The quest for companions to post-common envelope binaries IV: The 2:1 mean-motion resonance of the planets orbiting NN Serpentis

We present 69 new mid-eclipse times of the young post-common envelope binary (PCEB) NN Ser, which was previously suggested to possess two circumbinary planets. We have interpreted the observed eclipse-time variations in terms of the light-travel time effect caused by two planets, exhaustively covering the multi-dimensional parameter space by fits in the two binary and ten orbital parameters. We supplemented the fits by stability calculations for all models with an acceptable chi-square. An island of secularly stable 2:1 resonant solutions exists, which coincides with the global chi-square minimum. Our best-fit stable solution yields current orbital periods P_o = 15.47 yr and P_i = 7.65 yr and eccentricities e_o = 0.14 and e_i = 0.22 for the outer (o) and inner (i) planets, respectively. The companions qualify as giant planets, with masses of 7.0 M_Jup and 1.7 M_Jup for the case of orbits coplanar with that of the binary. The two-planet model that starts from the present system parameters has a lifetime greater than 10^8 yr, which significantly exceeds the age of NN Ser of 10^6 yr as a PCEB. The resonance is characterized by libration of the resonant variable Theta_1 and circulation of omega_i-omega_o, the difference between the arguments of periapse of the two planets. No stable non-resonant solutions were found, and the possibility of a 5:2 resonance suggested previously by us is now excluded at the 99.3% confidence level.Comment: 8 pages, 8 figure

Irradiated atmospheres of accreting magnetic white dwarfs with an application to the polar AM Herculis

We present a pilot study of atmospheres of accreting magnetic white dwarfs irradiated by intense fluxes at ultraviolet to infrared wavelengths. The model uses a standard LTE stellar atmosphere code which is expanded by introducing an angle-dependent external radiation source. The present results are obtained for an external source with the spectral shape of a 10 000 K blackbody and a freely adjustable spectral flux. The model provides an explanation for the observed largely filled-up Lyman lines in the prototype polar AM Herculis during its high states. It also confirms the hypotheses (i) that irradiation by cyclotron radiation and other radiation sources is the principle cause for the large heated polar caps surrounding the accretion spots on white dwarfs in polars and (ii) that much of the reprocessed light appears in the far ultraviolet and not in the soft X-ray regime as suggested in the original simple theories. We also briefly discuss the role played by hard X-rays in heating the polar cap

Zeeman tomography of magnetic white dwarfs. III, The 70–80 Megagauss magnetic field of PG 1015+014

Aims. We analyse the magnetic field geometry of the magnetic DA white dwarf PG 1015+014 with our Zeeman tomography method. Methods. This study is based on rotation-phase resolved optical flux and circular polarization spectra of PG 1015+014 obtained with FORS1 at the ESO VLT. Our tomographic code makes use of an extensive database of pre-computed Zeeman spectra. The general approach has been described in Papers I and II of this series. Results. The surface field strength distributions for all rotational phases of PG 1015+014 are characterised by a strong peak at 70 MG. A separate peak at 80 MG is seen for about one third of the rotation cycle. Significant contributions to the Zeeman features arise from regions with field strengths between 50 and 90 MG. We obtain equally good simultaneous fits to the observations, collected in five phase bins, for two different field parametrizations: (i) a superposition of individually tilted and off-centred zonal multipole components; and (ii) a truncated multipole expansion up to degree l = 4 including all zonal and tesseral components. The magnetic fields generated by both parametrizations exhibit a similar global structure of the absolute surface field values, but differ considerably in the topology of the field lines. An effective photospheric temperature of T eff = 10 000 ± 1000 K was found. Conclusions. Remaining discrepancies between the observations and our best-fit models suggest that additional small-scale structure of the magnetic field exists which our field models are unable to cover due to the restricted number of free parameters

Zeeman tomography of magnetic white dwarfs. IV, The complex field structure of the polars EF Eridani, BL Hydri and CP Tucanae

Context. The magnetic fields of the accreting white dwarfs in magnetic cataclysmic variables (mCVs) determine the accretion geometries, the emission properties, and the secular evolution of these objects. Aims. We determine the structure of the surface magnetic fields of the white dwarf primaries in magnetic CVs using Zeeman tomography. Methods. Our study is based on orbital-phase resolved optical flux and circular polarization spectra of the polars EF Eri, BL Hyi, and CP Tuc obtained with FORS1 at the ESO VLT. An evolutionary algorithm is used to synthesize best fits to these spectra from an extensive database of pre-computed Zeeman spectra. The general approach has been described in previous papers of this series. Results. The results achieved with simple geometries as centered or offset dipoles are not satisfactory. Significantly improved fits are obtained for multipole expansions that are truncated at degree lmax = 3 or 5 and include all tesseral and sectoral components with 0 ≤ m ≤ l. The most frequent field strengths of 13, 18, and 10MG for EF Eri, BL Hyi, and CP Tuc, and the ranges of field strength covered are similar for the dipole and multipole models, but only the latter provide access to accreting matter at the right locations on the white dwarf. The results suggest that the field geometries of the white dwarfs in short-period mCVs are quite complex, with strong contributions from multipoles higher than the dipole in spite of a typical age of the white dwarfs in CVs in excess of 1 Gyr. Conclusions. It is feasible to derive the surface field structure of an accreting white dwarf from phase-resolved low-state circular spectropolarimetry of sufficiently high signal-to-noise ratio. The fact that independent information is available on the strength and direction of the field in the accretion spot from high-state observations helps in unraveling the global field structure

On the HU Aquarii planetary system hypothesis

In this work, we investigate the eclipse timing of the polar binary HU Aquarii that has been observed for almost two decades. Recently, Qian et al. attributed large (O-C) deviations between the eclipse ephemeris and observations to a compact system of two massive jovian companions. We improve the Keplerian, kinematic model of the Light Travel Time (LTT) effect and re-analyse the whole currently available data set. We add almost 60 new, yet unpublished, mostly precision light curves obtained using the time high-resolution photo-polarimeter OPTIMA, as well as photometric observations performed at the MONET/N, PIRATE and TCS telescopes. We determine new mid--egress times with a mean uncertainty at the level of 1 second or better. We claim that because the observations that currently exist in the literature are non-homogeneous with respect to spectral windows (ultraviolet, X-ray, visual, polarimetric mode) and the reported mid--egress measurements errors, they may introduce systematics that affect orbital fits. Indeed, we find that the published data, when taken literally, cannot be explained by any unique solution. Many qualitatively different and best-fit 2-planet configurations, including self-consistent, Newtonian N-body solutions may be able to explain the data. However, using high resolution, precision OPTIMA light curves, we find that the (O-C) deviations are best explained by the presence of a single circumbinary companion orbiting at a distance of ~4.5 AU with a small eccentricity and having ~7 Jupiter-masses. This object could be the next circumbinary planet detected from the ground, similar to the announced companions around close binaries HW Vir, NN Ser, UZ For, DP Leo or SZ Her, and planets of this type around Kepler-16, Kepler-34 and Kepler-35.Comment: 20 pages, 18 figures, accepted to Monthly Notices of the Royal Astronomical Society (MNRAS