1. Planetary tides and solar activity Katya Georgieva
Solar-Terrestrial Influences Lab., Bulgarian Academy of Sciences
In collaboration with P.A. Semi

2. 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

3. 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

4. How the solar dynamo operates
Dipolar, or poloidal magnetic field in sunspot minimum
-effect (poloidal to toroidal field)
Differential rotation stretches the poloidal field in azimuthal direction at the base of the solar convective zone (~0.7 Rs) giving rise to the 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.

5. Toroidal to poloidal (-effect)
Babkock-Leighton mechanism
Due to the Coriolis force during the flux tube emergence, the sunspot pairs are tilted to the E-W direction
Late in the sunspot cycle, the leading spots diffuse across the equator and cancel with the opposite polarity leading spots in the other hemisphere.
The flux of the trailing spots and of the remaining sunspot pairs is carried to the poles where it cancels the flux of the previous cycle and then accumulates to form the poloidal field of the next solar cycle with the opposite polarity

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

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

8. Role of the meridional circulation
Poloidal to toroidal field: deep circulation Vdeep
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 during its transport through the convective zone  more generation of toroidal field  higher sunspot number
Advection dominated (low diffusivity, high speed): diffusive decay is less important and higher Vdeep  less time to induct toroidal field at the tachocline  lower sunspot number
higher Vdeep = higher sunspot max
diffusion-dominated regime
(Yeates, Nandy and Mackay, 2008)

9. The sequence of relations
Good correlation between the speed of the surface poleward circulation and the poloidal field of the next sunspot cycle
Good correlation between the poloidal field and the speed of the following deep circulation
Good correlation between the speed of the deep circulation and the toroidal field of the nest sunspot cycle
NO correlation between the toroidal field and the speed of the surface poleward circulation
Vsurf  Bpol  Vdeep  Btor… and the chain breaks

10. 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
But we are interested in the horizontal, not in the vertical component of the tidal force
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
For one only planet, all vectors directed to the planet’s subpoint

11. 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
movie

12. 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 d2
- the density is ~ gr/cm3
- 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:
- the tidal force is maximum
- the density is ~ 10-5 gr/cm3
- always equatorward

13. evaluation of the magnitude
a = F/
F ~ N/kg
 ~ 10-5 gr/cm3 = 10-2 kg/m3
 a ~ 10-8 m/s2
t ~ 108 s
 dVsurf ~ m/s
Corresponds to the observed variation of Vsurf

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

15. 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 of the next cycle

16. Forecast???

17. Thanks for your attention

18. Supporting material

19. Estimation of the speed of the solar meridional circulation from geomagnetic data
Double-peaked cycle of geomagnetic activity: one peak in sunspot max, the second one on the sunspot decline phase
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)

20. 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)

22. How can we derive the long-term variations of the solar poloidal and toroidal fields?
All points in the aa-sunspot scatterplot lie above a line (Feynman, 1982; Feynman and Ruzmaikin, 2001; Hathaway, 2004)
aaT = a + b*sunspot
aaT - the part of geomagnetic activity due to sunspot-related (toroidal) solar activity
The rest (aaP = aa - aaT) is due to non-sunspot-related (poloidal) solar activity

23. aaP/aaT increases after ~1960 The increase in aa in the recent decades is mainly due to the increase in aaP
The changing relative magnitude of the solar poloidal and toroidal fields is due to the changing relative speed of the surface and deep meridional circulation

25. Forecast???

27. Solar influences on climate?
good correlation between global temperature and sunspot number until about 3 decades ago
recently sunspot activity is declining while global temperature continues rising
Predominant (or only) anthropogenic effects?

28. Possible solar agents affecting terrestrial climate
Solar irradiance:
Total solar irradiance – total energy received from the Sun
Spectral solar irradiance – stratospheric chemistry and dynamics
Solar wind
Cosmic rays – atmospheric transparency, cloud microphysics, global electric circuit
Joule heating - atmospheric gravity waves, pressure distribution, atmospheric circulation

29. Long-term variations in solar irradiance are reconstructed from sunspot data, their effects are well understood and simulated in most general circulation models.
The effects of solar wind-related solar agents on climate are not clear, and are not included in any climate simulation models.
Solar irradiance is related to the solar toroidal field, solar wind is related to the solar poloidal field

30. Their long-term variations of are not identical
The variations of the solar poloidal field are very closely correlated to the global temperature variations