Magnetic field measurements of sharp-lined Ap stars

All spectropolarimetric observations used in our work were acquired with HARPSpol on the ESO 3.6-m telescope on La Silla, which has a resolving power of $R=115\,000$ and a wavelength coverage from 3780 to 6910 Å, with a small gap between 5259 and 5337 Å. Observations were carried out in 2019 June (Prg. ID 0103.C-0240). Additionally, we discuss archival observations for HD 137949 and HD 217522, which were obtained in 2012 August (Prg. ID 089.D-0383). The data reduction was carried out on La Silla using the HARPS data reduction pipeline. The normalization of the spectra to the continuum level is described in detail by Hubrig et al. (2013). More details on the observations are presented in Table 1. For each star in our sample, HARPSpol Stokes $I$ and Stokes $V$ spectra in the spectral region containing spectral lines characteristic for Ap stars are presented in Fig. 1.

To check the short- and long-term line profile variability of HD 138633, we extracted from the ESO archive high-resolution observations obtained with UVES (the Ultraviolet and Visual Echelle Spectrograph) mounted on Unit Telescope 2 (UT2) of the Very Large Telescope (VLT) at Cerro Paranal, Chile (Prg. ID 072.D-013, carried out on 2004 March 5), as well as two observations with the CES Very Long Camera, which was previously installed at the 1.4 m CAT telescope (Prg. ID 68.D-0445, carried out on 2002 January 25). The original UVES data consist of a large amount of very short, noisy exposures covering the wavelength range 4959–7071 Å and a spectral resolution $R=107\,000$. The individual UVES files were combined into one final spectrum with $S/N=456$ using the ESO Phase 3 UVES pipeline¹¹1http://www.eso.org/rm/api/v1/public/releaseDescriptions/163. Wavelength calibrations for the CES spectra were executed by utilising the Th-Ar comparison spectra obtained immediately before and after recording the stellar spectrum. The first spectrum has an exposure time of 600 s, whereas the second spectrum was obtained 14 minutes later with an exposure time of 780 s.

For three stars in our sample, HD 176196, HD 203932, and HD 217522, an analysis of TESS photometry was presented in the past. No variability was detected by Mathys, Kurtz & Holdsworth (2020) in the available TESS data for HD 176196 and HD 217522. Both stars were classified by these authors as super slowly rotating Ap (ssrAp) stars. Cunha et al. (2019) and Holdsworth et al. (2021) analysed TESS data for HD 203932 and reported a rotation period of $6.44\pm 0.01$ d, and pulsation periods of 2.6985 and 2.8048 mHz, confirming that this star is a rapidly oscillating Ap (roAp) star.

Three stars – HD 70702, HD 89393, and HD 174779 – were observed during Year 1 of the TESS mission, in sectors 8 and 9, sector 9, and sector 13, respectively²²2These observations occurred between 2018 July to 2019 July., but no analysis of the data for these stars has been reported in the past. In our study, the 2-minute cadence TESS observations in sectors 8–9 are used to search for periodicity in the light curve of HD 70702. HD 89393 has 2-min cadence data from sector 9 and 10-min full frame image (FFI) data from sector 36, while HD 174779 has 2-minute cadence data from sector 13. No TESS data exist for HD 137949, but it was observed as a part of the Kepler (Borucki et al., 2009) K2 (Howell et al., 2014) Campaign 15, from mid- to late-2017, in 1-minute cadence. In addition, we discuss the analysis of TESS data of HD 138633, which was observed in sector 51 in 2022 May. We do not have TESS data for HD 189832, which will be observed in sector 67, probably in 2023 July.

The shorter-cadence data from both Kepler and TESS are available in both simple aperture photometry (SAP) and presearch data conditioning SAP (PDCSAP) forms. Data processing was done using the Science Processing Operations Center (SPOC) pipeline at the NASA Ames Research Center (Jenkins et al., 2016). With the PDCSAP light curves, we performed a Discrete Fourier Transform (DFT; see, e.g. Kurtz, 1985) to identify the dominant frequency components of the signal and their amplitudes.

Not much is known about this star. It is classified as A0 SrCrEu in Renson & Manfroid (2009). Magnetic field measurements were not reported for this star in the past. In Fig. 3, we present the LSD Stokes $I$, Stokes $V$, and diagnostic null $N$ profiles for this star, calculated using five different masks. The mean longitudinal field strengths obtained at both epochs are almost identical (see also Tables 1 and 2 and Fig. 2), indicating the absence of any short-timescale variability. The amplitude of the Zeeman features and the measured field values clearly depend on the line masks constructed for individual elements, as the strongest mean longitudinal magnetic field is detected in the measurements using the Eu ii line mask, suggesting a slightly different location (probably closer to the magnetic pole) of the Eu concentration on the stellar surface in comparison to other elements.

The TESS light curve of HD 89383 is shown in the left panel of Fig. 4. The CROWDSAP parameter suggests that there is significant contamination from a nearby star (TYC 7712-2715-1). The CROWDSAP parameter refers to the fraction of flux that falls in the optimal aperture for the 2-minute data that is not directly attributable to the star in question (i.e. a “crowding parameter”) and is calculated as part of the SPOC pipeline when data products are produced. The Gaia BP–RP colour index (Gaia Collaboration, 2018) for this nearby contaminating star is greater than 1, suggesting that it is a cooler star. The periodogram shows just one marginal peak with a calculated $S/N$ of $\sim 4$ at a period of $0.34116\pm 0.00001$ d. Since our metric is the relative amplitude of the peaks in the periodograms, we do not attach any physical interpretation to this marginal peak and are not able to conclude whether this frequency could represent a pulsation mode or arises from some other physical phenomenon, such as rotation of either HD 89393 or the contaminating star. We assume that HD 89393 likely has a long rotation period; this must at least be longer than the length of the TESS observations over 27 d. Also the examination of the 10 min cadence TESS data in sector 36 did not reveal any significant peak in our periodogram.

The star is classified as F0 SrEuCr in Renson & Manfroid (2009). It is a roAp star with a pulsation period of 8.3 min (Kurtz, 1982). The study of Kervella et al. (2019) indicated the presence of a companion from an analysis of proper motions in the Gaia Data Release 2 (GDR2; Gaia Collaboration, 2018) and Hipparcos (van Leeuwen, 2007) catalogues. A strong mean longitudinal magnetic field with a value of more than 1 kG was initially discovered in this star by Babcock (1958). Given the presence of the strong magnetic field and the slow rotation, numerous spectral lines are resolved into their magnetically split components. The most complete review of the previous magnetic studies of 33 Lib is presented in Mathys (2017). Their seven measurements of the mean magnetic field modulus $\left<B\right>$ using magnetically resolved lines in observations acquired between 1996 and 1998 appear to be constant in the range from 4.63 to 4.69 kG, whereas the $\left<B_{\rm z}\right>$-values from the same observations range from 1.47 to 1.68 kG. Taking into account all previous measurements of $\left<B_{\rm z}\right>$-values, Mathys (2017) suggest that this star has a rotational period $P_{\rm rot}$ of 5195 d (approximately 14.25 yr).

On the other hand, Giarrusso et al. (2022) recently reported that $\left<B\right>$ and $\left<B_{\rm z}\right>$-values have shown a slight increase over several years, indicating that the rotation period should be longer than 27 yr. Our measurement of the mean field modulus using the HARPSpol observations obtained in 2012 August, $\left<B\right>=4.76\pm 0.02$ kG, is of the same order as reported by Giarrusso et al. (2022). As an illustration, we show the Zeeman subcomponents of the resolved magnetically split Fe ii line at 6149.258 Å in Fig. 5. No measurements of the mean longitudinal magnetic field after 2007 were presented by Giarrusso et al. (2022). Our measurement of the mean longitudinal field strength using all lines, $\left<B_{\rm z}\right>=1.54\pm 0.02$ kG, does not confirm the slight increase, but the small differences in the field values can be caused by the choice of spectral lines used in the measurements. As we see in Fig. 6, which presents the LSD Stokes $I$, Stokes $V$, and diagnostic null $N$ profiles calculated using five different masks, and in Table 2, the amplitude of the Zeeman features and the measured field values for this star depend on the line masks constructed for individual elements: We measure $\left<B_{\rm z}\right>=1.94\pm 0.05$ kG using 34 Pr iii lines, but only $\left<B_{\rm z}\right>=1.09\pm 0.04$ kG using 14 Nd iii lines. In any case, the comparison of our measurements with previous measurements confirm a long rotation period for HD 137949.

A full analysis of short-period oscillations (typical for roAp stars) was done for HD 137949 by Holdsworth et al. (2018) based on 60-s cadence K2 observations. The authors found that the low-frequency peaks were aliases of the frequency splitting, and that the rotation period was likely extremely long. The amplitude spectra of 33 Lib were presented in Figures 1 and 2 of Holdsworth et al. (2018).

This star is classified as F0 SrEuCr in Renson & Manfroid (2009). The presence of a weak magnetic field of the order of 0.7 kG was announced by Titarenko et al. (2013). They report that in contrast to ordinary Ap stars that exhibit strong REE lines in their spectra, these elements are represented only very poorly in the atmosphere of HD 138633. A photometric study using the STEREO satellites suggested that this star is constant or probably constant (Wraight et al., 2012). On the other hand, Romanyuk et al. (2017) report on the change of the field polarity in the measurements of the mean longitudinal magnetic field in spectra acquired in 2010 on two different nights separated by 5 days, with $\left<B_{\rm z}\right>=310\pm 30$ G and $\left<B_{\rm z}\right>=-290\pm 20$ G.

To check the short- and long-term line profile variability of HD 138633, we compared the line profile shapes observed with HARPSpol in 2019 with those observed using UVES on 2004 March 5 and CES on 2002 January 25. In Fig. 7, we display a few line profiles observed with these spectrographs in the same spectral region as shown in Fig. 1. Some tiny changes in the line shapes between the two CES spectra separated in time by 14 minutes seem to exist, but obviously higher $S/N$ data are needed to achieve any conclusion about any rapid spectral variability of this star.

In Fig. 8 we present the LSD Stokes $I$, Stokes $V$, and diagnostic null $N$ profiles calculated using five different masks. Using all lines for the measurements, we obtain a positive longitudinal magnetic field on the order of 200 G, which is comparable to measurements carried out using different line masks (see Tables 1–2). The strongest field, $\left<B_{\rm z}\right>=257\pm 30$ G, is detected for the Pr iii line mask. Based on the strengths of the LSD Stokes $I$ profiles of the studied REEs, we cannot confirm the finding of Titarenko et al. (2013) that these elements are represented very poorly in the atmosphere of HD 138633.

Due to significant scattered light from both the Moon and the Earth entering Camera 1, the short-cadence TESS data of HD 138633 suffers from a data gap of approximately 10 days. Using the available photometry, we performed a DFT (see, Fig. 9) and were unable to find any significant peaks in the periodogram that could correspond to either pulsations or rotation. This suggests that this star has a long rotational period that is at least longer than the length of the TESS observations. Due to the short length and poor quality of the TESS short-cadence data, we are unable to identify any evidence for the finding of Titarenko et al. (2013) that this star belongs to the group of rapidly oscillating Ap stars and possesses a pulsation period of $\sim 17$ min.

The star is classified as A0 Si in Renson & Manfroid (2009). Catalano & Renson (1998) noted that it exhibits variability in its luminosity and/or colour, but do not report an associated period. The study of Kervella et al. (2019) indicated the presence of a companion from an analysis of proper motions in the GDR2 and Hipparcos catalogues. Magnetic field measurements have not been reported for this star in the past. Our measurements presented in Tables 1 and 2 and in Figs. 2 and 10 show that the magnetic field is very weak, with $\left<B_{\rm z}\right>=-45\pm 3$ G measured using all lines. It is striking that for the Pr iii line mask our measurements yield a much higher field strength, $\left<B_{\rm z}\right>=-171\pm 25$ G, while the measurements using other masks are all below $-75$ G. These results show that great care should be taken in the selection of line lists for the measurements of weak magnetic fields.

The analysis of the TESS observations of HD 174779 reveals two marginal peaks in the periodogram (see Fig. 11). The first corresponds to a period of $3.7933\pm 0.0003$ d with S/N of 4.11. The second, higher-frequency peak with a similar S/N corresponds to the period of $1.11473\pm 0.0001$ d. We avoid any physical interpretation of these two peaks due to their marginal significance, and note that there is no clear, salient evidence of rotation from the light curve.

This star is classified as B9 EuCr in Renson & Manfroid (2009). The study of Kervella et al. (2019) indicated the presence of a companion from an analysis of proper motions in the GDR2 and Hipparcos catalogues. First detections of the mean longitudinal magnetic field, $\left<B_{\rm z}\right>=258\pm 69$ G and $\left<B_{\rm z}\right>=174\pm 58$ G, were reported by Hubrig et al. (2006) using low resolution spectropolarimetry with the FORS 1 instrument installed at the ESO VLT.

Our measurements, separated by two nights, are presented in Tables 1 and 2 and in Figs. 2 and 12 and show almost identical, rather low, mean longitudinal field strengths on the order of 100–120 G. For the measurements using the Pr iii line mask, the field strength reaches 180–190 G. Given the small change in the field strength since the first observations by Hubrig et al. (2006), it is very likely that the rotation period of HD 176196 is quite long.

Not much is known for this star. It is classified as A6 SrCrEu in Renson & Manfroid (2009). The study of Kervella et al. (2019) indicated the presence of a companion from an analysis of proper motions in the GDR2 and Hipparcos catalogues. A rotational period $P_{\rm rot}$ of 18.89 d was mentioned in Manfroid & Mathys (1985), who used ground-based photometry to arrive at this value. Magnetic field measurements have not been reported for this star in the past. Similar to HD 176196, our measurements for this star, displayed in Tables 1 and 2 and in Figs. 2 and 13, show the presence of a positive weak magnetic field, with a somewhat stronger field, $\left<B_{\rm z}\right>=184\pm 21$ G, measured using the Pr iii line mask.

This star is classified as A5 SrEu in Renson & Manfroid (2009). It is a roAp star (Kurtz, 1984), with a pulsation period of about 6.2 min. Holdsworth et al. (2021) reported a rotational period of 6.44 d, based on TESS data. Mathys & Hubrig (1997) were unable to identify the presence of a magnetic field. Later on, Hubrig et al. (2004b) reported $\left<B_{\rm z}\right>=-267\pm 72$ G measured in low-resolution FORS 1 polarimetric spectra acquired in 2002. Our analysis, shown in Tables 1 and 2 and in Figs. 2 and 14, yields the lowest mean longitudinal field strength when all lines are used in the measurement, but the field strength is as high as 150 G in the measurements using only the Eu ii line mask. Notably, the shape of the calculated Zeeman features in Figs. 2 and 14 corresponds to a typical crossover profile, which results from the correlation between the Zeeman effect and the rotation-induced Doppler effect across the stellar surface.

This star is classified as A5 SrEuCr in Renson & Manfroid (2009). It is a rapidly pulsating star with a pulsation period of about 13.7 min (Medupe et al., 2015). Hubrig et al. (2002) showed that HD 217522 is very similar to Przybylski’s star (HD 101065), which exhibits the most complex spectra known, with numerous lines of lanthanides and also rotates extremely slowly, with a probable $P_{\rm rot}$ of about 188 yr (Hubrig et al., 2018). The study of Kervella et al. (2019) indicated the presence of a companion from an analysis of proper motions in the GDR2 and Hipparcos catalogues, but no companion candidate was detected using diffraction-limited near-infrared imaging with NAOS-CONICA at the VLT by Schöller et al. (2012).

The first detection of a magnetic field of about $-400$ G was reported by Mathys & Hubrig (1997) using the ESO Cassegrain Echelle Spectrograph (CASPEC), fed by the ESO 3.6 m telescope, for observations acquired in 1992. One additional observation was obtained in 1997 with $\left<B_{\rm z}\right>=-559\pm 63$ G (Hubrig et al., 2002). Later, Hubrig et al. (2004b) reported $\left<B_{\rm z}\right>=-725\pm 88$ G using low-resolution spectropolarimetry with FORS 1. No variability of the field strength over the pulsation cycle was detected by Hubrig et al. (2004a) using a FORS 1 spectropolarimetric time series.

Our analysis presented in Tables 1 and 2 and in Figs. 2 and 15 is based on two HARPSpol observations, one from 2012 August and the second one from 2019 June. A comparison of the measurements indicates that the field in the measurements using all lines has slightly decreased from $\left<B_{\rm z}\right>=-401\pm 6$ G to $\left<B_{\rm z}\right>=-323\pm 6$ G. Assuming that the maximum field strength was reached in the year 2004, the expected rotation period should be at least of the order of a few tens of years. The strongest field strength was measured using the Pr iii line mask, reaching $\left<B_{\rm z}\right>=-552\pm 59$ G in the observations acquired in 2012.

This star is classified as B9 EuCrSr in Renson & Manfroid (2009) and was used in our observations as a standard star. It possesses an extremely strong magnetic field with a mean field modulus of the order of 14–15 kG. Because of the strength of this field, numerous lines in the spectra of HD 70702 appear resolved into their magnetically split components (Elkin, Kurtz & Nitschelm, 2012). Both of our HARPS spectra are rather noisy and, in addition, the precision of the measurements is limited by the distortion of the lines as a result of the combination of the Zeeman effect and the rotational Doppler effect. The measurements of the mean magnetic field modulus, $\left<B\right>=15.2\pm 0.9$ kG (from a spectrum obtained on 2019 July 13) and $\left<B\right>=14.0\pm 0.5$ kG (from a spectrum obtained on 2019 July 16), are presented in Fig. 16. They are in good agreement with the previously published value of 15 kG in Elkin, Kurtz & Nitschelm (2012). In Fig. 17, we present the LSD Stokes $I$, Stokes $V$, and diagnostic null $N$ profiles calculated for both observing epochs using five different masks. The strong variability of HD 70702 is obvious and is clearly reflected in the measurement results presented in Tables 1 and 2, as well as in the distinct changes of the amplitude of the Stokes $V$ profiles between both epochs. The strongest mean longitudinal magnetic field is detected using the Nd iii line mask in the observations from the first epoch, suggesting that this element, in comparison to other elements, is concentrated in a region of the surface located closer to the magnetic pole.

In the DFT for this star, we combined the data from Sectors 8 and 9 to find three significant periods. Contamination from other stars is likely minimal, since the CROWDSAP parameter suggests that only 1.5% of the flux in the optimal aperture does not belong to HD 70702. We observe a strong rotational modulation with $P_{\rm rot}=3.7601\pm 0.0007$ d, as well as a short-period modulation – perhaps due to pulsation – at $P_{\rm puls}=0.39019\pm 0.00001$ d. The other significant peak, at $P=1.8782\pm 0.0002$ d, has a lower $S/N$ than the others ($\sim 5$), but still meets our significance criterion. This peak can be identified as a harmonic of $P_{\rm rot}$, given that it is exactly twice the frequency (to within the uncertainty of the data) of the lower-frequency peak. Using the same argument, the small peak visible near $\nu=5$ d^-1 is almost certainly a harmonic of $P_{\rm puls}$. The light curve and Fourier transform for HD 70702 are shown in Fig. 18.

Since the TESS data show a clear rotation period, we can calculate the phases of our HARPS observations. Using as initial epoch $T_{0}$ the value TJD 1564.13520327 (=JD 2458564.13520327), which corresponds to the time of minimum light, we calculate $\varphi=0.306$ for the first observation and $\varphi=0.094$ for the second observation. Since this star has a rather short rotation period and possesses an extremely strong magnetic field, it is an excellent candidate for future spectropolarimetric monitoring to map its magnetic field and chemical spots using Zeeman Doppler Imaging.