Stellar Magnitude

(apparent), a measure of the illumination produced by a celestial body (star, planet, the sun) on the earth in a plane perpendicular to the incident rays; a measure of the brightness of a celestial body. It is generally assumed that corrections have been introduced into the values of stellar magnitudes that take into account the attenuation of the light in the earth’s atmosphere, and thus stellar magnitudes are extraatmospheric.

The concept of stellar magnitude was first introduced in the second century B.C. by Hipparchus, who divided all stars visible to the naked eye into six magnitudes. The brightest stars were relegated to the first magnitude and the weakest stars (of those visible to the naked eye), to the sixth. Stellar magnitudes m are related to the illuminations E that correspond to them by the formula

m = k log E + C₀

The value of the coefficient k, according to the suggestion of the British astronomer N. Pogson (mid-19th century), is taken to be equal to -2.5. It determines the steps of the stellar magnitude scale, whereas the constant C₀ determines its reference, or zero, point. A change in illumination by a factor of 100 corresponds to a change of 5 units in stellar magnitude. Moreover, the brighter the celestial object, the smaller the number expressing its magnitude; magnitudes may have both positive and negative values. The constant C₀ is determined from results of measurements of certain aggregates of stars selected as standards. In practice, it is rather difficult to carry out measurements of brightness with rigorous adherence to the generally accepted reference point and steps of the scale. In this connection, the parameters A: and C₀ may vary somewhat in different photometric catalogs of celestial bodies, as is evident from comparison.

Depending on the method of measurement, magnitudes are differentiated into visual (determined by the naked eye with the help of a visual photometer), photographic (from photographs), photoelectric (with the aid of a photoelectric photometer), and bolometric (with the aid of a bolometer) magnitudes. Stellar magnitudes obtained by photographing a celestial body on a photographic plate with an orthochromatic or panchromatic emulsion through a yellow filter are called photovisual (such magnitudes are close to visual). The use of different radiation detectors and light filters makes it possible to measure the brightness of celestial bodies in different regions of their spectra and thereby to determine the magnitudes belonging to different photometric systems. In the international photographic and photovisual systems (in the blue and yellow regions of the spectrum), the standard consists of 96 stars in the region of the north celestial pole, the so-called North Polar Sequence; selected areas in which secondary standards have been established are located throughout the entire sky. More convenient is the UBV system, in which stellar magnitudes are given in ultraviolet U (3500 Å), blue B (4350 Å), and yellow V (5550 Å) regions of the spectrum. The B magnitudes are close to the photographic magnitudes, and the V magnitudes coincide with the photovisual magnitudes of the international system. In addition to the UBV system, magnitudes in the red and infrared regions of the spectrum are used: R (0.7 μm), I (0.90 μm), J (1.25 μm), K(2.2 μm), L(3.7μm), and so on. It is accepted that, in the establishment of any new systems of stellar magnitudes, all types of magnitudes will coincide for selected stars of spectral type AO from the main sequence of the Hertzsprung-Russell diagram. Several dozen stars, situated throughout the entire sky, serve as the magnitude standards in the UBVRIJKL … system. Differences between magnitudes obtained in different photometric systems characterize the energy distribution in the spectra of stars. These are called color indexes, for example, B—V, U—B.

The stellar magnitudes and color indexes of more than 20,000 stars have been measured photoelectrically. The precision of the measurements is about 0.01–0.02 magnitude. The precision of photographic and visual measurements is about 0.05–0.1 magnitude. The brightest star in the sky, Sirius, has a magnitude V = -1.46; the weakest belong to the 23rd stellar magnitude. The magnitude of the sun is V = -26.78, while that of the full moon is V = -12.71. The magnitude of a light source producing an illumination of 1 lux is V = -13.78.

The magnitude that a celestial body would possess if it were located at a standard distance of 10 parsecs is termed its absolute stellar magnitude. Absolute magnitudes (in contrast to apparent magnitudes) characterize the physical properties of the bodies themselves, their luminosity. Absolute stellar magnitude M is related to apparent magnitude m by the formula

M = m + 5 - 5logr

where r is the distance to the body expressed in parsecs.