# Solar core

An illustration of the structure of the Sun

The core of the Sun is considered to extend from the center to about 0.2 to 0.25 solar radius.[1] It is the hottest part of the Sun and of the Solar System. It has a density of 150 g/cm³ (150 times the density of liquid water) at the center, and a temperature of close to 15,700,000 kelvin, or about 15,700,000 degrees Celsius; by contrast, the surface of the Sun is close to 6,000 kelvin. The core is made of hot, dense gas in the plasmic state, at a pressure estimated at 265 billion bar (26.5 quadrillion pascals or 3.84 trillion psi) at the center.

The core inside 0.20 of the solar radius, contains 34% of the Sun's mass, but only 0.8% of the Sun's volume. Inside 0.24 solar radius, the core generates 99% of the fusion power of the Sun.

## Energy production

Approximately 3.6×1038 protons (hydrogen nuclei) are converted into helium nuclei every second releasing energy at a rate of 3.86×1026 joules per second.[2]

The core produces almost all of the Sun's heat via fusion: the rest of the star is heated by the outward transfer of heat from the core. The energy produced by fusion in the core, except a small part carried out by neutrinos, must travel through many successive layers to the solar photosphere before it escapes into space as sunlight or kinetic energy of particles.

The energy production per unit time (power) of fusion in the core varies with distance from the solar center. At the center of the Sun, fusion power is estimated by models to be about 276.5 watts/m3.[3]

The power production density of the core overall is similar to the metabolic production density of a reptile.[4] The peak power production in the Sun's center, per volume, has been compared to the volumetric heat generated in an active compost heap.[5]

The low power outputs occurring inside the fusion core of the Sun may also be surprising, considering the large power which might be predicted by a simple application of the Stefan–Boltzmann law for temperatures of 10 to 15 million kelvin. However, layers of the Sun are radiating to outer layers only slightly lower in temperature, and it is this difference in radiation powers between layers which determines net power production and transfer in the solar core.

At 19% of the solar radius, near the edge of the core, temperatures are about 10 million kelvin and fusion power density is 6.9 watts/m3, which is about 2.5% of the maximum value at the solar center. The density here is about 40 g/cm3, or about 27% of that at the center.[6] Some 91% of the solar energy is produced within this radius. Within 24% of the radius (the outer "core" by some definitions), 99% of the Sun's power is produced. Beyond 30% of the solar radius, where temperature is 7 million K and density has fallen to 10 g/cm3 the rate of fusion is almost nil.[7]

There are two distinct reactions in which 4 H atoms may eventually result in one He atom. The first of these, known as the proton-proton chain, is:[2][8]

$\begin{cases} {}^1\!H + ^1\!H \rightarrow ^2\!D + e^+ + v \\ \mathrm{then}\quad{}^2\!D + ^1\!H \rightarrow ^3\!He + \gamma \\ \mathrm{then}\quad{}^3\!He + ^3\!He \rightarrow ^4\!He + ^1\!H + ^1\!H \end{cases}$

(1)

This reaction sequence is believed to be the most important one in the solar core. The total energy released by these reactions in turning 4 Hydrogen atoms into 1 Helium atom is 26.7 MeV.

The second reaction, called the CNO cycle, generates less than 10% of the total solar energy. This involves carbon atoms which are not consumed in the overall process. The details of this "carbon cycle" are as follows:

$\begin{cases} {}^{12}\!C + ^1\!H \rightarrow ^{13}\!N + \gamma \\ \mathrm{then}\quad{}^{13}\!N \rightarrow ^{13}\!C + e^+ + \nu \\ \mathrm{then}\quad{}^{13}\!C + ^1\!H \rightarrow ^{14}\!N + \gamma \\ \mathrm{then}\quad{}^{14}\!N + ^1\!H \rightarrow ^{15}\!O + \gamma \\ \mathrm{then}\quad{}^{15}\!O \rightarrow ^{15}\!N + e^+ + \nu \\ \mathrm{then}\quad{}^{15}\!N + ^1\!H \rightarrow ^{12}\!C + ^4\!He + \gamma \\ \end{cases}$

(2)

## Equilibrium

The rate of nuclear fusion depends strongly on density, so the fusion rate in the core is in a self-correcting equilibrium: a slightly higher rate of fusion would cause the core to heat up more and expand slightly against the weight of the outer layers, reducing the fusion rate and correcting the perturbation; and a slightly lower rate would cause the core to cool and shrink slightly, increasing the fusion rate and again reverting it to its present level.

## Energy transfer

The high-energy photons (gamma rays) released in fusion reactions take indirect paths to the Sun's surface. According to current models, random scattering from free electrons in the solar radiative zone (the zone within 75% of the solar radius, where heat transfer is by radiation) sets the photon diffusion time scale (or "photon travel time") from the core to the outer edge of the radiative zone at about 170,000 years. From there they cross into the convective zone (the remaining 25% of distance from the Sun's center), where the dominant transfer process changes to convection, and the speed at which heat moves outward becomes considerably faster.[9]

In the process of heat transfer from core to photosphere, each gamma ray in the Sun's core is converted during scattering into several million visible light photons before escaping into space. Neutrinos are also released by the fusion reactions in the core, but unlike photons they very rarely interact with matter, so almost all are able to escape the Sun immediately. For many years measurements of the number of neutrinos produced in the Sun were much lower than theories predicted, a problem which was recently resolved through a better understanding of neutrino oscillation.

## References

1. ^ García, Ra; Turck-Chièze, S; Jiménez-Reyes, Sj; Ballot, J; Pallé, Pl; Eff-Darwich, A; Mathur, S; Provost, J (Jun 2007). "Tracking solar gravity modes: the dynamics of the solar core.". Science 316 (5831): 1591–3. Bibcode:2007Sci...316.1591G. doi:10.1126/science.1140598. ISSN 0036-8075. PMID 17478682.
2. ^ a b McDonald, Andrew; Kennewell, John (2014). "The Source of Solar Energy". Bureau of Meteorology. Commonwealth of Australia.
3. ^ Table of temperatures, power densities, luminosities by radius in the sun
4. ^ A 50 kg adult human has a volume of about 0.05 m3, which would correspond to 13.8 watts at the volumetric power of the solar center. This is 285 Kcal = Cal/day, about 10% of the actual average caloric intake and output for humans in non-stressful conditions.
5. ^ Karl S. Kruszelnicki (17 April 2012). "Dr Karl's Great Moments In Science: Lazy Sun is less energetic than compost". Australian Broadcasting Corporation. Retrieved 25 February 2014.
6. ^ see p 54 and 55
7. ^ See
8. ^ al.], edited by Pascale Ehrenfreund ... [et (2004). Astrobiology: future perspectives. Dordrecht [u.a.]: Kluwer Academic. ISBN 1402023049. Retrieved 28 August 2014.
9. ^ Mitalas, R. & Sills, K. R. "On the photon diffusion time scale for the sun" http://adsabs.harvard.edu/full/1992ApJ...401..759M