119117392
Variability in mode amplitudes in the rapidly oscillating Ap star HR 1217
HR 1217 is one of the best studied rapidly oscillating Ap stars with eight known oscillation modes that are distorted by a strong, global magnetic field. We have reanalysed the multisite observations of HR 1217 taken in 1986 and 2000. We determined a weighting scheme for the 1986 and 2000 data to minimize the noise level. A wavelet analysis of the data has found that the modulation of the amplitude due to rotation for all frequencies is, in general, consistent with the expected modulation for modified l = 1, 2 or 3 modes. Unexpected variations in the rotational modulation are also seen, with variations in the modulation profile, time of maximal pulsation and pulsational energy in each mode. Interestingly, these changes take place on a short time-scale, of the order of days. We consider potential explanations for these behaviours.
59387646
Theory of rapidly oscillating Ap stars
I review recent theoretical work on rapidly oscillating Ap stars and discuss key aspects of the physics of the oscillations observed in this class of pulsators.
118476277
Probing tiny convective cores with the acoustic modes of lowest degree
Solar-like oscillations are expected to be excited in stars of up to about 1.6 solar masses. Most of these stars will have convective cores during their main-sequence evolution. At the edges of these convective cores, there is a rapid variation in the sound speed, which influences the frequencies of acoustic oscillations. In this paper we build on earlier work to investigate the impact that these rapid structural variations have on different p-mode frequency combinations, involving modes of low degree. In particular, we adopt a different expression to describe the sound speed variation at the edge of the core, which we show more closely reproduces the profiles derived from the equilibrium models. We analyse the impact of this change on the frequency perturbation derived for radial modes. Moreover, we consider three different small frequency separations involving modes of degree l = 0, 1, 2, 3, l = 0, 1, and l = 0, 2, and show that they are all significantly affected by the sharp sound speed variation at the edge of the core. In particular, we confirm that the frequency derivative of the diagnostic tool that combines modes of degree up to 3 can potentially be used to infer the amplitude of the relative sound speed variation directly at the edge of the core. We show that at high frequencies the other two diagnostic tools can be up to a few μHz smaller than what would be expected in the absence of the rapid structural variation at the edge of the core. Also, we show that the absolute values of their frequency derivatives are significantly increased, in a manner that strongly depends on stellar age.
14738827
Improved pulsating models of magnetic Ap stars ¿ I. Exploring different magnetic field configurations
Magnetic perturbations to the frequencies of low-degree, high radial order, axisymmetric pulsations in stellar models permeated by large-scale magnetic fields are presented. Magnetic fields with dipolar, quadrupolar and a superposition of aligned dipolar and quadrupolar components are considered. The results confirm that the magnetic field may produce strong anomalies in the power spectra of roAp stars. It is shown for the first time that anomalies may result both from a sudden decrease or a sudden increase of a mode frequency. Moreover, the results indicate that the anomalies depend essentially on the geometry of the problem, that is, on the configuration of the magnetic field and on the degree of the modes. This dependence opens the possibility of using these anomalies as a tool to learn about the magnetic field configuration in the magnetic boundary layer of pulsating stars permeated by large-scale magnetic fields.
119198538
Towards the understanding of radial velocity pulsation in roAp stars
High-resolution spectroscopic time series of rapidly oscillating Ap stars show evidence for a co-existence of standing and running waves in their atmospheric layers. With the purpose of understanding these observations we have carried out a theoretical analysis of the pulsations in the outermost layers of these stars, starting from the simplest possible model that still retains all important physical ingredients. In our analysis we considered an isothermal atmosphere in a plane-parallel approximation. Moreover we assumed that in the region considered the magnetic pressure is much larger than the gas pressure and, consequently, that the magnetoacoustic wave has decoupled into its acoustic and magnetic components. Using the analytical solutions for the velocity components appropriate to this model we estimate the velocity component parallel to the line of sight averaged over the visible stellar disk. Fitting the latter to a function of the form Acos(?t+phase), with ? the dimensionless oscillation frequency and t the dimensionless time, we derive the amplitude A and the phase for our model as function of height in the atmosphere.
14857158
A search for rapid pulsations among nine luminous Ap stars
The rapidly oscillating Ap (roAp) stars are of importance for studying the atmospheric structure of stars where the process of chemical element diffusion is significant. We have performed a survey for rapid oscillations in a sample of nine luminous Ap stars, selected from their location in the colour‐magnitude diagram as more evolved main-sequence Ap stars that are inside the instability strip for roAp stars. Until recently this region was devoid of stars with observed rapid pulsations. We used the Very Large Telescope UV‐Visual Echelle Spectrograph to obtain high time resolution spectroscopy to make the first systematic spectroscopic search for rapid oscillations in this region of the roAp instability strip. We report nine null detections with upper limits for radial velocity amplitudes of 20‐65 m s −1 and precisions of σ = 7‐ 20 m s −1 for combinations of Nd and Pr lines. Cross-correlations confirm these null results. At least six stars are magnetic and we provide magnetic field measurements for four of them, of which three are newly discovered magnetic stars. It is found that four stars have magnetic fields smaller than ∼2 kG, which according to theoretical predictions might be insufficient for suppressing envelope convection around the magnetic poles for more evolved Ap stars. Suppression of convection is expected to be essential for the opacity mechanism acting in the hydrogen ionization zone to drive the high-overtone roAp pulsations efficiently. Our null results suggest that the more evolved roAp stars may require particularly strong magnetic fields to pulsate. Three of the studied stars do, however, have magnetic fields stronger than 5 kG.
119279503
Exact solutions for a Maxwell-Kalb-Ramond action with dilaton: Localization of massless and massive modes in a sine-Gordon brane-world
We analytically find the exact propagation modes of the electromagnetic and the Kalb-Ramond fields together in a five-dimensional curved space-time. The existence and localization of gauge particles into our four-dimensional world (4D) is studied in detail on a brane-world scenario in which two gauge fields interact with a dilaton and a gravitational background. The coupling to the dilaton is different in each case causing the splitting between gauge spectra. The gauge-field zero-modes and an infinite tower of Kaluza-Klein massive states are analytically obtained. Relevant conditions on the dilaton coupling constant are found in order to identify with precision every finite tensor and vector eigenstate in the theory. An exact quantization condition on the whole mass spectrum, depending on the dilaton coupling constant and the bulk Planck mass, is inherited from the extra-dimension. This allows finding an exact rule to prevent tachyons in the theory and, by the same token, predicting a possible tensor zero-mode in 4D world. We also show that KK massive-modes contributions onto 4D physics are strongly suppressed.
54195021
Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant
Abstract We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R . To this end, we take into account a static and spherically symmetric solution of Hořava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.
119612595
Energy eigenfunctions for position-dependent mass particles in a new class of molecular Hamiltonians
Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. In the present paper, we consider the quantum differential equations resulting from position-dependent mass (PDM) particles. We first focus on the PDM version of the hyperbolic potential V(x) = asech2x + bsech4x, which we address analytically with no restrictioon the parameters and the energies. This is the celebrated Manning potential, a double-well widely used in molecular physics, until now not investigated for PDM. We also evaluate the PDM version of the sixth power hyperbolic potential V(x) = asech6x + bsech4x for which we could find exact expressions under some special settings. Finally, we address a triple-well case V(x) = asech6x + bsech4x + csech2x of particular interest for its connection to the new trends in atomtronics. The PDM Schrodinger equations studied in the present paper yield analytical eigenfunctions in terms of local Heun functions in its confluen...
119212554
Some remarks on Relativistic Diffusion and the Spectral Dimension Criterion
The spectral dimension $d_s$ for high energies is calculated using the Relativistic Schr\"{o}dinger Equation Analytically Continued (RSEAC) instead of the so-called Telegraph's Equation (TE), in both ultraviolet (UV) and infrared (IR) regimens. Regarding the TE, the recent literature presents difficulties related to its stochastic derivation and interpretation, advocating the use of the RSEAC to properly describe the relativistic diffusion phenomena. Taking into account that the Lorentz symmetry is broken in UV regime at Lifshitz point, we show that there exists a degeneracy in very high energies, meaning that both the RSEAC and the TE correctly describe the diffusion processes at these energy scales, at least under the spectral dimension criterion. In fact, both the equations yield the same result, namely, $d_s = 2$, a dimensional reduction that is compatible with several theories of quantum gravity. This result is reached even when one takes into account a cosmological model - the De Sitter one - for a flat Universe. On the other hand, in the IR regimen, such degeneracy is lifted in favor of the approach via TE, due to the fact that only this equation provides the correct value for $d_s$, which is equal to the actual number of spacetime dimensions, i. e., $d_s = 4$, while RSEAC furnishes $d_s=3$, so that a diffusing particle described by this latter experiences a three-dimensional spacetime.
119097979
Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials
We analytically solve the position-dependent mass (PDM) 1D Schrodinger equation for a new class of hyperbolic potentials Vqp(x)=−V0sinhpxcoshqx,p=−2,0,⋯q [see C. A. Downing, J. Math. Phys. 54, 072101 (2013)] among several hyperbolic single- and double-wells. For a solitonic mass distribution, m(x)=m0sech2(x), we obtain exact analytic solutions to the resulting differential equations. For several members of the class, the quantum mechanical problems map into confluent Heun differential equations. The PDM Poschl-Teller potential is considered and exactly solved as a particular case.