Preparing the Ground for Delving into the Stars

Shaviv, Giora

doi:10.1007/978-3-642-28385-7_2

Giora Shaviv²

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 387))

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Abstract

All our knowledge about the composition of cosmic objects is obtained via spectroscopy. Two key disciplines are required to extract this information from observations: the theory of radiative transfer through stellar material and the theory of atomic structure. Spectroscopy is as old as modern science. It began with Johannes Kepler (1571–1630m) and later Isaac Newton (1643–1727m), who knew about the effect of the prism on sunlight. When they cast the outgoing light of the prism on a screen, they discovered all the colors of the rainbow. Naturally, Newton used a circular aperture, and consequently his spectrum was not pure. Despite this early start, progress was slow at the beginning, and even after major breakthroughs, about 400 years were needed before reliable information about stellar composition could be obtained.

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Notes

1.
Kepler, J., Ad Vitellionem Paralipomena, Quibus Astronomiae Pars Optica Traditur, Claudius Marnius, Frankfurt, 1604.
2.
Newton, I., Treatise of the Reflections, Refractions, Inflections and Colours of Light, London, 1704. The discovery was in 1666, according to Newton’s letter to the secretary of the Royal Society dated 6 February 1672.
3.
Melvill, T., J. R. Astr. Soc. Can. 8, 231 (1914). This is a reprint of the original paper from 1752. And so says the special introduction: Had the ingenious author of this paper (who died December, 1853, at the age of 27) lived to put the finishing hand to it, he would probably, have added many things. I could not discover who wrote the introduction, nor the occasion on which the paper was reprinted.
4.
Roscoe, E.H., The Edinburgh Review CXVI, 295 (1862).
5.
Still, the question remains as to how Newton missed the discovery of the Fraunhofer lines in the solar spectrum. There is a claim (Johnson, A., Nature 26, 572, 12 October 1882) that Newton had to rely on a young assistant with better eyesight, and it was the assistant who missed the lines.
6.
Wollaston, W.H., Phil. Tran. R. Soc. Lond. 92, 365 (1802), read 24 June 1802. In a paper just after Wollaston’s in the journal, Young (Young, M.D.; ibid., 387, read 1 July 1802) describes how he repeated Wollaston’s experiment and got ‘perfectly’ identical results. In particular, he mentions ‘the line of yellow’.
7.
Cajori, F., A History of Physics, The Macmillan Comp., London, 1899.
8.
Fraunhofer, J. von, Denkschriften de K. Acad. der Wissenschaften zu Munchen, Band V, 193 (1817).
9.
Fraunhofer, Edinb. Phil. J. 9, 299 (1823); ibid. 10, 22 (1823).
10.
Jackson, M.W., Studies in History and Philosophy of Science Part A 25, 549 (1994). An interesting account of the way short-sighted politics on the one hand and military needs on the other affected progress in science on both sides of the English channel.
11.
Babbage, C. Reflections on the Decline of Science in England and on Some of Its Causes, London, Printed for B. Fellowes, Ludgate street, 1830, p. 210. Charles Babbage (1792–1871m) was a mathematician.
12.
The irony is that the German scientists thought the same way and expressed contempt for experimental work. When the brilliant self-taught optical inventor Fraunhofer applied for membership to the Bavarian Academy of Sciences, his application was rejected (1819) because Bavarian academics were convinced that the discoveries had only technological significance (what a shame!). Indeed, Fraunhofer regarded himself as an optical engineer. But the telescope lenses produced by Fraunhofer were considered the best in the world. In 1838, Friedrich Bessel (1784–1846m) used a Fraunhofer telescope to determine the first parallax of a nearby star (Bessel, F.W., MNRAS 4, 152, 1838). The star was 61 Cygni, with a mean annual parallax of 0.3135 arcsec. Johann Galle (1812–1910m) was using a Fraunhofer telescope when he discovered the theoretically predicted planet Neptune in the year 1846 (Galle, J.G., MNRAS 7, 153, 1846). It was estimated that Fraunhofer’s refractors of a given aperture were as effective as reflectors with an aperture three times as big. Better late than never, Fraunhofer was accepted as a member of the Bavarian Academy in 1823 and died three years later, before he turned forty.
13.
Bunsen invented the Bunsen burner sometime in 1855. The goal was mainly to develop a better heat source for laboratory work. The standard flames used were smoky and produced a low heat intensity. Bunsen’s breakthrough was simple: mix the gas with air before combustion instead of during combustion. Two years later in 1857, Bunsen and Roscoe described the new burner in Pogg. Ann. Phys. 100, 84 (1857). Mixing the air and gas before burning left the salt outside the burning volume.
14.
Swan, J.W., Edinb. Trans. 21, III, 411 (1857).
15.
Swan did not like the way Kirchhoff and Bunsen attributed the discovery to him, and found it necessary to write a letter to the editor stressing that he found it to be the case in all flames. Swan Phil. Mag. 20, 169 (1860).
16.
Young, T., A Course of Lectures on Natural Philosophy and the Mechanical Arts, London, Taylor & Walton, new edition, 1846, p. 489. The original edition was published in 1803. The relevant report is by Wolfe (Phil. Tran. 4, 1769), who stated that the first to concentrate heat like light was Hoffmann, although Buffon (Histoire Naturelle, Supplement, 1774, I, p. 146) gave a more rigorous proof than Hoffmann did.
17.
Pictet, M.A., Essais sur le feu, Geneva, 1790. Translated from French by W.B., printed for E. Jeffery, London, 1791.
18.
See Cornell, E.S., Ann. Sci. 1, 217 (1936) for a survey of previous experiments.
19.
Prévost was the first known case of a lawyer who turned into a physicist. The other famous cases are Edwin Hubble, who studied law before changing his mind and pursuing a unique career in astronomy, and Lewis Rutherfurd, an attorney and amateur astronomer, who built an observatory at the center of New York city in 1856. Avogadro studied law but reached the conclusion that physics is more interesting.
20.
Prévost, P., J. Phys. 38, 314 (1791).
21.
Prévost, P., Du calorique rayonnant, Paris, Chez Paschoud, J.J., Libraire, Quai des Grands Augustins, no. 11, près du pont Saint-Michel, à Genève, chez le même libraire, 1809. The proof of the radiation law in the book is only verbal. Mathematics appears only in some examples, and the cooling law is expressed algebraically, and not as a differential equation, although the latter techniques had been known since Newton’s times. Another interesting part of the book is Chap. VII, p. 298, where the author discusses the importance of the radiative heat exchange of the Earth in determining its global temperature, a key factor ignored by many in those days. This was at the time Fourier began his attempts to calculate the heat balance of the Earth.
22.
Rumford, An inquiry Concerning the Nature of Heat, and the Mode of Its Communication, 1804, in Collected Works of Count Rumford, Harvard Press, Cambridge, 1970.
23.
In 1796, on the basis of his research results for radiant heat, Rumford invented what is called today the Rumford fireplace. It reflects heat well and eliminates turbulence. The Rumford fireplace was popular until 1850.
24.
In The Gentleman’s Magazine, p. 394, October 1814, we find the following anecdote about Rumford, who applied his own research results:

Nor did any one follow (which is not to be wondered at) his whimsical winter dress, which was entirely white, even his hat. This he adapted agreeably to the law of nature, that more heated rays are thrown from a dark body than a light one; an experiment easily made, by taking two vessels of equal capacity, one blackened, the other white, and filling them with water heated to the same temperature: the water contained in the dark vessel will be found to arrive at the temperature of the surrounding bodies considerably sooner than the white, and vice versa.

The obituary is not signed. However, this is a good example of how physics may be important in fashion, even if it is wrong. Colors are meaningful only in the visible range. In the infrared, which is the relevant radiation in this case, there are no colors, and practically all materials behave the same way.
25.
This was even before 1817, when Dulong and Petit got the first result.
26.
Rumford, C., The Complete Works, Pub. Am. Acad. Arts Sci., Vol II, Boston, 1873.
27.
Leslie, J., An Experimental Inquiry into the Nature and Propagation of Heat, printed for J. Mawman, London, 1804. In 1805, Leslie was elected to the Chair of Mathematics at Edinburgh. His unsuccessful competitor for the chair was backed by some Edinburgh clerics, members of the moderate wing of the Scottish church. This group sought to have Leslie’s election overturned, invoking a clause in the university’s statutes requiring the electors to take the advice of the Edinburgh clergy! As evidence of Leslie’s unsuitability for the job, they cited a footnote from the book in which he agreed with David Hume’s view of cause and effect (p. 521), saying that Hume’s writings were a clear model of accurate reasoning. But Hume was hated by the church. Leslie’s opponents objected because his views challenged traditional arguments for the existence of God. Leslie denied any connection to Hume, however. What saved him was the fact that the different clerical groups hated each other more than they hated Leslie, and did not want one group (in this case the moderate one) to win the battle to change the decision. (Price, H., John Leslie, Oxford, Clarendon Press, 2001).
28.
Fine soot of incompletely burnt coal.
29.
Herschel, W., Phil. Trans. R. Soc. Lond. 90, 284 (1800).
30.
Young, T., A Course of Lectures on Natural Philosophy and the Mechanical Arts, printed for Taylor and Walton, London, 1845.
31.
The expression ‘full of hot air’ meaning nonsense or exaggerated, originated at some time during 1835–1845, but it is not clear to what extent Leslie’s idea contributed to it.
32.
Ritter, J.W., Ann. Phys. 7, 527 (1801).
33.
John was the father of Henry Draper (1837–1882m) from the Henry Draper (HD) catalogue, see Shaviv, The Life of the Stars, 2009. John William Draper took the first photograph of the Moon in 1840.
34.
Desains, P., Leçon de Physique, Tome second, Dezobry, E. Magdeleine et Co., Paris, 1865.
35.
Haüy, R-J., Traité de Physique, Berthollet, Daubenton, Paris, 1806. The translation into English by Gregory is from 1807. These are Haüy’s lectures at the Ecole Normale, Paris.
36.
Talbot, H.F., Brewster, D., Sci. 5, Phil. Mag. 3, 33 (1833); ibid. 9, 3 (1936).
37.
Miller, W.A., Phil. Mag. 27, 81 (1845).
38.
Simms was an acclaimed family of opticians who contributed to improvements in spectroscopy and telescopes through the company Troughton & Simms.
39.
Draper, J.W., Phil. Mag., May, 345 (1847).
40.
Stewart, B., An Account of Some Experiments on Radiant Heat, Involving an Extension of Prévost’s Theory of Exchanges, Trans. R. Soc. Edinb. XXII, PART I, 1 (March 1858) and Proc. R. Soc. Edinb. 6, 93, session of 1857–1858.
41.
Nobili, L., Univ. Sci. et Art Genève 29, 119 (1825).
42.
Melloni, M., Ann. Chim. Phys. 53, 5 (1833); also Pogg. Ann. 35, 112 (1835). His great work on thermal radiation was published in 1850 under the title La thermochrose, ou la coloration calorifique, Naples.
43.
Seebeck, T.J., Pogg. Ann. 6, 1 (1823).
44.
For an extended description of these experiments, see the book by Desains, P., Leçon de Physique, Dezobry, E., Magdeleine et Cie., Lib-Éditeurs, Paris, 1860.
45.
In the textbook Handbook of Natural Philosophy and Astronomy, by Lardner, D., Second Course, Blanchard & Lea Pub., Philadelphia, published in 1854, we already find a table showing the absorbing and reflecting power of various substances, as found by Melloni in the 1830s. The interesting point is that the title of the column is Radiating and Absorbing Powers, and a single number is given. This confirms that Melloni showed the emission to be equal to its absorption, as is also explicitly stated in the text. However, although Melloni gave more data than Leslie, Stewart did not mention him. As a matter of fact, in a textbook on physics from 1837, The Elements of Physics by Webster, T., Scott, Webster, and Geary Pub., London, 1837, it is stated that, in a state of equilibrium, the absorbing power is always equal to the radiating power (p. 257).
46.
The coefficient of proportionality is given by the radiation density at equilibrium. See later.
47.
Stewart, B., Researches on radiant heat, Trans. R. Soc. Edinb. XXII, Part I, 59 (April 1859).
48.
Note that lampblack is a perfect absorber in the infrared and was not really tested in the visible. However, in the visible, it has a black color. Colors have no meaning in the infrared as we cannot see in the infrared. So the term ‘black body’ really emerged from an object which behaved in the infrared as a perfect absorber and emitter, but has a black color in the visible range. Put another way, the name arose from an irrelevant property of the body, because it could have had any color in the visible.
49.
Stewart, B., Proc. R. Soc. Lond. 10, 385 (1859–1860).
50.
Kirchhoff, G., Monat. der König. Preussischen Akad. der Wissen. Berlin, October, 1858.
51.
Kirchhoff, G., Ann. Phys. 184, no. 12, 567 (1859); ibid. Ann. Phys. 185, no. 1, 148 (1859).
52.
Kirchhoff, G., Ann. Phys. 185, no. 2, 275 (1860); ibid. Ann. Physik und Chemie CIX, 6, 275 (1860); ibid. Ann. Chim. Phys. LXII, 3, 160 (1861).
53.
Kirchhoff, G. and Bunsen, R., Ann. Phys. und Chemie CX, 6, 161 (1860); ibid. CXIII, 7, 337 (1861); ibid. Ann. Chim. Phys. LXII, 3, 452 (1861); ibid. LXIV, 3, 257 (1862).
54.
Diathermanous means permeable by heat waves, so it describes a body which transmits heat as electromagnetic radiation. The term was apparently invented by Melloni somewhere between 1830 and 1840. Melloni proposed to use ‘diathermanous’ for bodies that let heat pass easily, and athermanous for those that do not let heat pass. However, see W.D.L.L. Nature 7, 242 (1873). In general, transparency in the visible and the property of being diathermanous are not related.
55.
Unsöld, A. and Baschek, B., The New Cosmos, 4th edn., Springer, 1991.
56.
Kirchhoff, G., Ann. Chim. Phys. 67, 160 (1861).
57.
This approximation is called the two-level atom. This simplification, which is frequently used even today, was introduced by Milne, E.A., J. Lond. Math. Soc. 1, 40, 1926.
58.
Kirchhoff, G., Ann. Phys. 194, 94 (1862). The English translation is: Phil. Mag. 25, 250 (1863).
59.
Stewart, B., Phil. Mag. 25, 354 (1863).
60.
Kirchhoff, G., Phil. Mag. Sect. 4, 20, 1 (1860).
61.
Kirchhoff wrote that de la Provostaye and Desains did the experiment, but did not provide any published reference. I suspect that he meant: de la Provostaye, F., and Desains, P., Ann. Phys. 150, 147 (1848), which was a translation from Compt. Rend. XXVI, 212 (1848).
62.
Kirchhoff mentions that, in the case of de la Provostaye and Desains, the rays were invisible, while he discussed visible light. The conclusions were nevertheless the same. In 1868, Desains wrote a review about French scientific achievements in La Théorie de la Chaleur and did not mention any ‘rays of heat’.
63.
Kirchhoff also argued incorrectly as follows: The wavelengths which correspond to maxima of the radiating and absorbing powers are, as will be fully explained in another place, altogether independent of the temperature. This was before the discovery of Wien’s displacement law, which is a relation between the temperature of a black body and the wavelength at which its emission power reaches maximum. The existence of such a law became clear once the shape of the spectral distribution had been found. Such a law had been suggested earlier by Wilhelm Weber (1804–1891) in his 1888 paper.
64.
Wien, W., Ann. Phys. 288, 132 (1894).
65.
Stewart, B., An Elementary Treatise on Heat, Clarendon press, Oxford, 1866.
66.
Rayleigh, Lord, Phil. Mag. 6, 1, 98 (1901); Scientific Papers 4, 494.
67.
Kayser, H., Handbuch der Spectroscopie, Hirzel, Leipzig, 1900.
68.
Larmor, J., Nature 115, 159 (16 January 1925).
69.
Foucault, L., Ann. Chim. Phys. 58, 476 (1860).
70.
De La Rive, A.-A., A Treatise on Electricity, London, Longman, Green, and Longman, 1853.
71.
de la Provostaye, F.H., and Desains, P., Compt. Rend. 38, 977 (1854).
72.
Kelvin was famous for many provocative statements which turned out later to be wrong, in particular in the discussion with Darwin. See Shaviv, G., The Life of Stars, Springer, 2009.
73.
Thomson, W., MacMillan’s Magazine, March, 1862, and Rep. Br. Assoc. 3, 27 (1871).
74.
Kelvin used the term ‘prismatic analysis’ rather than ‘spectroscopic analysis’ to refer to spectroscopic analysis by means of a prism. Today, spectroscopic analysis can be better carried out with a grating. The first to construct and apply a grating was David Rittenhouse (1732–1796) in 1785, followed later by Fraunhofer in 1821. However, the prisms were still better in those days. The priority of Rittenhouse in the use of a grating was established by Babb as late as 1932. See Cope, T.D., J. Frank. Inst. 214, 99 (1932). It was not until 1873 that Friedrich Nobert (1806–1881) perfected the grating to reach 9,000 lines per millimeter and eventually produce a superior resolution to prisms.
75.
Ångström, A.J., Optiska Undersokningar, Trans. R. Acad. Stockholm, 1853. Translated in Phil. Mag., fourth series, v, IX, 327.
76.
See Phil. Mag., fourth series, XXIV, 2, 3: Monatsberichte Akad. Wissen. Berlin, 1859, p. 662.
77.
Whitmell, C.T.L., Nature, p. 188 (January 1876).
78.
Irony of fate, there exists a Kirchhoff–Stokes equation for sound attenuation. The name was given after both heroes had passed away. Kirchhoff, who is mostly known for his work on electricity and radiation, derived a formula for the absorption of sound due to conduction (Kirchhoff, G., Ann. Phys. 134, 177, 1868) which is similar to the formula for viscosity deduced by Stokes (Stokes, G.G., Phil. Mag. I, 305, 1851) several years earlier.
79.
Brewster, D., Rep. Br. Assoc. 11, 15 (1842).
80.
Swan, J.W., On the Prismatic Spectra of the Flames of Compounds of Carbon and Hydrogen, Royal Society of Edinburgh. Transactions, 1857.
81.
Kirchhoff, G., Pogg. Ann. 118, 94 (1863).
82.
Talbot, W.H.F., Edinb. J. Sci. 5, 77 (1826). Talbot discusses experiments carried out by Herschel.
83.
Talbot claimed that the \(D\) line was due to sulphur and sodium salt. He was correct about the contribution of the sodium to the line, but wrong about the sulphur. Moreover, if two elements can produce the same line, then the lines cannot be used to identify elements.
84.
Herschel, J.F.W., A Treatise on Astronomy, 3rd edn., Carey, Lea & Blanchard, Philadelphia, 1835.
85.
Roscoe forwarded part of the letter to the Editor of the Philosophical Magazine and Journal, on 1 February 1860, and wrote: As it gives a later account of Kirchhoff and Bunsen’s most important researches than has yet appeared in the English journal, I think it may be of interest to you and to your readers. [...], signed: Henry E. Roscoe.
86.
Huggins, W., The New Astronomy, A Personal Retrospect, The Nineteenth Century 41, 911 (1897).
87.
Miller, W.A., Phil. Mag. III, 27, p. 81, 1845.
88.
Miller, W.A., Elements of Chemistry: Theoretical and Practical, Part I. Chemical Physics, 2nd edn. John W. Parker and Son, London, 1860, p. 146.
89.
Publisher Alexander Macmillan chose Lockyer as Nature’s founding editor in 1869. As Ruth Barton suggests (Barton, R., Lockyer’s columns of controversy in Nature, in History of the Journal Nature, Nature 16, October 2007), Lockyer endorsed discussions of controversies. Should we understand his remarks on the priority in terms of his passion for controversy?
90.
Lockyer, N., The Chemistry of the Sun, MacMillan, 1887. See Chap. V.
91.
Brewster, D., Edinb. Phil. Trans. 9, 433 (1823).
92.
Herschel, J.F.W., Edinb. Phil. Trans. 9, 445 (1823).
93.
Herschel, J.F.W., A Treatise on Astronomy, 3rd edn., Carey, Lea, & Blanchard, Philadelphia, 1835, p. 203.
94.
Herschel, J., Outline of Astronomy. The first edition came out in 1840 and the 11th edition was issued in 1871. The ‘new edition’ came out in 1893, London, Longmans, Green, 1893.
95.
Brewster, D., Phil. Trans. R. Soc. Lond. 127, 245, 1837.
96.
Brewster, D. and Gladstone, J.H., On the Lines of the Solar Spectrum, Proc. R. Soc. Lond. 150, 339, 1859.
97.
Miller, W.A., Phil. Mag., Ser. III, 27, 81, published in German Ann. Phys. 145, 404 (1846).
98.
Brewster, D., Phil. Trans. Edinb., 1833.
99.
Forbes, J.D., Phil. Trans. R. Soc. Lond. 126, 453 (1836).
100.
Pierce, A.K. and Slaughter, C.D., Solar Phys. 51, 25 (1977).
101.
In a footnote to his paper Forbes wrote:

I do not know with whom the idea of the absorptive action of the Sun’s atmosphere originated. The editors of the London and Edinburgh Phil. Mag. have, however, referred me to the mention of Sir John Herschel’s writings, particularly his Elementary Treatise on Astronomy, from which I extracted the following remarkable passage: “The prismatic analysis of the solar beam exhibits in the spectrum a series of fixed lines totally unlike those of any known terrestrial flame. This may hereafter lead us to clearer insight into its origin. But before we can draw any conclusions from such an indication, we must recollect that previous to reaching us it has undergone the whole absorptive action of our atmosphere, as well as of the Sun’s. [...] It deserves inquiry whether some or all of the fixed lines observed by Wollaston and Fraunhofer may not have their origin in our own atmosphere. [...] The effect of the Sun’s atmosphere, and possibly also of the medium surrounding it (whatever it be), which resists the motion of comets, cannot be eliminated.”

If we continued in this way, we would conclude that Herschel even predicted the effect of the solar wind on comets.
102.
Agnes Mary Clerke (1842–1907) was an astronomer and a well-known writer, mainly in the field of astronomy. She wrote a popular book on astronomy (Clerke, A.M., A Popular History of Astronomy During the Nineteenth Century, Edinburgh, A. & C. Black, 2nd edn. 1887).
103.
Very, F.W., Astrophys. J. 16, 73 (1902).
104.
\(z=\mathrm{ e}^{kt_0}\), \(\gamma =r/\mathrm{ R}_{\odot }\), and \(\sigma =1/\sqrt{1-\gamma }\), where \(t_0\) is the thickness of the absorbing layer, \(k\) the coefficient of absorption, \(r\) the perpendicular distance between any point on the Sun and the line drawn from the Sun’s surface towards the observer on the Earth, and \(\mathrm{ R}_{\odot }\) the radius of the Sun.
105.
Very, F.W., Astrophys. J. 19, 139 (1904).
106.
Schuster, A., Astrophys. J. 16, 320 (1902).
107.
See for example, Livingston, W.C., Milkey, R., and Sheeley, N., Jr., AAS meeting, no. 211, 159.06, 2008; Neckel, H., Solar Phys. 229, 13 (2005).
108.
Wheatstone, C., Prismatic decomposition of electric light, Reports to the British association for the Advancement of Science 5, 11 (1835); Crookes, Chem. News 3, 198 (1861).
109.
Wheatstone, C., Phil. Mag. 7, 299 (1835).
110.
Ångström, A.J., Pogg. Ann. 117, 290 (1862); Phil. Mag. 9, 327 (1855).
111.
Willigen, V.S.M., Ann. Phys. 182, 610 (1859).
112.
Roscoe (Roscoe, H.E., The Edinburgh Review or Critical Journal for July 1862 to October 1862, p. 295) gives the following example about the unbelievable way in which scientific discoveries are interpreted by laymen, and suggests that it could be an interesting branch of study to the psychologist: Kirchhoff and Bunsen got a letter form a Silesian farmer who thanked them for proving his theory that no inorganic materials should be added to plants as all the required minerals exist in solar light.
113.
Kirchhoff, G., Solar Spectra and the Spectra of the Chemical Elements, MacMillan, Cambridge, 1862.
114.
Recall the power of the excellent optical equipment produced by Fraunhofer. Similarly, the Steineil-Söhne company was founded in 1855 by Carl (1801–1870) and his son Adolf (1832–1893) Steineil, and excelled in spectrographs.
115.
Arago, F., Popular Astronomy. Translated by Smyth and Grant, Longman, Brown, Green and Longman, London, 1955. From 1813 and until 1845, Arago gave very popular non-technical lectures on astronomy. Chapter XXIX of the book is entitled: Is the Sun inhabited?
116.
The term photosphere was invented by Arago in Popular Astronomy, p. 411:

All the phenomena of which we have just been speaking, may be explained in a satisfactory manner, if we assume that the Sun is an obscure body surrounded to a certain distance by an atmosphere, which may be compared to the terrestrial atmosphere when the latter is occupied by a continuum stratum of opaque and light reflecting clouds. If moreover, we place above this first stratum a second luminous atmosphere which will assume the name of a photosphere, this photosphere, more or less remote from the interior cloudy atmosphere, determines by its contour the visible limits of the body.

Since then, this term has been adopted to describe the ‘last luminous visible layer of the Sun’.
117.
Penumbra literally means dim light, in this case, the outer filamentary region of a sunspot.
118.
The existence of magnetic fields in sunspots was demonstrated in 1908, shortly after the Zeeman effect was discovered. The Zeeman effect, the splitting of spectral lines in the presence of a magnetic field, was discovered by Zeeman (1865–1943m) in 1896 (Zeeman, P., Phil. Mag. [5], 43, 226, 1897; Astrophys. J. 5, 332, 1897). He observed in the laboratory how the two sodium \(D\) lines (the \(D\) lines played an important role once again) broaden when the flame is placed between the magnetic poles of a strong electromagnet. Hale used the Zeeman effect to identify the magnetic field in sunspots in 1908 (Hale, G.E., PASP 20, 287, 1908; Astrophys. J. 28, 315, 1908). In the wake of this discovery, Hale asked Zeeman to send his views about the discovery to Nature. While Hale was rather cautious about the discovery and its implication, Zeeman stated that:

Hale has given what appears to be a decisive evidence that sunspots have strong magnetic fields, the direction of these fields being mainly perpendicular to the Sun’s surface.

The effect was expected by Faraday (Maxwell, J.C., Collected Works, II, 790, Cambridge Press, 1890), who tried in vain to detect it as early as 1862. The temperature in the spot is about 4,000 K. The magnetic fields in the spots are about 1,000 times greater than the mean solar magnetic field, and may reach 1,000–4,000 gauss, while the magnetic field of the Earth is 0.3–0.6 gauss.
119.
Macpherson, H., Century Progress in Astronomy, William Blackwood and Sons, Edinb. and Lond. 1906.
120.
Stoney, G.J., Proc. R. Soc. XVII, 1, 1867.
121.
Knott, C.G., Life and Scientific Work of Peter Guthrie Tait, Cambridge University Press, 1911.
122.
Shaviv, G., The Life of the Stars, Springer, Heidelberg, 2009.
123.
Kirchhoff, G., On the relation between emission and absorption of light and heat, which was presented to the Berlin Academy of Sciences on 15 December 1859: Gustav Kirchhoff, Ueber den Zusammenhang von Emission und Absorption von Licht und Wärme, Akad. der Wissen. Berlin, pp. 783, 784, 786, reprinted in Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und das Spektrum der chemi schen Elemente und weitere ergänzende Arbeiten aus den Jahr en 1859–1862, Osnabrück, 1972, ed. Kangro. The more detailed paper was published in Ann. Phys., January 1860.
124.
Gustav Kirchhoff, Untersuchungen über das Sonnenspektrum und die Spektren der chemischen Elemente (2nd edn., Berlin, 1962), appendix, Über das Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermšgen der Körper für Wärme und Licht, 22–39; also in Gesammelte Abhandlungen. Vol. 1 (Leipzig, 1882) 571, English trans. in D.B. Brace, ed., The Laws of Radiation and Absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff, and Bunsen, New York, 1901, p. 75.
125.
Note that Kirchhoff’s one-wavelength plate is a perfect mirror for all radiation with a wavelength different from the specified one.
126.
Tyndall, J., Six Lectures on Light Delivered in America in 1872–1873, Appleton and Comp., New York, 1877.

127.

The Rumford Medal is awarded by the Royal Society every other year for an outstandingly important recent discovery in the field of thermal or optical properties of matter made by a scientist working in Europe. The medal is based on a donation by Rumford, who was the first to be awarded the prize! Of the names mentioned so far, the following were winners:

1804	Leslie	For his Experiments on Heat, published in his work, entitled, An Experimental
		Enquiry into the Nature and Propagation of Heat.
1816	Davy	For his Papers on Combustion and Flame, published in the last volume of the
		Philosophical Transactions.
1834	Melloni	For his discoveries relevant to radiant heat.
1838	Forbes	For his experiments on the polarization of heat, of which an account was
		published in the Transactions of the Royal Society of Edinburgh. Not for
		spectroscopy.
1842	Talbot	For his discoveries and improvements in photography. Not for heat research.
1852	Stokes	For his discovery of the change in the refrangibility of light.
1872	Ångström	For his researches on spectral analysis.
1874	Lockyer	For his spectroscopic researches on the Sun and on the chemical elements. Not
		for the helium discovery (it was too ‘risky’).
1876	Janssen	For his numerous and important researches in the radiation and absorption of
		light, carried on chiefly by means of the spectroscope. Not for
		discovering helium!
1880	Huggins	For his important researches in astronomical spectroscopy, and especially for
		his determination of the radical component of the proper motions of stars.
1886	Langley	For his researches on the spectrum by means of the bolometer.

Note those who did not get the prize, in particular, Herschel, Prévost, Pictet, Wheatston, Miller, de la Provostaye, Desains, and Bunsen. (Source: Rumford archives, 1800–1898.) Prize committeesare driven by internal politics.

128.
The following story is amusing. Kirchhoff (Smithsonian Report, p. 537, 1889) once told his banker about the discovery of terrestrial metals on the Sun. The banker responded somewhat indifferently, with: Of what use is gold on the Sun if I cannot get it down to Earth? Later, after Queen Victoria of England had presented Kirchhoff with a medal and a prize in gold sovereigns for work on the solar spectrum, he took the gold sovereigns to the banker and retorted: Here is some gold from the Sun!
129.
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131.
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132.
Wien was very nationalistic, and a defender of German science, so for him to raise such a claim was no a trivial matter.
133.
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134.
Paschen, F., Wied. Ann. 51, 41 (1894).
135.
A spectrometer which splits the light, combined with a bolometer which measures the power emitted in a certain wavelength range.
136.
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The two volume book by Courant, R. and Hilbert, D., Methods of Mathematical Physics, first published in 1924 and updated in 1953, Interscience Pub., served for many years as the ‘bible’ for mathematical physicists.
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For more details on this interesting and important debate, see Schirrmacher, A., Experimenting theory: The proofs of Kirchhoff’s radiation law before and after Planck, Historical Studies in the Physical and Biological Sciences 33, 299 (2003).
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147.
For historical justice, we mention, Ampère, Weber, and Robert Thomson (1822–1873).
148.
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152.
If matter is not completely evacuated from the cavity, the squared index of refraction of the matter enters the law. Here we leave this point aside and assume unity for the index of refraction (vacuum). If the walls are perfect reflectors, the radiation does not interact with the walls. If the radiation is to ‘feel’ the temperature of the walls, they must absorb at least part of the radiation (and then re-emit it). As for stars, the ‘enclosure’ is not empty, but full of matter and there are no walls to speak of.
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After Langley’s death, Abbot continued to measure the solar constant and searched for places with clear sky. Abbot discovered that the southern mountainous region of the Sinai Peninsula enjoyed excellent weather conditions all year round and established an observatory on Mount St. Katherine, only a few kilometers from the famous Santa Katherina monastery. One can still see the stairs with the sign ‘to the observatory’. The mountain on which, according to tradition, the ten commandments were announced provides an excellent place for measuring the solar constant! The observatory, established in 1931, operated for about 6 years and was then shut down. The reason for the consistent effort to measure the solar constant accurately was the belief by Langley and Abbot that the energy flux from the Sun dictates the weather on the Earth, so that an exact knowledge of this quantity would be a prerequisite for Earthly weather predictions. Langley suspected the solar radiation of varying periodically.
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A harmonic oscillator is any physical system that behaves like a spring attached to a mass or a pendulum, i.e., a system which, when displaced slightly from its equilibrium position where it would remain without motion, feels a restoring force proportional to its displacement from equilibrium. This is the simplest mechanical system one can conceive of, and many physical systems behave this way upon sufficiently small perturbation from their steady state. Hence, it was natural to assume the simplest possible system for the emitters and absorbers of radiation.
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According to Maxwell’s classical theory of a gas of molecules, or any collection of particles or systems, the distribution of energy of the molecules is exponential (\(\mathrm{ e}^{-E/kT}\)) and the mean energy is \(3/2kT\). This may sound complicated, but it can be shown that, if we bring two systems together and the energy of the new bigger system is the sum of the energies of the individual systems, then this law must follow.
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Strictly speaking, the wavelengths were discrete and of the form \(L/2n\), where \(L\) was the size of the cavity and \(n\) an integer. But these fine details make no difference for the final result and were added here for physical accuracy only.
191.
A degree of freedom of a physical system is a parameter needed to determine the state of the system uniquely. In the case of a monochromatic wave, there is one degree of freedom, the amplitude, and for a general wave there can be an infinite number of degrees of freedom.
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The irony is that much of the experimental work on the photoelectric effect on which Einstein based his theory was discovered by Lenard (1862–1947). Lenard, who got the Nobel prize in 1905, was an adamant promoter of the ‘Deutsche Physik’ idea and a declared anti-semite. As such, he did not believe in the ‘Jewish physics’ as reflected in the special theory of relativity. For him it was a bitter pill to watch Einstein being awarded the Nobel prize in 1921 for explaining the data obtained by an Aryan. Add to this his annoyance over the fact that the effect was named after Einstein and himself, since he did the experiment, and you will appreciate the rumor that he was even ready to declare his results wrong.
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In the photoelectric effect, a metal is illuminated by monochromatic light. Only when the frequency of the light is above a certain value are electrons emitted from the metal. Each metal has a different threshold frequency. A high intensity of light, but at a frequency below the threshold, does not release electrons.
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224.
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Shaviv, G. (2012). Preparing the Ground for Delving into the Stars. In: The Synthesis of the Elements. Astrophysics and Space Science Library, vol 387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28385-7_2

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