No Arabic abstract
We report here the detection of a weak magnetic field of 50 - 100 G on the O9.7 supergiant zeta Ori A, using spectropolarimetric observations obtained with NARVAL at the 2m Telescope Bernard Lyot atop Pic du Midi (France). zeta Ori A is the third O star known to host a magnetic field (along with theta^1 Ori C and HD 191612), and the first detection on a normal rapidly-rotating O star. The magnetic field of zeta Ori A is the weakest magnetic field ever detected on a massive star. The measured field is lower than the thermal equipartition limit (about 100 G). By fitting NLTE model atmospheres to our spectra, we determined that zeta Ori A is a 40 Msun star with a radius of 25 Rsun and an age of about 5 - 6 Myr, showing no surface nitrogen enhancement and losing mass at a rate of about 2x10^(-6) Msol/yr. The magnetic topology of zeta Ori A is apparently more complex than a dipole and involves two main magnetic polarities located on both sides of the same hemisphere; our data also suggest that zeta Ori A rotates in about 7.0 d and is about 40 degrees away from pole-on to an Earth-based observer. Despite its weakness, the detected magnetic field significantly affects the wind structure; the corresponding Alfven radius is however very close to the surface, thus generating a different rotational modulation in wind lines than that reported on the two other known magnetic O stars. The rapid rotation of zeta Ori A with respect to theta^1 Ori C appears as a surprise, both stars having similar unsigned magnetic fluxes (once rescaled to the same radius); it may suggest that the sub-equipartition field detected on zeta Ori A is not a fossil remnant (as opposed to that of theta^1 Ori C and HD 191612), but the result of an exotic dynamo action produced through MHD instabilities.
A close companion of Zeta Orionis A was found in 2000 with the Navy Precision Optical Interferometer (NPOI), and shown to be a physical companion. Because the primary is a supergiant of type O, for which dynamical mass measurements are very rare, the companion was observed with NPOI over the full 7-year orbit. Our aim was to determine the dynamical mass of a supergiant that, due to the physical separation of more than 10 AU between the components, cannot have undergone mass exchange with the companion. The interferometric observations allow measuring the relative positions of the binary components and their relative brightness. The data collected over the full orbital period allows all seven orbital elements to be determined. In addition to the interferometric observations, we analyzed archival spectra obtained at the Calar Alto, Haute Provence, Cerro Armazones, and La Silla observatories, as well as new spectra obtained at the VLT on Cerro Paranal. In the high-resolution spectra we identified a few lines that can be associated exclusively to one or the other component for the measurement of the radial velocities of both. The combination of astrometry and spectroscopy then yields the stellar masses and the distance to the binary star. The resulting masses for components Aa of 14.0 solar masses and Ab of 7.4 solar masses are low compared to theoretical expectations, with a distance of 294 pc which is smaller than a photometric distance estimate of 387 pc based on the spectral type B0III of the B component. If the latter (because it is also consistent with the distance to the Orion OB1 association) is adopted, the mass of the secondary component Ab of 14 solar masses would agree with classifying a star of type B0.5IV. It is fainter than the primary by about 2.2 magnitudes in the visual. The primary mass is then determined to be 33 solar masses.
Massive stars play a significant role in the chemical and dynamical evolution of galaxies. However, much of their variability, particularly during their evolved supergiant stage, is poorly understood. To understand the variability of evolved massive stars in more detail, we present a study of the O9.2Ib supergiant $zeta$ Ori Aa, the only currently confirmed supergiant to host a magnetic field. We have obtained two-color space-based BRIght Target Explorer photometry (BRITE) for $zeta$ Ori Aa during two observing campaigns, as well as simultaneous ground-based, high-resolution optical CHIRON spectroscopy. We perform a detailed frequency analysis to detect and characterize the stars periodic variability. We detect two significant, independent frequencies, their higher harmonics, and combination frequencies: the stellar rotation period $P_{mathrm{rot}} = 6.82pm0.18$ d, most likely related to the presence of the stable magnetic poles, and a variation with a period of $10.0pm0.3$ d attributed to circumstellar environment, also detected in the H$alpha$ and several He I lines, yet absent in the purely photospheric lines. We confirm the variability with $P_{mathrm{rot}}$/4, likely caused by surface inhomogeneities, being the possible photospheric drivers of the discrete absorption components. No stellar pulsations were detected in the data. The level of circumstellar activity clearly differs between the two BRITE observing campaigns. We demonstrate that $zeta$ Ori Aa is a highly variable star with both periodic and non-periodic variations, as well as episodic events. The rotation period we determined agrees well with the spectropolarimetric value from the literature. The changing activity level observed with BRITE could explain why the rotational modulation of the magnetic measurements was not clearly detected at all epochs.
Context: HD 54879 (O9.7 V) is one of a dozen O-stars for which an organized atmospheric magnetic field has been detected. To gain insights into the interplay between atmospheres, winds, and magnetic fields of massive stars, we acquired UV and X-ray data of HD 54879 using the Hubble Space Telescope and the XMM-Newton satellite. In addition, 35 optical amateur spectra were secured to study the variability of HD 54879. A multiwavelength (X-ray to optical) spectral analysis is performed using the Potsdam Wolf-Rayet (PoWR) model atmosphere code and the xspec software. Results: The photospheric parameters are typical for an O9.7 V star. The microturbulent, macroturbulent, and projected rotational velocities are lower than previously suggested (<4 km/s). An initial mass of 16$,M_odot$ and an age of 5 Myr are inferred from evolutionary tracks. We derive a mean X-ray emitting temperature of $log T_{rm X} = 6.7,$[K] and an X-ray luminosity of $log L_text{X} = 32,$[erg/s]. Short- and long-scale variability is seen in the H-alpha line, but only a very long period of $P approx 5,$yr could be estimated. Assessing the circumstellar density of HD 54879 using UV spectra, we can roughly estimate the mass-loss rate HD 54879 would have in the absence of a magnetic field as $log dot{M}_{B=0}approx -9.0,[{M_odot}/{rm yr}]$. The magnetic field traps the stellar wind up to the Alfven radius > $12,R_odot$, implying that its true mass-loss rate is $log dot{M}< -10.2,[{M_odot}/{rm yr}]$. Hence, density enhancements around magnetic stars can be exploited to estimate mass-loss rates of non-magnetic stars of similar spectral types, essential for resolving the weak wind problem. Conclusions: Our study confirms that strongly magnetized stars lose little or no mass, and supplies important constraints on the weak-wind problem of massive main sequence stars.
Using a weak limit for the hopping integral in one direction in the Hofstadter model, we show that the fermion states in the gaps of the spectrum are determined within the Kitaev chain. The proposed approach allows us to study the behavior of Chern insulators (CI) in different classes of symmetry. We consider the Hofstadter model on the square and honeycomb lattices in the case of rational and irrational magnetic fluxes $phi$, and discuss the behavior of the Hall conductance at a weak magnetic field in a sample of finite size. We show that in the semiclassical limit at the center of the fermion spectrum, the Bloch states of fermions turn into chiral Majorana fermion liquid when the magnetic scale $ frac{1}{ phi} $ is equal to the sample size N. We are talking about the dielectric-metal phase transition, which is determined by the behavior of the Landau levels in 2D fermion systems in a transverse magnetic field. When a magnetic scale, which determines the wave function of fermions, exceeds the size of the sample, a jump in the longitudinal conductance occurs. The wave function describes non-localized states of fermions, the sample becomes a conductor, the system changes from the dielectric state to the metallic one. It is shown, that at $1/phi>$N the quantum Hall effect and the Landau levels are not realized, which makes possibility to study the behavior of CI in irrational magnetic fluxes.
We combine UV spectra obtained with the HST/GHRS echelle, IMAPS, and Copernicus to study the abundances and physical conditions in the predominantly ionized gas seen at high (-105 to -65 km/s) and intermediate velocities (-60 to -10 km/s) toward zeta Ori. We have high resolution (FWHM ~ 3.3-4.5 km/s) and/or high S/N spectra for at least two significant ions of C, N, Al, Si, S, and Fe -- enabling accurate estimates for both the total N(H II) and the elemental depletions. C, N, and S have essentially solar relative abundances; Al, Si, and Fe appear to be depleted by about 0.8, 0.3-0.4, and 0.95 dex, respectively. While various ion ratios would be consistent with collisional ionization equilibrium (CIE) for T ~ 25,000-80,000 K, the widths of individual high-velocity absorption components indicate that T ~ 9000 K -- so the gas is not in CIE. Analysis of the C II fine-structure excitation equilibrium yields estimated densities (n_e ~ n_H ~ 0.1-0.2 cm^{-3}), thermal pressures (2 n_H T ~ 2000-4000 cm^{-3}K), and thicknesses (0.5-2.7 pc) for the individual clouds. We compare the abundances and physical properties derived for these clouds with those found for gas at similar velocities toward 23 Ori and tau CMa, and also with several models for shocked gas. While the shock models can reproduce some features of the observed line profiles and some of the observed ion ratios, there are also significant differences. The measured depletions suggest that ~10% of the Al, Si, and Fe originally locked in dust in the pre-shock medium may have been returned to the gas phase, consistent with predictions for the destruction of silicate dust in a 100 km/s shock. The near-solar gas phase abundance of carbon, however, seems inconsistent with the predicted longer time scales for the destruction of graphite grains.