1. Scientific astrology: planetary effects on solar activity Katya Georgieva Solar-Terrestrial Influences Lab., Bulgarian Academy of Sciences In collaboration with P.A. Semi IHY-ISWI Šibenic, Croatia, 7-13 September 2009

2. “…the conclusion seems to be inevitable, that my conjecture that the variations of spot-frequency depend on the influences of Venus, Earth, Jupiter and Saturn, will not prove to be wholly unfounded. The prepondering planet Jupiter will in such case mainly determine the length and height of the wave of the spot-period; Saturn will cause small variations in the length and height; and finally, the earth and Venus will change the smooth wave-line into a ripped one”. Wolf (1859)

3. Two mechanisms for planetary influences on solar activity Solar inertial motion about the barycenter of the solar system Tidal forces from the planets on the solar surface Sun’s axial rotation (or spin) changes due to changes in the Sun’s orbital revolution (speed along its orbit about the solar system barycenter) because of the varying distance from the barycenter Gravitational forces depending on the relative positions of the planets

4. Problems with the two mechanisms Solar inertial motion about the barycenter of the solar system Physics not clear: no mechanism to explain the exchange between rotation and revolution Tidal forces from the planets on the solar surface Forces very small: 10 12 times smaller than the Sun’s own gravity; the same during Maunder minimum

5. Our approach: Based on the solar dynamo theory, study the relation between the dynamics of the Sun and solar activity Look for possible planetary influences that could affect solar dynamics aspects relevant to solar activity Check whether these influences indeed correlate with solar activity

6. Basic concept Planetary influences do NOT cause solar activity. Solar (and stellar) magnetic activity is a natural consequence of the presence of a convective envelope Planetary influences can only modulate solar activity

7. The importance of a convective envelope convection of conducting plasma  generation of dipolar magnetic field convection + rotation  differential rotation (therefore no differential rotation in the radiative zone) differential rotation  meridional circulation

8. How the solar dynamo operates Dipolar, or poloidal magnetic field in sunspot min Differential rotation stretches the poloidal field in azimuthal direction at the base of the solar convective zone (~0.7 Rs)  E-W (toroidal) component of the field The buoyant magnetic field tubes rise up, piercing the surface at two spots (sunspots) with opposite magnetic polarities. Poloidal to toroidal field (  -effect)

9. Toroidal to poloidal (  -effect) Late in the sunspot cycle:  leading spots diffuse across the equator  cancel with the opposite polarity leading spots in the other hemisphere. Coriolis force during the flux tube emergence  sunspot pairs tilted to the E-W direction Babkock-Leighton mechanism  excess trailing spots flux carried to the poles  cancels the flux of the previous cycle  accumulates to form the poloidal field of the next solar cycle with the opposite polarity

10. Important solar dynamo parameters Differential rotationMeridional circulation

11. Role of the differential rotation Poloidal to toroidal field (rotation at the base of the convective zone) Bigger shear  stronger toroidal field  higher sunspot number (Howe, 2005)

12. Role of the meridional circulation: surface circulation - Toroidal to poloidal field: higher Vsurf  less time for the leading- polarity flux to diffuse across the equator  less uncanceled trailing-polarity flux reaches the pole  weaker poloidal field  lower sunspot number from it (Wang, 2004) Vsurf after sunspot max anticorrelated with the amplitude of the next sunspot max (note the reversed scale)

13. Role of the meridional circulation: deep circulation - poloidal to toroidal field: 2 regimes of operation (Yeates, Nandy and Mackay, 2008): Diffusion dominated (high diffusivity, low speed): higher Vdeep  less time for diffusive decay of the poloidal field  more generation of toroidal field  higher sunspot number Advection dominated (low diffusivity, high speed): diffusive decay less important  higher Vdeep  less time to induct toroidal field at the tachocline  lower sunspot number higher Vdeep = higher sunspot max  diffusion-dominated regime evaluated circulation speed

14. The sequence of relations Good negative correlation (r=-0.75) between Vsurf and the following Vdeep possible manifestation of the Malkus-Proctor mechanism

15. The sequence of relations Good correlation (r=0.81) between Vdeep and the following sunspot max (  toroidal field) Indication that solar dynamo operates in diffusion dominated regime

16. The sequence of relations NO correlation between the sunspot max (  toroidal field) and the speed of the following surface poleward circulation Vdeep

17. The sequence of relations Vsurf  Bpol  Vdeep  Btor… and the chain breaks  Vsurf is the factor which rules the amplitude of the sunspot cycle and through its influence on Vdeep, also the period of the sunspot cycle What factor modulates Vsurf?

18. This dynamo mechanism works without any planets What if the star has a planet? The simplest case: one planet on a circular orbit in the star’s equatorial plane In the case of the Sun, the elevation caused by all planets together is very small The elevation is due to the vertical component of the tidal force But we are interested in the horizontal, not in the vertical component of the tidal force For one only planet, all vectors directed to the planet’s subpoint

19. the case of the Sun with a number of planets The tidal forces depend on the distance and relative positions of the major tide-creating planets (Jupiter, Earth, Venus, Mercury) which change with time view from the pole (elevation)

20. Tidal acceleration in the horizontal plane Meridional acceleration can change the meridional circulation speed ~ 10 m/s

21. Tidal forces create acceleration in both zonal and meridional directions Zonal acceleration can change the rotation speed ~2000 m/s important for the magnetic field generation at the base of the convective zone (0.7 R  ) where: - the tidal force decreases with depth as d 2 - the density is ~ gr/cm 3 - both eastward and westward = 0 average over a solar rotation Meridional acceleration can change the meridional circulation speed ~ 10 m/s important for the magnetic field generation at the surface where: maximum - the tidal force is maximum - the density is ~ 10 -5 gr/cm 3 - always equatorward

22. evaluation of the magnitude a = F/  F ~ 10 -10 N/kg  ~ 10 -5 gr/cm 3 = 10 -2 kg/m 3  a ~ 10 -8 m/s 2 t ~ 10 8 s  dVsurf ~ m/s Corresponds to the observed variation of Vsurf

23. The average tidal force depends on the period when the surface meridional circulation carries the flux to the poles

24. bigger meridional tidal force = higher sunspot number of the next cycle

25. conclusion Planetary tides modulate the long-term variations of solar activity through modulation of the speed of the large- scale surface meridional circulation Bigger meridional tidal force = slower poleward surface circulation = higher sunspot maximum

26. Forecast???

27. Thanks for your attention

28. Supporting material

29. Estimation of the speed of the solar meridional circulation from geomagnetic data The lag between the peaks has been changing in the last century (Kishcha et al., 1999; Echer et al., 2004) Sunspot max peak – max in sporadic geomagnetic activity (solar toroidal field) Sunspot decline phase peak – max in recurrent geomagnetic activity (solar poloidal field) Double-peaked cycle of geomagnetic activity: one peak in sunspot max, the second one on the sunspot decline phase

30. Highest aa max on sunspot decline phase occurs when the trailing polarity flux has reached the pole  the time from sunspot max to aa max = the time it takes the surface meridional circulation to carry the flux from sunspot max latitudes to the pole (PINK) The time between aa max and next sunspot max = the time for the flux to sink to the base of the convective zone, to be carried by the deep meridional circulation to sunspot max latitudes and to emerge as the sunspots of the next cycle (BLUE)