mechanism applies, and the properties and study of the Higgs bosons. [K2000]


The superpartner of the Higgs boson. [K2000]

High-Energy Particles

Particles of electromagnetic radiation that contain high energies, measured in terms of electron volts. The energy in gamma radiation is of the order of 8 x 107 to 8 x 105 electron volts and in X-rays of 8 x 103 to 8 × 101 electron volts. [A84]

High-Energy Physics

See particle physics. [F88]

High-Luminosity Early Type Objects

A collective designation for some early type stars with very peculiar spectra, like S Dor and P Cyg. [JJ95]

High-Velocity Object

Generally a celestial object in the galactic halo whose orbital velocity around the galactic center is less than that of the Sun, and that thus, relative to the Sun, has a high space motion. A "high-velocity" object usually travels around the galactic center in an eccentric orbit, often of large inclination to the galactic plane. [H76]

High-Velocity Star

(a) A star whose U and/or V and/or W velocities are much greater or much less than zero. Such stars usually have eccentric orbits around the Galaxy. [C95]
(b) Late type stars whose spatial velocities are greater than 100 km s-1. Other authors prefer the definition, with radial velocities greater than 60 km s-1. [JJ95]

Higher-Dimensional Supergravity

Class of supergravity theories in more than four spacetime dimensions. [G99]

Hilbert Space

A mathematical tool used in the formalism of quantum mechanics. The dimensions of a Hilbert space consist of wave functions, instead of length, width, and breadth. (See quantum mechanics; wave function.) [LB90]

Hind's Nebula

A reflection nebula (q.v.) discovered by Hind in 1852, which is illuminated by the star T Tauri. It is remarkable for its changes in brightness. (NGC 1554-5) [H76]


HIgh-Precision PARallax COllecting Satellite. [LLM96]
A European satellite that from 1989 to 1993 measured the parallaxes of stars. [C95]

Hirayama Families

Groups of minor planets with similar orbital elements. The members of a given family are widely believed to have resulted from collisions between larger parent bodies. [H76]


The time taken to use up all the liquid cryogens, like LN2, in a cooled CCD cryostat. [McL97]

Holmberg Radius

The radius of an external galaxy at which the surface brightness is 26.6 mag arcsec-2. This criterion was developed by Holmberg in 1958 to estimate the actual dimensions of the major and minor axes of a galaxy without regard to its orientation in space. [H76]


A soft malleable silvery element of the lanthanoid series of metals. It occurs in association with other lanthanoids. It has few applications.
Symbol: Ho; m.p. 1474°C; b.p. 2695°C; r.d. 8.795 (25°C); p.n. 67; r.a.m. 164.93032. [DC99]


An interferometric method of recording information about the three-dimensional nature of an object which relies on preserving both the amplitudes and phases of the wavefronts which reach the detector, instead of merely the amplitudes. Hologram means "whole record". The basic principle was outlined by D. Gabor in 1948. [McL97]


Same as complex analytic. [LB90]

Holtsmark Approximation

An approximation in which the lines emitted and absorbed by atoms are subject to the fluctuating electrostatic fields to which the atom is subject in an ionized atmosphere. [H76]


(a) In cosmology, the property that any large volume of the universe looks the same as any other large volume. Most cosmological models assume homogeneity. [LB90]
(b) This expresses the power of a mathematical function. Thus x3 has homogeneity of +3, while 1/x4 has homogeneity of -4. The homogeneity of twistor functions is of key importance in expressing fields in twistor terms. [P88]

Homogeneity Problem

Same as horizon problem. [LB90]


A universe is called homogeneous if it would look the same to all observers, no matter where they were located. The real universe is not precisely homogeneous, but it appears to be homogeneous on large scales. That is, if we averaged the mass density or other property of the matter in the universe over cubes of a few hundred million light-years on each side, all such cubes would be very similar to each other. See also isotropic. [G97]

Homogeneous Expansion

To a good approximation, our universe appears to be undergoing homogeneous expansion, which means that successive snapshots of a given region would each look like a photographic blowup of the first snapshot. Homogeneous expansion is also called Hubble expansion, since it implies Hubble's law. See Figure 2.1 on page 21. [G97]

Honeycomb Mirrors

A construction method for a large mirror in which the back is hollowed-out to leave a ribbed structure that resembles a honeycomb. [McL97]


(a) The maximum distance that an observer can see. In cosmology, our horizon is the distance from us that light has traveled since the beginning of the universe. Objects more distant than our horizon are invisible to us because there hasn't been enough time for light to have traveled from there to here. [LB90]
(b) A plane perpendicular to the line from an observer to the zenith. The great circle formed by the intersection of the celestial sphere with a plane perpendicular to the line from an observer to the zenith is called the astronomical horizon. [S92]

Horizon Distance

the maximum distance, at any given time, that a light signal could have travelled since the beginning of the Universe. [D89]
(b) Since the big bang theory assigns a finite age to the universe, at any given time there is a maximum distance that light could have traveled since the beginning, called the horizon distance. Since no signal propagates faster than light, the horizon distance is the maximum distance over which any information can be obtained. [G97]

Horizon Problem

(a) A quandary in standard big bang theory, which indicates that few of the particles of the early universe would have had time to be in causal contact with one another at the outset of cosmic expansion. It appears to have been resolved in the inflationary universe theory. [F88]
(b) The puzzle that widely separated regions of the universe are observed to share the same physical properties, such as temperature, even though these regions were too far apart when they emitted their radiation to have exchanged heat and homogenized during the time since the beginning of the universe. In particular, we detect the same intensity of cosmic radio waves (cosmic background radiation) from all directions of space, suggesting that the regions that emitted that radiation had the same temperature at the time of emission. However, at the time of emission, when the universe was about 1 million years old, those regions were separated by roughly 100 million light years, much exceeding the distance light or heat could have traveled since the big bang. The horizon problem is also called the causality puzzle. (See horizon.) [LB90]
(c) A problem of the traditional big bang theory (without inflation) related to the large scale uniformity of the observed universe. The problem is seen most clearly in the cosmic background radiation, which is believed to have been released at about 300,000 years after the big bang, and has been observed to have the same temperature in all directions to an accuracy of one part in 100,000. Calculations in the traditional big bang theory show that the sources of the background radiation arriving today from two opposite directions in the sky were separated from each other, at 300,000 years after the big bang, by about 100 horizon distances. Since no energy or information can be transported further than one horizon distance, the observed uniformity can be reconciled only by postulating that the universe began in a state of near-perfect uniformity. See also Flatness Problem. [G97]
(d) Cosmological puzzle associated with the fact that regions of the universe that are separated by vast distances nevertheless have nearly identical properties such as temperature. Inflationary cosmology offers a solution. [G99]

Horizontal Branch

That part of the H-R diagram of a typical globular cluster that extends shortward from the asymptotic branch at an approximately constant absolute bolometric magnitude of about 0.3. A star appears on the horizontal branch after it has undergone the helium flash and begins to burn helium quietly in its core and hydrogen in a surrounding envelope. [H76]

Horizontal Branch Star

A metal-poor star, similar in mass to the Sun, that fuses helium into carbon and oxygen at its core. Such stars range in color from blue to yellow. RR Lyrae stars are horizontal-branch stars. Stars bluer than RR Lyraes are called blue horizontal-branch stars; stars redder are called red horizontal-branch stars, even though they are actually yellow. All other things being equal, the more metal-poor a globular cluster, the bluer its horizontal branch; the older a globular cluster, the bluer its horizontal branch, too. [C95]

Horizontal Parallax

The difference between the topocentric and geocentric positions of an object, when the object is on the astronomical horizon. [S92]

Horsehead Nebula

An absorption nebula in the middle of Orion. See Omega Nebula. (NGC 2024) [H76]

Host Computer

The main or master computer in an instrumentation system. The computer responsible for interacting with the user. [McL97]

Hot Big Bang

Later, but fundamental, concept within the big-bang theory, that the primordial explosion occurred in terms of almost unimaginable heat. The concept, formulated by George Gamow, led to considerable study of thermonuclear reactions and the search for background radiation. [A84]

Hot Dark Matter

Any form of dark matter which was relativistic at its point of decoupling. [C97]

Hour Angle

Angular distance on the celestial sphere measured westward along the celestial equator from the meridian to the hour circle that passes through a celestial object. [S92]

Hour Circle

A great circle passing through the celestial poles - i.e., perpendicular to the celestial equator. [H76]

Hourglass Nebula

A compact H II region in the center of M8. [H76]

Hoyle-Narlikar Theory

A reformulation of the general theory of relativity that incorporates and extends Mach's principle (q.v.). In this theory, the inertial mass of a particle is a function of the masses of all other particles, multiplied by a coupling constant which is a function of cosmic epoch. In cosmologies based on this theory, the gravitational constant G decreases strongly with time. [H76]


Half Power Beam Width. The angle across the main lobe of an antenna pattern between the two directions where the sensitivity of the antenna is half the value at the center of the lobe. This is the nominal resolving power of the antenna system. [H76]


Highly Polarized Quasar

H-R Diagram

See Hertzsprung-Russell Diagram. [C95]


High-Resolution Spectrograph (Hubble). [LLM96]


Hubble Space Telescope. A space-based reflecting telescope with a primary mirror diameter of 2.4 m (94 in) capable of high-resolution imaging from the far ultraviolet to the near infrared. A joint NASA/ESA mission. Launched in 1990 with a planned lifetime of 15 years. Encountered reduced performance when the mirror was found to have spherical aberration. Solved by the installation of corrective optics (COSTAR) in 1994. [McL97]


Hyper-Text Mark-up language.


Hyper-Text Transfer Protocol.

Hubble Classification

A morphological classification sequence of galaxies devised by Edwin Hubble. It splits galaxies into ellipticals, lenticulars, spirals, barred spirals and irregulars. [C97]

Hubble Constant

(a) The present expansion rate of the universe, in units of kilometers per second per megaparsec. The larger the Hubble constant, the younger the universe. [C95]
(b) According to Hubble's law, discovered by Edwin Hubble in 1929, distant galaxies are receding from us, on average, with a speed equal to the product of the Hubble constant and the distance to the galaxy. Hubble's "constant" is independent of distance, but actually decreases slowly in time as the expansion is slowed by the gravitational pull of each galaxy on all the others. The present value is somewhere between 15 and 30 kilometers per second per million light-years. [G97]
(c) The constant of proportionality in the Hubble law. Its value must vary with time, so it is often referred to as the Hubble parameter. The Hubble constant is generally used to mean the value of the Hubble parameter at the current epoch, and is somewhere between 50 and 100 km/s/Mpc with possibly a value close to 75 km/s/Mpc. [C97]
(b) The rate at which the universe expands, equal to approximately fifty kilometers of velocity per megaparsec of distance. [F88]
(d) The rate of expansion of the universe. The Hubble constant actually changes in time, even though it is called a constant, because gravity is slowing down the rate of expansion of the universe. The Hubble constant is equal to the recessional speed of a distant galaxy, divided by its distance from us. Assuming a homogeneous and isotropic universe, the recessional speed of a distant galaxy is proportional to its distance; thus the Hubble constant as determined by any receding galaxy should be the same, yielding a universal rate of expansion of the universe. According to estimates, the current value of the Hubble constant is approximately 1 per 10 billion years, meaning that the distance between any two distant galaxies will double in about 10 billion years at the current rate of expansion. Astronomers measure the Hubble constant in units of kilometers per second per megaparsec. For example, a Hubble constant of 100 kilometers per second per megaparsec - which astronomers would refer to simply as a Hubble constant of 100 - corresponds to 1 per 10 billion years. The Hubble constant is denoted by the symbol H0. [LB90]

Hubble Diagram

Plot of galaxy redsifts against their distances. This was the first evidence of the expansion of the universe. [F88]

Hubble Expansion

... of the Universe. There are billions of other galaxies and all except the closest ones (the Local Group) are receding from us as deduced from the Doppler redshift effect of their spectra. Thus the Universe appears to be expanding. Moreover, the greater the distance the faster the speed of recession. This is interpreted as the expansion of spacetime itself since an event called the Big Bang. [McL97]

Hubble Flow

The movement of the galaxies away from us caused by the expansion of the Universe. [C97]

Hubble Law

(a) The law that recessional speed is proportional to distance for a homogeneous and isotropic universe. Galaxies moving away from us with a speed precisely following this law are said to follow the Hubble flow. Because the actual universe is not precisely homogeneous, with lumpiness arising from clustering of galaxies and voids of empty space, the motions of actual galaxies deviate somewhat from the Hubble flow. [LB90]
(b) The observation, first made by E.P. Hubble in the 1920s, that distant galaxies are receding from us with a velocity proportional to their distance; one infers that any two galaxies are receding from each other with a velocity proportional to their separation. [D89]

Hubble nebula

A cometary nebula whose apex star is R Mon. (NGC 2261) [H76]

Hubble Program

The research program carried out in the 1920s and 1930s by Edwin Hubble to measure the recessional speeds and distances of a large number of galaxies and to attempt to measure the deceleration parameter. This last parameter can in principle be determined by measuring the apparent brightness and redshift of a large number of objects of identical intrinsic luminosity. (See deceleration parameter; Sandage program; standard candle.) [LB90]

Hubble Radius

c/H The radius of the observable universe (> 1027 cm). [H76]

Hubble Time

(a) The Hubble time is one divided by the Hubble constant, which gives a number from 10 to 20 billion years. For a flat universe with no cosmological constant, the age of the universe is two-thirds of the Hubble time. [G97]
(b) The inverse of the Hubble constant and a crude measure of the universe's age. (H0-1) For a Hubble constant of 50, one can calculate that the Hubble time is 19.6 billion years; for a Hubble constant of 80, the Hubble time is 12.2 billion years. If there is no cosmological constant, the universe is younger than the Hubble time. In particular, if the mass density of the universe (designated Omega) is 0.1, the universe's age is 90 percent of the Hubble time; if Omega is 1.0, the universe's age is 67 percent of the Hubble time. [C95]

Hugoniot Relations

Relations expressing conservation of baryon number, momentum, and energy across a shock front. [H76]

Hulse-Taylor Pulsar

A binary pulsar discovered in 1974, probably consisting of a neutron star and an even more compact object in an eccentric orbit, with an orbital period of 0.3230 days and a pulsation period of 59 milliseconds. (PSR 1913+16) [H76]

Hund's Rule

The larger the value of S (total spin angular momentum), the lower the value of the average perturbation energy <V>SL. [H76]

Huyghenian Region

The brightest portion of the Orion Nebula. [H76]


A single member of the Hyades. [H76]


A young (5 × 108 yr) moving cluster (radial velocity, + 36 km s-1) of more than 200 stars (spectral types A1-K) visible to the naked eye in Taurus, about 40 pc distant. Aldebaran is a foreground star in that region of the sky. [H76]

Hybrid Array

A device in which the roles of radiation (infrared mostly) detector and signal multiplexer are separated. The device is a sandwich of two slabs. Other names include focal plane array (FPA) and sensor chip assembly (SCA). [McL97]


Molecule which contains only hydrogen and carbon. Type of organic molecule. [SEF01]


The study of how gases and fluids flow under applied forces. [LB90]


(a) Element that is the lightest and the most abundant in the Universe. Its atom comprises one proton and one electron. The element occurs both in stars and as interstellar clouds, in regions where it may be neutral (H I regions) or ionized (H II regions). [A84]
(b) The lightest and most common element in the universe. It has atomic number one and was produced by the big bang. Hydrogen-1 (one proton and no neutrons) is the most common isotope; hydrogen-2 (one proton and one neutron), or deuterium, is rarer; and hydrogen-3 (one proton and two neutrons), or tritium, is radioactive. [C95]
(c) A colorless gaseous element; the least dense and most abundant element in the Universe and the ninth most abundant element in the Earth's crust and atmosphere (by mass). It occurs principally in the form of water and petroleum products; traces of molecular hydrogen are found in some natural gases and in the upper atmosphere. Hydrogen occupies a unique position among the elements as hydrogen atoms are the simplest of all atoms. The hydrogen atom consists of a proton (positive charge) with one extranuclear electron (1s1).
Atomic nuclei possess the property of `spin' and for diatomic molecules there exists the possibility of having the spins of adjacent nuclei aligned (ortho) or opposed (para). Because of the small mass of hydrogen, these forms are more important in hydrogen molecules than in other diatomic molecules. The two forms are in equilibrium with parahydrogen dominant at low temperatures, rising to 75% orthohydrogen at room temperatures. Although chemically identical the melting point and boiling point of the para form are both about 0.1° lower than the 3:1 equilibrium mixture.
Natural hydrogen in molecular or combined forms contains about one part in 2000 of deuterium, D, an isotope of hydrogen that contains one proton and one neutron in its nucleus.
Symbol: H; m.p. 14.01 K; b.p. 20.28 K; d. 0.089 88 kg m-3 (0°C); p.n. 1; r.a.m. 1.0079. [DC99]

Hydrogen Burning

The fusion of hydrogen into helium and the process by which all main-sequence stars generate energy. Every star born with more than 0.08 solar masses burns hydrogen. [C95]

Hydrogen-Deficient C-type Stars

A subgroup of high-luminosity C stars with weak or absent hydrogen lines, mostly of types F and G. Variable stars having such characteristics are called R CrB stars. [JJ95]

Hydrogen-Deficient Early-Type Stars

Early type stars of type O, B or A in which the hydrogen lines are very weak or absent. [JJ95]


See magnetohydrodynamics. [H76]

Hydrostatic Equilibrium

A balance between the gravitational force inward and the gas and radiation forces outward in a star. [H76]

Hyperbolic Space

A three-dimensional space whose geometry resembles that of a saddle-shaped surface and is said to have negative curvature. [Silk90]


Twice the charge of a charge multiplet (q.v.). [H76]


Involving more than the customary four dimensions (three of space plus one of time) of relativistic space-time. [F88]

Hyperfine Structure

Splitting of spectral lines due to the spin and consequent magnetic moment of an atomic nucleus. It can be observed only at very high resolution. [H76]


A system consisting of a dominant spiral galaxy surrounded by a cloud of dwarf satellite galaxies, often ellipticals. Our galaxy and the Andromeda galaxy are hypergalaxies. [Silk90]


Eighth satellite of Saturn about 160 km in diameter. P = 21d6h38m. Discovered by Bond in 1848. [H76]


(a) A baryon with non-zero strangeness. [CD99]
(b) An unstable heavy baryon (q.v.) with an average life of 10-8 to 10-10 seconds. [H76]


A scientific proposition that purports to explain a given set of phenomena; less comprehensive and less well established than a theory. [F88]


(a) The ability to follow two different branches of states, as a parameter built in the system varies first in a monotonic fashion and subsequently comes back to its initial value by varying in the opposite direction. [D89]
(b) In general, an apparent lag of an effect behind whatever is causing it. Magnetic Hysteresis is the behavior of ferromagnetic materials as they are magnetized and demagnetized. The flux density, B, lags behind the external field strength H. See hysteresis cycle. [DC99]

Hysteresis Cycle

A closed loop obtained by plotting the flux density, B, of a ferromagnetic substance against the magnetizing field strength, H. The substance is first brought to magnetic saturation from an unmagnetized state - this produces curve OA (see illustration). As the field strength is taken through one cycle of reductions, reversals, and increases, the curve follows the path ACDEFGA. This is known as a hysteresis loop.
The area of the loop equals the energy loss in taking the sample once through the cycle. This is known as hysteresis loss and depends on the substance.
OC (or OF) represents the remanence, the magnetic flux density remaining in the specimen when the saturating field is removed. OD (or OG) represents the coercivity, the value of the magnetizing field strength needed to reduce this remaining flux density to zero. All these details are readily explained by the domain behavior of ferrogmagnetics. [DC99]


Hertz A unit of frequency equal to one cycle (or wave) per second. [F88]

HZ Stars

Blue horizontal-branch stars, the first catalog of which was compiled by Humason and Zwicky. [H76]

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