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
• “…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)
Two mechanisms for planetary influences
on solar activity
• Solar inertial motion
about the barycenter of
the solar system
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
• Tidal forces from the
planets on the solar
surface
Gravitational forces depending on the
relative positions of the planets
Problems with the two mechanisms
• Solar inertial
motion about the
barycenter of the
solar system
• Tidal forces from
the planets on the
solar surface
• Physics not clear:
no mechanism to
explain the
exchange between
rotation and
revolution
• Forces very small:
1012 times smaller
than the Sun’s own
gravity; the same
during Maunder
minimum
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
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
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
How the solar dynamo operates
Poloidal to toroidal field (-effect)
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.
Toroidal to poloidal (-effect)
Babkock-Leighton mechanism
Coriolis force during the flux
tube emergence  sunspot pairs
tilted to the E-W direction
Late in the sunspot
cycle:
 leading spots
diffuse across the
equator
 cancel with the
opposite polarity
leading spots in the
other hemisphere.
 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
Important solar dynamo parameters
• Differential rotation
• Meridional circulation
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)
Role of the meridional circulation:
surface circulation - Toroidal to poloidal field:
higher Vsurf
 less time for the leadingpolarity 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)
Role of the meridional circulation:
deep circulation - poloidal to toroidal field:
2 regimes of operation
(Yeates, Nandy and Mackay, 2008):
evaluated circulation speed
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
The sequence of relations
• Good negative
correlation
(r=-0.75) between
Vsurf and the
following Vdeep
possible manifestation
of the Malkus-Proctor
mechanism
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
The sequence of relations
NO correlation between
the sunspot max
( toroidal field) and
the speed of the
following surface
poleward circulation
Vdeep
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?
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
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)
Tidal acceleration in the horizontal plane
Meridional acceleration can change the meridional circulation
speed ~ 10 m/s
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
evaluation of the magnitude
• a = F/
• F ~ 10-10 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
The average tidal force depends on the period when the
surface meridional circulation carries the flux to the poles
bigger meridional tidal force = higher
sunspot number of the next cycle
conclusion
• Planetary tides modulate the long-term
variations of solar activity through
modulation of the speed of the largescale surface meridional circulation
• Bigger meridional tidal force = slower
poleward surface circulation = higher
sunspot maximum
Forecast???
Thanks for your attention
Supporting material
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)
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)