Tables 798-800 



TABLE 798. — Brightness of the Stars 



623 



_ Stellar magnitudes give the apparent brightness of the stars on a logarithmic scale, — a numerical 

 increase of one magnitude corresponding to a decrease of the common logarithm of the light by 0.400, 

 and a change of five magnitudes to a factor of 100. The brightest objects have negative stellar magni- 

 tudes. The visual magnitude of the Sun is —26.7; of the mean full Moon, —12.5; of Venus at her 

 brightest, —4.3; of Jupiter, at opposition, —2.3; of Sirius, —1.6; of Vega, + 0.2; of Polaris, + 2.1. 

 (The stellar magnitude of a standard candle 1 m distant is — 14.18.) The faintest stars visible with 

 the naked eye on a clear dark night are of about the sixth magnitude (though a single luminous point as 

 faint as the eighth magnitude can be seen on a perfectly black background). The faintest stars visible 

 with a telescope of aperture A in. are approximately of magnitude q + 5 login A. The faintest photo- 

 graphed with the 100-inch reflector at Mt. Wilson are of about the 22nd magnitude. A standard candle, 

 of the same color as the stars, would appear of magnitude + 0.8 at a distance of one kilometer. 



Ine actual luminosity (absolute magnitude) is the stellar magnitude which the star would have if 

 placed at a distance of ten parsecs. The faintest star at present known (Innes), a distant companion to 

 a Centaun, has the (visual) absolute magnitude + 15.4, and a luminosity 0.00006 that of the sun. The 

 brightest so far definitely measured. Orionis, has (Kapteyn) the abs. mag. — 5.5 and a luminosity 

 13.000 times the sun s. Canopus, and some other stars, may be still brighter. Note 1931: S. Doradus 

 abs. mag. probably > — 8. 



The absolute magnitudes of 6 planetary nebulae average 9.1; average diameter, 4000 astronomical 

 units (Solar system to Neptune = 60 astr. units), van Maanen, Proc. Nat. Acad. Sci. 4, p. 394, 1918. 



TABLE 799.— Giant and Dwarf Stars 



The stars of Class B are all bright, and nearly all above the absolute magnitude zero. Stars of com- 

 parable brightness occur in all the other spectral classes, but the inferior limit of brightness diminishes 

 steadily for the " later " or redder types. The distribution of absolute magnitudes conforms to the 

 superposition of two series, in each of which the individual stars of each spectral class range through 

 one or two magnitudes 011 each side of the mean absolute magnitude. Absolute magnitude supergiants 

 — 2 to —8; giants roughly o to -I- 1 ; dwarfs A, 1 to 2; F. 2 to 4; G, 4 to 6; K, 6 to 9; M, 9 to 11. 

 The two series overlap in Classes A and F, are fairly well separated in Class K, and sharply so in 

 Class M. Two very faint stars of Classes A and F fall into neither series. 



The majority of the stars visible to the naked eye are giants since these, being brighter, can be seen 

 at much greater distances. The greatest percentage of dwarf stars among those visible to the eye is 

 found in Classes F and G. The dwarf stars of Classes K and M are actually much more numerous per 

 unit of volume, but are so faint that few of the former, and none of the latter, are visible to the 

 naked eye. 



TABLE 800. — Masses and Densities 



Stars differ less in mass than in any other characteristic. The most massive star known is the brighter 

 component of the spectroscopic binary B.l). 6°i309, 86 times the sun's mass, 113 times its luminosity, 

 and spectrum Oe. The smallest known mass is that of the faint component of the visual binary Krueger 

 60, whose mass is 0.15, and luminosity 0.0004 of the sun's, and spectrum M. Note: Plaskett notes 

 giant double star 184 sun's mass. 



The giant stars are in general more massive than the dwarfs. According to Russell (Publ. Astron. 

 Soc. America, 3, 327, 19 17) the mean values of Binary systems are: 



Spectrum B2 



Ratio of mass to Sun 12 



Ao 

 6-5 



Fs giant K5 giant 



F2 dwarf 

 3-o 



G2 dwarf 

 1.2 



K8 dwarf 

 0.9 



The densities can be determined only for eclipsing variables. Stars of Classes B and A have densities 

 averaging about one tenth that of the sun and a relatively small range; Classes F to K show a wide 

 range in density, from 1.8 times that of the sun (W Urs. Maj.) to 0.000002 (W Crucis). 



The surface brightness probably diminishes by at least one magnitude for each step along the Harvard 

 scale from B to M. It follows that the dwarf stars are, in general, closely comparable with the sun in 

 diameter, while the stars of Classes B and A, though larger, rarely exceed ten times the sun's diameter. 

 The redder giant stars must be much larger, and a few, such as Antares, may have diameters exceeding 

 that of the earth's orbit. The densities of these stars must be exceedingly low. 



Arranged in order of increasing density, the stars form a single sequence starting with the giant stars 

 of Class M, proceeding up that series to Class B, and then down the dwarf series to Class M. 



Computed by Plaskett, Publ. Ast. Soc. Pac. 1922: Interferometer measurements, 

 30,600,000 km; Betelgeuse, 0.047", 386,000,000 km. (1921). 



Smithsonian Tables 



Antares, 0.024" 



