Magnetic field evolution in OBA stars

The applications of the spectral analysis methods discovered by Kirchhoff for the investigation of stellar magnetic fields are considered. The statistical properties of the mean magnetic fields for OBA stars have been investigated by analyzing data from two catalogs of magnetic fields. It is shown that the mean effective magnetic field ℬ of a star can be used as a statistically significant characteristic of its magnetic field. The magnetic field distribution functions F(ℬ) have been constructed for B-type and chemically peculiar (CP) stars, which exhibit a power-law dependence on ℬ. A sharp decrease in F(ℬ) in the range of weak magnetic fields has been found. The statistical properties of the magnetic fluxes for main-sequence stars, white dwarfs, and neutron stars are analyzed.     

New magnetic field measurements of β Cephei stars and slowly pulsating B stars

We present the results of the continuation of our magnetic survey with FORS 1 at the VLT of a sample of B‐type stars consisting of confirmed or candidate β Cephei stars and Slowly Pulsating B (hereafter SPB) stars, along with a small number of normal B‐type stars. A weak mean longitudinal magnetic field of the order of a few hundred Gauss was detected in three β Cephei stars and two stars suspected to be β Cephei stars, in five SPB stars and eight stars suspected to be SPB stars. Additionally, a longitudinal magnetic field at a level larger than 3σ has been diagnosed in two normal B‐type stars, the nitrogen‐rich early B‐type star HD 52089 and in the B5 IV star HD 153716. Roughly one third of β Cephei stars have detected magnetic fields: Out of 13 β Cephei stars studied to date with FORS 1, four stars possess weak magnetic fields, and out of the sample of six suspected β Cephei stars two show a weak magnetic field. The fraction of magnetic SPBs and candidate SPBs is found to be higher: Roughly half of the 34 SPB stars have been found to be magnetic and among the 16 candidate SPBs eight stars possess magnetic fields. In an attempt to understand why only a fraction of pulsating stars exhibit magnetic fields, we studied the position of magnetic and non‐magnetic pulsating stars in the H‐R diagram. We find that their domains in the H‐R diagram largely overlap, and no clear picture emerges as to the possible evolution of the magnetic field across the main sequence. It is possible that stronger fields tend to be found in stars with lower pulsating frequencies and smaller pulsating amplitudes. A somewhat similar trend is found if we consider a correlation between the field strength and the v sin i ‐values, i.e. stronger magnetic fields tend to be found in more slowly rotating stars (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effects of intense magnetic fields on Landau levels in a neutron star

In this paper, an approximate method of calculating the Fermi energy of electrons (E _F (e)) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: E _F (e) is related to density ρ, the mean electron number per baryon Y _e and magnetic field strength B.     

Studies of magnetic fields in the solar photosphere using the line-ratio method

The longitudinal magnetic field measured using the Fe I λ 525 and Fe I λ 524.7 nm lines and global magnetic field of the sun differ depending on the observatory. To study the cause of these discrepancies, we calculate the H _‖(525)/H _‖(524.7) ratios for various combinations of magnetic elements and compare them with the corresponding observed values. We use the standard quiet model of the solar photosphere suggesting that there are magnetic fields of different polarities in the range between zero and several kilogauss. The magnetic element distribution is found as a function of magnetic field strength and the parameters of this distribution are determined for which the calculated H _‖(525)/H _‖(524.7) ratio agrees with the observed one. The sigma-components are found to be shifted differently for various points of the Fe I λ 525 nm profile calculated for the inhomogeneous magnetic field. The farther the point is from the line center, the larger the sigma-components shift. Such a peculiarity of the profiles may be responsible for the discrepancies in the measured values of the global magnetic field obtained at different observatories. The increase in modulus of the global magnetic field during the maxima of solar activity can be due to a larger fraction of magnetic elements with kilogauss magnetic fields.     

Evolution of magnetic fields in stars across the upper main sequence: II. Observed distribution of the magnetic field geometry

We re‐discuss the evolutionary state of upper main sequence magnetic stars using a sample of Ap and Bp stars with accurate Hipparcos parallaxes and definitely determined longitudinal magnetic fields. We confirm our previous results obtained from the study of Ap and Bp stars with accurate measurements of the mean magnetic field modulus and mean quadratic magnetic fields that magnetic stars of mass M < 3 M_⊙ are concentrated towards the centre of the main‐sequence band. In contrast, stars with masses M > 3 M_⊙ seem to be concentrated closer to the ZAMS. The study of a few known members of nearby open clusters with accurate Hipparcos parallaxes confirms these conclusions. Stronger magnetic fields tend to be found in hotter, younger and more massive stars, as well as in stars with shorter rotation periods. The longest rotation periods are found only in stars which spent already more than 40% of their main sequence life, in the mass domain between 1.8 and 3 M_⊙ and with log g values ranging from 3.80 to 4.13. No evidence is found for any loss of angular momentum during the main‐sequence life. The magnetic flux remains constant over the stellar life time on the main sequence. An excess of stars with large obliquities β is detected in both higher and lower mass stars. It is quite possible that the angle β becomes close to 0. in slower rotating stars of mass M > 3 M_⊙ too, analog to the behaviour of angles β in slowly rotating stars of M < 3 M_⊙. The obliquity angle distribution as inferred from the distribution of r ‐values appears random at the time magnetic stars become observable on the H‐R diagram. After quite a short time spent on the main sequence, the obliquity angle β tends to reach values close to either 90. or 0. for M < 3 M_⊙. The evolution of the obliquity angle β seems to be somewhat different for low and high mass stars. While we find a strong hint for an increase of β with the elapsed time on the main sequence for stars with M > 3 M_⊙, no similar trend is found for stars with M < 3 M_⊙. However, the predominance of high values of β at advanced ages in these stars is notable. As the physics governing the processes taking place in magnetised atmospheres remains poorly understood, magnetic field properties have to be considered in the framework of dynamo or fossil field theories. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comprehensive study of the magnetic stars HD 5797 and HD 40711 with large chromium and iron overabundances

We present the results of a comprehensive study of the chemically peculiar stars HD 5797 and HD 40711. The stars have the same effective^temperature, T _eff = 8900 K, and a similar chemical composition with large iron (+1.5 dex) and chromium (+3 dex) overabundances compared to the Sun. The overabundance of rare-earth elements typically reaches +3 dex. We have measured the magnetic field of HD 5797. The longitudinal field component B _e has been found to vary sinusoidally between −100 and +1000 G with a period of 69 days. Our estimate of the evolutionary status of the stars suggests that HD 5797 and HD 40711, old objects with an age t ≈ 5 × 10⁸ yr, are near the end of the core hydrogen burning phase.     

HARPS spectropolarimetry of Herbig Ae/Be stars

Our knowledge of the presence and the strength of magnetic fields in intermediate‐mass pre‐main‐sequence stars remains very poor. We present new magnetic field measurements in six Herbig Ae/Be stars observed with HARPS in spectropolarimetric mode. We downloaded from the European Southern Observatory (ESO) archive the publically available HARPS spectra for six Herbig Ae/Be stars. Wavelength shifts between right‐ and left‐hand side circularly polarised spectra were interpreted in terms of a longitudinal magnetic field 〈B_z〉, using the moment technique introduced by Mathys. The application of the moment technique to the HARPS spectra allowed us in addition to study the presence of the crossover effect and quadratic magnetic fields. Our search for longitudinal magnetic fields resulted in first detections of weak magnetic fields in the Herbig Ae/Be stars HD 58647 and HD 98922. Further, we confirm the previous tentative detection of a weak magnetic field in HD 104237 by Donati et al. and confirm the previous detection of a magnetic field in the Herbig Ae star HD 190073. Surprisingly, the measured longitudinal magnetic field of HD 190073, 〈B_z〉 = 91 ± 18 G at a significance level of 5σ is not in agreement with the measurement results of Alecian et al. (2013), 〈B_z〉 = –10 ± 20 G, who applied the LSD method to exactly the same data. No crossover effect was detected for any star in the sample. Only for HD 98922 the crossover effect was found tobe close to 3σ with a measured value of –4228 ± 1443 km s^–1 G. A quadratic magnetic field of the order of 10 kG was detected in HD 98922, and of ∼3.5 kG in HD 104237. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic survey of emission line B‐type stars with FORS 1 at the VLT

We report the results of our search for magnetic fields in a sample of 16 field Be stars, the binary emission‐line B‐type star υ Sgr, and in a sample of fourteen members of the open young cluster NGC3766 in the Carina spiral arm. The sample of cluster members includes Be stars, normal B‐type stars and He‐strong/He‐weak stars. Nine Be stars have been studied with magnetic field time series obtained over ∼1 hour to get an insight into the temporal behaviour and the correlation of magnetic field properties with dynamical phenomena taking place in Be star atmospheres. The spectropolarimetric data were obtained at the European Southern Observatory with the multi‐mode instrument FORS1 installed at the 8m Kueyen telescope. We detect weak photospheric magnetic fields in four field Be stars, HD 62367, μ Cen, o Aqr, and ε Tuc. The strongest longitudinal magnetic field, 〈B_z〉 = 117 ± 38 G, was detected in the Be star HD 62367. Among the Be stars studied with time series, one Be star, λ Eri, displays cyclic variability of the magnetic field with a period of 21.12 min. The binary star υ Sgr, in the initial rapid phase of mass exchange between the two components with strong emission lines in the visible spectrum, is a magnetic variable star, probably on a timescale of a few months. The maximum longitudinal magnetic field 〈B_z〉 = –102 ± 10 G at MJD 54333.018 was measured using hydrogen lines. The cluster NGC3766 seems to be extremely interesting, where we find evidence for the presence of a magnetic field in seven early B‐type stars out of the observed fourteen cluster members (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The atmospheres of helium-deficient Bp stars

Based on spectra taken with a 6-m telescope, we analyzed the abundances of chemical elements in the He-weak stars HD 21699 and HD 217833, estimated their surface magnetic fields (B_s = 4000 and 4500 G, respectively) from the magnetic intensification of spectral lines, and determined their microturbulences (V _t = 0.80 and 0.75 km s⁻¹, respectively). The low values of V _t show that the stellar atmospheres are stabilized by a magnetic field, which explains the presence of diffusion processes that lead to chemical anomalies. Helium is strongly underabundant, and its deficiency is −1.50 and −1.81 dex in HD 21699 and HD 217833, respectively. We used model atmospheres to determine the effective temperatures, T _eff = 16 000 and 15 450 K, and surface gravities, log g = 4.15 and 3.88, for the stars from the Hδ line, implying that they lie on the main sequence near the stars of luminosity class V.     

One-photon and two-photon annihilation of positronium in strong magnetic fields

In the presence of a strong magnetic field (such as those believed to be characteristic of neutron stars:B-10¹² Gauss) positronium may annihilate through the emission of a single photon, the magnetic field providing the photon momentum. We report on calculations of the one-photon and two-photon annihilation rates for the ground state of positronium, for magnetic fields in the range (1–44)×10¹² Gauss, and give, in the two-photon case, the minimum energy half-width of the emission line due to the momentum contributions from the magnetic field. We find that unless neutron stars have magnetic fields in excess of 10¹³ Gauss, it is unlikely that the one-photon process will be observable.Research supported in part by the National Research Council of Canada.     

Magnetic field models of CP stars HD18296, HD19832, HD22470, HD24712

We model the magnetic fields of four magnetic stars using published longitudinal (Be) field measurements. The structure of the magnetic field of each of the four stars is close to that of the central dipole. Unfortunately, the number of measurements for each star is insufficient for accurate finding of the field parameters, and therefore we find no dipole shift exceeding its error Δa ≈ 0.1, expressed as a fraction of the stellar radius. Our data support the opinion that the results of modeling depend most strongly on the adopted inclination of the star’s rotation axis i.     

Discovery of magnetic fields in three He variable Bp stars with He and Si spots

It is essential for the understanding of stellar structure models of high mass stars to explain why constant stars, nonpulsating chemically peculiar hot Bp stars and pulsating stars co‐exist in the slowly pulsating B stars and β Cephei instability strips. We have conducted a search for magnetic fields in the four Bp stars HD55522, HD105382, HD131120, and HD138769 which previously have been wrongly identified as slowly pulsating B stars. A recent study of these stars using the Doppler Imaging technique revealed that the elements He and Si are inhomogeneously distributed on the stellar surface, causing the periodic variability. Using FORS 1 in spectropolarimetric mode at the VLT, we have acquired circular polarisation spectra to test the presence of a magnetic field in these stars. A variable magnetic field is clearly detected in HD55522 and HD105382, but no evidence for the existence of a magnetic field was found in HD131120. The presence of a magnetic field in HD138769 is suggested by one measurement at 3σ level. We discuss the occurrence of magnetic B stars among the confirmed pulsating B stars and find strong magnetic fields of order kG and oscillations to be mutually exclusive. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zonal structure and meridional drift of large-scale solar magnetic fields

Digitized synoptic charts of photospheric magnetic fields were analyzed for the past 4 incomplete solar activity cycles (1969–2000). The zonal structure and cyclic evolution of large-scale solar magnetic fields were investigated using the calculated values of the radial B _r, |B _r|, meridional B _θ, |B _θ|, and azimuthal B _φ, |B _φ| components of the solar magnetic field averaged over a Carrington rotation (CR). The time–latitude diagrams of all 6 parameters and their correlation analysis clearly reveal a zonal structure and two types of the meridional poleward drift of magnetic fields with the characteristic times of travel from the equator to the poles equal to ∼16–18 and ∼2–3 years. A conclusion is made that we observe two different processes of reorganization of magnetic fields in the Sun that are related to generation of magnetic fields and their subsequent redistribution in the process of emergence from the field generation region to the solar surface. Redistribution is supposed to be caused by some external forces (presumably, by sub-surface plasma flows in the convection zone).     

Magnetic fields of active galactic nuclei and quasars from the SDSS catalog

We analyze the spectropolarimetric observations of 12 candidates for quasars from the spectroscopic database of the SDSS Catalog. The magnetic fields of these objects are estimated in the context of a theory that includes the Faraday rotation of the polarization plane on the mean free path of a photon in the outflow from an accretion disk. As a result, we have determined the column density in the outflow, N _H ∼ 6 × 10²³ cm⁻², and the radial, B ∼ 1 G, and toroidal, B ∼ 600 G, magnetic fields.     

Magnetic fields of chemically peculiar stars. II: Magnetic fields and rotation of stars with strong and weak anomalies in the continuum energy distribution

We make a comparative analysis of magnetic fields and rotation parameters of magnetic CP stars with strong and weak anomalies in the spectral energy distribution. Stars with strong depressions in the continuum at 5200 Å are shown to have significantly stronger fields (the mean longitudinal component of the fields of these stars is 〈B _e〉 = 1341 ± 98 G) compared to objects with weaker depressions (〈B _e〉 = 645 ± 58 G). Stars with stronger depressions are also found to occur more commonly among slow rotators. Their rotation periods are, on the average, about 10 days long, three times longer than these of stars with weak depressions (about three days). This fact is indicative of a decrease of the degree of anomality of the magnetic stars continuum spectrum with increasing rotational velocity. Yet another proof has been obtained suggesting that slow rotation is one of the crucial factors contributing to the development of the phenomenon of magnetic chemically peculiar stars.Magnetic CP stars with weak depressions at 5200 Å are intermediate objects between stars with strong depressions and normal A- and B-type stars both in terms of field strength and rotational velocity.     

Photometrically determined mean surface magnetic fields of Ap stars

The photometrically determined mean surface magnetic fields B_S need a revision. None of the stars for which B_S can be measured directly by Zeeman line splitting fulfils the relation between the photometric parameter Δ(V₁ – G) and the mean surface field B_S, which is used by NORTH , CRAMER and MAEDER to determine B_S for other B2 – A3 stars. The ratio B_eff^Max/B_S for stars, which define North's relation, shows unreasonable large values.     

Longitude variations of solar magnetic fields of different intensity in cycle 23 as inferred from the SOHO/MDI data

SOHO/MDI magnetograms have been used to analyze the longitude distribution of the squared solar magnetic field 〈B ²〉 in the activity cycle no. 23. The energy of the magnetic field (〈B ²〉) is shown to change with longitude. However, these variations hardly fit the concept of active longitudes. In the epochs of high solar activity, one can readily see a relationship between longitude variations of the medium-strong ((|B| > 50 G or |B| > 100 G) and relatively weak (|B| ≤ 50 G or |B| ≤ 100 G) fields at all latitudes. In other periods, this relationship is revealed mainly at the latitudes not higher than 30°. The background fields (|B| ≤ 25 G) also display longitude variations, which are, however, not related to those of the strong fields. This makes us think that the fields of solar activity are rather inclusions to the general field than the source of the latter.     

Intensity and Magnetic Field Distribution of Sunspots

We study the relationship between the brightness (I) and magnetic field (B) distributions of sunspots using 272 samples observed at the San Fernando Observatory and the National Solar Observatory, Kitt Peak, whose characteristics varied widely. We find that the I – B relationship has a quadratic form for the spots with magnetic field less than about 2000 G. The slope of the linear part of the I – B curve varies by about a factor of three for different types of spots. In general the slope increases as the spot approaches disk center. The I – B slope does not have a clear dependency on the spot size but the lower limit appears to increase as a function of the ratio of umbra and penumbra area. The I – B slope changes as a function of age of the sunspots. We discuss various sunspot models using these results.     

Magnetic Flux Imbalance of the Solar and Heliospheric Magnetic Fields

A comparative analysis of solar and heliospheric magnetic fields in terms of their cumulative sums reveals cyclic and long-term changes that appear as a magnetic flux imbalance and alternations of dominant magnetic polarities. The global magnetic flux imbalance of the Sun manifests itself in the solar mean magnetic field (SMMF) signal. The north – south asymmetry of solar activity and the quadrupole mode of the solar magnetic field contribute the most to the observed magnetic flux imbalance. The polarity asymmetry exhibits the Hale magnetic cycle in both the radial and azimuthal components of the interplanetary magnetic field (IMF). Analysis of the cumulative sums of the IMF components clearly reveals cyclic changes in the IMF geometry. The accumulated deviations in the IMF spiral angle from its nominal value also demonstrate long-term changes resulting from a slow increase of the solar wind speed over 1965 – 2006. A predominance of the positive IMF B _z with a significant linear trend in its cumulative signal is interpreted as a manifestation of the relic magnetic field of the Sun. Long-term changes in the IMF B _z are revealed. They demonstrate decadal changes owing to the 11/22-year solar cycle. Long-duration time intervals with a dominant negative B _z component were found in temporal patterns of the cumulative sum of the IMF B _z .     

Evolution of superhigh magnetic fields of magnetars

In this paper, we consider the effect of Landau levels on the decay of superhigh magnetic fields of magnetars. Applying ³ P ₂ anisotropic neutron superfluid theory yield a second-order differential equation for a superhigh magnetic field B and its evolutionary timescale t. The superhigh magnetic fields may evolve on timescales ∼(10⁶–10⁷) yrs for common magnetars. According to our model, the activity of a magnetar may originate from instability caused by the high electron Fermi energy.