10

The answer to your first question is (now) fairly simple: No, brown dwarfs are not more common than red dwarfs. A crude approximation is that stars (which are indeed mostly red dwarfs) outnumber brown dwarfs 4 or 5 to 1; see, for example, the review article by Chabrier et al. (2014). This is supported by extensive surveys done in the 2000s and 2010s, ...


8

Red dwarfs, depending on your definition, can range from 2.5 to 150 times more dense than the Sun. What is the cause of this discrepancy? They give no calculations, so I can only guess. The article is from 1946 and we've gotten a lot better at science. It's 1946 and information exchange is limited. No internet, no TV, and long distance calls are expensive....


7

This is an important question to ask about the initial mass function of objects in the Galaxy - and the final answer hasn't been cast as it is a matter of research. Yet, observational data (e.g. see the mass functions for various clusters in this talk), and simulations in more or less good agreement with that (e.g. here or here), seem to indicate that this ...


7

The brown dwarf "limit" is about $0.072 M_{\odot}$ at solar metallicity (e.g. Chabrier et al. 2000) and is composition dependent. It gets a little higher in metal-poor gas and a little lower in metal-rich gas. $0.064 \pm 0.012 M_\odot$ (the third significant figure is superfluous) is within one error bar of that limit, which in itself is only a 68% ...


3

If we take 1 atmosphere of optical depth to mean looking though the Earth's atmosphere at zenith, then the optical depth to scattering is small - probably of order 0.3 for blue light and much smaller (according to $\lambda^{-4}$) for red light. That means that when the Sun is at zenith, most of the light reaches the ground but some blue light is scattered ...


3

This is a brief letter to Nature from 1946, containing no quantitative justification of the density estimate In 1946, whilst the radius of some of the nearest red dwarfs could be estimated from their luminosities and blackbody temperatures, there would be little information about masses. There is little else to say. Modern models and measurements of masses ...


3

According to the wiki article on sub-brown dwarfs, the lowest mass object that can form from collapse of gas cloud is about 1 Jupiter mass. Original source: Boss, Alan P.; Basri, Gibor; Kumar, Shiv S.; Liebert, James; Martín, Eduardo L.; Reipurth, Bo; Zinnecker, Hans (2003), "Nomenclature: Brown Dwarfs, Gas Giant Planets, and ?"


2

A "star" has significant hydrogen fusion occuring in its core. This energy prevents collapse and allows the star to reach a stable position state. A Brown dwarf does not have significant hydrogen fusion. Its core is heated by the release of gravitational energy (the Kelvin–Helmholtz mechanism). The transition between brown and red dwarfs is at ...


2

This mechanism, being actively emitting in the radio-wavelengths, is certainly negligible for the overall atmospheric energetics at Proxima b. One can conclude this by taking the band luminosities from the cited paper ($\rm 2.51\times10^{20} erg/s$, p.3, first paragraph) and compare them to the solar constant at the planets orbit, which should amount to $\...


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