Stars as Laboratories for Fundamental Physics - MPP Theory Group

Miscellaneous Exotica 549
15.2.3 Properties of the Sun
If G N did vary in time one would expect a modification of the standard
course of stellar evolution as first stressed by Teller (1948). By means
of a beautifully simple homology argument, Teller showed that the luminosity
of the Sun is approximately proportional to G 7 NM 5 with M
the solar mass which was also allowed to vary in the spirit of Dirac’s
(1937, 1938) large numbers hypothesis. Teller then proceeded to estimate
the temperature on Earth in the past, taking a modification of its
orbit from the G N variation into account. Depending on whether G N
was larger or smaller in the past the average terrestrial surface temperature
would have been larger or smaller. Teller estimated that if
G N fell outside ±10% of its standard value it would be unlikely that
life on Earth could be sustained. Therefore, G N should have remained
constant to within this accuracy at least during the past 500 million
years or more where life has been known to exist on Earth. 95
Later, a similar homology argument based on the solar age was presented
by Gamow (1967). Detailed models of the Sun with a varying
G N were constructed by Pochoda and Schwarzschild (1964), Ezer and
Cameron (1966), Roeder and Demarque (1966), Shaviv and Bahcall
(1969), Chin and Stothers (1975, 1976), Demarque et al. (1994), and
Guenther et al. (1995). The crux with constraining ĠN from the Sun
is that the presolar helium abundance Y initial and the mixing-length parameter
α can and must be tuned to reproduce the Sun’s present-day
luminosity and radius. In Sect. 1.3.2 it became clear that even extreme
anomalous energy-loss rates could be compensated by an adjustment
of Y initial ; a similar effect pertains to variable-G N solar models. Even
though the present-day central temperature, density, and helium abundance
could differ vastly from standard predictions, their main impact
would be on the neutrino flux which, however, is not a reliable probe
of the solar central conditions as it may get modified by neutrino oscillations.
At the present time the most sensitive probe of a variant internal
solar structure is afforded by the measured p-mode frequencies which
agree well with standard predictions, especially when the gravitational
settling of helium is taken into account. Demarque et al. (1994) have
constructed solar models with a varying G N and then analyzed their
p-mode spectra in comparison with the observations. They assumed a
G N time variation of the form Eq. (15.1) with t 0 = 15 Gyr for the age of
95 Apparently there is more recent evidence for primitive lifeforms on Earth as
early as 3.5 Gyr ago (e.g. Gould 1994).