Context: Long-term variability in solar cycles represents a challenging
constraint for theoretical models. Mean-field Babcock-Leighton dynamos that
consider non-instantaneous rising flux tubes have been shown to exhibit
long-term variability in their magnetic cycle. However a relation that
parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of
stellar parameters is still missing. Aims: We aim to find a general
parameterization of the rise-time of magnetic flux tubes for solar-like stars.
Methods: By considering the influence of magnetic tension on the rise of
non-axisymmetric flux tubes, we predict the existence of a control parameter
referred as \$\Gamma\_\alpha\_1^\alpha\_2\$. This parameter is a measure of the
balance between rotational effects and magnetic effects (buoyancy and tension)
acting on the magnetic flux tube. We carry out two series of numerical
experiments (one for axisymmetric rise and one for non-axisymmetric rise) and
demonstrate that \$\Gamma\_\alpha\_1^\alpha\_2\$ indeed controls the rise-time
of magnetic flux tubes. Results: We find that the rise-time follows a power law
of \$\Gamma\_\alpha\_1^\alpha\_2\$ with an exponent that depends on the
azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility
does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In
the case of non-axisymmetric rise, the tension force modifies the force balance
acting on the magnetic flux tube. We identified the three independent
parameters required to predict the rise-time of magnetic flux tubes, that is,
the stellar rotation rate, the magnetic flux density of the flux tube, and its
azimuthal wavenumber. We combined these into one single relation that is valid
for any solar-like star. We suggest using this generalized relation to
constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo
models.
%0 Generic
%1 citeulike:14409278
%A Fournier, Yori
%A Arlt, Rainer
%A Ziegler, Udo
%A Strassmeier, Klaus G.
%D 2017
%K imported
%T 3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension
%U http://arxiv.org/abs/1707.06781
%X Context: Long-term variability in solar cycles represents a challenging
constraint for theoretical models. Mean-field Babcock-Leighton dynamos that
consider non-instantaneous rising flux tubes have been shown to exhibit
long-term variability in their magnetic cycle. However a relation that
parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of
stellar parameters is still missing. Aims: We aim to find a general
parameterization of the rise-time of magnetic flux tubes for solar-like stars.
Methods: By considering the influence of magnetic tension on the rise of
non-axisymmetric flux tubes, we predict the existence of a control parameter
referred as \$\Gamma\_\alpha\_1^\alpha\_2\$. This parameter is a measure of the
balance between rotational effects and magnetic effects (buoyancy and tension)
acting on the magnetic flux tube. We carry out two series of numerical
experiments (one for axisymmetric rise and one for non-axisymmetric rise) and
demonstrate that \$\Gamma\_\alpha\_1^\alpha\_2\$ indeed controls the rise-time
of magnetic flux tubes. Results: We find that the rise-time follows a power law
of \$\Gamma\_\alpha\_1^\alpha\_2\$ with an exponent that depends on the
azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility
does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In
the case of non-axisymmetric rise, the tension force modifies the force balance
acting on the magnetic flux tube. We identified the three independent
parameters required to predict the rise-time of magnetic flux tubes, that is,
the stellar rotation rate, the magnetic flux density of the flux tube, and its
azimuthal wavenumber. We combined these into one single relation that is valid
for any solar-like star. We suggest using this generalized relation to
constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo
models.
@misc{citeulike:14409278,
abstract = {Context: Long-term variability in solar cycles represents a challenging
constraint for theoretical models. Mean-field Babcock-Leighton dynamos that
consider non-instantaneous rising flux tubes have been shown to exhibit
long-term variability in their magnetic cycle. However a relation that
parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of
stellar parameters is still missing. Aims: We aim to find a general
parameterization of the rise-time of magnetic flux tubes for solar-like stars.
Methods: By considering the influence of magnetic tension on the rise of
non-axisymmetric flux tubes, we predict the existence of a control parameter
referred as \$\Gamma\_{\alpha\_1}^{\alpha\_2}\$. This parameter is a measure of the
balance between rotational effects and magnetic effects (buoyancy and tension)
acting on the magnetic flux tube. We carry out two series of numerical
experiments (one for axisymmetric rise and one for non-axisymmetric rise) and
demonstrate that \$\Gamma\_{\alpha\_1}^{\alpha\_2}\$ indeed controls the rise-time
of magnetic flux tubes. Results: We find that the rise-time follows a power law
of \$\Gamma\_{\alpha\_1}^{\alpha\_2}\$ with an exponent that depends on the
azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility
does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In
the case of non-axisymmetric rise, the tension force modifies the force balance
acting on the magnetic flux tube. We identified the three independent
parameters required to predict the rise-time of magnetic flux tubes, that is,
the stellar rotation rate, the magnetic flux density of the flux tube, and its
azimuthal wavenumber. We combined these into one single relation that is valid
for any solar-like star. We suggest using this generalized relation to
constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo
models.},
added-at = {2019-03-25T08:20:55.000+0100},
archiveprefix = {arXiv},
author = {Fournier, Yori and Arlt, Rainer and Ziegler, Udo and Strassmeier, Klaus G.},
biburl = {https://www.bibsonomy.org/bibtex/2bd09109f928a98b2b4497a2a52cb3a03/ericblackman},
citeulike-article-id = {14409278},
citeulike-linkout-0 = {http://arxiv.org/abs/1707.06781},
citeulike-linkout-1 = {http://arxiv.org/pdf/1707.06781},
day = 21,
eprint = {1707.06781},
interhash = {3743105ff5dc0e1f7858cb38d0509e24},
intrahash = {bd09109f928a98b2b4497a2a52cb3a03},
keywords = {imported},
month = jul,
posted-at = {2017-08-06 07:54:29},
priority = {2},
timestamp = {2019-03-25T08:20:55.000+0100},
title = {{3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension}},
url = {http://arxiv.org/abs/1707.06781},
year = 2017
}