On the possibility of a bimodal solar dynamo

A simple way to couple an interface dynamo model to a fast tachocline model is presented, under the assumption that the dynamo saturation is due to a quadratic process and that the effect of finite shear layer thickness on the dynamo wave frequency is analoguous to the effect of finite water depth on surface gravity waves. The model contains one free parameter which is fixed by the requirement that a solution should reproduce the helioseismically determined thickness of the tachocline. In this case it is found that, in addition to this solution, another steady solution exists, characterized by a four times thicker tachocline and 4-5 times weaker magnetic fields. It is tempting to relate the existence of this second solution to the occurrence of grand minima in solar activity.Comment: 4 pages, 1 figure; Astr. Nachr., in pres

Dynamics of the fast solar tachocline: II. Migrating field

We present detailed numerical calculations of the fast solar tachocline based on the assumption that the dynamo field dominates over the dynamics of the tachocline. In the present paper of the series, we focus on three shortfalls of the earlier models. First, instead of the simple oscillating dipole poloidal field we study the more general magnetic field structures reminiscent of the butterfly diagram. The migrating field is prescribed as the observed axisymmetric radial magnetic field Stenflo (1988, 1994). Our results are in good agreement with our analitical estimate and our previous works in Forgacs-Dajka & Petrovay (2001,2002), but the polar "dip" in isorotational surfaces is strongly reduced in this case. On the other hand, a more realistic model should have a magnetic diffusivity decreasing significantly inside the radiative interior, so we also explore the effect of diffusivity and magnetic Prandtl number varying with depth. We found that the downwards decreasing magnetic diffusivity and Prandtl number have no significant effect on the solution, although the temporal variation of the tachocline thickness has decreased.Comment: 9 page

The evolution of collision debris near the ν6\nu_6 secular resonance and its role in the origin of terrestrial water

This work presents novel findings that broadens our understanding of the amount of water that can be transported to Earth. The key innovation lies in the combined usage of Smoothed Particle Hydrodynamics (SPH) and $N$-body codes to assess the role of collision fragments in water delivery. We also present a method for generating initial conditions that enables the projectile to impact at the designated location on the target's surface with the specified velocity. The primary objective of this study is to simulate giant collisions between two Ceres-sized bodies by SPH near the $\nu_6$ secular resonance and follow the evolution of the ejected debris by numerical $N$-body code. With our method 6 different initial conditions for the collision were determined and the corresponding impacts were simulated by SPH. Examining the orbital evolution of the debris ejected after collisions, we measured the amount of water delivered to Earth, which is broadly 0.001 ocean equivalents of water, except in one case where one large body transported 7\% oceans of water to the planet. Based on this, and taking into account the frequency of collisions, the amount of delivered water varies between 1.2 and 8.3 ocean's worth of water, depending on the primordial disk mass. According to our results, the prevailing external pollution model effectively accounts for the assumed water content on Earth, whether it's estimated at 1 or 10 ocean's worth of water.Comment: 15 pages, 13 figure

Transit timing variations in eccentric hierarchical triple exoplanetary systems. I. Perturbations on the time-scale of the orbital period of the perturber

We study the long-term time-scale (i.e. period comaprable to the orbital period of the outer perturber object) transit timing variations in transiting exoplanetary systems which contain a further, more distant (a_2>>a_1) either planetary, or stellar companion. We give an analytical form of the O-C diagram (which describes such TTV-s) in trigonometric series, valid for arbitrary mutual inclinations, up to the sixth order in the inner eccentricity. We show that the dependence of the O-C on the orbital and physical parameters can be separated into three parts. Two of these are independent of the real physical parameters (i.e. masses, separations, periods) of a concrete system, and depend only on dimensionless orbital elements, and so, can be analyzed in general. We analyze these dimensionless amplitudes for different arbitrary initial parameters, as well as for two particular systems CoRoT-9b and HD 80606b. We find in general, that while the shape of the O-C strongly varies with the angular orbital elements, the net amplitude (departing from some specific configurations) depends only weakly on these elements, but strongly on the eccentricities. As an application, we illustrate how the formulae work for the weakly eccentric CoRoT-9b, and the highly eccentric HD 80606b. We consider also the question of detection, as well as the correct identification of such perturbations. Finally, we illustrate the operation and effectiveness of Kozai cycles with tidal friction (KCTF) in the case of HD 80606b.Comment: Submitted to Astronomy and Astrophysics; Revised versio

Dynamics of the fast solar tachocline: I. Dipolar field

One possible scenario for the origin of the solar tachocline, known as the "fast tachocline", assumes that the turbulent diffusivity exceeds eta>10^9 cm^2/s. In this case the dynamics will be governed by the dynamo-generated oscillatory magnetic field on relatively short timescales. Here, for the first time, we present detailed numerical models for the fast solar tachocline with all components of the magnetic field calculated explicitly, assuming axial symmetry and a constant turbulent diffusivity eta and viscosity nu. We find that a sufficiently strong oscillatory poloidal field with dipolar latitude dependence at the tachocline-convective zone boundary is able to confine the tachocline. Exploring the three-dimensional parameter space defined by the viscosity in the range log(nu)=9-11, the magnetic Prandtl number in the range Prm=0.1-10, and the meridional flow amplitude (-3 to +3 cm/s), we also find that the confining field strength B_conf, necessary to reproduce the observed thickness of the tachocline, increases with viscosity nu, with magnetic Prandtl number nu/eta, and with equatorward meridional flow speed. Nevertheless, the resulting B_conf values remain quite reasonable, in the range 10^3-10^4 G, for all parameter combinations considered here. The thickness of the tachocline shows a marked dependence on both time and latitude. A comparison with seismic constraints suggests that best agreement with our models is achieved for the highest values of nu and Prm considered here.Comment: 11 page

A fast method to identify mean motion resonances

The identification of mean motion resonances in exoplanetary systems or in the Solar System might be cumbersome when several planets and large number of smaller bodies are to be considered. Based on the geometrical meaning of the resonance variable, an efficient method is introduced and described here, by which mean motion resonances can be easily find without any a priori knowledge on them. The efficiency of this method is clearly demonstrated by using known exoplanets engaged in mean motion resonances, and also some members of different families of asteroids and Kuiper-belt objects being in mean motion resonances with Jupiter and Neptune respectively.Comment: 7 pages, 13 figures, accepted by Monthly Notices of the Royal Astronomical Societ

A BABCOCK-LEIGHTON SOLAR DYNAMO MODEL WITH MULTI-CELLULAR MERIDIONAL CIRCULATION IN ADVECTION- AND DIFFUSION-DOMINATED REGIMES

Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock-Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of butterfly wing to an anti-solar type. A butterfly diagram constructed from middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow-speed is strong enough, of similar order of magnitude as the surface flow-speed.Comment: 40 pages, 19 figures, accepted in Ap

SPH-based simulation of multi-material asteroid collisions

We give a brief introduction to smoothed particle hydrodynamics methods for continuum mechanics. Specifically, we present our 3D SPH code to simulate and analyze collisions of asteroids consisting of two types of material: basaltic rock and ice. We consider effects like brittle failure, fragmentation, and merging in different impact scenarios. After validating our code against previously published results we present first collision results based on measured values for the Weibull flaw distribution parameters of basalt.Comment: Accepted and to be published in Astronomical Note