# Mass of sun's core

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?

• Can you give references for these numbers? Oct 22 '14 at 5:54

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.

• Change in what over the change in density?
– LDC3
Oct 24 '14 at 1:40
• @LCD3 pressure. Oct 24 '14 at 1:41

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.

• With 0.25 radius, the volume is 0.0156 the total volume, which is 1.56%. If 0.8% is 34% of the mass, than 1.56% should be 50% of the mass. Now all that is needed is a probe to determine if it is 20% or 25% of the radius.
– LDC3
Oct 23 '14 at 0:26
• I'm not sure I follow some of the numbers. Oct 23 '14 at 0:29
• Which numbers are you confused about?
– LDC3
Oct 23 '14 at 0:33
• Are you justifying the data you found, or mine? If 0.8% is 34% of the mass, then (assuming constant density, which might not be true), 1.56% should be roughly 2/3 of the mass, not 50%. Oct 23 '14 at 0:34
• Actually, I was justifying yours. But remember, the density between 20% and 25% is a lot less than that below 20% so the mass wouldn't double.
– LDC3
Oct 23 '14 at 0:36

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