Main-sequence magnetic CP stars III. Results of magnetic field measurements

We present the third part of the survey of magnetic parameters of main-sequence magnetic CP stars. We analyze the main definitions and terminology, basic data on the magnetic fields of CP stars (catalogs, the history of the stellar magnetism research, the main observational results obtained over 60 years of studies). We describe the modern views on the properties of magnetic CP stars, i.e. their geometric structure, distribution of field strengths, magnetic field and rotation, magnetic field and energy distribution anomalies, and the evolutionary status of magnetic CP stars. We conclude that the observational data mostly support the theory of the relict origin and evolution of magnetic fields of CP stars.     

Analysis of magnetic field measurements for T Tau

The presence of hot spots on the surface of T Tau attributable to mass accretion from the protoplanetary disk is shown to have virtually no effect on the accuracy of estimating the magnetic field strength for this star. By comparing the magnetic field strengths for T Tau at the photospheric level measured by various methods, we found that if the angle i at which we see T Tau does not exceed 10°, then the magnetic field of the star could be dipolar with the angle between the dipole axis and the rotation axis of the star ?85°. If, however, it later emerges that i > 10°, its magnetic field is essentially nondipolar and/or nonstationary.     

New results of magnetic field measurements for BP Tau

We present measurements of the longitudinal magnetic field component B _‖ of the young star BP Tau in the He I 5876 emission line formation region, i.e., in the accretion flow near the stellar surface. The values obtained (?1.7 kG and ?1.0 kG in 2000 and 2001, respectively) agree with the results of similar measurements by other authors. At the same time, we show that the previously obtained field strength at the magnetic pole, B _p, and the inclination of the magnetic axis to the rotation axis, β, are untrustworthy. In our opinion, based on the B _‖ measurements available to date, it is not possible to conclude whether the star’s magnetic field is a dipole one or has a more complex configuration and to solve the question of whether this field is stationary. However, we argue that at least in the He I 5876 line formation region, the star’s magnetic field is not stationary and can be restructured in a time of the order of several hours. Nonstationary small-scale magnetic fields of active regions on the stellar surface and/or magnetospheric field line reconnection due to the twisting of these field lines as the star rotates could be responsible for the short-term magnetic field variability. It seems highly likely that there are no strictly periodic variations in brightness and emission line profiles in BP Tau due to the irregular restructuring of the star’s magnetic field.     

High-precision magnetic field measurements of Ap and Bp stars

In this paper we describe a new approach for measuring the mean longitudinal magnetic field and net linear polarization of Ap and Bp stars. As was demonstrated by Wade et al., least-squares deconvolution (LSD; Donati et al.) provides a powerful technique for detecting weak Stokes V , Q and U Zeeman signatures in stellar spectral lines. These signatures have the potential to apply strong new constraints to models of stellar magnetic field structure. Here we point out two important uses of LSD Stokes profiles. First, they can provide very precise determinations of the mean longitudinal magnetic field. In particular, this method allows one frequently to obtain 1 σ error bars better than 50 G, and smaller than 20 G in some cases. This method is applicable to both broad- and sharp-lined stars, with both weak and strong magnetic fields, and effectively redefines the quality standard of longitudinal field determinations. Secondly, LSD profiles can in some cases provide a measure of the net linear polarization, a quantity analogous to the broad-band linear polarization recently used to derive detailed magnetic field models for a few stars (e.g. Leroy et al.). In this paper we report new high-precision measurements of the longitudinal fields of 14 magnetic Ap/Bp stars, as well as net linear polarization measurements for four of these stars, derived from LSD profiles.     

Fossil magnetic field of accretion disks of young stars

We elaborate the model of accretion disks of young stars with the fossil large-scale magnetic field in the frame of Shakura and Sunyaev approximation. Equations of the MHD model include Shakura and Sunyaev equations, induction equation and equations of ionization balance. Magnetic field is determined taking into account ohmic diffusion, magnetic ambipolar diffusion and buoyancy. Ionization fraction is calculated considering ionization by cosmic rays and X-rays, thermal ionization, radiative recombinations and recombinations on the dust grains. Analytical solution and numerical investigations show that the magnetic field is coupled to the gas in the case of radiative recombinations. Magnetic field is quasi-azimuthal close to accretion disk inner boundary and quasi-radial in the outer regions. Magnetic field is quasi-poloidal in the dusty “dead” zones with low ionization degree, where ohmic diffusion is efficient. Magnetic ambipolar diffusion reduces vertical magnetic field in 10 times comparing to the frozen-in field in this region. Magnetic field is quasi-azimuthal close to the outer boundary of accretion disks for standard ionization rates and dust grain size a _d=0.1 μm. In the case of large dust grains (a _d>0.1 μm) or enhanced ionization rates, the magnetic field is quasi-radial in the outer regions. It is shown that the inner boundary of dusty “dead” zone is placed at r=(0.1–0.6) AU for accretion disks of stars with M=(0.5–2)?M _⊙. Outer boundary of “dead” zone is placed at r=(3–21) AU and it is determined by magnetic ambipolar diffusion. Mass of solid material in the “dead” zone is more than 3?M _⊕ for stars with M≥1?M _⊙.     

Analysis of HST ultraviolet spectra for T Tauri stars: DR Tau

We analyze the spectra of DR Tau in the wavelength range 1200 to 3100 Å obtained with the GHRS and STIS spectrographs from the Hubble Space Telescope. The profiles for the C IV 1550 and He II 1640 emission lines and for the absorption features of some lines indicate that matter falls to the star at a velocity ～300 km s^?1. At the same time, absorption features were detected in the blue wings of the N I, Mg I, Fe II, Mg II, C II, and Si II lines, suggesting mass outflow at a velocity up to 400 km s^?1. The C II, Si II, and Al II intercombination lines exhibit symmetric profiles whose peaks have the same radial velocity as the star. This is also true for the emission features of the Fe II and H₂ lines. We believe that stellar activity is attributable to disk accretion of circumstellar matter, with matter reaching the star mainly through the disk and the boundary layer. At the time of observations, the accretion luminosity was L_ac ? 2L_⊙ at an accretion rate ?10^?7M_⊙ yr^?1. Concurrently, a small (<10%) fraction of matter falls to the star along magnetospheric magnetic field lines from a height ～R_*. Within a region of size ?3.5R_*, the disk atmosphere has a thickness ～0.1R_* and a temperature ?1.5 × 10⁴ K. We assume that disk rotation in this region significantly differs from Keplerian rotation. The molecular hydrogen lines are formed in the disk at a distance <1.4 AU from the star. Accretion is accompanied by mass outflow from the accretion-disk surface. In a region of size <10R_*, the wind gas has a temperature ～7000 K, but at the same time, almost all iron is singly ionized by H I L _α photons from inner disk regions. Where the warm-wind velocity reaches ?400 km s^?1, the gas moves at an angle of no less than 30° to the disk plane. We found no evidence of regions with a temperature above 10⁴ K in the wind and leave open the question of whether there is outflow in the H₂ line formation region. According to our estimate, the star has the following set of parameters: M_* ? 0.9M_⊙, R_* ? 1.8R_⊙, L_* ? 0.9L_⊙, and \(A_V \simeq 0\mathop .\limits^m 9\). The inclination i of the disk axis to the line of sight cannot be very small; however, i≤60°.     

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)     

Soft X-ray and magnetic field of late-type stars

We used four coronal models to fit ROSAT data of a sample of late-type stars. The merits and demerits of each was discussed. We found a good correlation between the cornoal temperature so derived and the magnetic field strength. This indicates magnetic heating of the corona and provides a possible, indirect means of estimating the photospheric magnetic field.     

Possible variability of the magnetic field of T Tau

Using the Main Stellar Spectrograph of the 6-m Special Astrophysical Observatory telescope equipped with a polametric analyzer, we measured the longitudinal magnetic field component B_∥ for the T Tauri stars T Tau and AS 507 on January 16 and 18 and February 15, 2003. For both stars, we determined only the upper limits on B_∥ from photospheric lines: +15±30 G for T Tau and ?70±90 G for AS 507. The magnetic field of AS 507 was not measured previously, while B_∥ for T Tau is lower than its values that we obtained in 1996 and 2002 (B_∥?150±50G), suggesting that the longitudinal magnetic field component in the photosphere of T Tau is variable. We also measured the longitudinal magnetic field component for T Tau in the formation region of the He I 5876 Å emission line. We found B_∥ in this region to be ?+650, ?+350, and ?+1100 G on January 16, 18, and February 15, 2003, respectively. Our observations on January 18 and February 15 correspond to virtually the same phase of the star's rotation period, but the profiles of the He I 5876 Å line differ markedly on these two nights. Therefore, we believe that the threefold difference between the B_∥ values on these nights does not result from observational errors. We discuss the possible causes of the B_∥ variability in the photosphere and the magnetosphere of T Tau.     

Features of multi-dipole magnetic field structures in CP stars

Ten of the sixty investigated magnetic stars have two- or three-dipole structures. From the viewpoint of the relic hypothesis a wide variety of magnetic field structures and strengths allows to assume that in the initial phases of formation of magnetic stars, their fields were even more entangled and heterogeneous than now. This may be due to the complex structure of protostellar clouds, the consequence of non-stationary processes during the collapse, and, probably, the result of subsequent accretion interactions. The expected variation of the large-scale structure with age is lost at the background of a wide variety of structures, depending on the initial conditions. Complex structures occur both in the stars at ZAMS, and in the stars leaving the Main Sequence. As a result of quadratic dependence of the magnetic structure lifetime on their characteristic dimensions, large-scale configurations can exist for times comparable to the lifetime of stellar magnetic field, i.e. τ ≥ 10⁹ yrs. One of the common properties of multi-dipole stars is that the centers of the dipoles are predominantly located in the equatorial plane of rotation. In the majority of studied objects magnetic dipoles (i.e. the regions with the maximum field) are shifted from the center of the star by the distance greater than the radius of the convective core (approximately 0.1R*). This may indicate that the poloidal field is not compatible with the convective core and is not generated therein. Large distances between the monopoles, comparable to the radii of the stars are typical. This may be a sign indicating that inside the stars the field structure is slightly different from the dipole, what implies that the dipole is not a mathematical point, but rather some highly magnetized volume inside the star, comparable to a magnetized rod.     

Specificities of magnetic field structures in chemically peculiar stars

We continue our program of the study of large-scale structures of magnetic fields in chemically peculiar stars. In this paper we analyze eight stars, out of which three stars have the structure of a central dipole, three—the structure of a dipole shifted along the axis, and two—of a dipole shifted across the axis. High-precision measurements (with σ = 50 and 80 G) are available for two stars (HD62140 and HD71866, respectively). The model phase dependences agree with the measurements within the errors. This result shows that the hypothesis about the dipole structure of the magnetic fields of CP stars is well founded.     

Evolution of the multipolar magnetic field in isolated neutron stars

The evolution of the multipolar structure of the magnetic field of isolated neutron stars is studied assuming the currents to be confined to the crust. We find that, except for multipoles of very high order ( l ≳25), the evolution is similar to that of a dipole. Therefore no significant evolution is expected in the pulse shape of isolated radio pulsars because of the evolution of the multipole structure of the magnetic field.     

Diamagnetic screening of the magnetic field in accreting neutron stars

A possible mechanism for screening of the surface magnetic field of an accreting neutron star, by the accreted material, is investigated. We model the material flow in the surface layers of the star by an assumed two-dimensional velocity field satisfying all the physical requirements. Using this model velocity we find that, in the absence of magnetic buoyancy, the surface field is screened (i.e. there is submergence of the field by advection) within the time-scale of material flow of the top layers. On the other hand, if magnetic buoyancy is present, the screening happens over a time-scale that is characteristic of the slower flow of the deeper (and hence, denser) layers. For accreting neutron stars, this longer time-scale turns out to be about 10⁵ yr, which is of a similar order of magnitude to the accretion time-scale of most massive X-ray binaries.     

Enigmas in measurements of solar magnetic field

The mean magnetic field (MMF) of the photosphere of the Sun as a star was measured in 2001?C2010 at the Crimean Astrophysical Observatory using two Fe I absorption lines with ?? = 524.7 nm and ?? = 525.0 nm. The regression coefficient b for 1054 pairs of daily values measured simultaneously on both lines equals 0.82 (a correlation coefficient is 0.94; magnetic field strengths determined by the line with ?? = 525.0 nm are lower than those for the line with ?? = 524.7 nm). However, the b value varied significantly along with phases of the 11-year cycle from 0.88 in 2003 to 0.49 in 2009. It is difficult to ascribe these variations to purely instrumental or solar causes. Moreover, the semiannual value of b decreased with the decrease in the absolute strength of the MMF, which contradicts the model of thin magnetic flux ropes of the photosphere. Similar behavior of b was also observed in the comparison of MMF measured at the Crimean Astrophysical Observatory and Stanford by the line with ?? = 525.0 nm. The inconsistency of the results obtained by these two iron lines on different instruments has been noted. It has been concluded that the variance in and odd behavior of b are predetermined not only by the instrument and the Sun (by the so-called fine structure of the photosphere field), but also by the act of measuring. When recording solar (and stellar) magnetic fields and modeling atmospheric processes, quantum effects have to be taken into account, such as nonlocality, indistinguishability, and the entanglement of photons, as well as that a photon only acquires its properties at the exact moment of its detection. The best approximation to reality can be achieved by averaging the MMF measurements carried out with different magnetographs and in different spectral lines.     

An investigation of planetary nebulae accompanying PG 1159 central stars,based on Gaia DR2 measurements

This article discusses the physical and kinematical characteristics of planetary nebulae accompanying PG 1159 central stars. The study is based on the parallax and proper motion measurements recently offered by the Gaia space mission. Two approaches were used to investigate the kinematical properties of the sample. The results revealed that most of the studied nebulae arise from progenitor stars in the mass range 0.9-1.75 M⊙. Furthermore, they tend to live within the Galactic thick disk and move with an average peculiar velocity of 61.7 ± 19.2 km s~(-1) at a mean vertical height of 469 ± 79 pc. The locations of the PG 1159 stars on the H-R diagram indicate that they have an average final stellar mass and evolutionary age of 0.58 ± 0.08 M_⊙and 25.5 ± 5.3×10~3 yr, respectively. We found a good agreement between the mean evolutionary age of the PG 1159 stars and the mean dynamical age of their companion planetary nebulae(28.0 ± 6.4×10~3 yr).     

Generation of a toroidal magnetic field in rotating neutron stars

The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).