Stars as Laboratories for Fundamental Physics - MPP Theory Group

550 Chapter 15
Table 15.2. Characteristics of the Demarque et al. (1994) solar models with
a varying G N according to Eq. (15.1).
β α X initial X c T c ρ c R env 37 Cl 71 Ga
[%] [%] [10 6 K] [g/cm 3 ] [R ⊙ ] [SNU] [SNU]
−0.4 1.832 69.42 45.6 15.14 125.5 0.739
−0.2 1.895 70.10 42.1 15.28 134.0 0.731 5.5 117
−0.1 1.936 70.51 40.0 15.37 139.5 0.724
0.0 1.983 70.98 37.6 15.47 146.2 0.721 6.8 124
0.1 2.036 71.51 34.8 15.58 154.6 0.716
0.2 2.104 72.11 31.7 15.72 165.1 0.710 8.7 134
0.4 2.291 73.56 23.9 16.07 197.3 0.695
the universe. Some characterisitics of their solar models as a function of
β are summarized in Tab. 15.2 where α is the mixing-length parameter,
X initial the presolar hydrogen abundance, the quantitites with index c
refer to central conditions of the present-day Sun, and R env to the radius
of its convective envelope. The last two columns are the predicted
counting rates in the chlorine and gallium solar neutrino experiments
under the assumption that there are no neutrino oscillations.
The most important effect of the G N variation is a shift of the base
of the convective envelope which is caused by the required change of α
and the initial helium abundance Y initial . It is this modification of the
convection zone which has the largest impact on the observable p-mode
frequencies. However, an identical shift can be produced by other effects
such as modified opacities, equation of state, surface boundary conditions,
degree of gravitational helium settling, and perhaps by magnetic
fields. Therefore, only relatively crude limits can be extracted at the
present time. Demarque et al. (1994) believe that |β| < ∼ 0.4 is a reasonably
conservative limit which probably can be improved by a factor
of four within the next decade by more precise p-mode observations.
With Eq. (15.1) the current limit corresponds to
|ĠN/G N | ∼ < 30×10 −12 yr −1 , (15.2)
similar to the celestial-mechanics bounds of Tab. 15.1. The precise functional
form Eq. (15.1) is not crucial for the solar bound as it probes G N
only for the last 4.5 Gyr of the assumed 15 Gyr cosmic age. Therefore,
one could have equally assumed a linear form for G N (t).