Do Planets Affect the Behavior of the Long-term Solar Activity?

TL;DR

This work tests the planetary hypothesis for long-term solar activity by modeling the collective planetary influence as a single barycentric tidal field and decomposing it into radial and meridional components. Using $V=- \frac{\gamma M r^2}{2R^3}(3 \cos^2 \phi -1)$ and the meridional acceleration $F_M= -\frac{1}{r} \frac{\partial V}{\partial \phi} = \frac{2G}{r} \sin 2\phi$ with $G= \frac{3}{4} \gamma M r^2/R^3$, the authors estimate potential meridional flow speeds and compare them to solar activity proxies over multi-century intervals, employing the DE431 ephemerides to compute the solar-system barycenter's motion. They find no consistent phase relation or synchronization between the planetary tide variations and the 11-year sunspot cycle or longer cycles, such as the 178-year oscillation, thereby not supporting planets as a driver of long-term solar modulation. The results reinforce the view that the solar dynamo is the primary endogenous driver of solar activity, with planetary influences being either absent or too weak to establish a stable coupling.

Abstract

Solar activity is a process driven by many independent but interconnected phenomena. Although the 11-year cycle is the result of operation of the dynamo mechanism, the cause of longer secular variations is not clear. In search of such a cause, it was proposed to take into account the influence of the planetary system. In order to verify the idea, we consider the action of all planets in the solar system reduced to the effect of a single barycenter. The tidal force is decomposed into radial and meridional components. The radial tidal force is too small compared to the powerful radial gravity of the Sun. The meridional force is not compensated for by solar gravity and depends on latitude. As the latitude of the barycenter changes quite slowly, the sign of this component changes over a characteristic time scale of about 5 years, during which the meridional acceleration constantly acts on the surface of the Sun. This could ultimately lead to speeds of several meters per second and, in principle, could significantly change the speeds of the meridional currents involved in generating the magnetic field. However, it turned out that the calculated speed variation does not agree with the observed periodicity of solar activity. Earlier, the relation was analyzed between the activity periods on solar-type stars and the rotation periods of exoplanets, and no correspondence was observed either. Thus, the planetary hypothesis as a cause of long-term modulation of solar activity is not confirmed.

Figures (5)

• Figure 1: Distribution of horizontal tidal forces from the single planet located above the equator of the star(a). The structure of the vertical tidal forces on the Sun in September 2005 (b).
• Figure 2: Meridional tidal acceleration $F_M$ (force per unit mass) measured in m/s$^{2}$ on the surface of the Sun (red) and sunspot numbers (SSN, blue) over the past 120 years.
• Figure 3: Meridional tidal acceleration $F_M$ measured in m/s$^{2}$ on the surface of the Sun (thin red line) and sunspot numbers (SSN, thin blue line) over the past 320 years. The thick lines show the corresponding 20-yrs averaging.
• Figure 4: Meridional acceleration (thin red line) and its 20-year average (thick red line) compared to reconstructed SSN data (blue). The legends OM, WM, SM, MM DM mark the epochs of special behavior of solar activity: the Oort Minimum, Wolf Minimum, Spörer Minimum, Maunder Minimum, and Dalton Minimum.
• Figure 5: Accumulated meridional velocity $V_M$ (red) versus the reconstructed SSN data (blue) over the past millennium.