Photon Residence Time in the Stellar Core

Kevin Hurlbutt
March 12, 2014

Submitted as coursework for PH241, Stanford University, Winter 2014

It is well known fact even among non-scientists that light from the sun takes 8 minutes to reach Earth, and the light from more distant astronomical bodies was produced when dinosaurs roamed the Earth. Less commonly acknowledged is the fact that light created at the core of our sun today will not escape into the radiative layer of the sun (~25% solar radius) for another 170,000 years. [1]

The Sun's Core

The sun is composed of several layers. The innermost layer, comprising the first 25% of the solar radius, is the core. The core is made of approximately three-quarters hydrogen, and most of the rest of the mass is helium. [2] The core, as with all other layers of the sun, is in a plasma state. Energies in the sun are high enough that most atoms are completely ionized. The core has a large density at 150 g/cm3 and a high temperature of 1.5 × 107 °K. It is at a pressure of 2.65 × 1016 Pa. It is in this layer that virtually all stellar fusion happens. [3] As we will see soon, the high pressure and density are key to confining electromagnetic radiation generated in fusion. In the core, free protons combine through nuclear fusion to form predominantly helium nuclei. The energy released due to the high mass defect of the helium nuclear is emitted as a high energy photon from the excited helium nucleus.

Photon Production in the Core

During fusion, energy is released as a gamma ray. [3] A high-energy photon proceeds at c away from the helium nucleus from which it was emitted. However, the great density and pressure of the sun's core means that almost immediately after being emitted, the incident photon will interact with another atom of either hydrogen or helium. It will either scatter, changing direction, or be absorbed by the new nucleus. This nucleus, now in an excited state, will immediately re-emit the photon in a different, random direction. The photon will soon encounter a new nucleus, and the process continues...for 170,000 years.

Random Walk Through the Core

The value 1.7 × 105 years for photon escape from the core is derived from the application of a random walk in three dimensions. [4] Mitalas et. al. showed that a diffusing photon has an mean free path of 9.2 × 10-4 m. The average photon will have a net velocity on its journey to outer space of just under 1 cm/s, and it will interact with other nuclei (through scattering or absorption and re-emission) and astounding 1025 times before it reaches the next layer of the sun. From there, significant and rapid decreases in density allow for significant radiative and, eventually, conductive heat transfer, corresponding to greater radial mobility for the photon.


If asked about the interior of the sun, everyone could tell you it was very, very hot, and they could probably at least guess that it is very dense as well. The true extremity of the conditions internal to our star is lost in orders of magnitude beyond our human imaginings. It serves as good reminder to scientists and lay people alike that to speak of the sun is to speak of a place so intense that it can lengthen a trip that should take light a mere six-tenths of one second into one hundred seventy millennia.

© Kevin Hurlbutt. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] F. H. Shu,The Physical Universe: An Introduction to Astronomy (University Science Books, 1982).

[2] M. Stix, The Sun: an Introduction (Springer, 1989).

[3] I. J. Thompson and F. Nunes, Nuclear Reactions for Astrophysics: Principles, Calculation and Applications of Low-energy Reactions (Cambridge U. Press, 2009).

[4] R. Mitalas and K. R. Sills, "On the Photon Diffusion Time Scale for the Sun," Astrophys. J 401, 759 (1992).