Line formation in microturbulent magnetic fields

The formation of Zeeman lines in Gaussian microturbulent magnetic fields is considered assuming LTE. General formulae are derived for the local mean values of the transfer matrix elements. The cases of one-dimensional (longitudinal), isotropic, and two-dimensional (transversal) magnetic microturbulence are studied in some detail. Asymptotic formulae are given for small mean as well as for small microturbulent magnetic fields. Characteristic effects of magnetic microturbulence on the transfer coefficients are: (i) the broadening of the frequency contours, although only for the case of longitudinal Zeeman effect and longitudinal magnetic microturbulence this effect can be described analogous to Doppler broadening, (ii) the appearance of a pseudo-Zeeman structure for nonlongitudinal magnetic microturbulence, (iii) the reduction of maximal values of circular polarization, and (iv) the appearance of characteristic linear polarization effects due to the anisotropy of the magnetic microturbulence.Line contours and polarization of Zeeman triplets are computed for Milne-Edddington atmospheres. It is shown that magnetic intensification due to microturbulent magnetic fields may be much more efficient than that due to regular fields. The gravity center of a Zeeman line observed in circularly polarized light remains a reasonable measure of the line of sight component of the mean magnetic field for a line strength47-1. For saturated lines, the gravity center distance depends significantly on the magnetic microturbulence and its anisotropy. The influence of magnetic microturbulence on the ratio of longitudinal field magnetographic signals shows that unique conclusions about the magnetic microstructure can be drawn from the line ratio measurement only in combination with further spectroscopic data or physical reasoning.     

Hydrogen and helium spectra in large magnetic fields

The energy levels and wave functions of hydrogen and helium atoms in the presence of large (10⁷G) magnetic fields are found by assuming that the eigenvalues and eigenvectors may be approximated by those of a truncated Hamiltonian matrix. In these atoms, fields of this size produce, in addition to the usual Paschen-Back effect, a quadratic Zeeman effect. This contributes an upward shift to the energy of all levels, which at sufficiently high fields dominates the Paschen-Back splitting.The behavior of a number of eigenvalues and wave functions as a function of magnetic field is presented. The effects of the field on the wavelengths and strengths of the components of H and the helium lines 4471, 4026 and 4120 as well as the forbidden 4025 are examined. In hydrogen the lines are split into components attributed to the now nondegenerate transitionsnlm _lnlm_l. In helium forbidden lines are excited, which may develop strengths larger than those of the allowed lines.     

Zeeman-Doppler imaging of solar-type stars: Multi line technique

In this work, a multi-line spectropolarimetric detection using an Echelle spectrograph is described. The polarization of Zeeman effect is detected by the use of more than 200 lines observed in the solar type star, HR1099. Using the statistics analysis in a sample of 200 lines, we found on the average a polarization signal of about 3 × 10^–4.     

The Zeeman broadening of high n solar recombination lines

The Zeeman broadening of high n lines is derived. While in areas of the quiet Sun with field strengths of 1 G the upper boundary of the observable frequency region of recombination lines is defined by electron impact broadening, in active regions with field strengths 25 G the Zeeman broadening will shift this boundary to higher frequencies. The frequency region most favourable for observations is derived and the corresponding Doppler, electron impact and Zeeman broadening are discussed. The strengths of the recombination lines obtained in earlier calculations is reduced when one considers besides the Doppler broadening the electron impact and Zeeman broadening also. The frequency region favourable for observations is compared with the atmospheric transparency of the microwave region; it is found that observations require at least high altitude stations or space-based platforms. Details of using the Zeeman broadening of high n recombination lines for mapping (coronal) magnetic fields are given.     

Magnetic fields and Fe I line profiles in the major solar flare on October 28, 2003

Strong (“kilogauss”) small-scale magnetic fields were detected outside a sunspot near the seismic source of the major X17.2/4B solar flare on October 28, 2003. Echelle Zeeman spectrograms of the flare were obtained with the horizontal solar telescope at the Astronomical Observatory of the Taras Shevchenko Kiev National University. Analysis of the Stokes I ± V profiles for the Fe I 5232.9, 5247.1, 5250.2, and 5397.1 Å lines has revealed a number of characteristic spectral features. These are indicative of both background fields with a strength of ≈300 G and small-scale fields with a strength of 1300–3100 G. Evidence for the presence of another small-scale field component of opposite polarity with a strength of 8–10 kG has been found. A redshift (downflow) with a velocity of 1 km s^?1 was observed in the latter component.     

Structure and physics of solar faculae

The OSO-8 satellite enabled us to study various characteristics of the profiles of Si ii, Si iv, C iv, and O vi lines above active areas of the Sun, as well as above quiet areas, and to derive some physical properties of the transition region between chromosphere and corona (CCT): (i) The study of the lines shows a general tendency for the microvelocity fields on the average to be nearly constant for the heights corresponding to T > 10⁵ K; however they seem to slightly increase with height in quiet areas, and decrease in active areas. (ii) A multicomponent model of the CCT is however quite necessary, and its geometry is far from being a set of plane-parallel columns. It is similar to an association of moving knots within the non-moving principal component of the matter. (iii) The proportion of mass, in the knots relative to that in the non-moving component, is several times larger in active regions than in quiet regions. (iv) In the knots, the non-thermal microvelocity fields are smaller in active regions and seem to decrease for T increasing above 10⁵ K, contrary to what happens in the steady principal component. Of course, we consider that microturbulence and Doppler shift are two aspects of the same distribution of velocity.     

Eruptive prominence and associated CME observed with SUMER, CDS and LASCO (SOHO)

Observations of an eruptive prominence were obtained on 1 May 1996, with the SUMER and CDS instruments aboard SOHO during the preparatory phase of the Joint Observing Programme JOP12. A coronal mass ejection observed with LASCO is associated temporally and spatially with this prominence. The main objective of JOP12 is to study the dynamics of prominences and the prominence–corona interface. By analysing the spectra of Oiv and Siiv lines observed with SUMER and the spectra of 15 lines with CDS, Doppler shifts, temperatures and electron densities (ratio of Oiv 1401 to 1399Å) were derived in different structures of the prominence. The eruptive part of the prominence consists of a bubble (plasmoid) of material already at transition region temperatures with red shifts up to 100 km s^-1 and an electron density of the order of 10¹⁰cm^-3. The whole prominence was very active. It developed both a large helical loop and several smaller loops consisting of twisted threads or multiple ropes. These may be studied in the SUMER movie (movie 2). The profiles of the SUMER lines show a large dispersion of velocities (±50 km s^-1) and the ratio of the Oiv lines indicates a large dispersion in electron density (3 x 10⁹cm^-3 to 3x 10¹¹cm^-3). The CME observed by LASCO left the corona some tens of minutes before the prominence erupted. This is evidence that the prominence eruptions are probably the result of the removal of the restraining coronal magnetic fields which are in part responsible for the original stability of the prominence.     

Polarization of the atmosphere as a foreground for cosmic microwave background polarization experiments

We quantify the level of polarization of the atmosphere due to Zeeman splitting of oxygen in the Earth’s magnetic field and compare it to the level of polarization expected from the polarization of the cosmic microwave background radiation. The analysis focuses on the effect at mid-latitudes and at large angular scales. We find that from stratospheric balloon borne platforms and for observations near 100 GHz the atmospheric linear and circular polarized intensities are about 10⁻¹² and 100 × 10⁻⁹ K, respectively, making the atmosphere a negligible source of foreground. From the ground the linear and circular polarized intensities are about 10⁻⁹ and 100 × 10⁻⁶ K, making the atmosphere a potential source of foreground for the CMB E (B) mode signal if there is even a 1% (0.01%) conversion of circular to linear polarization in the instrument.     

The Hanle effect and the diagnostics of turbulent magnetic fields in the solar atmosphere

The theory of the Hanle effect is used to interpret the linear polarization measured in a number of spectral lines on the solar disk near the heliographic north and south poles, in search for a turbulent magnetic field in the solar atmosphere. The Hanle depolarization is separated from a number of other effects, including collisional depolarization and scattering geometry. Although the main aim of the paper is to elucidate the physics of the Hanle effect as applied to the Sun, our results indicate the existence of hidden or turbulent magnetic flux near the temperature minimum of the solar atmosphere, with a field strength between 10 and 100 G. This field is hidden in the sense that it is not seen in measurements of the longitudinal Zeeman effect (solar magnetograms). It carries more total magnetic flux than the kG network fields.     

Solar magnetic fields as revealed by Stokes polarimetry

Observational astrophysics started when spectroscopy could be applied to astronomy. Similarly, observational work on stellar magnetic fields became possible with the application of spectro-polarimetry. In recent decades there have been dramatic advances in the observational tools for spectro-polarimetry. The four Stokes parameters that provide a complete representation of partially polarized light can now be simultaneously imaged with megapixel array detectors with high polarimetric precision (10^?5 in the degree of polarization). This has led to new insights about the nature and properties of the magnetic field, and has helped pave the way for the use of the Hanle effect as a diagnostic tool beside the Zeeman effect. The magnetic structuring continues on scales orders of magnitudes smaller than the resolved ones, but various types of spectro-polarimetric signatures can be identified, which let us determine the field strengths and angular distributions of the field vectors in the spatially unresolved domain. Here we review the observational properties of the magnetic field, from the global patterns to the smallest scales at the magnetic diffusion limit, and relate them to the global and local dynamos.     

Circular Polarization in a Solar Filament

Integrating 26 624 pairs of video frames, the authors have mapped the circular polarization in an active-region filament against the solar disk by using a traditional magnetograph working at the Hβ line. This filament, offset the disk center, appeared at the boundary of three decayed active regions. It was quiet and away from any strong enhanced network. The mapped circular polarization in the filament has an average polarization degree of 1.1×10⁻³ with a measurement precision of 4×10⁻⁴. The mapping of circular polarization in a filament may provide a supplementary diagnosis of the filament magnetic field, in addition to the mapping of linear polarization via the Hanle effect. However, the interpretation of the circular polarization requires treatment of the full quantum problem of Zeeman and non-Zeeman effects of Stokes line profiles.     

Comparison of the magnetic fields in active prominences measured from the He I D3 and Hα lines

We present the results of magnetic field measurements in three active prominences, July 24, 1981, July 24, 1999, and July 12, 2004, obtained from observations with the echelle spectrograph of the horizontal solar telescope at the Astronomical Observatory of the Taras Shevchenko Kiev National University. The magnetic fields were measured from the Zeeman splitting of the I ± V profiles in the He I D₃ and H?? lines in the atmosphere at heights from 3 to 14 Mm. Our measurements of the effective magnetic fields B _eff from the shift of the profile centroids have shown that the magnetic fields averaged over the entrance slit area were within the range from ?600 to +1500 G. The amplitude values of the local fields have been estimated from the splitting of the bisectors of the central parts of the line profiles at 0.9 of the peak intensity. The corresponding fields B _0.9 have turned out to be approximately twice B _eff and reached 4000 G in absolute value. Narrow (1?C2 Mm) height peaks at heights of 6?C11 Mm have been found in the height distributions of the magnetic field. We have found an interesting effect in two prominences-an anticorrelation between the magnetic field strengths measured from the D₃ and H?? lines.     

The post-Newtonian mean anomaly advance as further post-Keplerian parameter in pulsar binary systems

The post-Newtonian gravitoelectric secular rate of the mean anomaly ℳ is worked out for a two-body system in the framework of the General Theory of Relativity. The possibility of using such an effect, which is different from the well known decrease of the orbital period due to gravitational wave emission, as a further post-Keplerian parameter in binary systems including at least one pulsar is examined. The resulting effect is almost three times larger than the periastron advance . E.g., for the recently discovered double pulsar system PSR J0737-3039 A+B it would amount to −47.79 deg yr⁻¹. This implies that it could be extracted from the linear part of a quadratic fit of the orbital phase because the uncertainties both in the linear drift due to the mean motion and in the quadratic shift due to the gravitational wave are smaller. The availability of such additional post-Keplerian parameter would be helpful in further constraining the General Theory of Relativity, especially for such systems in which some of the other post-Keplerian parameters can be measured with limited accuracy. Moreover, also certain pulsar-white dwarf binary systems, characterized by circular orbits like PSR B1855+09 and a limited number of measured post-Keplerian parameters, could be used for constraining competing theories of gravity.     

The hydrogen emission spectrum of a shock wave in a stellar atmosphere

Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M₁?10 and unperturbed gas densities σ₁=10^?10 g cm^?3, the Doppler shift is approximately one third of the shock velocity U₁. The FWHM of the emission-line profile δ _? is related to the shock velocity by δ _? ≈ k _? U₁, where k _? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.     

Non,thermal Cosmic Gravitational Radiation and Redshift Fluctuations

Intergalactic gravitational radiation fields with wavelengths in the range of 1 to 10³ Megaparsecs have remarkable observational effects if the energy density of the fields becomes comparable to the equivalent “critical” cosmological matter density χo = 3H₀². In this case the perturbation in the space-time metric caused by the radiation field is high enough to change the frequency and to shift the path of light rays of extragalactic objects in a random manner by observable amounts. The present paper discusses the wave spectrum as a function of cosmic time and gives a statistical treatment of the redshift fluctuations.     

Polarization measurements of molecular lines

ALMA observations of circular (Zeeman) and linear (Goldreich–Kylafis) polarization in spectral lines will significantly enhance sensitivity and angular resolution over currently available data, and should lead to major breakthroughs in our understanding of the role of magnetic fields in the star formation process. This work was partially supported by NSF grants AST 0540459 and 0606822.     

The polarization of optical radiation from the magnetic white dwarfs

It is pointed out that, because of the large Faraday rotation an outlet of linear polarization from the photosphere of a white dwarf is hampered. In accordance with this fact it is proposed to distinguish two types of magnetic white dwarfs. The first type (its representative is Grw 70°8247) has a linear polarization which is comparable in magnitude with the circular one. Polarization of radiation from the white dwarfs of the first type cannot arise in the photosphere. It arises in the corona of the star either as a result of cyclotron emission of hot electrons (T～10⁶ K) or as a result of scattering of slightly polarized emission from the photosphere in the corona. For the first type dwarfs such magnetic fields are required thatω _B ω_opt, i.e.B(1?3)×10⁸G. The white dwarfs of the second type (its representative is G 99-37) have their linear polarization much smaller than the circular one. Polarization of these white dwarfs can arise as a result of the transfer of radiation in the nonisothermal photosphere. Magnetic fields required for the second type can be much smaller:B cos γ=(1?10)×10⁶ G. It is shown that the photospheric model allows to obtain the quantitative accordance of the theory with all the observational data for G 99-37 and is not in accordance with the data for Grw 70°8247, at the same time the model with cyclotron emission from the corona explains the magnitude of both linear and circular polarization and their wavelength dependence for Grw 70°8247.     

Modeling of Stark–Zeeman Lines in Magnetized Hydrogen Plasmas

The action of electric and magnetic fields on atomic species results in a perturbation of the energy level structure, which alters the shape of spectral lines. In this work, we present the Zeeman–Stark line shape simulation method and perform new calculations of hydrogen Lyman and Balmer lines, in the framework of magnetic fusion research. The role of the Zeeman effect, fine structure and the plasma’s non-homogeneity along the line-of-sight are investigated. Under specific conditions, our results are applicable to DA white dwarf atmospheres.     

The Ultraviolet Spectrometer and Polarimeter on the Solar Maximum Mission

The Ultraviolet Spectrometer and Polarimeter (UVSP) on the Solar Maximum Mission spacecraft is described, including the experiment objectives, system design, performance, and modes of operation. The instrument operates in the wavelength range 1150–3600 Å with better than 2 arc sec spatial resolution, raster range 256 × 256 arc sec², and 20 mÅ spectral resolution in second order. Observations can be made with specific sets of 4 lines simultaneously, or with both sides of 2 lines simultaneously for velocity and polarization. A rotatable retarder can be inserted into the spectrometer beam for measurement of Zeeman splitting and linear polarization in the transition region and chromosphere.Currently at MMTO, University of Arizona, Tucson, Ariz. 85721, U.S.A.     

Interpretation of Solar Magnetic Field Strength Observations

This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compared the synoptic program λ5250 Å line of Fe?i to the line of Fe?i at λ5233 Å since this latter line has a broad shape with a profile that is nearly linear over a large portion of its wings. The present study uses five pairs of sampling points on the λ5233 Å line. Line profile observations show that the determination of the field strength from the Stokes V parameter or from line bisectors in the circularly polarized line profiles lead to similar dependencies on the spectral sampling of the lines, with the bisector method being the less sensitive. We recommend adoption of the field determined with the line bisector method as the best estimate of the emergent photospheric flux and further recommend the use of a sampling point as close to the line core as is practical. The combination of the line profile measurements and the cross-correlation of fields measured simultaneously with λ5250 Å and λ5233 Å yields a formula for the scale factor δ ^?1 that multiplies the MWO synoptic magnetic fields. By using ρ as the center-to-limb angle (CLA), a fit to this scale factor is δ ^?1=4.15?2.82sin?²(ρ). Previously δ ^?1=4.5?2.5sin?²(ρ) had been used. The new calibration shows that magnetic fields measured by the MDI system on the SOHO spacecraft are equal to 0.619±0.018 times the true value at a center-to-limb position 30°. Berger and Lites (2003, Solar Phys. 213, 213) found this factor to be 0.64±0.013 based on a comparison using the Advanced Stokes Polarimeter.