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 paper on juvenile stars.

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

1° If it concerns 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 concerns 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: " 7.09.2024 15:22"

Notes

• 1 Guillaume Bigourdan was a member, along with Poincaré, of the Bureau of Longitudes; he was also 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 and astrophysics, the Bulletin astronomique, directed by Poincaré since 1896. Verschaffel probably sent Bigourdan his paper for publication in the Bulletin. 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 that appeared in August, 1911 (Halm, 1911; Verschaffel, 1914). Halm’s paper focused on stellar velocity in the constellation of Orion, and on the hypothesis advanced by Kapteyn and Frost (1910), according to which these stars belong to a third stream (or “third drift”), different from the two streams identified 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. Verschaffel’s paper contests the use of statistical mechanics in astrophysics and cosmology, and was thus certain to attract Poincaré’s attention.
• 2 Verschaffel’s essay (1914) neglects to repair the defects pointed out by Poincaré, and in all likelihood, Verschaffel’s neglect of Poincaré’s request for revisions explains the publication delay in the Bulletin astronomique. The rejection of Verschaffel’s manuscript would have been an embarassment both for Verschaffel and the Paris Academy of Sciences, where Verschaffel became a corresponding member in December, 1911. Poincaré’s successor as editor-in-chief, Benjamin Baillaud, decided to publish Verschaffel’s essay in spite of its defects. However, he took the unusual step of inserting a commentary by Pierre Puiseux (1914), which defends Poincaré’s deployment of statistical mechanics in astrophysics and cosmology. By 1914, several astrophysicists were pursuing research based on statistical mechanics, including Jeans and von Zeipel, although Eddington (1914, 160) found that observations of stellar motion in some regions did not support the law of equipartition of energy.
• 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 loosely arranged.
• 4 Halm referred to the Maxwell-Boltzmann law describing the distribution of molecular velocity of a perfect mono-atomic 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 carefully observed. Verschaffel’s essay (1914) mentions no law of velocity distribution, but like Halm, Verschaffel observes that, if equipartition of energy were applicable to stellar populations, the ratio of two stellar velocities $v$ and $v^{\prime}$ would equal the inverse of the square root of mass: $v/v^{\prime}=\sqrt{m^{\prime}}/\sqrt{m}$. Verschaffel does not identify his reference frame and, unlike both Halm and Poincaré, he finds that, if equipartition of energy has an empirical foundation for systems of gas molecules, it is not so founded for “cosmic masses”: stars, planets and nebulae. With respect to stellar evolution, Verschaffel adopts Halm’s view of the so-called “third drift” discovered by Kapteyn and Frost in Orion (see note 1), whereby this stream results from collision of the two star-streams identified by Kapteyn in 1904. Verschaffel conjectures that stellar collisions result in novae, while allowing that fission, or what he termed “auto-sectionnement” may also explain stellar origin. In 1911, the Poincaré-Darwin fission theory of binary-star formation was in full swing; see, for example, Arthur Eddington’s entry “Star” in the Encyclopaedia Britannica (Eddington, 1911). On the fission theory, see also Myers to Poincaré, 24.09.1901 (§ 3-36-1), the correspondence with George Howard Darwin, and the overview in Walter (2023).