We present the evidence for abundance stratication in the atmosphere of the rapidly oscillating Ap star Equ. Ca, Cr, Fe, Ba, Si, Na seem to be overabundant in deeper atmospheric layers, but normal to underabundant in the upper layers with a transition in the typical line forming region of 1:5 < log5000 < 0:5. This stratication prole agrees well with diusion theory for Ca and Cr, developed for cool magnetic stars with a weak mass loss of 2:5 10 15 M yr 1 . Pr and Nd from the rare earth elements have an opposite prole. Their abundance is more than 6 dex higher above log5000 8:0 than in the deeper atmospheric layers. We further discuss the implications of abundance stratication in the context of radial velocity amplitudes and phases observed by Kochukhov & Ryabchikova (2001) for a variety of spectral lines and elements using high spectral and time resolved, high S/N observations.

/pdf/abundance-stratification-and-pulsation-in-the-atmosphere-of-4zdqfp69ly.pdf

Abundance stratification and pulsation in the atmosphere of the roAp star $\boldmath\gamma$ Equulei

This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a 1.9-M ○. , main-sequence model (log T eff = 3.913). The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the Hen ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.

A non-adiabatic analysis for axisymmetric pulsations of magnetic stars

Received xx/Accepted yy Abstract. With FORS1 at the VLT we have tried for the first time to measure the magnetic field variation over the pulsation cycle in six roAp stars to begin the study of how the magnetic field and pulsation interact. For the star HD101065, which has one of the highest photometric pulsation amplitudes of any roAp star, we found a signal at the known photometric pulsation frequency at the 3� level in one data set; however this could not be confirmed by later observations. A preliminary simple calculation of the expected magnetic variations over the pulsation cycle suggests that they are of the same order as our current noise levels, leading us to expect that further observations with increased S/N have a good chance of achieving an unequivocal detection.

/pdf/measurements-of-magnetic-fields-over-the-pulsation-cycle-in-33qv62k87r.pdf

Measurements of magnetic fields over the pulsation cycle in six roAp stars with FORS 1 at the VLT

We investigate magnetic field geometry and surface distribution of chemical elements in the rapidly oscillating Ap star HR 3831. Results of the model atmosphere analysis of the spectra of this star are combined with the Hipparcos parallax and evolutionary models to obtain new accurate estimates of the fundamental stellar parameters: Teff = 7650 K, log L/L� = 1.09, M/M� = 1.77 and an inclination angle i = 68 ◦ of the stellar axis of rotation. We find that the variation of the longitudinal magnetic field of HR 3831 and the results of our analysis of the magnetic intensification of Fe  lines in the spectrum of this star are consistent with a dipolar magnetic topology with a magnetic obliquity β = 87 ◦ and a polar strength Bp = 2. 5k G. We apply a multi-element abundance Doppler imaging inversion code for the analysis of the spectrum variability of HR 3831, and recover surface distributions of 17 chemical elements, including Li, C, O, Na, Mg, Si, Ca, Ti, Cr, Mn, Fe, Co, Ba, Y, Pr, Nd, Eu. Our study represents the most thorough examination of the surface chemical structure in a magnetic Ap star and provides important observational constraints for modelling radiative diffusion in magnetic stars. The exceedingly high quality of some of our spectroscopic data allowed us to reconstruct unprecedented details of abundance distributions, demonstrating a high level of complexity in the surface structure down to the resolution limit of the Doppler maps. The Doppler imaging analysis of HR 3831 forms a basis for subsequent detailed observational investigations and theoretical modelling of non-radial oscillations in this star. We discuss the compound effect of the chemical nonuniformities and pulsational velocity field on the rapid line profile variations, and assess the possibility of identifying pulsation modes by using spatial filtering produced by an inhomogeneous abundance distribution. The results of our study of the surface chemical structure suggest that differences in pulsational behaviour of lines of different ions observed for HR 3831 are not a consequence of horizontal atmospheric inhomogeneities, but predominantly a depth effect.

https://www.aanda.org/articles/aa/pdf/2004/36/aa0517-04.pdf

Multi-element abundance Doppler imaging of the rapidly oscillating Ap star HR 3831

The effect of a dipole magnetic field on adiabatic axisymmetric non-radial p-mode pulsations is studied numerically. The angular dependence of pulsation, which cannot be represented by a single spherical harmonic in the presence of a magnetic field, is expanded into a series of spherical harmonics with different degrees l. The presence of a magnetic field not only shifts the pulsation frequency, the pulsations are also damped due to the generation of magnetic slow waves. In agreement with the results of Cunha & Gough, who used a different approach from ours, we find that the effect of a magnetic field on the intermediate-to-high-order p-modes is not monotonic but cyclic with respect to the pulsation frequency and the magnetic field strength. The damping rate of a high-order p-mode becomes very small at about 3 kG and 8 kG; the corresponding field strengths are higher for lower overtones. The diminished magnetic damping is favourable for the corresponding modes, if they are excited by the classical K-mechanism, to survive even in the presence of a strong magnetic field. This picture could explain the mode selection as observed in the rapidly oscillating Ap stars. For a low-order p-mode, the damping rate increases as the strength of the magnetic field increases. We find that in the presence of a magnetic field of a few kG, magnetic damping seems to exceed the driving owing to the K-mechanism of oscillations representative of δ Scuti variability. This may explain why δ Scuti-type oscillations are unlikely to be seen in magnetic Ap stars. The amplitude of a mainly dipole (or quadrupole) mode is strongly confined to the magnetic axis in the outer layers. Furthermore, horizontal motion can be comparable to radial motion even for high-order p-modes. We discuss the influence of the magnetic distortion of the eigenfunction on the pulsation amplitude modulation with respect to the rotation phase.

Axisymmetric p‐mode pulsations of stars with dipole magnetic fields

We present an investigation of the magnetic field geometries and inhomogeneous distribution of chemical elements in the atmospheres of peculiar A and B stars. Our study combines high-quality spectroscopic and spectropolarimetric stellar observations with the development and application of novel techniques for theoretical interpretation of the shapes and variability of stellar line profiles. In particular, we extend the method of Doppler imaging to the analysis of spectra in the four Stokes parameters, making it possible to derive detailed and reliable stellar magnetic maps simultaneously with the imaging chemical inhomogeneities.The magnetic Doppler imaging is applied to study of magnetic topologies and distributions of chemical elements in the peculiar stars α2 CVn and 53 Cam. We found that the magnetic field geometry of 53 Cam is considerably more complex than a low-order multipolar topology, commonly assumed for magnetic A and B stars. Our Doppler imaging analysis also led to a discovery and study of spots of enhanced mercury abundance in the atmosphere of α And, a star where the presence of a global magnetic field is unlikely.The ESO 3.6-m telescope is used to collect unique, very high spectral- and time-resolution observations of rapidly oscillating peculiar A (roAp) stars and to reveal line profile variations due to stellar pulsations. We present a detailed characterization of the spectroscopic pulsational behaviour and demonstrate a remarkable diversity of pulsations in different spectral lines. The outstanding variability of the lines of rare-earth elements is used to study propagation of pulsation waves through the stellar atmospheres and identify pulsation modes. This analysis led to a discovery of a non-axisymmetric character of pulsations in roAp stars.Our study of chemical stratification in the atmosphere of the roAp star γ Equ provides a compelling evidence for significant variation of the chemical composition with depth. We find a combined effect of extreme chemical anomalies and a growth of pulsation amplitude in the outermost atmospheric layers to be the most likely origin of the high-amplitude pulsational variations of the lines of rare-earth elements.Observations of cool magnetic CP stars are obtained with the ESO Very Large Telescope and are used for empirical investigation of the anomalies in the atmospheric temperature structure. We show that the core-wing anomaly of the hydrogen Balmer lines observed in some cool CP stars can be attributed to a hot layer at an intermediate atmospheric depth.

/pdf/time-resolved-spectroscopy-of-the-roap-star-gamma-equ-c967o85zb4.pdf

O. Kochukhov

Papers

Time-resolved spectroscopy of the roAp star gamma Equ