SearcharxivSearch

arXiv subjects

L. Lehmann

Publications and source records attributed to L. Lehmann.

2 recordsLinked to original sources

The magnetic field vector of the Sun-as-a-star. II. Evolution of the large-scale vector field through activity cycle 24

In the present work, we investigate how the large-scale magnetic field of the Sun, in its three vector components, has evolved during most of cycle 24, from 2010 Jan to 2018 Apr. To filter out the small-scale field of the Sun, present in high-resolution synoptic maps, we use a spherical harmonic decomposition method, which decomposes the solar field in multipoles with different l degrees. By summing together the low-l multipoles, we reconstruct the large-scale field at a resolution similar to observed stellar magnetic fields, which allows the direct comparison between solar and stellar magnetic maps. During cycle 24, the `Sun-as-a-star' magnetic field shows a polarity reversal in the radial and meridional components, but not in the azimuthal component. The large-scale solar field remains mainly poloidal with > 70% of its energy contained in the poloidal component. During its evolution, the large-scale field is more axisymmetric and more poloidal when near minima in sunspot numbers, and with a larger intensity near maximum. There is a correlation between toroidal energy and sunspot number, which indicates that spot fields are major contributors to the toroidal large-scale energy of the Sun. The solar large-scale magnetic properties fit smoothly with observational trends of stellar magnetism reported in See et al. The toroidal (Etor) and poloidal (Epol) energies are related as Etor ~Epol^{1.38 \pm 0.04}. Similar to the stellar sample, the large-scale field of the Sun shows a lack of toroidal non-axisymmetric field.

astro-ph.SR

Algorithmic Differentiation of Linear Algebra Functions with Application in Optimum Experimental Design (Extended Version)

We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using univariate Taylor propagation of matrices (UTPM). Linear algebra functions are regarded as elementary functions and not as algorithms. The presented algorithms are implemented in the BSD licensed AD tool \texttt{ALGOPY}. Numerical tests show that the UTPM algorithms derived in this paper produce results close to machine precision accuracy. The theory developed in this paper is applied to compute the gradient of an objective function motivated from optimum experimental design: $\nabla_x \Phi(C(J(F(x,y))))$, where $\Phi = \{\lambda_1 : \lambda_1 C\}$, $C = (J^T J)^{-1}$, $J = \frac{\dd F}{\dd y}$ and $F = F(x,y)$.

cs.DS