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

Meta-Functional Benefit Transfer for Wetland Valuation: Making the Most of Small Samples

This study applies functional Benefit Transfer via Meta-Regression Modeling to derive valuation estimates for wetlands in an actual policy setting of proposed groundwater transfers in Eastern Nevada. We illustrate how Bayesian estimation techniques can be used to overcome small sample problems notoriously present in Meta-functional Benefit Transfer. The highlights of our methodology are (i) The hierarchical modeling of heteroskedasticity, (ii) The ability to incorporate additional information via refined priors, and (ii) The derivation of measures of model performance with the corresponding option of model-averaged Benefit Transfer predictions. Our results indicate that economic losses associated with the disappearance of these wetlands can be substantial and that primary valuation studies are warranted.Bayesian Model Averaging; t-Error Regression Model; Meta-Analysis; Benefit Transfer; Wetland Valuation

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