In this paper, we present the physics of the gravitational effect of the Galactic bar. Our equations differ from those recently used in the literature. We apply the simultaneous action of the Galactic bar and spiral structure, together with the action of the Galactic halo and disc, to the motion of the Sun.
The true multipolar model of the Galactic bar does not generate any relevant radial migration of the Sun. The Galactocentric distance of the Sun R changes by 1 per cent from the current value R0, for the bar model based on Cosmic Background Explorer (COBE) observations, if the gravity of the spiral arms is not considered. Spiral arms can generate more relevant radial migration. If we take into account the values of 220 km s−1, recommended by the International Astronomical Union, and R0 = 8.0 kpc, together with the bar model based on the COBE observations, then we find the following.
- R ∈ 〈7.85, 8.10〉 kpc, and the results are practically independent of the spiral structure strength εs, for the four-armed spiral structure.
- R ∈ 〈7.55, 8.90〉 kpc, and the results strongly depend on the spiral structure strength, for the two-armed spiral structure. If we admit that the absolute value of the radial velocity component is smaller than about 10 per cent of the speed of the Sun during its motion, then εs ≤ 0.03 and R ∈ 〈7.75, 8.45〉 kpc. There is significant radial migration of the Sun for the corotation resonance of the spiral arms with the Sun and εs = 0.06: R ∈ 〈4.18, 15.15〉 kpc.
The radial migration of the Sun is not a consequence of the existence of the Galactic bar. The same result would yield a spherically symmetric Galactic bulge, except for the special case of the corotation resonance of the spiral arms with the Sun and εs = 0.06.