The BOES Spectropolarimeter for Zeeman Measurements of Stellar Magnetic Fields

The polarimetric analyzer that we use in the spectropolarimetric mode consists of a rotatable QWP for polarimetric modulation and a Savart plate as a beam splitter. In the present design we have decided to use a polymer QWP (Samoylov et al. 2004) instead of the frequently used quartz/MgF₂ crystal wave plate or Fresnel rhombs. It is a well‐known fact that the quartz/MgF₂ QWP produces significant artificial polarization ripples of 0.05%–2% (Harris & Howarth 1996; Donati et al. 1999) due to the interference within the cemented layers of the retarder. And the well‐known solution based on Fresnel rhombs cannot easily be used in our design due to the considerable size of this optics. At the same time, the polymer QWP that we used retards the wave at a rate of 0.25 ± 0.007λ in the 4000–8000 Å range (Samoylov et al. 2004), and the ripple is below 0.1% (Ikeda et al. 2003). Such good parameters of the plate make it possible to use it instead of other available plates. With these optical elements the available working wavelength range of the polarimeter is 4000–8000 Å.

The optics is installed at the Cassegrain focus in front of the fiber input as shown in Figure 2. It is mounted on rotary stages to be removable from the optical axis in case of ordinary spectral observations. The spectropolarimetric observations are available with a resolving power of 45,000 or 60,000.

Before each run of the polarimetric observations, the adjustment of the polarimeter is examined using a laboratory source of light (for example, a similar procedure is described in detail by Plachinda 2005). Some important examples of these tests are presented in Figure 6, where the upper plot illustrates the analyzer assembled for measurements of the modulation by the QWP in observations of circular polarization. Artificial circularly polarized light is created by the combination of an additional QWP (QWP1) and polarizer (polarizer 1) as shown in the figure. The efficiency of the modulation is better than 99.7%. The lower plot (graph) illustrates the results of cross talk measurements obtained at different orientation angles (the horizontal axis) of polarizer 1 (QWP1 is removed in this case). As one can see, the maximum cross talk (vertical axis in the figure), which characterizes artificial circular polarization from linearly polarized light, is not higher than 5.5%. To our knowledge, this result is practically standard for modern polarimeters.

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As the design concept of the CIM and the fiber assembly was described in Kim et al. (2002), we do not mention it here in detail. Since then, we have revised the flat‐fielding lamps and the fiber assembly that was adopted for polarimetric observations. For the white balance of the flat fielding, we use three tungsten halogen lamps with an integration sphere—a 10 W lamp with a half‐inch diameter aperture for the red wavelengths, a 100 W with 1 inch diameter filters (3 mm KG3 + 1 mm BG24A + 1 mm BG39) for the medium wavelengths, and a 100 W with 2 inch diameter filters (3 mm KG3 + 1 mm UG5 + 1 mm S8612) for the blue region (see the cube‐type integrating sphere in Fig. 3).

The BOES is furnished with nine fibers of 80, 100, 150, 200, and 300 μm in core diameters that provide corresponding spectral resolutions λ/Δλ∼90,000, 75,000, 60,000, 45,000, and 30,000, respectively (Fig. 4). Five of them are used for ordinary spectroscopy, and two pairs of 150 and 200 μm fibers, for spectropolarimetry. At the fiber input, fibers in each pair are separated by 500 μm distance that corresponds to the separation of the beams split by the polarimetric analyzer. At the fiber exit, these are separated to 380 μm to avoid overlapping of spectral orders. All the fibers except the 80 μm one (STU; Schötz et al. 1998) are FBP,⁶ the transmission of which is improved relative to STU fiber, especially in the blue region.

The spectrometer (BOES) was designed by S. S. V. and is shown in Figure 5. It is a quasi‐Littrow configuration in the dual‐white‐pupil (DWP) configuration pioneered by the UV‐Visual Echelle Spectrograph (UVES; Dekker et al. 1992) on the VLT. Other similar‐style DWP spectrometers are FOCES (Pfeiffer et al. 1998) of the 2.2 m telescope at Calar Alto Observatory, HRS (Tull 1998) on the Hobby‐Eberly Telescope (HET), and FEROS (Kaufer & Pasquini 1998) at ESO.

In the BOES design, the f/8 beam exiting the fiber is collimated by the main off‐axis collimator into a 136 mm diameter beam, which is then dispersed by a 41.59 groove mm⁻¹ R4 echelle of size 203 × 813 mm. This echelle is a replica of the master ruled for the blue side of UVES. The dispersed light from the echelle returns in quasi‐Littrow mode (0.6° out of plane) back to the main collimator and, via the folding mirror, to the transfer collimator. The transfer collimator is identical to the main collimator, and the optical axes of both are colinear. The transfer collimator corrects, to a high degree, the aberrations introduced by the main collimator and provides a white pupil near the cross‐disperser to minimize the required clear apertures of the prisms and camera. Both collimators are cut from a common f/1.8 parent parabola of 600 mm diameter. All the mirrors have durable high‐reflectance silver coatings.

Most if not all previous versions of DWP spectrometers incorporated a toroidal rear surface in the optical train (near the focal plane) to counteract astigmatism introduced by the quasi‐Littrow white pupil collimation combination. However, we found that slightly pistoning the transfer collimator provides an equally viable solution that eliminates the need for this aspheric optics.

For the cross‐disperser, we adopted the use of a pair of 55° prisms instead of a grating. Prisms provide more uniform order separation and higher efficiency across the very wide spectral bandpass of BOES. We used S‐BSL7Y, a BK‐7–like glass with enhanced ultraviolet transmission available from Ohara, Inc. It was selected on the basis of its unusually high ratio of red to blue dispersion, creating a more uniform order separation across the echelle format and thus more efficient order packing. The f/1.6 camera has an effective focal length of 389 mm and consists of six spherical lenses in three groups. It works over about a 9.5° diameter field of view and spans the entire 3500–10,500 Å range with adequate image quality. All prisms and camera lenses were treated with wideband antireflection coatings, which provide reflectance below 1.5% across the 3500–10,500 Å range. Overall, 86 spectral orders, from the 46th to the 131st, are captured on the CCD. Interorder stray light appears to be at less than 2% of the intensities of the neighboring orders.

Figure 7 illustrates the typical efficiency of the BOES measured on 2003 November 3 with different (300, 200, and 80 μm in diameter) single fibers. This shows that maximum efficiency is up to 12% including the light loss due to the atmospheric extinction, the reflectance of the telescope, and the light cutoff at the fiber input. While the efficiency was measured, the target star was at an air mass of 1.13 with the seeing size around 2.3^''. The small efficiency of the 80 μm fiber comes from the light cutoff at the fiber input due to the small diameter (Kim et al. 2002).

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Good mechanical stability of the spectrograph makes it possible to use the instrument in a wide range of observational programs, for example, asteroseismology as well as Zeeman observations. Figure 8 illustrates the typical accuracy of the stellar radial velocity measurements achieved in observations with the BOES equipped with an iodine cell. The standard star τ Ceti (G8 V) does not exhibit any variations in radial velocity within a typical accuracy of about 9 m s⁻¹ on a 3 yr time base.

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Directly, stellar magnetic fields are detected mainly through the observations of the Zeeman effect in spectral lines. According to basic physical principles (for more details see, for example, Landstreet 1980), if an atom is placed in a magnetic field B, its individual energy levels are split into 2J + 1 sublevels separated by energy ΔE = geB/2mc, where g is the Lande factor. As a result, stellar magnetosensitive spectral lines are split into a number of π‐ and σ‐components, which are polarized depending on the orientation of the magnetic field relative to the observer.

In a longitudinal (parallel to the line of sight) magnetic field the σ‐components, which are generally displaced symmetrically to shorter and longer wavelengths relative to the nonshifted central π‐components of spectral lines, have opposite circular polarizations. Thus, by observing circular polarization in the spectral lines we are able to measure the longitudinal component of the stellar magnetic field. To reconstruct the full vector of the field, additional observations of linearly polarized π‐ and σ‐components are needed. These observations allow us to estimate a transverse field component that, together with observations of the longitudinal component, gives a full vector magnetic field averaged over the stellar disk. In this paper, we discuss observations of the longitudinal fields only.

The averaged circularly polarized σ‐components are displaced relative to the rest wavelength λ₀ of a spectral line by a factor of

where B_l is the longitudinal field component in gauss, z is the effective Lande factor, and λ is the wavelength in angstroms. Due to the fact that these displaced components have opposite circular polarizations and are shifted relative to each other, in the stellar circular polarization spectra (Stokes V spectra, or V spectra) they form nonzero features within magnetosensitive spectral lines. In most cases of spectropolarimetric observations these features show well‐known ‐shaped features (Fig. 9) at the cores of spectral lines. Their amplitudes and forms depend on magnetic field strengths, Lande factors, gradients of the line profiles, and the spectral resolution of the spectrograph:

where dI/dλ describes the gradient of a spectral line convolved with the instrumental function of a spectrograph (e.g., Landstreet 2001). The mean longitudinal magnetic field can be estimated by applying model methods of Doppler‐Zeeman spectropolarimetric tomography to the analysis of the Stokes V spectra (e.g., Euchner et al. 2002), or the LSD method (Donati et al. 1997). Alternatively (and traditionally), longitudinal magnetic fields can simply be measured via analysis of the displacement (eq. [1]) between the positions of spectral lines in the spectra of opposite circular polarizations split by the analyzer.

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Each exposure in observations of circular polarization with the BOES yields two spectra on the CCD—one from the ordinary beam and the other from the extraordinary beam split by the analyzer. In the case of an ideal spectropolarimeter (which has no intrinsic distortion factors), this single exposure obtained at one of the orthogonal orientations of the quarter‐wave plate would practically be enough to build V Stokes spectra and to measure the magnetic field. However, due to the presence of a large number of instrumental biases such as pixel‐to‐pixel inhomogeneity, slightly different dispersion relationships at each of the split beams, and other factors, it is recommended to obtain an additional exposure with inverted sign of the polarization effects by rotating the quarter‐wave plate by 90°. Such a technique makes it possible to reconstruct the Stokes V spectra in a pixel coordinate system separately for the spectra of the ordinary and extraordinary beams that significantly increases the quality of the output results (for details see, e.g., Plachinda & Tarasova 1999, Bagnulo et al. 2002, or Aznar Cuadrado et al. 2004).

Due to the above‐mentioned reasons and in order to increase the reliability of our observations of circular polarization, one observation with the BOES consists of four short, consecutive exposures at two orthogonal orientations of the quarter‐wave plate (the sequence of its position angles is +45°, −45°, −45°, +45°). Assuming a priori that the timescale of possible physical variability of polarization features in spectra of nondegenerate stars would be as short as a few hours, we usually set the integration time for each of the individual exposures from a few minutes to 0.5 hr depending on stellar magnitude and sky conditions.

The data reduction was processed with IRAF. The procedures are mostly standard, including the following steps: cosmic‐ray hit removal, electronic bias subtraction, flat‐fielding, 2‐D wavelength calibration, sky background subtraction, and spectrum extraction. As an output result we obtained a series of pairs of left and right circular polarized spectra that we used to build V Stokes spectra and measure stellar longitudinal magnetic fields. We obtained the individual Stokes V spectra for each of the echelle spectral orders by applying the technique presented by Bagnulo et al. (2002).

In order to illustrate the results of the reduction in our first polarimetric observations with the BOES, we present fragments of circular polarization spectra of the magnetic stars HD 215441, HD 32633, HD 40312, and the star HD 61421 (Procyon) in Figures 9 and 10. We have chosen these stars as the remarkable cases of typical magnetic stars (HD 215441, HD 32633, HD 40312) having polarization features of different intensities (details on these stars are also presented below) and a zero‐field star (Procyon). As one can see (Fig. 9), the circular polarization of different intensities can easily be resolved and studied with our polarimeter.

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Examination of the zero‐field star Procyon has not revealed any artificial circular polarization features at a characteristic level of about 0.5% within the working wavelength region from 4000 to 8000 Å. The bottom plot in Figure 9 demonstrates zero polarization of Procyon at the Hβ region. An example of another wavelength region is presented in Figure 10.

Finally, before presentation of the results of the longitudinal magnetic field measurements in the standard stars, we would also like to briefly discuss the possibility of obtaining Stokes Q/U (linear polarization) spectra, which is necessary for measurements of the transverse magnetic fields. It should be noted that linear polarization features in spectral lines due to the Zeeman effect are intrinsically weaker than the corresponding circular polarization features. This strongly complicates observations of linear polarization with 2 m class telescopes. To simplify the solution, special methods of data reduction (Donati et al. 1997) and the LSD method for obtaining linear polarization measurements that are averaged over all spectral lines (Donati et al. 1997) should be applied. In this paper we do not discuss these details, leaving them for future investigations for application to the BOES data. Here we just briefly present and illustrate test observations of the Stokes Q/U spectra with the BOES.

There are several designs of polarimetric optics for obtaining all Stokes parameters including Stokes Q/U. Due to technical limitations, for linear polarization measurements we have chosen the simplest configuration of polarimetric optics, similar to that presented by Naydenov et al. (2002). According to their scheme, the Stokes Q/U spectra can simply be obtained by using the beam splitter only (without the QWP). In this case, the necessary observational basis is achieved by rotation of the Cassegrain assembly to obtain four consecutive exposures at different position angles of the beam splitter relative to the sky plane (for details see Naydenov et al. 2002). Applying this method, we observed the magnetic star α² CVn, which shows rotationally modulated linear polarization in its spectral lines.

According to Wade et al. (2000) net linear polarization of this star varies from about −0.2% to about +0.6%. We observed α² CVn at two phases of the star's rotation when the polarization is nearly zero (ϕ ≈ 0.03) and at one of the extrema (ϕ ≈ 0.2) where the star's spectrum exhibits nonzero positive linear polarization (Stokes Q ≈ + 0.6% and Stokes U ≈ + 0.3%; see Fig. 6 in Wade et al. 2000). Such a weak polarization level cannot simply be registered within consideration of one individual spectral line. However, the problem can be resolved if several spectral lines are considered together. For instance, considering net polarization as a function of the distance from the line cores (in the radial velocity scale), the LSD method of obtaining polarization that is averaged over all available spectral lines can be applied (Wade et al. 2000). To illustrate this, in Figure 11 we present Stokes Q/U spectra of α² CVn that are averaged over all available Balmer lines. The left two plots illustrate zero polarization at the rotation phase ϕ ≈ 0.03. The right plots present nearly maximum positive polarization at the rotation phase ϕ ≈ 0.2. Signatures of the narrow ∼0.6% polarization features are clearly seen at the line cores in this case. As one can see, even such a weak polarization level can also be registered with our polarimeter, which enables us to measure the transverse magnetic field. This problem, however, deserves an additional special paper where we will present all the necessary tools for these measurements and details on linear polarization observations of the standard stars including α² CVn that we briefly touched on here. In this paper we limit ourselves to presentation of the polarimeter and consideration of the longitudinal magnetic field measurements only.

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In our first Zeeman observations of stellar magnetic fields with the BOES we measured longitudinal fields via analysis of the displacement (eq. [1]) between the positions of spectral lines in the spectra of opposite circular polarizations (see, e.g., Monin et al. 2002 and references therein). This technique, if applied to all selected spectral lines in a spectrum with further statistical averaging of the result, is quite robust for the determination of longitudinal magnetic fields averaged over the stellar disks. The atomic data necessary for the identification of spectral lines and their Lande factors were taken from the VALD database (Piskunov et al. 1995; Ryabchikova et al. 1999; Kupka et al. 1999).

Measurements at individual spectral lines were carried out in a pixel coordinate system separately for spectra obtained at the ordinary and extraordinary beams split by the analyzer to avoid uncertainties in the wavelength calibration. In this case, Zeeman displacement between σ‐components of opposite circular polarizations can be measured as a shift between the centers of gravity of a spectral line extracted from the same pixels of two neighboring CCD frames obtained at two orthogonal orientations (+45° and −45°) of the quarter‐wave plate. The longitudinal magnetic field B_l based on these measurements can be found as an averaged mean of B^o_l and B^e_l estimates of the magnetic field obtained from spectra of the corresponding ordinary and extraordinary beams. It is clear that B^o_l and B^e_l are not free of any biases due to the influence of mechanical instabilities from exposure to exposure. Their averaging, however, significantly reduces them as we now illustrate.

Denoting the center of gravity of spectral lines from the ordinary/extraordinary spectrum obtained at the +45° or −45° position of the quarter‐wave plate as λ^o_+45°/λ^e_+45° or λ^o_-45°/λ^e_-45°, the B^o_l and B^e_l estimations have the following forms:

where k = 1/(4.67 × 10^-13zλ²); Δλ_B is Zeeman displacement between the σ‐components in the spectral line; and Δλ_o and Δλ_e are instrumental shifts between spectra of the ordinary/extraordinary beam obtained at different moments in time due to the requirement of having two consecutive exposures at +45° and −45° orientations of the QWP. The sign inversion in B^e_l estimation appears due to the inverse polarimetric properties of the extraordinary beam relative to the ordinary one. Averaging the data, we have

In equation (5), the instrumental shift is taken with opposite sign due to the polarimetric inversion in the beams. In practically all cases of any instrumental effect these shifts are equal in linear guess approximation and eliminated each other in the applied method.

Obtaining an estimate of the averaged mean longitudinal magnetic fields and error bars within one observation of a star (consisting of four consecutive exposures) was done by weighting and statistically averaging all the individual measurements. Here we weighted individual line‐by‐line measurements by residual intensities and signal‐to‐noise ratios as described by Monin et al. (2002). Alternatively, we also applied the Monte Carlo simulation method (Plachinda 2004a) of obtaining error bars and weights for the individual measurements.

This work was supported by the Korea Astronomy and Space Science Institute (KASI) under grant 2007‐1‐310‐A0. We wish to thank our anonymous referee for comments on the first draft of this paper, which led to considerable improvement of this paper. K. M. K. thanks A. Kaufer, J.‐L. Lizon, and H. Dekker of ESO, D. Fabricant of SAO, J. Zajac of Oak Ridge Observatory, H. Epps of UCO/Lick Observatory, J. Lee of Chong Ju University, and D. Shakhovskoy of CrAO for their kind help while manufacturing the BOES process. I. Han acknowledges partial financial support by KFICST through grant 07‐179. G. V. is grateful to the Korean MOST (Ministry of Science and Technology; grant M1‐022‐00‐0005) and KOFST (Korean Federation of Science and Technology Societies) for providing him an opportunity to work at KASI through the Brain Pool program. B. C. L. acknowledges his work as part of the research activity of the Astrophysical Research Center for the Structure and Evolution of the Cosmos (ARCSEC, Sejong University) of the Korea Science and Engineering Foundation (KOSEF) through the Science Research Center (SRC) program.