Discovery of Resolved Magnetically Split Lines in SDSS/APOGEE Spectra of 157 Ap/Bp Stars

Globally ordered magnetic fields are observed in roughly 10%–20% of intermediate and massive main sequence stars with spectral types between approximately F0 and B2. These stars, generally called chemically peculiar Ap and Bp stars (referred to as Ap stars in the rest of this Letter, for simplicity's sake), exhibit strong overabundances of certain iron peak elements and rare earths. The majority also exhibit underabundances of He, C, and O relative to solar abundances (e.g., Ghazaryan et al. 2018), though the more massive Bp stars usually show overabundances of He and Si (e.g., Castro et al. 2017). These effects are caused by the disruption of normal diffusion processes by the strong magnetic fields. As stars of more than a few solar masses are expected to lack significant surface convection zones in which magnetic dynamos are generated in low-mass stars, the strong magnetic fields of Ap stars are unexpected and often attributed to fossil fields inherited from the collapsed gas clouds (Moss 2001).

The magnetic fields of Ap stars are most frequently diagnosed through spectropolarimetric measurements of the mean longitudinal field, $\langle {B}_{{\rm{z}}}\rangle$, which is strongly dependent on the line of sight but can be obtained for the majority of Ap stars regardless of their rotation rates. However, an important group is formed by the Ap stars with low projected rotational velocities and strong kG magnetic fields. For these stars, conventional spectroscopy of sufficient resolution can be used to measure the mean magnetic field modulus, $\langle B\rangle$, based on the wavelength separations of resolved, magnetically split lines (RMSLs). Although somewhat dependent on the geometry of the observation, $\langle B\rangle$ has the advantage of being primarily determined by the intrinsic stellar magnetic field strength. Prior to this work, 84 Ap stars with RMSLs were known (Mathys 2017), and their study allowed the measurement of their magnetic fields and the establishment of a number of general properties. The star with the strongest magnetic field currently known, "Babcock's Star" (HD 215441), is a B8V star with a surface dipole field strength of 34 kG (Babcock 1960; Preston 1969).

The vast majority of past studies of Ap stars with RSMLs have relied on optical data of very slowly rotating stars (for which the Doppler effect does not serve to blend the split components), but spectroscopy at longer wavelengths provides several advantages in terms of resolving magnetically split lines. For example, the wavelength separation of magnetically split components is proportional to the square of the wavelength, such that for the fixed effective Landé factor, the spectral resolution required to resolve the split components of a line is significantly lower in the H-band than it would be in the optical. Further, the Doppler effect has a linear dependence on wavelength, such that magnetic splitting can be resolved in the H-band for stars that are rotating too fast for the splitting to be resolved in the optical.

In this Letter we present the analysis of a sub-sample of 154 new stars with RMSLs in the H-band, as well as of 3 stars for which RMSLs had been observed previously in the optical. The 157 stars were identified among the largest-ever spectroscopic survey of Ap stars to date, being carried out by the Sloan Digital Sky Survey (SDSS-III and SDSS-IV; Eisenstein et al. 2011; Blanton et al. 2017) sub-survey known as the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017). This near-tripling of the number of Ap stars with $\langle B\rangle$ measurement is due partially to the volume and depth of the APOGEE survey. The 157 RSML stars were identified among a much larger sample of ∼1000 Ap/Am stars with multi-epoch APOGEE observations, and the 91/157 stars with V magnitudes greater than 10 represents a 3000% increase in the number of $V\gt 10$ Ap stars for which $\langle B\rangle$ has been measured.

2.1. APOGEE H-band Spectroscopy

2.2. ARCES Optical Spectroscopy

The APOGEE Ap star sample currently consists of 986 stars that APOGEE has observed together more than 5500 times, with the about 85% of the stars having been identified among the APOGEE telluric standard stars via an algorithm designed to search for the presence of the doubly ionized Cerium (Ce iii) lines that are usually the strongest absorption features aside from the broad hydrogen Bracket series lines. The other 15% of the stars lack the Ce iii lines and were instead added to the sample based on literature Ap/Bp/Am classifications (for detailed definitions of these spectral classes, see Chapter 5.2 of Gray & Corbally 2009). These 986 Ap/Bp/Am stars therefore account for just over 2% of the APOGEE telluric standard stars, but this should be taken as a lower limit to the true fraction.

Whereas the overall sample will be discussed in future work, this Letter deals with the 157 stars (886 total spectra) for which RMSLs were visually identified in one or more APOGEE spectra. For the majority of the 157 stars, RMSLs appear in multiple observations such that absorption lines in the combined spectra clearly exhibit splitting. However, 17/157 stars have only been observed once to date, and in another 49/157 cases, the RMSLs were noticed and measured in an individual spectrum rather than the combined spectrum. Usually this was due to one of the individual spectra having significantly higher S/N than the others, but in some cases, it was almost certainly due to temporal variability of the magnetic field strength.

We used the APOGEE linelist (Shetrone et al. 2015) to identify the majority of absorption lines present in the H-band spectra. Atomic data for the Ce iii lines was obtained from a Ce iii linelist computed by Biémont et al. (2002). This linelist was previously used by Hubrig et al. (2012; provided to them as private communication by Biemont et al.), who were the first to confirm the presence of Ce iii lines in H-band spectra of Ap stars. For the optical follow-up spectra, we relied on the Kurucz linelist¹² for line identification.

One or more ions are clearly missing from our H-band linelist, as indicated by several unidentified lines exhibiting RMSLs in the spectra of numerous stars. These features are usually detected simultaneously and they are occasionally the only metallic absorption features beyond Ce iii. They are probably due to some heavy element that cannot be identified owing to the limited availability of atomic data for λ > 10000 Å. The strongest of these unknown lines is the 16184 Å line, for which magnetically split components are observed in ∼31% of the larger Ap star sample. We used a sub-sample of 20 narrow-lined Ap stars exhibiting the unknown lines to measure accurate wavelengths for the features. Figure 1 displays the full APOGEE spectrum of one such narrow-lined star (2MASSJ 01023033+7438487) along with a star for which the unknown lines are magnetically split (2MASSJ 06010117+3214538).

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The Ce iii lines (15961, 15965, 16133 Å, and in cases of strong Ce iii, also 16292 and 15720 Å) are present in 100% of the sample at hand, with the 16133 Å line exhibiting RMSLs for 63% of the sample and with the weaker 15961 Å and 16292 Å lines being split for 43% and 32% of the sample, respectively. The Ce iii 15965 Å line is often blended with the strongest Si i line covered (15964 Å), such that the splitting of Ce iii 15965 Å can only be measured when the presence of Si i lines can be ruled out by confirming absence of Si i 15893 Å and 16685 Å. The fraction of stars with Ce iii 16133 Å measurements would be even higher were it not for a strong airglow feature (16129 Å) that is often poorly subtracted and may coincide with the blue wing of the Ce iii line depending on the stellar radial velocity.

Cr ii is the next most frequently magnetically split ion, with the splitting of the 15370 and 15470 Å lines being measurable in 50% and 39% of the sample, respectively. Other particularly useful lines include Fe i 15299 Å (34%), Fe i 15626 Å (31%), Fe i 16491 Å (27%), Si i 16685 Å (25%), as well as the unidentified line at 16184 Å (31%). Unlike the situation in the optical, where Ap stars typically exhibit numerous Fe ii and Ti ii lines, no Fe ii lines are confidently detected in the spectra of any stars, and Ti ii detections are quite rare. The star 2MASS J23102121+4717017 is the only available example where more than two magnetically split Ti ii lines were resolved.

Given the measurements of the wavelength separations of magnetically split components in a given absorption line and knowledge of the Landé g factors of the associated energy levels, it is straightforward to compute the mean magnetic field modulus $\langle B\rangle$ in units of Gauss according to

$$\begin{eqnarray}&&\langle B\rangle =\displaystyle \frac{{\rm{\Delta }}\lambda }{k\,{g}_{\mathrm{eff}}\,{\lambda }_{0}^{2}}.\end{eqnarray} \tag{ 1 }$$

Here, Δλ is the separation in Å between an outer and the central split component or else half of the separation between outer components in a triplet profile. λ₀ is the rest wavelength of the line in Å and k is a constant, 4.67 × 10⁻¹³ Å⁻¹ G⁻¹. It is important to note that although we have only analyzed spectral lines exhibiting apparent triplet profiles like those shown in the lower panels of Figure 1, the Zeeman patterns (see Mathys 1990) of the H-band lines have not been investigated and Equation (1) is therefore an approximation.

The effective Landé factor (g_eff) of a given transition is calculated using the total angular momentum quantum numbers (J) and Landé factors (g) of the lower (1) and upper level (2) as follows:

$$\begin{eqnarray}&&{g}_{\mathrm{eff}}=\displaystyle \frac{1}{2}({g}_{1}+{g}_{2})+\displaystyle \frac{1}{4}({g}_{1}-{g}_{2})\left[{J}_{1}({J}_{1}+1)-{J}_{2}({J}_{2}+1)\right],\end{eqnarray} \tag{ 2 }$$

where in the case of J₁ = J₂, g_eff is simply the average of the Landé factors of the lower and upper levels.

To measure Δλ, we either fit Gaussians to the absorption features or simply estimated their positions visually. This was done interactively using the splot program in IRAF. For each star, the splitting was measured for as many lines as possible and the results were averaged, with assumed or derived errors on g_eff being propagated appropriately. On average, measurements from ∼13 lines per star were used, but the range of number of lines used is quite large. In a few cases, the magnetic splitting could only be measured in two to three lines, often because the only metallic lines present are Ce iii. In the case of 2MASS J06365367+0118455 however, the splitting of 61 lines was measured.

The J and g values used here were taken from the Kurucz linelist, and we assumed a constant uncertainty of 0.02 for the g_eff of lines with existing laboratory data. However, laboratory data are unavailable for the Ce iii lines and for the unknown lines (see Section 4), such that it was necessary to estimate the g_eff of these lines. To do so, we defined a sub-sample of 34/157 stars with high-S/N spectra, particularly well-resolved magnetically split features, and measurements of lines with known g_eff in addition to Ce iii and the unknown lines. The lines with known g_eff were used to calculate preliminary $\langle B\rangle$ measurements for the 34 stars. These values were then used derive average estimates of g_eff for the Ce iii and unknown lines.

Table 1 summarizes the 149 lines used for measurement of $\langle B\rangle$, providing the vacuum wavelength, log(gf), energy levels, and g_eff for each line, as well as the number of stars for which magnetic splitting was measured. Overall, we find relatively low g_eff for Ce iii and the unknown lines, which together average g_eff ∼ 1.07. The weak Ce iii 15720 Å line has the highest estimated value at g_eff ∼ 1.39, but unfortunately this line is rarely observed.

5.1. H-band Results

The upper panel of Figure 2 shows the distribution of measured $\langle B\rangle$ of all Ap stars known to exhibit RMSLs, with the new discoveries presented in this Letter shaded in green and with those from Mathys (2017) shaded in gray. The average for the APOGEE sample is $\langle B\rangle$ ∼ 7.1 kG, while the average for all stars including those of Mathys (2017) is a bit higher at $\langle B\rangle$ ∼ 7.3 kG due to the inclusion of Babcock's Star. The distribution of $\langle B\rangle$ measured using APOGEE spectra ranges from ∼3.6 kG in the case of 2MASS J02463240+0001145 up to ∼25 kG in the case of 2MASS J02563098+4534239. A total of 19 new examples of stars with $\langle B\rangle$ > 10 kG are identified, thus filling in the previous gap between 10–11 kG.

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The lower limit on $\langle B\rangle$ of ∼3.5 kG measurable from the APOGEE spectra is a consequence of resolving power, whereby the smallest splitting that we can measure is about 0.6 Å. For a star with strong Mn i 15222 Å (g_eff = 1.969), splitting should be visible down to $\langle B\rangle$ of just below 3 kG. No such examples have been found, however, meaning that it is not possible to investigate the notion of an intrinsic lower limit to measurable field strength of $\langle B\rangle$ ∼ 2 kG (Mathys 2017).

Figure 3 shows an example of a magnetically split line for each of the 157 stars, generally showing the most clearly resolved line. In the cases where Ce iii 16133 Å is displayed, narrow spikes blueward of the line are residuals from the imperfect removal of the aforementioned strong airglow line at 16129 Å.

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5.2. Optical Results

The same procedure described in Section 5 was applied to the 29 optical follow-up spectra obtained with the ARC 3.5 m telescope and ARCES spectrograph in order to provide a sanity check on the H-band measurements of $\langle B\rangle$. As expected, the stars exhibit numerous RMSLs in the optical. For the 19/29 stars with $\langle B\rangle$ < 8 kG, we relied primarily on limited numbers of long wavelength lines (7000–10200 Å), while for the 10/29 stars with $\langle B\rangle$ > 9 kG, we measured hundreds of RMSLs for each star, keeping the 50 lines nearest to the average. Another 3 of the 157 stars were included in the Mathys (2017) sample of stars for which magnetically split lines had been previously resolved in optical spectra.

As demonstrated in the lower panel of Figure 2, we find good agreement overall between the H-band and optical measurements, with the results agreeing to within a kG in most cases. The most discrepant results pertain to the star 2MASSJ 07123042-2103537 (HD 55540), where we find $\langle B\rangle$ = 15.0 kG despite Freyhammer et al. (2008) having found $\langle B\rangle$ = 12.7 kG. The three available APOGEE spectra of this star allow us to confirm that not only is the difference due to temporal variability of the observed $\langle B\rangle$, but also that the star is indeed radial velocity variable as pointed out by Freyhammer et al. (2008).

We also used the optical spectra to estimate traditional spectral types based on comparison of the target stars to a sample of 30 bright A and B stars with spectra in the ELODIE Archive (Prugniel & Soubiran 2001). Stars with clear detections of He i 4471 Å and weak or missing Fe i, Mg i, Ca i, and Mn i lines were assigned temperature classes of B8 or B9, while the A stars were classified based on the equivalent widths of temperature-dependent lines (e.g., Fe i 4045 Å, Mg i 5183 Å, Ca i 4227 Å, Mn i 4031 Å) as well the ratios of neutral versus singly ionized lines (e.g., Mg i/Mg ii and Fe i/Fe ii). Due in part to difficulty finding the continuum around the wings of the hydrogen Balmer series lines in the ARCES camera's small wavelength ranges per order, luminosity classes were not estimated. Anomalously strong absorption lines from Si, Cr, Sr, and Eu are specifically flagged.

Table 2 summarizes the H-band and optical magnetic field modulus measurements, giving 2MASS designations, alternate identifiers, V magnitudes from UCAC4 (Zacharias et al. 2013), H magnitudes from 2MASS, the number of APOGEE spectra of each star, the S/N of the combined spectrum, a literature or estimated spectral type if available, the magnetic field modulus $\langle B\rangle$, and the number of spectral lines used to measure $\langle B\rangle$. In the cases where optical measurements were available, the final columns of Table 2 provide the associated $\langle B\rangle$ measurement and the number of spectral lines used. Less reliable measurements of $\langle B\rangle$, usually due to large scatter between different lines and/or measurements near the resolution limit of APOGEE are given in parentheses in Table 2.

Table 2.  Magnetic Field Modulus Estimates

2MASS ID	Other ID	V	H	Nspectra	S/N	Spec. Type	$\langle B\rangle$ (kG)	Nlines	$\langle B\rangle$ (kG)	Nlines
		(mag)	(mag)				H-band	H-band	Optical	Optical
00033808+7018217	HD 225114	8.10	8.19	12	726	A0p SrCrSia	7.46 ± 0.54	8	7.43 ± 0.32a	36
00102704+7337035	TYC 4306-1062-1	10.84	10.07	9	537	⋯	4.17 ± 0.28	16	⋯	⋯
00283062+6947472	TYC 4299-696-1	10.53	9.45	12	682	⋯	7.92 ± 0.89	4	⋯	⋯
00284036+8418313	TYC 4615-2915-1	10.96	10.54	14	332	A2Vb	5.10 ± 0.22	17	⋯	⋯
00323366+5512530	HD 2887	9.79	8.17	13	1793	A2:p SrCra	4.95 ± 0.24	25	4.97 ± 0.22a	27
00331847+5716167	TYC 3662-378-1	10.70	10.37	6	481	⋯	(8.53 ± 0.79)	5	⋯	⋯
00564145+5739255	TYC 3676-505-1	11.19	10.96	3	86	⋯	18.49 ± 0.76	6	⋯	⋯
00584870+6240562	TYC 4021-632-1	11.22	10.45	6	411	A2:p Eua	4.25 ± 0.29	15	4.60 ± 0.19a	22
01052242+5010296	TYC 3271-1597-1	10.49	10.22	3	266	⋯	(6.79 ± 1.13)	3	⋯	⋯
01184266+5844433	TYC 3681-1528-1	10.49	9.99	4	355	B8b	9.67 ± 0.50	9	⋯	⋯

Notes.

^aOwn data (ARC 3.5 m/ARCES). ^bSkiff (2014). ^cRenson & Manfroid (2009). ^dSIMBAD. ^eMathys (2017). ^fFreyhammer et al. (2008).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Although spectroscopic observations at long wavelengths such as in the H-band help to maximize the Δλ term of Equation (1) and to lessen the impact of blending due to the Doppler effect, this Letter represents the first serious exploitation of this wavelength regime for investigating the magnetic fields of Ap stars. The APOGEE sample of Ap stars with RMSLs represents a 183% increase in the number of Ap stars with $\langle B\rangle$ measurements, bringing the total to 238 stars. As the SDSS/APOGEE survey is still ongoing, this number is expected to increase. Detailed characterization of the now much larger sample of Ap stars with RSMLs may help to shed light on the origin of magnetic fields in stars with radiative envelopes as well as the relations between magnetism and other factors such as binarity and rotation. In particular, the investigation of the stellar parameters and chemical abundances of the sample would be a worthwhile effort, as would be high-resolution spectroscopic monitoring to measure the average value of $\langle B\rangle$ and the rotational period.

As demonstrated in the histogram of magnetic field modulus presented in Figure 2, more than 50% of Ap stars with magnetically split lines possess magnetic fields in the range of 4–7 kG. Despite the identification among the APOGEE sample of 19 new examples of stars with $\langle B\rangle$ > 10 kG, led by 2MASS J02563098+4534239 ($\langle B\rangle$ = 25 kG), the high-$\langle B\rangle$ tail of the distribution remains capped by the 34 kG magnetic field of Babcock's Star (HD 215441; Babcock 1960). The only other non-degenerate star known to approach 30 kG is HD 75049 (Elkin et al. 2010), for which $\langle B\rangle$ ranges from 24 to 30 kG over an orbital period. Among the more massive magnetic stars, which are He-rich early-type B stars, the strongest known magnetic field is only 21 kG (Hubrig et al. 2017). We can speculate that the magnetic field value of 34 kG likely represents a critical field strength above which stable magnetic fields do not exist in Ap stars. Such a limit would be probably be related to the restricted range of seed fields, of the order of milli-Gauss, that are observed in star-forming regions (Han & Zhang 2007).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is www.sdss.org.

SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

D.A.G.H. and O.Z. acknowledge support from the State Research Agency (AEI) of the Spanish Ministry of Science, Innovation and Universities (MCIU) and the European Regional Development Fund (FEDER) under grant AYA2017-88254-P.

We thank the referee for numerous useful suggestions that improved this Letter.