Mean Field Modulus Research Articles

Statistical relations between spectropolarimetric observables and the polar strength of the stellar dipolar magnetic field

Global magnetic fields of early-type stars are commonly characterised by the mean longitudinal magnetic field 〈Bz〉 and the mean field modulus 〈B〉, derived from the circular polarisation and intensity spectra, respectively. Observational studies often report a root mean square (rms) of 〈Bz〉 and an average value of 〈B〉. In this work, I used numerical simulations to establish statistical relationships between these cumulative magnetic observables and the polar strength, Bd, of a dipolar magnetic field. I show that in the limit of many measurements randomly distributed in rotational phase, 〈Bz〉rms = 0.179−0.043+0.031 Bd and 〈B〉avg = 0.691−0.023+0.020 Bd. The same values can be recovered with only three measurements, provided that the observations are distributed uniformly in the rotational phase. These conversion factors are suitable for ensemble analyses of large stellar samples, where each target is covered by a small number of magnetic measurements.

Testing pulsation diagnostics in the rapidly oscillating magnetic Ap star γ Equ using near-infrared CRIRES+ observations

Context. Pulsations of rapidly oscillating Ap stars and their interaction with the stellar magnetic field have not been studied in the near-infrared (near-IR) region despite the benefits these observations offer compared to visual wavelengths. The main advantage of the near-IR is the quadratic dependence of the Zeeman effect on the wavelength, as opposed to the linear dependence of the Doppler effect. Aims. To test pulsation diagnostics of roAp stars in the near-IR, we aim to investigate the pulsation behaviour of one of the brightest magnetic roAp stars, γ Equ, which possesses a strong surface magnetic field of the order of several kilogauss and exhibits magnetically split spectral lines in its spectra. Methods. Two magnetically split spectral lines belonging to different elements, the triplet Fe I at 1563.63 nm and the pseudo-doublet Ce III at 1629.2 nm, were recorded with CRIRES+ over about one hour in the H band with the aim of understanding the character of the line profile variability and the pulsation behaviour of the magnetic field modulus. Results. The profile shapes of both studied magnetically split spectral lines vary in a rather complex manner probably due to a significant decrease in the strength of the longitudinal field component and an increase in the strength of the transverse field components over the last decade. A mean magnetic field modulus of 3.9 kG was determined for the Zeeman triplet Fe I at 1563.63 nm, whereas for the pseudo-doublet Ce III at 1629.2 nm we observe a much lower value of only about 2.9 kG. For comparison, a mean field modulus of 3.4kG was determined using the Zeeman doublet Fe II at 6249.25 in optical PEPSI spectra recorded just about two weeks before the CRIRES+ observations. Different effects that may lead to the differences in the field modulus values are discussed. Our measurements of the mean magnetic field modulus using the line profiles recorded in different pulsational phase bins suggest a field modulus variability of 32 G for the Zeeman triplet Fe I at 1563.63 nm and 102 G for the pseudo-doublet Ce III at 1629.2 nm.

Magnetic field geometry and magnetospheric environment of the strongly magnetic Of?p star NGC 1624-2

ABSTRACT NGC 1624-2 is an O7f?p star with a reported probable polar magnetic field strength ≥20 kG, which is the strongest magnetic field ever measured in an O-type star. We study the variability of the mean longitudinal magnetic field 〈Bz〉 and the mean field modulus 〈B〉 to obtain constraints on its field geometry. Only one magnetic pole is observable over the rotation cycle. The approximately sinusoidal variation of 〈Bz〉 and the ratio of the values of the extrema of 〈B〉 indicate that there is an important component of the field that is dipolar. The 〈Bz〉 values measured over the rotation cycle are in the range from −0.2 to 4.5 kG, whereas the values for 〈B〉 vary between 9 and 12 kG. The 〈Bz〉 values obtained using the O iii λ7455 emission line are in the range from 0.4 to 2.3 kG and show a variability pattern similar to that detected for the absorption lines. The fact that the phase of the 〈Bz〉 minimum coincides with the phase of the 〈B〉 maximum, indicates that the field structure must significantly depart from a centred dipole. Further, we discuss the nature of the observed variable Stokes V profiles corresponding to a longitudinal field of negative polarity detected in the emission He i lines and present the first magnetohydrodynamical numerical simulations of the gas flow in the magnetosphere of this star.

The Magnetic Field of the Active Planet-hosting M Dwarf AU Mic

Abstract AU Mic is a young, very active M dwarf star with a debris disk and at least one transiting Neptune-size planet. Here we present a detailed analysis of the magnetic field of AU Mic based on previously unpublished high-resolution optical and near-infrared spectropolarimetric observations. We report a systematic detection of circular and linear polarization signatures in the stellar photospheric lines. Tentative Zeeman Doppler imaging modeling of the former data suggests a nonaxisymmetric global field with a surface-averaged strength of about 90 G. At the same time, linear polarization observations indicate the presence of a much stronger ≈2 kG axisymmetric dipolar field, which contributes no circular polarization signal due to the equator-on orientation of AU Mic. A separate Zeeman broadening and intensification analysis allowed us to determine a mean field modulus of 2.3 and 2.1 kG from the Y- and K-band atomic lines, respectively. These magnetic field measurements are essential for understanding environmental conditions within the AU Mic planetary system.

A new weak-field magnetic DA white dwarf in the local 20 pc volume

We report the discovery of a new magnetic DA white dwarf (WD), WD 0011 − 721, which is located within the very important 20 pc volume-limited sample of the closest WDs to the Sun. This star has a mean field modulus ⟨|B|⟩ of 343 kG, and from the polarisation signal we deduce a line-of-sight field component of 75 kG. The magnetic field is sufficiently weak to have escaped detection in classification spectra. We then present a preliminary exploration of the data concerning the frequency of such fields among WDs with hydrogen-rich atmospheres (DA stars). We find that 20 ± 5% of the DA WDs in this volume have magnetic fields, mostly weaker than 1 MG. Unlike the slow field decay found among the magnetic Bp stars of the upper main sequence, the WDs in this sample show no evidence of magnetic field or flux changes over several Gyr.

Monitoring and modelling of white dwarfs with extremely weak magnetic fields

Magnetic fields are detected in a few percent of white dwarfs. The number of such magnetic white dwarfs known is now some hundreds. Fields range in strength from a few kG to several hundred MG. Almost all the known magnetic white dwarfs have a mean field modulus >= 1 MG. We are trying to fill a major gap in observational knowledge at the low field limit (<= 200 kG) using circular spectro-polarimetry. In this paper we report the discovery and monitoring of strong, periodic magnetic variability in two previously discovered "super-weak field" magnetic white dwarfs, WD2047+372 and WD2359-434. WD2047+372 has a mean longitudinal field that reverses between about -12 and +15 kG, with a period of 0.243 d, while its mean field modulus appears nearly constant at 60 kG. The observations can be intepreted in terms of a dipolar field tilted with respect to the stellar rotation axis. WD2359-434 always shows a weak positive longitudinal field with values between about 0 and +12 kG, varying only weakly with stellar rotation, while the mean field modulus varies between about 50 and 100 kG. The rotation period is found to be 0.112 d using the variable shape of the Halpha line core, consistent with available photometry. The field of this star appears to be much more complex than a dipole, and is probably not axisymmetric. Available photometry shows that WD2359-434 is a light variable with an amplitude of only 0.005 mag, our own photometry shows that if WD2047+372 is photometrically variable, the amplitude is below about 0.01 mag. These are the first models for magnetic white dwarfs with fields below about 100 kG based on magnetic measurements through the full stellar rotation. They reveal two very different magnetic surface configurations, and that, contrary to simple ohmic decay theory, WD2359-434 has a much more complex surface field than the much younger WD2047+372.

Discovery of an extremely weak magnetic field in the white dwarf LTT 16093 = WD 2047+372

Magnetic fields have been detected in several hundred white dwarfs, with strengths ranging from a few kG to several hundred MG. Only a few of the known fields have a mean magnetic field modulus below about 1 MG. We are searching for new examples of magnetic white dwarfs with very weak fields, and trying to model the few known examples. Our search is intended to be sensitive enough to detect fields at the few kG level. We have been surveying bright white dwarfs for very weak fields using spectropolarimeters at the Canada-France-Hawaii telescope, the William Herschel telescope, the European Southern Observatory, and the Russian Special Astrophysical Observatory. We discuss in some detail tests of the WHT spectropolarimeter ISIS using the known magnetic strong-field Ap star HD 215441 (Babcock's star) and the long-period Ap star HD 201601 (gamma Equ). We report the discovery of a field with a mean field modulus of about 57 kG in the white dwarf LTT 16093 = WD2047+372. The field is clearly detected through the Zeeman splitting of Halpha seen in two separate circularly polarised spectra from two different spectropolarimeters. Zeeman circular polarisation is also detected, but only barely above the 3 sigma level. The discovery of this field is significant because it is the third weakest field ever unambiguously discovered in a white dwarf, while still being large enough that we should be able to model the field structure in some detail with future observations.

Linear theory and violent relaxation in long-range systems: a test case

In this paper, several aspects of the dynamics of a toy model for long-range Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian mean field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, N → ∞, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports the mean field modulus in the vicinity of its equilibrium value within some linear e-folding times.

Observing and Modelling Stellar Magnetic Fields

In this chapter, we examine the question of how spectropo- larimetric observations of magnetic stars may be modelled, and how modelling techniques may be used to extract much detailed informa- tion about the stellar magnetic field and other characteristics of the magnetized stellar atmosphere. In the preceding chapter, we discussed how the energy levels of atoms are split by a magnetic field, and how this leads in turn to splitting of spectral lines in to multiple components, an effect called the Zeeman or Paschen-Back effect depending on the field strength. We saw that the polarisation characteristics of these components provide valuable tools for detection and measurement of stellar magnetic fields, and that polarisation measurements allow one to obtain, in a straight-forward way, an estimate of the mean line-of-sight field component averaged over the visible hemisphere (the mean longitudinal field h Bzi ). We also saw that, if the field is large enough and ve sin i small enough, observation of splitting of spectral lines into discrete components makes it possible to estimate the mean field modulus h Bi , again averaged over the visible hemisphere. Finally, we looked at some simple multipole models of stellar field structure that can reproduce simple data-sets such as observed values of h Bzi , or of h Bzi and h Bi , over a stellar rotation, and how these models lead to the fundamental conceptual model known as the oblique rotator. Determination of mean field values directly from the spectra (in the same way as radial velocities and projected rotation velocities are derived), and the modelling of such integral or moment data with simple geometric field structures, provide a useful and valuable source of information about global characteristics of the stellar field. However, such models are based on data-sets that are often

The Peculiar Magnetic Field Morphology of the White Dwarf WD 1953−011: Evidence for a Large‐Scale Magnetic Flux Tube?

We present and interpret new spectropolarimetric observations of the magnetic white dwarf WD 1953–011. Circular polarization and intensity spectra of the Hα spectral line demonstrate the presence of two-component magnetic field in the photosphere of this star. The geometry consists of a weak, large-scale component, and a strong, localized component. Analyzing the rotationally modulated low-field component, we establish a rotation period -->Prot = 1.4480 ± 0.0001 days. Modeling the measured magnetic observables, we find that the low-field component can be described by the superposition of a dipole and quadrupole. According to the best-fit model, the inclination of the stellar rotation axis with respect to the line of sight is -->i ≈ 20°, and the angle between the rotation axis and the dipolar axis is -->β ≈ 10°. The dipole strength at the pole is about 180 kG, and the quadrupolar strength is about 230 kG. These data suggest a fossil origin of the low-field component. In contrast, the strong-field component exhibits a peculiar, localized structure (magnetic spot) that confirms the conclusions of Maxted and coworkers. The mean field modulus of the spot ( -->|Bspot| = 520 ± 7 kG) together with its variable longitudinal magnetic field having a maximum of about +400 kG make it difficult to describe it naturally as a high-order component of the star's global poloidal field. Instead, we suggest that the observed strong-field region has a geometry similar to a magnetic flux tube.

Atmospheric parameters and chemical composition of the ultra-cool roAp star HD 213637

A high-resolution spectrum obtained with the UVES instrument at the ESO VLT is used to determine atmospheric parameters and chemical composition of the roAp star HD 213637. Resolved Zeeman split lines are discovered in the spectrum of this star, indicating a mean field modulus of 5.5 kG. Effective temperature, K determined from the profiles of the hydrogen Hα and Hβ lines, makes HD 213637 one of the coolest (ro)Ap stars known, suggesting that the class of magnetic chemically peculiar stars extends to lower effective temperatures than previously thought. Furthermore, the low temperature of HD 213637 poses serious challenge to some excitation mechanisms suggested as an explanation of the roAp phenomenon. This peculiar star is also unique in its evolutionary stage: it is either located near the very end of its main sequence life or has already ascended the giant branch. Abundance analysis reveals that HD 213637 is iron-deficient and has abundance pattern typical of the cool pulsating Ap stars. An inconsistency between abundances derived from the weak and strong spectral lines and the lines of different ions provide a clear evidence for prominent vertical abundance stratification of many chemical species, notably Na, Mg, Ca, Fe, Pr, Nd, Tb, and Er.

Discovery of a 14.5 kG magnetic field in the NGC 2516 star HD 66318

We have been searching for magnetic Ap stars in open clusters, in order to clarify the time evolution of magnetic fields in middle main sequence stars from the ZAMS to the TAMS. We have discovered that the star HD 66318 in the open cluster NGC 2516 has an extraordinarily large magnetic field: the measured mean longitudinal component B 1 4.5 kG, and the mean field modulus B s 14.5 kG. This star thus has one of the largest fields so far discovered in a non-degenerate star, and the largest field known in a current Ap star cluster member. We estimate that HD 66318 has completed about 16 ′ 5% of its main sequence life. It thus appears to contradict the hypothesis of Hubrig et al. that magnetic fields are only found in stars that have completed at least 30% of their main sequence lifetimes. There is no indication that the spectrum or brightness of the star is variable, and the spectral lines are very sharp. The star probably has a very long rotation period (years). We have modelled some parts of the observed spectrum, assuming that the chemical composition is uniform both horizontally and vertically, and using a simple multipolar expansion for the field stricture; although our model does not reproduce exactly the observed spectrum, it is clear that the atmospheric chemical composition of the star is very peculiar, with Ti, Cr and Fe overabundant by between 1.5 and 2.5 dex. Both La II and III are apparently about 4 dex overabundant. In contrast, evidence for the presence of other rare earths is difficult to find in the spectrum. It appears that Ce III, Pr III, Nd II and III, and Eu II are detected with inferred overabundances ranging between 1.5 and 5 dex, but for most of these elements, the abundance of the non-detected ionization state is significantly lower than that inferred for the detected state. HD 66318 thus seems to exhibit strong discrepancies between abundances deduced for different ionization states of rare earths, a phenomenon so far found only in somewhat cooler stars. Even within one ionization state it has not been found possible to fit most observed lines with a single value of abundance. For example, when we fit medium strength lines of Fe II, the calculated strong lines of this ion are deeper than observed, and the calculated weak lines are less deep than observed. This situation is probably due to strong vertical abundance stratification of most of the elements studied. Finally, HD 66318 also shows a new form of core-wing anomaly in Ha in which the observed line profile falls below the computed one in the core. These characteristics clearly suggest that the atmospheric structure of HD 66318 is not closely similar to that of a normal main sequence A star of similar parameters.

The mean magnetic field modulus of Ap stars

We present new measurements of the mean magnetic field modulus of a sample of Ap stars with spectral lines resolved into magnetically split components. We report the discovery of 16 new stars having this property. This brings the total number of such stars known to 42. We have performed more than 750 measurements of the mean field modulus of 40 of these 42 stars, between May 1988 and August 1995. The best of them have an estimated accuracy of . The availability of such a large number of measurements allows us to discuss for the first time the distribution of the field modulus intensities. A most intriguing result is the apparent existence of a sharp cutoff at the low end of this distribution, since no star with a field modulus (averaged over the rotation period) smaller than 2.8 kG has been found in this study. For more than one third of the studied stars, enough field determinations well distributed throughout the stellar rotation cycle have been achieved to allow us to characterize at least to some extent the variations of the field modulus. These variations are often significantly anharmonic, and it is not unusual for their extrema not to coincide in phase with the extrema of the longitudinal field (for the few stars for which enough data exist about the latter). This, together with considerations on the distribution of the relative amplitude of variation of the studied stars, supports the recently emerging evidence for markedly non-dipolar geometry and fine structure of the magnetic fields of most Ap stars. New or improved determinations of the rotation periods of 9 Ap stars have been achieved from the analysis of the variations of their mean magnetic field modulus. Tentative values of the period have been derived for 5 additional stars, and lower limits have been established for 10 stars. The shortest definite rotation period of an Ap star with magnetically resolved lines is 34, while those stars that rotate slowest appear to have periods in excess of 70 or 75 years. As a result of this study, the number of known Ap stars with rotation periods longer than 30 days is almost doubled. We briefly rediscuss the slow-rotation tail of the period distribution of Ap stars. This study also yielded the discovery of radial velocity variations in 8 stars. There seems to be a deficiency of binaries with short orbital periods among Ap stars with magnetically resolved lines.

Magnetic Fields: Observations and Topology

AbstractTo understand the complex physical processes revealed by the wide variety of surface chemical abundances and the inhomogeneous distributions of various elements over the surfaces of magnetic Ap and Bp stars, it is important to be able to describe the surface magnetic field structure. For most magnetic stars, the available observations are far from sufficient to define the surface magnetic structure even with low resolution, but more extensive and constraining observations are gradually becoming available for a small set of stars. This paper discusses the extent to which the surface field structure can be defined for stars for which only the usual measurements (essentially the variation of the mean longitudinal field strength Bɩ with rotational phase) are available, and how further information (variation of mean field modulus Bs with phase, line profile observations, and circular and linear spectropolarimetry of absorption lines or broad-band radiation) can be used to obtain a much more detailed picture of the magnetic field structure.