Tables 538-539 

 ASTRONOMICAL DATA. 



413 



TABLE 538. - Brightness of tlie Stars. 



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

 magnitude corresponding tp 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 magnitudes. 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 i 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 9 + 5 logm .4. The faintest photographed with the 60-inch reflector 

 at Mt. Wilson are of about the 21st magnitude. A standard candle, of the same color as the stars, would appear of 

 magnitude -j-0.8 at a distance of one kilometer. 



The 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 Centauri, has the (visual) absolute 

 magnitude +15.4, and a luminosity 0.00006 that of the sun. The brightest so far definitely measured, /S Ononis, 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. 



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

 system to Neptune = 60 astr. units), van Maanen, Pr. Nat. Acad. 4, p. 394, 1918. 



Giant and Dwarf Stars. 



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

 ness 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 on each side of the mean absolute 

 magnitude. Absolute magnitude giants roughly o to +1; dwarfs A, i 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 vi.sible to the naked eye. 



Adams and Stromberg have shown that the mean peculiar velocities of the giant stars are all small, — increasing 

 only from about 6 kra/sec. for Class B to 12 for Class M, — while those of the dwarf stars are much greater, increas- 

 ing within each spectral class by about 1.5 km per unit of absolute magnitude, and reaching fully 30 km for stars of 

 Class M and abs. mag. 10. Both giant and dwarf stars show the phenomenon of preferential motion. 



TABLE 539. — 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.D. 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. 



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

 3, 327, 1917) the mean values of Binary systems are: 



Spectrum B2 Ac Fs giant Ks giant F2 dwarf G2 dwarf K8 dwarf 



Ratio of mass to Sun 1 2 6.5 8 10 3.0 1.2 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 ex- 

 ceedingly low. 



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

 ceeding up that series to Class B, and then down the dwarf series to Class M. Russell and others believe this sequence 

 indicates the order of evolution, — a star at first rising in temperature as it contracts and then cooling off again. 



Computed by Plaskett, Pub. Ast. Soc. Pac. 1922; Interferometer measurements, Antares, 0,024", 30,600,000 km; Betel- 

 geuse, 0.047", 386, 000,000 km. (1921) 



Smithsonian Tables. 



