by Arthurs S. Eddington
Cambridge University Press
First published 1926
Reissued in the Cambridge Science Classics series 1988
p.371
CHAPTER XIII
DIFFUSE MATTER IN SPACE
The Temperature of Space
256. The total light received by us from the stars is estimated to be equivalent to about 1000 stars of the first magnitude. Allowing an average correction to reduce visual to bolometric magnitude for stars of types other than F and G, the heat received from the stars may be taken to correspond to 2000 stars of apparent bolometric magnitude 1･0. We shall first calculate the energy-density of this radiation,
A star of absolute bolometric magnitude 1･0 radiates 36･3 times as much energy as the sun or 1･37.1035 ergs per sec. This gives 1･15.10-5 ergs per sq.cm.per sec. over a sphere of 10 parsecs(3･08.1019cm.)radius. The corresponding energy-density is obtained by dividing by the velosity of propagation and amounts to 3･83.10-16 ergs per cu.cm. At 10 parsecs distance the apparent magnitude is equal to the absolute magnitude; hence the energy-density 3･83.10-16 corresponds to apparent bolometric magnitude 1･0.
Accordingly the total radiation of the stars has an energy-density
2000 × 3･83.10-16 = 7･67.10-13 ergs/cm.3
By the formula E = αT4 the effective temperature corresponding to this density is
3°･18 absolute
In a region of space not in the neighbourhood of any star this constitutes the whole field of radiation, and a black body, e.g. a black bulb thermometer, will there take up a temperature of 3°･18 so that its emission may balance the radiation falling on it and absorbed by it. This is sometimes called the "temperature of intersteller space."
