Mass of sun's core

Question

It is estimated that the sun's core is about 1/5 of the radius of the sun (from Wikipedia). I know that the density of the plasma increases substantially the near the center, and that the volume of the core is 0.008 times the total volume.

$$\frac {V_{core}}{V_{sun}}=\frac {4/3\pi (0.2)^3}{4/3\pi (1)^3}$$ $$\frac {V_{core}}{V_{sun}}=\frac {(0.008)}{(1)}$$

What is the mass of the core compared to the total mass?

Answer 1

Here are the results of some arbitrary cutoffs for the "core" based on $2010$ solar models calculated by Guenther et al:

• Contributing $99\%$ of the total luminosity:
  $R = 25.5\%$, $M = 9.88\times10^{29}\,\mathrm{kg}$ ($49.7\%$).
• Nuclear reaction rate falls below $1\%$ of central rate:
  $R= 27.2\%$, $M = 1.07\times10^{30}\,\mathrm{kg}$ ($54.0\%$).

Overall, $\sim 1/4$ the radius ($\sim 1/64$ the volume) and $\sim 1/2$ the mass decently with some other sources. Unfortunately, there does not seem to be a clear dividing line demarcating the "core" like there is between the radiative zone and the convection zone.

Perhaps an alternative condition would be a local maximum of $\mathrm{d}(\ln P)/\mathrm{d}(\ln\rho)$, which occurs under $20\%$ of solar radius and is roughly constant until the convection zone.

Answer 2

I'm getting a slightly different figure from space.com (not my favorite source, but a source nonetheless), which says

The core extends from the sun's center to about a quarter of the way to its surface. Although it only makes up roughly 2 percent of the sun's volume, it is almost 15 times the density of lead and holds nearly half of the sun's mass.

I would expect it to be fairly dense because of the extreme conditions at the center, primarily the force of gravity pushing in on it. The "15 times the density of lead" is not constant throughout the Sun, and only applies in the very center of the core.

Answer 3

I found out it is 34% of the Sun's mass on Wikipedia.