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In 1931, Chandrasekhar was able to show that there is a certain critical mass (Chandrasekhar's limit) beyond which a white dwarf cannot exist, since the electronic fluid at that point cannot support its weight no matter how compressed it is.

The core of such a star will simply collapse inward.

The critical mass, Chandrasekhar showed, is 1.4 times that of the Sun.

When I first heard this, I was totally confused. Sun is a star too. The Sun will eventually enter the Red Giant Phase, and then it will eventually become a white-dwarf.

How and why did Chandrasekar express his limit relative to Sun?

James K
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Senthil Kumaran
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The mass of the sun is just a unit of convenience in a astronomy. The sun's mass and luminosity, in particular, are relatively easy for us to measure precisely, and when we're talking about stars, provide a convenient scale where the numbers won't be too "astronomical" (be too high a power of $10$ to picture easily). You could derive the Chandrasekhar limit in grams, kilograms, or slugs from the relevant physics, if you wanted. The relevant equation (from the Wikipedia article) is: $$M_{\mathrm{limit}} = \frac{\omega_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^{3/2} \frac{1}{(\mu_e m_\mathrm{H})^2},$$ where $\mu_e$ is the average molecular weight per electron (stellar composition dependent), $m_\mathrm{H}$ is the mass of hydrogen, and $\omega_3^0$ is a numerical constant that is approximately $2.018236\ldots$.

It should be noted that the Chandrasekhar limit is a limit on the mass of the final white dwarf, not of the object that will produce the white dwarf.

Sean Lake
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    The conversion factor for the mass of the Sun to kilograms is 1 solar mass equals 1.9885 × 10^30 kg. Thus, 1.4 solar masses equals 2.7846 x 10^30 kg. – ohwilleke Sep 18 '17 at 21:43
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    +1 The first sentence, "The mass of the sun is just a unit of convenience in a astronomy." summarises it very nicely. Our Solar System is often used as a reference - Sun, Earth, Jupiter, distance from Sun to Earth (1 au) etc. – Mick Sep 19 '17 at 06:29
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    Obligatory request for someone to workout the Chandrasekhar limit in slugs. – SGR Sep 19 '17 at 07:42
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    @SGR It's just a unit conversion; https://www.wolframalpha.com/input/?i=Chandrasekhar+limit+in+slugs – Taemyr Sep 19 '17 at 08:04
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    @Taemyr The internet is a wonderful thing. For anyone interested: 1.9×10^29 slugs – SGR Sep 19 '17 at 08:11
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    That would make a slug 14.65kg – r_ahlskog Sep 19 '17 at 10:46
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    Yes, it's using this Imperial Slug rather than this invertebrate slug – Useless Sep 19 '17 at 11:49
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    @Useless you ninja'd me, tho' I was going to suggest banana slugs because they taste better – Carl Witthoft Sep 19 '17 at 11:51
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    Wolfram Alpha is surprisingly bad at explaining what it thinks a unit means! – Useless Sep 19 '17 at 11:52
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    @Mick The au wasn't originally a unit of convenience. It sits at the base of the cosmological distance ladder and, before radar ranging had really nailed down the size of the solar system, was a significant source of correlated uncertainties in measurements. By making the au a unit, you isolate that source of error, and prevent underestimation of your uncertainty. For more, see: https://astronomy.stackexchange.com/questions/20466/why-dont-astronomers-use-meters-to-measure-astronomical-distances/20469#20469 – Sean Lake Sep 19 '17 at 20:39
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    As far as I know, though, the mass of the sun has always been a unit of convenience, since all that's required to measure it is Kepler's laws, plus Newton's law of gravitation, and $G$. So it would initially have been fixed by the radius of the Earth (via $g$ and the Earth's radius to get $GM_{\mathrm{Earth}}$), it would have been pretty well nailed down as soon as Cavendish measured $G$ directly. The unit of luminosity that sits at the base of measurements in astronomy, though, is usually the that of Vega, not the sun. https://www.astro.umd.edu/~ssm/ASTR620/mags.html – Sean Lake Sep 19 '17 at 20:46
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    Why, Vega? Ask Ptolemy: https://en.wikipedia.org/wiki/Apparent_magnitude – Sean Lake Sep 19 '17 at 20:48