Steady flows in the core of precessing planets : effects of the geometry and an applied magnetic field.

2020 ◽  
Author(s):  
Raphael Laguerre ◽  
Aymeric Houliez ◽  
David Cébron ◽  
Véronique Dehant
Keyword(s):  
Magnetic Field ◽  
Analytical Model ◽  
Inner Core ◽  
Rotation Axis ◽  
The Body ◽  
External Boundary ◽  
Core Size ◽  
Major Purpose ◽  
Resonance Amplitude ◽  
The Magnetic Field

<p>The Earth is submitted to the gravitational effect of different objects,  resulting  in  small  variations  of  the  orientation  of  its  axis  rotation.   The  precession corresponds to the rotation of the body spin axis around the normal to the elliptic plane. The primary flow forced by precession in a sphere is mainly a tilted solid body rotation, a flow of uniform vorticity. In this study we focused on the pseudo-resonance between the precessional forcing  and  the  spin-over  mode,  detected  as  a  peak  of  amplitude  of  the  norm  of the  vorticity  of  the  fluid.   We  show  the  influences  of  both  the  geometry and the application of an uniform external magnetic field on the external boundary, onto this pseudo-resonance.  The major purpose is to validate a semi-analytical model to allow its interpolation to planetary bodies.  We compared the semi-analytical model [Noir and C ́ebron, 2013] with numerical simulations performed with XSHELLS [Schaeffer, 2013],  which give us the components of the fluid vorticity in a precessing frame. We compared also the spin-over mode coefficients, used to simulate the viscous  effect  on  the  model,  with  two  methods :  an  empirical  equation  and  the numerical solver Tintin [Triana et al., 2019], taking into account the solid inner-core size (η=RI/R).  The differential rotation between the flow and the container, obtained with the model and the XSHELLS simulations, show us a verygood agreement especially for a small Ekman number (E= 10^−5), thus the spin-over mode coefficients for small E and η≤0.5.  An increase of the inner-core size  implies  a  decrease  of  the  resonance  amplitude  caused  by  the  supplementary Ekman layer added at the Inner Core Boundary (ICB); nevertheless thecolatitude (αf) and the longitude (φf) of the fluid don’t change significantly.The  application  of  a  uniform  magnetic  field  at  the  CMB  implies  a  decrease of the resonance amplitude, but also a modification of the mean rotation axis direction.  Indeed, the coupling between the viscous flow and the magnetic field induces a modification of the αfand φf, which follow the main direction angle of the magnetic field axis.  We observe small discrepancies between the simulations (XSHELLS and Tintin) and the model but the behavior following different parameters (Po,α angle,Ro,η,β angle, Λ) is well understood.  As a result, we applied the models at few parameter ”realistic values” of planetary objects like terrestrial planets but also ice’s satellites.</p><p>References</p><p>[Noir and C ́ebron, 2013]  Noir,  J.  and  C ́ebron,  D.  (2013).    Precession-driven flows in non-axisymmetric ellipsoids.Journal of Fluid Mechanics, 737:412–439.</p><p>[Schaeffer, 2013]  Schaeffer, N. (2013).  Efficient spherical harmonic transforms aimed  at pseudospectral numerical  simulations.Geochemistry, Geophysics,Geosystems, 14(3):751–758.</p><p>[Triana et al., 2019]  Triana, S. A., Rekier, J., Trinh, A., and Dehant, V. (2019).The coupling between inertial and rotational eigenmodes in planets with liq-uid cores.Geophysical Journal International.</p>

scholarly journals Broadband Linear Polarization in Ap Stars

1993 ◽  
Vol 138 ◽  
pp. 305-309
Author(s):  
Marco Landolfi ◽  
Egidio Landi Degl’Innocenti ◽  
Maurizio Landi Degl’Innocenti ◽  
Jean-Louis Leroy ◽  
Stefano Bagnulo
Keyword(s):  
Magnetic Field ◽  
Circular Polarization ◽  
Linear Polarization ◽  
Rotation Axis ◽  
Spectral Lines ◽  
Line Of Sight ◽  
Long Time ◽  
Rotating Star ◽  
Ap Stars ◽  
The Magnetic Field

AbstractBroadband linear polarization in the spectra of Ap stars is believed to be due to differential saturation between σ and π Zeeman components in spectral lines. This mechanism has been known for a long time to be the main agent of a similar phenomenon observed in sunspots. Since this phenomenon has been carefully calibrated in the solar case, it can be confidently used to deduce the magnetic field of Ap stars.Given the magnetic configuration of a rotating star, it is possible to deduce the broadband polarization at any phase. Calculations performed for the oblique dipole model show that the resulting polarization diagrams are very sensitive to the values of i (the angle between the rotation axis and the line of sight) and β (the angle between the rotation and magnetic axes). The dependence on i and β is such that the four-fold ambiguity typical of the circular polarization observations ((i,β), (β,i), (π-i,π-β), (π-β,π-i)) can be removed.

scholarly journals Circumstellar environment of 55 Cancri

2020 ◽  
Vol 633 ◽  
pp. A48 ◽  
Author(s):  
C. P. Folsom ◽  
D. Ó Fionnagáin ◽  
L. Fossati ◽  
A. A. Vidotto ◽  
C. Moutou ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Stellar Wind ◽  
Large Scale ◽  
Rotation Axis ◽  
Doppler Imaging ◽  
Magnetic Pole ◽  
Average Strength ◽  
Detailed Understanding ◽  
The Magnetic Field ◽  
Circumstellar Environment

Context. 55 Cancri hosts five known exoplanets, most notably the hot super-Earth 55 Cnc e, which is one of the hottest known transiting super-Earths. Aims. Because of the short orbital separation and host star brightness, 55 Cnc e provides one of the best opportunities for studying star-planet interactions (SPIs). We aim to understand possible SPIs in this system, which requires a detailed understanding of the stellar magnetic field and wind impinging on the planet. Methods. Using spectropolarimetric observations and Zeeman Doppler Imaging, we derived a map of the large-scale stellar magnetic field. We then simulated the stellar wind starting from the magnetic field map, using a 3D magneto-hydrodynamic model. Results. The map of the large-scale stellar magnetic field we derive has an average strength of 3.4 G. The field has a mostly dipolar geometry; the dipole is tilted by 90° with respect to the rotation axis and the dipolar strength is 5.8 G at the magnetic pole. The wind simulations based on this magnetic geometry lead us to conclude that 55 Cnc e orbits inside the Alfvén surface of the stellar wind, implying that effects from the planet on the wind can propagate back to the stellar surface and result in SPI.

scholarly journals Hydromagnetic dynamos in rotating spherical fluid shells in dependence on the Prandtl number, density stratification and electromagnetic boundary conditions

2014 ◽  
Vol 44 (4) ◽  
pp. 293-312 ◽  
Author(s):  
Tomáš Šoltis ◽  
Ján Šimkanin
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Prandtl Number ◽  
Inner Core ◽  
Polar Regions ◽  
Number Density ◽  
Magnetic Diffusion ◽  
Spherical Fluid ◽  
The Magnetic Field

Abstract We present an investigation of dynamo in a simultaneous dependence on the non-uniform stratification, electrical conductivity of the inner core and the Prandtl number. Computations are performed using the MAG dynamo code. In all the investigated cases, the generated magnetic fields are dipolar. Our results show that the dynamos, especially magnetic field structures, are independent in our investigated cases on the electrical conductivity of the inner core. This is in agreement with results obtained in previous analyses. The influence of non-uniform stratification is for our parameters weak, which is understandable because most of the shell is unstably stratified, and the stably stratified region is only a thin layer near the CMB. The teleconvection is not observed in our study. However, the influence of the Prandtl number is strong. The generated magnetic fields do not become weak in the polar regions because the magnetic field inside the tangent cylinder is always regenerated due to the weak magnetic diffusion.

COMPARISON OF CARDIAC MAGNETIC FIELD DISTRIBUTIONS DURING DEPOLARIZATION AND REPOLARIZATION

2003 ◽  
Vol 13 (12) ◽  
pp. 3783-3789 ◽  
Author(s):  
F. E. SMITH ◽  
P. LANGLEY ◽  
L. TRAHMS ◽  
U. STEINHOFF ◽  
J. P. BOURKE ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Field Distribution ◽  
Normal Subjects ◽  
The Body ◽  
Magnetic Field Distribution ◽  
T Wave ◽  
High Magnetic Field Strength ◽  
The Magnetic Field

Multichannel magnetocardiography measures the magnetic field distribution of the human heart noninvasively from many sites over the body surface. Multichannel magnetocardiogram (MCG) analysis enables regional temporal differences in the distribution of cardiac magnetic field strength during depolarization and repolarization to be identified, allowing estimation of the global and local inhomogeneity of the cardiac activation process. The aim of this study was to compare the spatial distribution of cardiac magnetic field strength during ventricular depolarization and repolarization in both normal subjects and patients with cardiac abnormalities, obtaining amplitude measurements by magnetocardiography. MCGs were recorded at 49 sites over the heart from three normal subjects and two patients with inverted T-wave conditions. The magnetic field intensity during depolarization and repolarization was measured automatically for each channel and displayed spatially as contour maps. A Pearson correlation was used to determine the spatial relationship between the variables. For normal subjects, magnetic field strength maps during depolarization (R-wave) showed two asymmetric regions of magnetic field strength with a high positive value in the lower half of the chest and a high negative value above this. The regions of high R-wave amplitude corresponded spatially to concentrated asymmetric regions of high magnetic field strength during repolarization (T-wave). Pearson-r correlation coefficients of 0.7 (p<0.01), 0.8 (p<0.01) and 0.9 (p<0.01) were obtained from this analysis for the three normal subjects. A negative correlation coefficient of -0.7 (p<0.01) was obtained for one of the subjects with inverted T-wave abnormalities, suggesting similar but inverted magnetic field and current distributions to normal subjects. Even with the high correlation values in these four subjects, the MCG was able to identify differences in the distribution of magnetic field strength, with a shift in the T-wave relative to the R-wave. The measurement of cardiac magnetic field distribution during depolarization and repolarization of normal subjects and patients with clinical abnormalities should enable the improvement of theoretical models for the explanation of the cardiac depolarization and repolarization processes.

scholarly journals Magnetohydrodynamic simulations of a Uranus-at-equinox type rotating magnetosphere

2020 ◽  
Vol 633 ◽  
pp. A87 ◽  
Author(s):  
L. Griton ◽  
F. Pantellini
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Supersonic Flow ◽  
Magnetic Dipole ◽  
Stellar Wind ◽  
Rotation Axis ◽  
Spin Axis ◽  
Mhd Equations ◽  
Field Lines ◽  
The Magnetic Field

Context. As proven by measurements at Uranus and Neptune, the magnetic dipole axis and planetary spin axis can be off by a large angle exceeding 45°. The magnetosphere of such an (exo-)planet is highly variable over a one-day period and it does potentially exhibit a complex magnetic tail structure. The dynamics and shape of rotating magnetospheres do obviously depend on the planet’s characteristics but also, and very substantially, on the orientation of the planetary spin axis with respect to the impinging, generally highly supersonic, stellar wind. Aims. On its orbit around the Sun, the orientation of Uranus’ spin axis with respect to the solar wind changes from quasi-perpendicular (solstice) to quasi-parallel (equinox). In this paper, we simulate the magnetosphere of a fictitious Uranus-like planet plunged in a supersonic plasma (the stellar wind) at equinox. A simulation with zero wind velocity is also presented in order to help disentangle the effects of the rotation from the effects of the supersonic wind in the structuring of the planetary magnetic tail. Methods. The ideal magnetohydrodynamic (MHD) equations in conservative form are integrated on a structured spherical grid using the Message-Passing Interface-Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). In order to limit diffusivity at grid level, we used background and residual decomposition of the magnetic field. The magnetic field is thus made of the sum of a prescribed time-dependent background field B0(t) and a residual field B1(t) computed by the code. In our simulations, B0(t) is essentially made of a rigidly rotating potential dipole field. Results. The first simulation shows that, while plunged in a non-magnetised plasma, a magnetic dipole rotating about an axis oriented at 90° with respect to itself does naturally accelerate the plasma away from the dipole around the rotation axis. The acceleration occurs over a spatial scale of the order of the Alfvénic co-rotation scale r*. During the acceleration, the dipole lines become stretched and twisted. The observed asymptotic fluid velocities are of the order of the phase speed of the fast MHD mode. In two simulations where the surrounding non-magnetised plasma was chosen to move at supersonic speed perpendicularly to the rotation axis (a situation that is reminiscent of Uranus in the solar wind at equinox), the lines of each hemisphere are symmetrically twisted and stretched as before. However, they are also bent by the supersonic flow, thus forming a magnetic tail of interlaced field lines of opposite polarity. Similarly to the case with no wind, the interlaced field lines and the attached plasma are accelerated by the rotation and also by the transfer of kinetic energy flux from the surrounding supersonic flow. The tailwards fluid velocity increases asymptotically towards the externally imposed flow velocity, or wind. In one more simulation, a transverse magnetic field, to both the spin axis and flow direction, was added to the impinging flow so that magnetic reconnection could occur between the dipole anchored field lines and the impinging field lines. No major difference with respect to the no-magnetised flow case is observed, except that the tailwards acceleration occurs in two steps and is slightly more efficient. In order to emphasise the effect of rotation, we only address the case of a fast-rotating planet where the co-rotation scale r* is of the order of the planetary counter-flow magnetopause stand-off distance rm. For Uranus, r*≫ rm and the effects of rotation are only visible at large tailwards distances r ≫ rm.

scholarly journals Magnetic field disturbances in the sheath region of a super-sonic interplanetary magnetic cloud

2008 ◽  
Vol 26 (10) ◽  
pp. 3153-3158 ◽  
Author(s):  
E. Romashets ◽  
M. Vandas ◽  
S. Poedts
Keyword(s):  
Magnetic Field ◽  
Geomagnetic Storms ◽  
Magnetic Cloud ◽  
The Body ◽  
Magnetic Clouds ◽  
Shock Surface ◽  
Sheath Region ◽  
Magnetic Field Magnitude ◽  
The Magnetic Field ◽  
Magnetic Disturbances

Abstract. It is well-known that interplanetary magnetic clouds can cause strong geomagnetic storms due to the high magnetic field magnitude in their interior, especially if there is a large negative Bz component present. In addition, the magnetic disturbances around such objects can play an important role in their "geo-effectiveness". On the other hand, the magnetic and flow fields in the CME sheath region in front of the body and in the rear of the cloud are important for understanding both the dynamics and the evolution of the interplanetary cloud. The "eventual" aim of this work is to calculate the magnetic field in this CME sheath region in order to evaluate the possible geo-efficiency of the cloud in terms of the maximum |Bz|-component in this region. In this paper we assess the potential of this approach by introducing a model with a simplified geometry. We describe the magnetic field between the CME shock surface and the cloud's boundary by means of a vector potential. We also apply our model and present the magnetic field distribution in the CME sheath region in front of the body and in the rear of the cloud formed after the event of 20 November 2003.

scholarly journals Period spacings of gravity modes in rapidly rotating magnetic stars

2020 ◽  
Vol 636 ◽  
pp. A100 ◽  
Author(s):  
V. Prat ◽  
S. Mathis ◽  
C. Neiner ◽  
J. Van Beeck ◽  
D. M. Bowman ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Rotation Axis ◽  
Equatorial Region ◽  
Rotating Stars ◽  
Frequency Shifts ◽  
New Formalism ◽  
Magnetic Stars ◽  
Internal Oblique ◽  
Rapidly Rotating Stars ◽  
The Magnetic Field

Context. Stellar internal magnetic fields have recently been shown to leave a detectable signature on period spacing patterns of gravity modes. Aims. We aim to investigate the effect of the obliquity of a mixed (poloidal and toroidal) dipolar internal fossil magnetic field with respect to the rotation axis on the frequency of gravity modes in rapidly rotating stars. Methods. We used the traditional approximation of rotation to compute non-magnetic modes, and a perturbative treatment of the magnetic field to compute the corresponding frequency shifts. We applied the new formalism to HD 43317, a magnetic, rapidly rotating, slowly pulsating B-type star, whose field has an obliquity angle of about 80°. Results. We find that frequency shifts induced by the magnetic field on high-radial-order gravity modes are larger with increasing obliquity angle, when the magnetic axis is closer to the equatorial region, where these modes are trapped. The maximum value is reached for an obliquity angle of 90°. This trend is observed for all mode geometries. Conclusions. Our results predict that the signature of an internal oblique dipolar magnetic field is detectable using asteroseismology of gravity modes.

Relation between wave speeds in the crust of dense magnetic stars

1978 ◽  
Vol 364 (1719) ◽  
pp. 537-552 ◽  
Keyword(s):  
Magnetic Field ◽  
Initial Pressure ◽  
The Body ◽  
Perfect Conductor ◽  
Initial State ◽  
Wave Speeds ◽  
Magnetic Stars ◽  
Arbitrary Strength ◽  
The Magnetic Field ◽  
Relativistic Framework

By studying, within the relativistic framework, the propagation of so-called infinitesimal discontinuities throughout a magnetized elastic perfect conductor in an initial state of high hydrostatic pressure p 0 and in the presence of a magnetic field of arbitrary strength, it is proven that there hold universal relations (i. e., that do not depend on the exact equation of state of the body) between the speeds U f and U s of so-called fast and slow magnetoelastic modes. These results, which should hold true in the crust of dense magnetic stars, have the following form. If A 0 is the relativistic Alfvén number of the initial state and a 0 is the sound speed of a fictitious relativistic perfect fluid whose law of compression would yield the initial pressure p o , then (with nondimensional speeds) U 2 / f = 4/3[ U 2 s (1+ A 2 0 ]+( a 2 0 -4/3 A 2 0 ) for a propagation along the magnetic field and U 2 f (1+ A 2 0 )=4/3 U 2 s +( a 2 0 + A 2 0 ) for a propagation in a direction orthogonal to the magnetic field. These results generalize previous results obtained in relativistic elasticity by Carter and Maugin.

The effect of a strongly stratified layer in the upper part of Mercury’s core on its magnetic field

2020 ◽  
Author(s):  
Patrick Kolhey ◽  
Daniel Heyner ◽  
Johannes Wicht ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Dipole Moment ◽  
Magnetic Dipole ◽  
Magnetic Dipole Moment ◽  
Rotation Axis ◽  
Outer Core ◽  
Magnetic Field Generation ◽  
Fluid Core ◽  
Planetary Magnetic Fields ◽  
The Magnetic Field

&lt;p&gt;In the 1970&amp;#8217;s the flybys of NASA&amp;#8217;s Mariner 10 spacecraft confirmed the existence of an internally generated magnetic field at Mercury. The measurements taken during its flybys already revealed, that Mercury&amp;#8216;s magnetic field is unique along other planetary magnetic fields, since the magnetic dipole moment of ~190 nT &amp;#8729; R&lt;sub&gt;M&lt;/sub&gt;&lt;sup&gt;3 &lt;/sup&gt;is very weak, e.g. compared to Earth&amp;#8217;s magnetic dipole moment. The following MESSENGER mission from NASA investigated Mercury and its magnetic field more precisely and exposed additional interesting properties about the planet&amp;#8217;s magnetic field. The tilt of its dipole component is less than 1&amp;#176;, which indicates a strong alignment of the field along the planet&amp;#8217;s rotation axis. Additionally the measurement showed that the magnetic field equator is shifted roughly 0.2 &amp;#8729; R&lt;sub&gt;M&lt;/sub&gt; towards north compared to Mercury&amp;#8216;s actual geographic equator.&lt;/p&gt;&lt;p&gt;Since its discovery Mercury&amp;#8216;s magnetic field has puzzled the community and modelling the dynamo process inside the planet&amp;#8217;s interior is still a challenging task. Adapting the typical control parameters and the geometry in the models of the geodynamo for Mercury does not lead to the observed field morphology and strength. Therefore new non-Earth-like models were developed over the past decades trying to match Mercury&amp;#8217;s peculiar magnetic field. One promising model suggests a stably stratified layer on the upper part of Mercury&amp;#8217;s core. Such a layer divides the fluid core in a convecting part and a non-convecting part, where the magnetic field generation is mainly inhibited. As a consequence the magnetic field inside the outer core is damped very efficiently passing through the stably stratified layer by a so-called skin effect. Additionally, the non-axisymmetric parts of the magnetic field are vanishing, too, such that a dipole dominated magnetic is left at the planet&amp;#8217;s surface.&lt;/p&gt;&lt;p&gt;In this study we present new direct numerical simulations of the magnetohydrodynamical dynamo problem which include a stably stratified layer on top of the outer core. We explore a wide parameter range, varying mainly the Rayleigh and Ekman number in the model under the aspect of a strong stratification of the stable layer. We show which conditions are necessary to produce a Mercury-like magnetic field and give a inside about the planets interior structure.&lt;/p&gt;

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