7-2-77. H. Poincaré to Aloys Verschaffel, English translation

[After 1 August 1911]

Bureau des longitudes — Palais de l’institut — 3, rue Mazarine

Dear Colleague,

M. Bigourdan showed me your article on young stars.

This seems interesting; let me nonetheless make the following remarks. It would be best to provide the numbers on which you rely, since we have to know:

1° If it is only angular proper motion or radial velocities, since in the first case one could suppose that they are slow because they are distant.

2° If it has to do with observed proper motion, i.e., motion with respect to the sun, or motion corrected for parallax, i.e., absolute motion. In the presentation of your theory, it would be necessary to explain clearly the hypotheses with which you begin. Are the velocities $v$ and $v^{\prime}$ taken with respect to the sun or to the center of gravity of the solar system? Which law of probability are the velocities supposed to satisfy, is it that of Maxwell?

Your much devoted colleague

Poincaré

ALS 2p. Château-Observatoire d’Abbadia. Translated from the original French (§ 3-45-1) and annotated by S. A. Walter.

Time-stamp: "18.11.2023 23:19"

Notes

• 1 Guillaume Bigourdan was a member of the astronomy section of the Paris Academy of Sciences, and served on the editorial board of the leading French journal of astronomy, the Bulletin astronomique, directed by Poincaré since 1896. It appears likely that Verschaffel sent him a paper for publication in the Bulletin, or perhaps in the Comptes rendus hebdomadaires of the Paris Academy of Sciences. However, no paper by Verschaffel on the topic of stellar evolution was published until June, 1914, when the Bulletin published an essay in response to a paper by Jacob Halm, published in August, 1911 (Halm, 1911; Verschaffel, 1914). Halm focussed on stellar velocity in the constellation of Orion, and on the hypothesis advanced by Kapteyn and Frost (1910), according to which these stars form a third stream, over and above the two streams announced earlier by Kapteyn (1906); see Paul (1993). Poincaré discussed Kapteyn’s discovery in his Leçons sur les hypothèses cosmogoniques from the standpoint of statistical mechanics (Poincaré, 1911, 104–111). Notably, Poincaré observed that Kapteyn’s star streams show that the Milky Way has not reached a state of thermodynamic equilibrium.
• 2 Verschaffel’s essay (1914) neglects to repair the defects pointed out by Poincaré, and in all likelihood, this neglect explains the three-year publication delay in the Bulletin astronomique. Poincaré’s successor as editor-in-chief, Benjamin Baillaud, decided to publish the essay, in spite of the defects. However, he inserted a commentary by Pierre Puiseux (1914), which defended Poincaré’s deployment of statistical mechanics in astrophysics and cosmology.
• 3 Halm’s tightly-structured paper features several pages of calculations and numerical data, including values for proper motion and radial velocity, while Verschaffel’s essay is discursive and meandering.
• 4 By absolute motion, Poincaré means motion corrected for the velocity of the solar system.
• 5 While Verschaffel’s essay (1914) mentions no law of velocity distribution, Halm refers to the Maxwell-Boltzmann law describing the distribution of molecular velocity of a perfect monoatomic gas at thermodynamic equilibrium. According to Halm (and to Poincaré), under the same equilibrium condition, the Maxwell-Boltzmann law describes the velocity distribution of a stellar system. The law of equipartition of energy is a consequence of the Maxwell-Boltzmann law, as Halm observed. Verschaffel (1914) n’a pas précisé de loi de distribution de vitesses. Tout comme Halm, il a observé que si la loi d’équipartition de l’énergie était applicable aux étoiles, le rapport des vitesses de deux étoiles $v$ et $v^{\prime}$ serait égal au rapport inverse de la racine carrée de leurs masses: $v/v^{\prime}=\sqrt{m^{\prime}}/\sqrt{m}$. Verschaffel n’a pas précisé le système de référence auquel sont rattachées les vitesses stellaires $v$ et $v^{\prime}$ et, à la différence de Halm (et de Poincaré), Verschaffel trouvait que si l’application de la loi d’équipartition de l’énergie fut fondée empiriquement pour les molécules gazeuses, il ne le fut pas pour les “masses cosmiques”, dont les étoiles, les planètes, et les nébuleuses. En ce qui concerne la jeunesse des étoiles, Verschaffel a repris la suggestion de Halm, selon laquelle les étoiles de ce troisième essaim (“third drift”) dans la constellation d’Orion avaient pour origine la collision d’étoiles des deux essaims de Kapteyn. He conjectured these collisions result in novae, while allowing that fission, or what he termed “auto-sectionnement” may also explain stellar origin. The Poincaré-Darwin fission theory grew out of Poincaré’s work on the equilibrium figures of rotating fluid masses (Poincaré, 1885). On the astrophysical interpretation of this work, see Myers à Poincaré, 24.09.1901 (§ 3-36-1) and Walter (2023).