Solar Pole and Prime Meridian

Heliographic coordinate systems use the position of the solar rotation axis which is defined by its declination $\delta_{\odot}$ and the right ascension $\alpha_{\odot}$ with respect to the celestial pole ( $GEI_{J2000} +Z$). Values for J2000.0 are [S. Table 15.7]:

$$\delta_{\odot}=63^{\circ}.87 \hspace{1cm} \alpha_{\odot} = 286^{\circ}.13 \hspace{1cm}$$ (13)

The traditional definition refers to the ecliptic of date with the values for the inclination $i_{\odot}$ of the solar equator and longitude of the ascending node $\Omega_{\odot}$ [S. 7.2, note the typo]:

$$i_{\odot} = 7^\circ.25 \hspace{1cm} \Omega_{\odot} = 75^\circ.76 + 1^\circ.397 T_0$$ (14)

The ecliptic values for the polar axis have been in use since their first determination by Carrington. Newer measurements show that the axis direction is less well defined (Balthasar et al., 1987) but for the purpose of coordinate transformations one sticks with the original values. The same is true for the Solar rotation period for which the adopted values are [A. C3] :

$$r_{sid}=25.38 days \hspace{1cm}\mbox{ and }\hspace{1cm} r_{syn} = 27.2753 days,$$ (15)

where the sidereal period $r_{sid}$ is relative to the celestial sphere, and the synodic relative to the rotating Earth (see also Rosa et al. (1995)). The time dependence in $\Omega_{\odot}$ takes approximate account of the ecliptic precession such that no further precessional transformation should be applied but there is of course a small difference between the ecliptic and the equatorial definition. In transformation of datasets always the equatorial values should be used.

Physical observations of the Sun refer to the apparent center of the visible disk from Earth (subterrestrial point) whose heliocentric ecliptic longitude is the apparent longitude of the Earth $\lambda_{\odot}=\lambda_{geo}-a$ defined in eqn.36 corrected for light aberration ( $a \approx 20''$, see Appendix A.3).