August 4, 1923] 



NA TURE 



167 



The Temperatures of the Stars. 



By Herbert Dingle. 



THE measurement of the temperature of a star is 

 one of the most difficult problems of physical 

 astronomy. The difficulties are of two general kinds. 

 In the first place^ the very phrase, " the temperature 

 of a star/' has no meaning : we may as well speak of 

 the latitude of the land surface of the earth. There 

 can be no doubt whatever that the temperature varies 

 from one part of a star to another over an enormous 

 range — probably thousands of times greater than the 

 interval between the temperatures of liquid hydrogen 

 and the electric furnace. Secondly, for experimental 

 methods of measurement the only available data are 

 wrapped up in an inconceivably small fraction of the 

 total radiation of the star which reaches the earth after 

 the possible wear and tear of many years' journey 

 through interstellar space and our own atmosphere. 

 From the character of that radiation we have to deduce 

 the temperature of the star. From these two general 

 sources difficulties of many kinds issue forth. 



Happily, the resources of modern physics make the 

 problem anything but hopeless. The " temperatures " 

 of a number of stars have been determined by different 

 methods, though exactly what the figures mean, and 

 how much reliance can be placed on them, are perhaps 

 still matters of doubt. With regard to the first source 

 of difficulty, considerable help is received from the 

 spectroscope. More than ninety-nine per cent, of 

 recorded stellar spectra consist of absorption lines on 

 a continuous background — conclusive evidence that a 

 star consists of at least two distinct parts. In the 

 light of Kirchhoff's principle, the continuous spectrum 

 is attributed, to the hotter, deeper-lying part, and the 

 absorption lines to a surrounding cooler, but still 

 luminous, atmosphere. Accordingly, temperatures 

 measured from the characteristics of the absorption 

 lines must apply to the atmosphere, and temperatures 

 measured from the continuous spectrum must apply 

 to the interior. 



The next questions are evidently : Do the atmosphere 

 and the interior, as thus defined, comprise the whole 

 star, or are there regions outside the one and beneath 

 the other ? In the former event, what parts of the 

 atmosphere and the interior have the respective 

 measured temperatures, and, in the latter event, what 

 are the temperatures of the unconsidered regions ? 

 For the answers to these questions we are indebted 

 mainly to the nearest star — our sun. We know, from 

 observations made possible by a total solar echpse, that 

 outside the sun's atmosphere (j.e. the source of the 

 absorption spectrum lines) there is the corona — 

 evidently a permanent though ever-changing part of 

 the solar structure. We know also that the source 

 of the sun's continuous spectrum is effectively a layer 

 of limited thickness near the surface, because the 

 luminosity of the sun's disc does not fall off appreciably 

 outwards from the centre until the limb is nearly 

 reached. There must, therefore, be a core inside what 

 we have called the " interior," about which, from 

 direct observation, we know nothing. We may assume, 

 then, that in addition to the regions the temperatures 

 of which we measure from the spectrum of a star, 

 there are other very extensive regions, the tempera- 



NO. 2805, VOL. 112] 



tures of which it is at present quite impossible to 

 determine by any experimental means. 



The temperature throughout the atmosphere of a 

 star may be regarded as a constant quantity. To 

 solar eclipses, again, we owe the knowledge that the 

 sun's atmosphere is very thin compared with the depth 

 of the whole globe. It is true that there are indications 

 that its physical condition varies at different levels, but 

 these variations are refinements of analysis which we 

 cannot hope to apply to the stars for a long time to 

 come. If we can determine a temperature from the 

 absorption lines in the spectrum of a star, we are 

 justified in supposing that we can state definitely the 

 temperature at a particular part of the star. The case 

 is not so clear when we come to the continuous spectrum. 

 We do not know at all definitely from what part of 

 the star the continuous spectrum comes. We know 

 that it must come from beneath the atmosphere, and 

 it has just been pointed out that it represents the 

 radiation of a surface layer, which we may call the 

 " photosphere," but how thick that layer is, and 

 what part of it has the temperature deduced from its 

 spectrum, are questions that are still unanswered. 



The first set of difficulties, then, can be partly over- 

 come. Assuming that the sun is a type of its kind, we 

 can divide a star into four distinct parts — a corona, 

 an atmosphere, a photosphere, and a core. Of the 

 temperatures of the first and last, we know, by direct 

 experiment, nothing. The temperature of the second 

 can possibly be measured definitely, and that of the 

 third, vaguely. Supposing these measurements to be 

 made, theory indicates, for certain stars, what must be 

 the temperatures at different parts of the core. 



Turning now to the second set of difficulties — those 

 connected with the actual measurement of the tempera- 

 tures — we note that these may be subdivided into the 

 difficulties of obtaining the requisite data, and those 

 of interpreting the data when they are obtained. It 

 is probably fair to say that, in measuring atmospheric 

 temperatures, the former preponderate, while the latter 

 are most in evidence in the measurement of photo- 

 spheric temperatures. It was Lockyer who first 

 showed the influence of temperature on the line 

 spectrum of a substance, and urged that the relative 

 temperatures of stellar atmospheres could be deter- 

 mined from a study of the lines by which particular 

 substances were represented. More recent investiga- 

 tions, originated by Saha, have confirmed Lockyer's 

 views, and have shown how the actual temperatures 

 can be calculated. But it appears that, while tempera- 

 ture is probably the chief factor in determining the line 

 spectrum, it is by no means the only one. Pressure, 

 the absorption of photospheric radiation, the relative 

 amounts of different substances in the atmosphere, the 

 ionisation potentials of the elements — these at least 

 play a part, and must be determined before the tempera- 

 tures can be found. Unfortunately, they are, in most 

 instances, unknown, and their values have to be 

 assumed, on more or less plausible grounds. There 

 is, therefore, a considerable element of uncertainty 

 in existing estimates of the temperatures of stellar 

 atmospheres. 



