48 research outputs found
A New Formula for Predicting Solar Cycles
A new formula for predicting solar cycles based on the current theoretical
understanding of the solar cycle from flux transport dynamo is presented. Two
important processes---fluctuations in the Babcock-Leighton mechanism and
variations in the meridional circulation, which are believed to be responsible
for irregularities of the solar cycle---are constrained by using observational
data. We take the polar field near minima of the cycle as a measure of the
randomness in the Babcock-Leighton process, and the decay rate near the minima
as a consequence of the change in meridional circulation. We couple these two
observationally derived quantities into a single formula to predict the
amplitude of the future solar cycle. Our new formula suggests that the cycle 25
would be a moderate cycle. Whether this formula for predicting the future solar
cycle can be justified theoretically is also discussed using simulations from
the flux transport dynamo model.Comment: 12 pages, 6 figures, Accepted for publication in Ap
A theoretical model of the variation of the meridional circulation with the solar cycle
Observations of the meridional circulation of the Sun, which plays a key role
in the operation of the solar dynamo, indicate that its speed varies with the
solar cycle, becoming faster during the solar minima and slower during the
solar maxima. To explain this variation of the meridional circulation with the
solar cycle, we construct a theoretical model by coupling the equation of the
meridional circulation (the component of the vorticity equation within
the solar convection zone) with the equations of the flux transport dynamo
model. We consider the back reaction due to the Lorentz force of the
dynamo-generated magnetic fields and study the perturbations produced in the
meridional circulation due to it. This enables us to model the variations of
the meridional circulation without developing a full theory of the meridional
circulation itself. We obtain results which reproduce the observational data of
solar cycle variations of the meridional circulation reasonably well. We get
the best results on assuming the turbulent viscosity acting on the velocity
field to be comparable to the magnetic diffusivity (i.e. on assuming the
magnetic Prandtl number to be close to unity). We have to assume an appropriate
bottom boundary condition to ensure that the Lorentz force cannot drive a flow
in the subadiabatic layers below the bottom of the tachocline. Our results are
sensitive to this bottom boundary condition. We also suggest a hypothesis how
the observed inward flow towards the active regions may be produced.Comment: 15 pages, 11 figures, accepted for publication in MNRA
A theoretical study of the build-up of the Sun's polar magnetic field by using a 3D kinematic dynamo model
We develop a three-dimensional kinematic self-sustaining model of the solar
dynamo in which the poloidal field generation is from tilted bipolar sunspot
pairs placed on the solar surface above regions of strong toroidal field by
using the SpotMaker algorithm, and then the transport of this poloidal field to
the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar
solution within a certain range of parameters. We use this model to study the
build-up of the polar magnetic field and show that some insights obtained from
surface flux transport (SFT) models have to be revised. We present results
obtained by putting a single bipolar sunspot pair in a hemisphere and two
symmetrical sunspot pairs in two hemispheres.We find that the polar fields
produced by them disappear due to the upward advection of poloidal flux at low
latitudes, which emerges as oppositely-signed radial flux and which is then
advected poleward by the meridional flow. We also study the effect that a large
sunspot pair, violating Hale's polarity law would have on the polar field. We
find that there would be some effect---especially if the anti-Hale pair appears
at high latitudes in the mid-phase of the cycle---though the effect is not very
dramatic.Comment: 18 pages, 18 figures, published in Ap
Is a deep one-cell meridional circulation essential for the flux transport Solar Dynamo?
The solar activity cycle is successfully modeled by the flux transport
dynamo, in which the meridional circulation of the Sun plays an important role.
Most of the kinematic dynamo simulations assume a one-cell structure of the
meridional circulation within the convection zone, with the equatorward return
flow at its bottom. In view of the recent claims that the return flow occurs at
a much shallower depth, we explore whether a meridional circulation with such a
shallow return flow can still retain the attractive features of the flux
transport dynamo (such as a proper butterfly diagram, the proper phase relation
between the toroidal and poloidal fields). We consider additional cells of the
meridional circulation below the shallow return flow---both the case of
multiple cells radially stacked above one another and the case of more
complicated cell patterns. As long as there is an equatorward flow in low
latitudes at the bottom of the convection zone, we find that the solar behavior
is approximately reproduced. However, if there is either no flow or a poleward
flow at the bottom of the convection zone, then we cannot reproduce solar
behavior. On making the turbulent diffusivity low, we still find periodic
behavior, although the period of the cycle becomes unrealistically large. Also,
with a low diffusivity, we do not get the observed correlation between the
polar field at the sunspot minimum and the strength of the next cycle, which is
reproduced when diffusivity is high. On introducing radially downward pumping,
we get a more reasonable period and more solar-like behavior even with low
diffusivity.Comment: 12 pages, 13 figure
Incorporating Surface Convection into a 3D Babcock-Leighton Solar Dynamo Model
The observed convective flows on the photosphere (e.g., supergranulation,
granulation) play a key role in the Babcock-Leighton (BL) process to generate
large-scale polar fields from sunspots fields. In most surface flux transport
(SFT) and BL dynamo models, the dispersal and migration of surface fields is
modeled as an effective turbulent diffusion. Recent SFT models have
incorporated explicit, realistic convective flows in order to improve the
fidelity of convective transport but, to our knowledge, this has not yet been
implemented in previous BL models. Since most Flux-Transport (FT)/BL models are
axisymmetric, they do not have the capacity to include such flows. We present
the first kinematic 3D FT/BL model to explicitly incorporate realistic
convective flows based on solar observations. Though we describe a means to
generalize these flows to 3D, we find that the kinematic small-scale dynamo
action they produce disrupts the operation of the cyclic dynamo. Cyclic
solution is found by limiting the convective flow to act only on the vertical
radial component of the magnetic field. The results obtained are generally in
good agreement with the observed surface flux evolution and with non-convective
models that have a turbulent diffusivity on the order of
cm s (300 km s). However, we find that the use of a
turbulent diffusivity underestimates the dynamo efficiency, producing weaker
mean fields and shorter cycle than in the convective models. Also, the
convective models exhibit mixed polarity bands in the polar regions that have
no counterpart in solar observations. Also, the explicitly computed turbulent
electromotive force (emf) bears little resemblance to a diffusive flux. We also
find that the poleward migration speed of poloidal flux is determined mainly by
the meridional flow and the vertical diffusion.Comment: 21 pages, 14 figures, Revised version is submitted to Ap
Incorporating Surface Convection into a 3D Babcock-Leighton Solar Dynamo Model
The observed convective flows on the photosphere (e.g., supergranulation,
granulation) play a key role in the Babcock-Leighton (BL) process to generate
large-scale polar fields from sunspots fields. In most surface flux transport
(SFT) and BL dynamo models, the dispersal and migration of surface fields is
modeled as an effective turbulent diffusion. Recent SFT models have
incorporated explicit, realistic convective flows in order to improve the
fidelity of convective transport but, to our knowledge, this has not yet been
implemented in previous BL models. Since most Flux-Transport (FT)/BL models are
axisymmetric, they do not have the capacity to include such flows. We present
the first kinematic 3D FT/BL model to explicitly incorporate realistic
convective flows based on solar observations. Though we describe a means to
generalize these flows to 3D, we find that the kinematic small-scale dynamo
action they produce disrupts the operation of the cyclic dynamo. Cyclic
solution is found by limiting the convective flow to act only on the vertical
radial component of the magnetic field. The results obtained are generally in
good agreement with the observed surface flux evolution and with non-convective
models that have a turbulent diffusivity on the order of
cm s (300 km s). However, we find that the use of a
turbulent diffusivity underestimates the dynamo efficiency, producing weaker
mean fields and shorter cycle than in the convective models. Also, the
convective models exhibit mixed polarity bands in the polar regions that have
no counterpart in solar observations. Also, the explicitly computed turbulent
electromotive force (emf) bears little resemblance to a diffusive flux. We also
find that the poleward migration speed of poloidal flux is determined mainly by
the meridional flow and the vertical diffusion.Comment: 21 pages, 14 figures, Revised version is submitted to Ap