Abstract

1 INTRODUCTION

About 1 in 15 early-type stars possess a detectable magnetic field (Grunhut, Wade & MiMeS Collaboration2012b; Grunhut et al.2017). Their magnetic fields are typically strong (10²–10⁴ G), topologically simple (mostly tilted dipoles), stable over at least thousands of rotational cycles (e.g. Shultz et al.2018b), and their strength shows no correlation with rotation (unlike what would be expected for magnetic fields maintained by contemporaneous dynamos). These properties lead to their characterization as fossil magnetic fields (e.g. Neiner et al.2015). Magnetic OB stars are particularly interesting due to their magnetically confined winds, which often lead to magnetospheres that can be detected via X-ray, ultraviolet, optical, and infrared emission lines (e.g. Petit et al.2013, hereafterP13). Magnetic wind confinement also leads to rapid spin-down (e.g. ud-Doula, Owocki & Townsend2009), an effect that should intensify with increasing mass-loss rate and increasing magnetic field strength.

Magnetospheres can be divided into those in which rotation plays a negligible role (dynamical magnetospheres or DMs), and those in which centrifugal support due to rapid rotation is decisive in sculpting the circumstellar plasma distribution (centrifugal magnetospheres or CMs).P13 introduced a rotation–magnetic confinement diagram, and showed that the position of a star on the diagram is broadly predictive of its magnetospheric H α emission status. O-type stars (with high mass-loss rates and typically very slow rotation) are almost invariably predicted to have DMs, and always possess detectable H α emission. Conversely, B-type stars only possess detectable magnetospheric emission when they are both very rapidly rotating and very strongly magnetized, i.e. when they are predicted to have very large CMs.

For most of the stars studied byP13, rotational periods and surface magnetic field strengths were unknown, meaning that only limiting values of their magnetic and rotational properties were available, and their positions on the rotation–magnetic confinement diagram were only limiting values. In consequence, the conditions under which CMs become detectable were not observationally constrained.

Shultz et al. (2018b, hereafterPaper I) presented magnetic field measurements, rotational periods, and projected surface rotational velocitiesvsin i for all known main-sequence early B-type stars in theP13 sample for which sufficient magnetic data had been obtained for accurate characterization of their surface magnetic properties. Before these results can be used to obtain surface rotational properties and magnetic oblique rotator models, fundamental stellar parameters (masses and radii) must also be determined, which in turn require stellar atmospheric parametersT_eff, log g, and log L. For many of the stars, only photometric measurements of the first two parameters are available. The newly availableGaia Data Release 2 (DR2; Gaia Collaboration2018) parallaxes mean that distances and luminosities can be obtained with higher precision for many of the more distant stars in the sample. The purpose of this paper is to combine the available high-resolution spectroscopic data withGaia DR2 parallaxes to determine high-precision atmospheric parameters.

An overview of the sample and observations is provided in Section 2. Section 3 describes the measurements and the resulting properties of the sample, together with an examination of some of the systematics arising from different measurement methods. Results are discussed, and conclusions drawn, in Section 4. Previously unreported magnetic measurements are provided for HD 47777 in Appendix  A. Surface gravity measurements of individual single stars are detailed in Appendix  B, and those of binary systems in Appendix  C.

2 SAMPLE AND OBSERVATIONS

The sample consists of essentially all known magnetic main-sequence stars with spectral types between B5 and B0. The selection criteria and properties of the sample were described inPaper I. One star, HD 35912, has been removed as we demonstrated inPaper I the absence of a detectable surface magnetic field. The study is based primarily upon an extensive data base of high-resolution ESPaDOnS, Narval, and HARPSpol spectropolarimetry, in some cases supplemented with FEROS spectroscopy; these data were also described inPaper I. The majority of these data were acquired by the MiMeS and BinaMIcS large programs (LPs). The basic observational techniques and strategy of the MiMeS LPs, as well as the reduction and analysis of ESPaDOnS, Narval, and HARPSpol data, were described by Wade et al. (2016). The BinaMIcS LPs used the same instruments as MiMeS. Additional observations were acquired by the BRIght Target Explorer Constellation polarimetric survey (Neiner et al.2017), the B-fields in OB stars (Fossati et al.2015b; Schöller et al.2017) LP at the European Southern Observatory, and by various independent ESPaDOnS observing programs (listed inPaper I) at the Canada–France–Hawaii Telescope (CFHT).

SincePaper I five stars satisfying the selection criteria have been added to this sample, the magnetic and rotational properties of these stars, along with the available high- and low-resolution spectropolarimetric measurements, are given together with the relevant references in Table 1. In the case of HD 47777, the magnetic data are published here for the first time, and are described in Appendix  A. The final sample consists of 56 stars, listed in Table 2.

3 ATMOSPHERIC PARAMETERS

This section collects prior determinations of atmospheric parameters from the literature, and describes the steps taken to obtain more precise constraints when the high-resolution spectroscopic data described inPaper I provide the opportunity to improve on previous measurements.

We began with the surface parameters provided byP13, who collected spectroscopic modelling measurements from the literature determined (for hotter stars) with non-local thermodynamic equilibrium (NLTE) FASTWIND or TLUSTY model atmospheres (Lanz & Hubeny2003), or (for cooler stars) LTE models such asatlas (Kurucz1979). Where spectral modelling is already available, literature values are adopted without modification.

In those cases for which spectral modelling was unavailable,P13 used photometry to deriveT_eff and log g, with appropriate spectral-type calibrations. In several cases, spectral modelling has since been performed. For the remaining stars, we present new measurements based on spectroscopic modelling next (Sections 3.1–3.3). Table 2 collects the stellar surface parameters, together with the references when values were adopted from the literature. In the end, literature values were adopted without modification for 20 stars; entirely new values are presented for 15 stars; and for the remaining 21 stars, one parameter or more has been modified.

3.1 Effective temperatures

PhotometricT_eff calibrations are often inaccurate for chemically peculiar stars since their non-standard, variable surface chemical abundance patterns (in particular He, Si, and Fe) redistribute flux across the spectrum in a fashion that is unique to each star and thus impossible to properly account for without detailed modelling. As a sanity check on photometricT_eff determinations, we used equivalent width (EW) ratios ofT_eff-sensitive spectral lines of different ionizations but the same atomic species (Gray et al.1992), and compared these to EW ratios measured from a grid of model spectra. These measurements were performed for all stars for which high-resolution spectra are available. This is less precise than detailed comparison of observed to synthetic spectra, but it is based on the same physics, yields similar results (e.g. Shultz et al.2015,2017), is computationally cheaper, and is to first order independent of abundance peculiarities.

EWs were measured using mean (i.e. rotationally averaged) spectra created from all available ESPaDOnS, Narval, and HARPSpol observations for each star, thus maximizing the signal-to-noise ratio (S/N) and minimizing the potential effects of stellar variability due to, e.g. chemical spots and/or pulsations. For the hotter stars (T_eff ≥ 25 kK), EWs of He i 587.6 nm and He i 667.8 nm versus He ii 468.6 nm, and Si iii 455.3 nm and 456.8 nm versus Si iv 411.6 nm were compared. For cooler stars, the ratios used were Si ii 413.1, 505.6, 634.7, and 637.1  nm versus Si iii 455.3 and 456.8 nm; P ii 604.3 nm versus P iii 422.2 nm; S ii 564.0 nm versus S iii 425.4 nm; and Fe ii 516.9 nm versus Fe iii 507.4 and 512.7 nm. These lines were selected by searching Vienna Atomic Line Data base (VALD3: Piskunov et al.1995; Ryabchikova et al.1997; Kupka et al.1999,2000; Ryabchikova et al.2015) line lists with the criteria that the lines be both isolated and strong within theT_eff range of interest. Many of the sample stars are chemically peculiar He-weak or He-strong stars (see Table 2), and may therefore possess numerous spectral lines that would not be expected in a star with standard solar abundances. The broad spectral lines of rapid rotators may also be strongly blended. These considerations required the line lists to be individually tailored for each star by excluding obvious blends. When one of the ionizations does not appear at all in the spectrum, the chemical species in question was discarded from consideration (although this did provide an additional upper or lower bound onT_eff).

We compared the EW ratios measured from the mean spectra to a grid of EW ratios determined from the non-LTE solar metallicity grid of BSTAR2006 synthetic spectra (Lanz & Hubeny2007), i.e. essentially the method described by Shultz et al. (2015). The grid was limited to the range of the star’s approximate log g. TheT_eff was calculated as the mean value across the grid, with the uncertainty obtained from the standard deviation of these values; since only those regions of the grid corresponding to log g were included, the uncertainty also includes the uncertainty in log g.

Special care was required for spectroscopic binaries. Where possible, we measured EW ratios from individual (rather than mean) spectra, using only those observations in which the stellar components are clearly separated. The finalT_eff was determined from the mean across all such observations and all chemical ionizations examined. This was possible for HD 136504 and HD 149277. It was not practical for the remaining systems, but in these cases detailed spectral modelling is generally already available in the literature and these values were adopted without modification.

Fig. 1 compares ourT_eff measurements to the values adopted byP13. PhotometricT_eff values are indicated with the blue solid circles, and spectroscopicT_eff measurements by the black open circles. Our measurements are consistent with those from spectral modelling, suggesting they are fairly reliable. They are also consistent with those from photometry, albeit more precise. The only significant outlier is NU Ori (the filled red square in Fig. 1). In this case, it was determined that the magnetic field detection is associated with a previously undetected companion, rather than with the B0V primary as originally assumed (Petit et al.2008; Shultz et al.2019). The magnetic star’sT_eff was inferred from orbital and evolutionary models. After NU Ori, the next most significant change inT_eff is in ALS 3694, which shows no Si ii or Si iv lines in its spectrum, but does possess fairly prominent Si iii lines. Despite the low S/N, a weak He  ii 468.6 nm line can also be discerned. These indicateT_eff = 23 ± 2 kK, 3 kK hotter than (although formally consistent with) the photometric determination of 20 ± 3 kK (Landstreet et al.2007).

Figure 1.

Top: comparison of measurements ofT_eff obtained via EW ratios with those obtained from the literature. The filled blue circles indicate stars for whichP13 determinedT_eff using photometric data; the open black circles indicate stars for which spectral modelling has already been performed. The filled red square indicates HD 37061/NU Ori (see text).Bottom: the distribution of adopted effective temperatures.

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As the error bars from EW ratios are smaller than measurements obtained from photometry (with a median uncertainty ratio of 60 per cent), and as they are additionally independent of reddening, we adopted these values in preference to the photometric measurements used byP13.

The finalT_eff distribution is shown in the bottom panel of Fig. 1. The histogram uncertainties were determined by a Monte Carlo process, in which 10⁴ synthetic data sets were created with the values of individual data points varying randomly within Gaussian distrbutions normalized to the (presumed 1σ) error bars. The error bars in each bin represent the standard deviation in bin number across all synthetic data sets. The distribution peaks at about 19 kK, and is approximately Gaussian, with an upper range of 32 kK and a lower cut-off of 15 kK. The MiMeS survey, from which the majority of the sample was drawn, focused primarily upon the hottest stars, and declines in completeness from 30 per cent at B0 to about 10 per cent at B5 (Wade et al.2016). This is the most likely explanation for the declining number of stars in the sample at the cooler end.

3.2 Surface gravities

Spectroscopic surface gravities are not available in the literature for many of the sample stars. While surface gravity can be determined photometrically, this is a less sensitive diagnostic than the pressure-broadened wings of H Balmer lines.

We used H β in the majority of cases. In comparison to higher-numbered Balmer lines, H β has a high S/N in ESPaDOnS and Narval spectra, and is generally free of blending with strong metallic or He lines. Some stars display strong magnetospheric H Balmer line emission; this is most prominent in H α but also affects H β therefore for these stars H γ was often used instead as the next-best available line.

Both H β and H γ are close to the edges of their respective spectral orders in ESPaDOnS/Narval spectra. To avoid warping of the line wings, the two overlapping orders of the unnormalized spectra were first merged, with the merging wavelength chosen as the point at which the flux uncertainties intersect, and the merged spectra were then normalized using a linear fit between continuum regions. In order to maximize the S/N, initially unnormalized spectra were co-added, with merging and normalization performed after co-addition.

We determined log g with a goodness-of-fit test. We convolved synthetic BSTAR2006 TLUSTY spectra (Lanz & Hubeny2007) with rotational profiles corresponding to thevsin i values found inPaper I, and then calculated the reduced χ² for each synthetic spectrum, with an integration range extending from 483 to 489 nm for H β and 431 to 437 nm for H γ. In most cases, we used a range of 3.5–4.5 in log g. Balmer lines are weakly sensitive toT_eff therefore we tested fits at the minimum, mean, and maximumT_eff (using the values and uncertainties adopted in Section 3.1). The rotationally broadened cores of H Balmer lines may be subject to effects that may not have been accounted for by TLUSTY (e.g. the core-wing anomaly; Kochukhov, Bagnulo & Barklem2002) therefore we excluded the region inside ±vsin i. Where relevant we also excluded the range of velocities containing the majority of the emission (as evaluated by eye from H α, which is much more sensitive to emission). For eachT_eff, we then fit a low-order polynomial to the reduced χ² as a function of log g in order to locate the χ² minimum for thatT_eff; the final value of log g and its uncertainty were, respectively, the mean of the values at the χ² minima for minimum, mean, and maximumT_eff, and one-half of the range of these values. Due to the very high S/N, systematic uncertainty from the models dominates over the contribution from photon noise. The resulting best-fitting line profiles for single stars are shown in Appendix  B. The special considerations involved in modelling the H β lines of spectroscopic binary stars, and the results of those analyses, are given in Appendix  C.

The spectroscopic data set is somewhat heterogeneous. While the majority of stars were observed with ESPaDOnS and/or Narval, which are identical instruments yielding indistinguishable results, in some cases FEROS and HARPSpol measurements are also available, while in some other cases only HARPSpol measurements are available (see table 1 inPaper I, and Table 1 in this work). For stars with data from multiple spectrographs, log g was measured using mean spectra from each available instrument. ESPaDOnS, Narval, and FEROS all yield compatible results. However, log g measurements performed with HARPSpol are systematically about 0.1 dex lower than measurements performed using ESPaDOnS, as illustrated in Fig. 2. This is likely due to the narrower wavelength range of the spectral orders of the HARPS spectrograph, combined with the reduction pipeline, which does not provide un-normalized spectra; since the orders are shorter than the line widths of H lines, it is very likely that these are overnormalized, leading to lower apparent surface gravities. Where ESPaDOnS, Narval, or FEROS data are available, the values found from these instruments were adopted. Where only HARPSpol data are available (HD 96446, HD 105382, HD 122451, CPD −57°3509, and CPD −62°2124) we increased log g by 0.1 dex.

Figure 2.

Comparison of log g measured with HARPSpol to values obtained from ESPaDOnS.

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The surface gravities measured here are compared to those adopted byP13 in the top panel of Fig. 3. As in Fig. 1, the open circles denote values determined via spectral modelling, while the filled blue circles indicate stars for whichP13 used photometric calibrations. There is good agreement between our spectral modelling and results from the literature. The photometric measurements cluster around log g = 4.0; our spectroscopic measurements are more dispersed. The lower panel of Fig. 3 shows the distribution of adopted log g measurements. Histogram errors were determined using the same Monte Carlo process described in Section 3.1. log g values span the main sequence, from about 3.5 to 4.5, but peak at around 4.1. Thus, while the sample in principle probes the entire main sequence, it is somewhat biased towards stars in the first half of the main sequence (between about 4.0 and 4.3).

Figure 3.

Top: Surface gravities from the literature as a function of those measured in this work. Stars for whichP13 used a photometric calibration are indicated by the filled blue circles; the open circles represent stars for which spectroscopic measurements are available.Bottom: histogram of log g. The median value is about 4.05.

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Figure 4.

Correlation of the slope of the rate of change of log g withT_eff as a function ofT_eff. The dashed line indicates the best linear fit.

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3.3 Luminosities

The photometric parameters used to determine log L are provided in Table 3. Visual magnitudesV were obtained fromsimbad. Distance Moduli (DMs) were obtained fromHipparcos (Perryman et al.1997; van Leeuwen2007) orGaia DR2 (Gaia Collaboration2018)¹ parallaxes π as DM = 5log (1/π) − 5, for π in arcseconds.

A comparison ofHipparcos andGaia parallaxes for our sample is shown in Fig. 5. Most stars agree within 3σ of theHipparcos error bar. Outliers are divided into two classes. The first are binary systems. DR2 treated all sources as single stars; since orbital motion was not accounted for in the astrometric solution, the parallaxes of binary systems may be unreliable. The second class of outliers are relatively bright stars (V < 6); sinceGaia is optimized for dimmer targets, the parallaxes of bright stars may be unreliable (Lindegren et al.2018). Indeed, a bias towards higherGaia parallaxes is seen in stars with the largest parallaxes, which also tend to be the brightest. WhenHipparcos parallaxes were available, we adoptedGaia parallaxes only for systems withV > 6 and at least 3σ agreement betweenGaia andHipparcos results. In the end, we used DR2 parallaxes for 27 stars, or about half the sample, and retained theHipparcos parallaxes for 24 stars.

Figure 5.

Comparison ofHipparcos andGaia parallaxes. The circles indicate dim stars (V > 6), the squares bright stars (V < 6) for whichGaia parallaxes are expected to be inaccurate. The filled symbols indicate stars for whichGaia andHipparcos agree within 3σ of theHipparcos parallax error.Gaia uncertainties are smaller than the symbol size in most cases. The large red circles indicate binaries. With the exception of two binaries, theHipparcos andGaia parallaxes are in agreement for all dim stars. The obvious outlier, with aHipparcos parallax of about 3 mas and aGaia parallax of about 0.5 mas, is HD 37017; this star is discussed further in the text.

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