Mixed Modes and Asteroseismic Surface Effects. II. Subgiant Systematics

Models of solar-like oscillators yield acoustic modes at different frequencies than would be seen in actual stars possessing identical interior structure, due to modeling error near the surface. This asteroseismic “surface term” must be corrected when mode frequencies are used to infer stellar structure. Subgiants exhibit oscillations of mixed acoustic (p-mode) and gravity (g-mode) character, which defy description by the traditional p-mode asymptotic relation. Since nonparametric diagnostics of the surface term rely on this description, they cannot be applied to subgiants directly. In Paper I, we generalized such nonparametric methods to mixed modes, and showed that traditional surface-term corrections only account for mixed-mode coupling to, at best, first order in a perturbative expansion. Here, we apply those results, modeling subgiants using asteroseismic data. We demonstrate that, for grid-based inference of subgiant properties using individual mode frequencies, neglecting higher-order effects of mode coupling in the surface term results in significant systematic differences in the inferred stellar masses, and measurable systematics in other fundamental properties. While these systematics are smaller than those resulting from other choices of model construction, they persist for both parametric and nonparametric formulations of the surface term. This suggests that mode coupling should be fully accounted for when correcting for the surface term in seismic modeling with mixed modes, irrespective of the choice of correction used. The inferred properties of subgiants, in particular masses and ages, also depend on the choice of surface-term correction, in a different manner from those of both main-sequence and red giant stars.

The hidden fluxes, that control the fluctuations of scalar fields

The fluctuations of scalar fields, that are invariant under rotations of the worldvolume, in Euclidian signature, can be described by a system of Langevin equations. These equations can be understood as defining a change of variables in the functional integral for the noise, with which the physical degrees of freedom are in equilibrium. The absolute value of the Jacobian of this change of variables therefore repackages the fluctuations. This provides a new way of relating the number and properties of scalar fields with the consistent and complete description of their fluctuations and is another way of understanding the relevance of supersymmetry, which, in this way, determines the minimal number of real scalar fields (e.g. two in two dimensions, four in three dimensions and eight in four dimensions), in order for the system to be consistently closed. The classical action of the scalar fields, obtained in this way, contains a surface term and a remainder, in addition to the canonical kinetic and potential terms. The surface term describes possible flux contributions in the presence of boundaries, while the remainder describes additional interactions, that can’t be absorbed in a redefinition of the canonical terms. It is, however, through its combination with the surface term that the noise fields can be recovered, in all cases. However their identities can be subject to anomalies. What is of particular, practical, interest is the identification of the noise fields, as functions of the scalars, whose correlation functions are Gaussian. This implies new identities, between the scalars, that can be probed in real, or computer, experiments.

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630–651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400–408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision–performance balance.

Sphere-valued harmonic maps with surface energy and the K13 problem

We consider an energy functional motivated by the celebrated {K_{13}} problem in the Oseen–Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an additional surface term. It is known that this energy is unbounded from below and our aim has been to study the local minimisers. We show that even having a critical point in a suitable energy space imposes severe restrictions on the boundary conditions. Having suitable boundary conditions makes the energy functional bounded and in this case we study the partial regularity of the global minimisers.

Volume and surface nonlocality terms in the neutron–nucleus elastic scattering using the velocity-dependent optical potential

In this work, we tested the effect of adding a volume term to the surface term in our modified optical potential in the case of elastic neutron scattering of spin-zero 40Ca nucleus in the incident energy range between 30–50 MeV. This is achieved in two steps. First, we fit our theoretical elastic angular distribution scattering using the surface term in our velocity-dependent optical potential concerning the experimental data. Then, we adjust our theoretical elastic angular distribution scattering with the experimental data after adding the volume term into our velocity-dependent optical potential. The second step is comparing the two fits and noticing the effect of adding a volume term to the surface term. Clearly, the modified optical potential using the volume term resulted in excellent fits to the experimental data, most notably the pronounced large angle, backscattering minima, which depend sensitively on the incident energies and which have long been associated with nonlocalities. We assume the nonlocality to be due to interaction between the incident neutrons and the nucleons inside the target.