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Influence of a variation of the fine-structure constant

on the sun and the habitability of earth

By Björn Sörgel (08.01.2013)

In modern physics four different forces are believed to govern the interaction between particles and bodies: gravitation, electromagnetism, weak and strong force. With each of these interactions a coupling constant is associated. This is a dimensionless number expressing the strength of the respective force in comparison to the other ones. The electromagnetic coupling constant, also called fine-structure constant [1], is given by 

Some modern theories of high energy physics suggest that these coupling constants may change during the evolution of the universe. We therefore determine the effects of a variation of the fine-structure constant on the sun and the consequences for the earth. By requiring the conditions on our planet to be suitable for developing and sustaining intelligent life, we constrain a possible variation of αem.

The sun generates energy by the fusion of hydrogen nuclei (protons) into helium nuclei. This reaction can only take place due to quantum tunneling. The probability of this process depends on the strength of the electric repulsion between the two positively charged protons. Therefore it is also affected by a variation of the fine-structure constant. By calculating the thermonuclear reaction rates with a variable αem we find an analytic expression for the energy generation rate (energy per unit time and volume) in the solar interior.

The state of matter inside the sun is governed by the equations of stellar structure. These are four coupled differential equations which are in general only solvable by numerical models. Instead of these, we use a solar model based on an ansatz for the pressure gradient [2]. Using analytic calculations only, this provides a solution for mass, density, pressure and temperature in the solar interior as functions of the radius. These functions and the energy generation rate from above can be used to calculate the solar luminosity depending on αem. We find that an increase of αem lowers the luminosity and vice versa. As a larger fine-structure constant increases the strength of the repulsion between the protons and therefore lowers the reaction rate, the qualitative behaviour of the luminosity can be understood intuitively. As a consistency check for our model we also calculate the solar radius and get Rsun = 6.95 x 1010 cm, which is in good agreement with the actual value.

To develop and sustain intelligent life on a planet like the earth, liquid water on its surface is believed to be a necessary condition. This allows to determine a habitable zone around a star. For this purpose we estimate the surface temperature of the earth by assuming an equilibrium between incoming radiation from the sun and outgoing thermal radiation.

The inner and outer limit of the habitable zone depend on the fine-structure constant for two reasons: On the one hand, the luminosity varies with αem as explained above. On the other hand, the boiling and melting point of water also change with αem because the molecules interact with each other via electromagnetic forces. Taking these two effects into account, we constrain a variation of the fine-structure constant by requiring the habitable zone to contain the earth. For increasing αem , we find

to prevent the earth from freezing. Assuming a linear change over the earth's age of about 4.6 billion years, an upper bound for the growth rate of αem  is given by

On the other hand, αem  may decrease by only a few percent to prevent the water on earth from boiling. Although stricter constraints than ours can be obtained by observations of distant quasar spectra [3], we find it most exciting to see how far we can get using only solar system data and mostly analytic calculations.


Bachelor's thesis at the University Observatory of LMU Munich
B. Sörgel, D. Boneberg and H. Lesch



[1] As this combination of constants first appeared in the fine structure of atomic spectra, it was called fine-structure constant.
[2] Clayton, D.D.: Solar structure without computers. Am. J. Phys., 54 (4): 354-362, 1986
[3] Uzan, J.-P.: The fundamental constants and their variation: observational status and theoretical motivations. Rev.Mod.Phys., 75:403-455, 2003


  • 2008-2011
  • Bachelor Physik plus Astronomie (LMU München)
  • Seit 2011
  • Master Physik mit Schwerpunkt Astrophysik (LMU, Universitätssternwarte München)
  • Seit 09/2012
  • Auslandsstudium Universidad de La Laguna (Teneriffa): Mitarbeit an einem Forschungsprojekt

  • 2011
  • Tutor für Klassische Mechanik
  • 2011
  • Tutor für Probestudium Physik
  • 2011/12
  • Tutor für Quantenmechanik
  • 2012
  • Tutor für Elektrodynamik

  • 03/2012
  • UK-Germany National Astronomy Meeting 2012 (mit Poster-Präsentation)
  • 07/2012
  • Lindau Nobel Laureate Meeting (als "Young Researcher")

Stipendien und Auszeichnungen
  • * Max-Weber-Programm (seit 2008)
  • * e-fellows.net-Stipendium (seit 2008)
  • * Stipendium der Studienstiftung des deutschen Volkes (seit 2011)