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Glossary & Formulas

Some abbreviations used in ChView files are:

a = semi-major axis of an elliptical orbit
badHipPlx = Hipparcos catalogue parallax with very large standard error
B1900/B1950 = stardate 1900/1950 of celestial position (of RA and Dec following)
brownDwarfComp = star has brown dwarf companion
comp"x"? = possible companion object"x"
Dec = declination of celestial position
double-lineB = spectroscopic binary ("double") inferred from double-line spectra.
dia = diameter (e.g., as a fraction of Sol's diameter)e = eccentricity of an orbit; or
e = eccentricity of orbit
e = standard error of parallax (e_Plx), if following "Plx=xx.xx,e=x.xx."
HerbigObj = pre-main sequence, Herbig-Haro (HH) object
inclin="xxx"d = degrees of inclination of orbit
Jmass = equivalent Jupiter masses
Mv = absolute magnitude
optComp"x" = the star's visual companion "x" is not gravitationally bound
optComp"x"?= gravitation binding of companion "x" is unknown from reference
P = period of orbit
planetComp = star has planetary companion
Plx = parallax (usually from Hipparcos satellite mission)
PreMainSeq = pre-main sequence object (e.g., T-Tauri star)
RA = right ascension of celestial position
sep" = binary separation in arcseconds (")
single-lineB = spectroscopic binary inferred from single-line spectra
SolMass = equivalent solar masses
spec.dou. = star has a spectroscopic double (or "binary")
spec.dou.B = this star is a spectroscopic binary
TycPlx = Tycho catalogue parallax; has larger error than Hipparcos parallax
V(AB) = apparent magnitude of stars A and B
var = variable star
YalePlxBetter = Yale parallax believed to be better than Hipparcos parallax

Absolute Visual Magnitude (Mv) and Luminosity (L):
Absolute visual magnitude is the intrinsic brightness (luminosity) of a celestial body when viewed at a distance of 10 parsecs from Earth. The luminosity of a star is typically defined as the quantity of light (radiant energy) emitted by that celestial body relative to that radiated by Sol, our sun. Astronomers relate the two in the following manner:
     Mv = 4.8 - [2.5 * log (Lstar/Lsol)]
Astronomical Unit (AU):
Distance from Earth to the Sun, 149,598,770 kilometers (km) or about 93 million miles.

Binary Separation:
For close angular separations, where gravitational binding is likely, the following formula can be used to convert angular separation to distance:
     d  = distance between stars 1 and 2,
     r1 = distance to star 1,
     r2 = distance to star 2, and
     theta = degrees of angular separation, then

     d^2 = (r1)^2 + (r2)^2 - [2(r1)(r2)*cosine(theta)].
Where separation -- compared to distance from Earth -- is very close so that, for example, we're trying to measure a separation of less than a tenth of a light-year, the above formula can be collapsed to:
     r ~ r1 ~ r2, so that:  d = r * {[2(1 - cosine(theta))]^(1/2)},
where binary separation is given arcseconds(", at 3600" per degree), or fractions thereof such as 0.1", and distance is converted to astronomical units from light-years (ly), so that:
     r = ly * (206,265 AU/3.2616pc) and 
     theta = ("/3600) * (@Pi/180, for Lotus/Quattro Pro).  
Black Hole:
A hypothetical celestial body of extreme density whose gravitational strength is great enough -- within a certain distance dependent on its mass -- to prevent the escape of light (i.e., photons). In theory, black holes that result from the collapse of very large stars should have over six solar masses. Matter falling into black holes may emit detectable x-rays; one x-ray source in the star files is a possible companion to NN, an unnumbered Gliese and Jahreiss catalogue star, that may be located 68 light-years away.

Distance Modulus:
Absolute visual magnitude (Mv) is derived from apparent magnitude (M), the apparent visual brightness of a celestial body without adjusting for distance from Earth, using distance (d) in parsecs from Earth, in the following manner:
     Mv - M = 5 - [5 * log d]
Dust, Stellar Disks:
In recent years, astronomers have been able to detect enormous disks of dust around some stars, especially young T-Tauri types. Some young, local stars with substantial dust include Beta Pictoris, Fomalhaut, and Vega. At least one astronomer may have detected gaps within the inner dust disk of Beta Pictoris, possible evidence of planetary formation. Dust has also been detected around Epsilon Eridani, Ross 128, 61 Cygni2, and Tau Ceti.

Equatorial System Coordinates (x,y,z):
In ChView, x,y,z equatorial system (celestial) coordinates are presented in light-years (d) from Earth/Sol, where z is along the Earth's polar axis (+ towards celestial north), x is in the plane of the equator (+ in the direction of the vernal equinox), and y is perpendicular to x. These coordinates are derived from the distance of a celestial object from Earth/Sol and converting right ascension (RA) from hours to degrees (multiply by 15) and declination (Dec) in degrees; trigonometic functions in Lotus and Quattro Pro spreadsheets require that degrees be converted to radians, by multiplying by @Pi/180.

     x =      d * Cosine(RA*15) * Cosine(Dec);
     y =      d * Sine(RA*15)   * Cosine(Dec);  and
     z =      d * Sine(Dec).  
Flare Stars (UV Ceti type):
Some low mass (M or K) dwarfs can "flare" suddenly and enormously (compared with our own sun's puny "solar" flares), brightening the star from one to six magnitudes and lasting for several minutes (e.g., UV Ceti B, Luyten 726-8 B, Kruger 60 B, Ross 154, or Proxima Centauri).

Habitable Zone (HZ):
From Kaltenegger et al, 2010 (page 5): "For a given planet (assuming a certain atmosphere composition and albedo) the surface temperature depends on the distance from the host star, the luminosity [L] of the host star, and the normalized solar flux factor Seff that takes the wavelength dependent intensity distribution of the spectrum of different spectral classes into account. The distance d of the HZ can be calculated as (Kasting et al, 1993) :

d = 1 AU * [ (L = Lsun) / Seff ] ([take square root])

where Seff is 1.90, 1.41, 1.05, and 1.05 for F, G, K, and M stars respectively for the inner edge of the HZ (where runaway greenhouse occurs) and 0.46, 0.36, 0.27, and 0.27 for F, G, K, and M stars respectively for the outer edge of the HZ (assuming a maximum greenhouse effect in the planet's atmosphere). These calculations were originally done for F0, G2, and M0 spectra and will be updated for all spectral sub classes (Kaltenegger, Segura, and Kasting in prep)."

Lifetime, Stellar:
Lifetime = (Solar lifetime = 10 billion years)
           * [(1 / solar masses) raised to 2.5 power)]
M7-8     = (10) * [(1/0.1)^2.5)] = 10 * 316     =  3.2 trillion years
M0       =            0.5        =      5.7     = 57   billion years
K0       =            0.7        =      2.4     = 24   billion years
Sol(G2)  =            1.0        =      1.0     = 10   billion years
F-class  =            1.3        =      0.52    =  5.2 billion years
A-class  =            2.5        =      0.10    =  1.0 billion years
B-class  =           10          =      0.0032  = 32   million years
O-class  =           25          =      0.00032 =  3.2 million years
O3       =          120          =      0.00006 = 63   thousand years
9.4 trillion km, almost six trillion miles, or 0.3066 parsecs.

Luminosity (L) and Mass (m):
O  - K2:  Lstar/Lsol = [m(star)/m(sol)] to 4th power.  
K5 - M5:  Lstar/Lsol = 0.6 * {[m(star)/m(sol)] squared}.  
A number representing the intrinsic or apparent brightness of a celestial body on a logarithmic scale, in which a difference of one unit corresponds to the multiplication or division of the brightness of light by 2.512.

Mass of a Binary System:
When orbital information is available, the total mass of a binary system can be calculated as follows:
     m1 + m2 = (a^3) / (P^2), where

     m1, m2 = masses of objects 1 and 2, as a ratio of Sol's,
     a = angular separation of the objects in AUs, and
     P = period in years.  
Neutron Star:
A super dense, stellar remnant of between 1.4 and six solar masses and of small, asteroid-like size (e.g., a mile in diameter) that: may result from the supernova explosion of a very large star; is composed of closely packed nuclear particles (primarily neutrons); and may be detectable through the emission of X rays. One x-ray source in the star files is NN, an unnumbered Gliese and Jahreiss star, which may be 68 light-years from Earth.

Optical Companion (optComp):
A star's visual companion. "OptCompC?" means that the reference used did not indicate or rule out that visual companion "C" may be gravitationally bound to stars A and B.

Parsec (pc):
3.2616 light-years or 206,265 AUs; the distance at which the Earth's orbital radius would subtend an angle of one second of arc.

Speed of Light:
299,792.458 km/second or over 186 thousand miles/second.

Spectroscopic Doubles (spec.dou. or SB):
The stars in these binary systems are so close together that only analysis of the spectra of their light (resulting in spectral lines that are doubled and/or that oscillate) reveals their binary nature (e.g., Groombridge 34 A or Algol).

Some sun-like ("Sol-type") stars occasionally produce flares that release between 100 and 10 million times more energy than the largest flares ever observed on the sun. These "superflares" last from one hour to one week and increase the normal luminosity of a star as much as 1,000 times. If our sun were to produce a large superflare, Earth's ozone layer would be destroyed and ice on the daylight side of moons as far out as those of Jupiter or even Saturn would be melted, producing vast floodplains that refreeze after the flare subsides. None have been detected in our solar system. In 1998, nine Sol-type stars (naked-eye objects Omicron Aquilae, Kappa Ceti, and Pi1 Ursae Majoris, as well as MQ or 5 Serpentis, UU Coronae Borealis, S Fornacis, MT Tauri, BD+10 2783, and Groombridge 1830) were found to have produced superflares, on average, about once per century. None of these stars rotate particularly fast, have close binary companions, or are very young. Unlike previously known "flare stars" (M-class), a superflare in a Sol-type star (as hypothesized by a member of the Yale team conducting the three-year spectroscopic study of F8-G8, main-sequence stars) may be caused by the interaction of the magnetic field of a giant planet ("hot Jupiter") in a tight orbit with the star's own magnetic field.

Variables, Eclipsing:
Also known as "eclipsing binaries", changes in the apparent brightness of these stars are caused by one star of the binary system passing in front of the other -- relative to an observer on Earth. Some are at maximum brightness most of the time (Algol type, EA). Others involve stars that are so close together that their shapes are distorted into two "eggs" in near physical contact; of these, dwarf pairs may have periods of less than one day (W Ursae Majoris type, EW), while others exhibit continuous light-variations that alternate in length between short and long (Beta Lyrae, EB).

Variables, Pulsating:
Some stars actually expand and contract in size over time (months to seconds), which changes their brightness. Many such stars (Mira, semi-regular, Cepheids, RR Lyrae, RV Tauri, Beta Canis Majoris or Beta Cephei, Alpha Cygni and irregular types) are evolving off the main sequence, and thus include many subgiant, giant, and supergiant stars that are exhausting their core supply of hydrogen and fusing heavier elements in concentric gaseous shells. Delta Scuti type (which have small amplitudes and periods from 0.02 to 0.25 of a day) are young A and F stars, and many are spectroscopic binaries; subdwarfs of this type are call SX Phoenicis stars. ZZ Ceti type are white dwarfs with small amplitudes and periods as short as 30 seconds.

Variables, Eruptive:
These stars include novae and dwarf novae, flare stars, nova-like, P Cygni, nebular, and R Coronae Borealis variables.

Variables, Rotating:
Exhibiting small amplitudes, variations in brightness may be due to non-uniform surface brightness, fast rotation and great chromospheric activity, and binaries where one companion is rapidly rotating and large (FGK giant or subgiant) or where the stars are very close and gravitationally distorted (ellipsoidal variables).

Variables, Secular:
Stars such as Beta Leonis, Theta Eridani, and Delta Ursae Majoris may have brightened or faded over historical time periods. These "estimated" variations, however, are generally thought to be suspect, due to the subjectiveness of eye-ball observation in less technologically advanced times.
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