### Why is Chandrasekar Limit expressed relative to Sun?

• 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?

@JamesK - thank you. corrected my description.

Note that the red giant phase of the sun will not increase its mass, only its radius.

5 years ago

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.

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.

+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.

Obligatory request for someone to workout the Chandrasekhar limit in slugs.

@Taemyr The internet is a wonderful thing. For anyone interested: 1.9×10^29 slugs

That would make a slug 14.65kg

Yes, it's using this Imperial Slug) rather than this invertebrate slug

@Useless you ninja'd me, tho' I was going to suggest banana slugs because they taste better

Wolfram Alpha is surprisingly bad at explaining what it thinks a unit means!

@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

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