A rare phosphorus-rich star in an eclipsing binary from TESS

Our spectral observations sampled 11 individual nights over a baseline of ${\approx}10\,$months. This allowed us to determine the radial velocity amplitude $K_{\rm RV}$ of the primary and constrain the nature of the transiting companion. Radial velocity (RV) measurements were performed on the long-slit spectra using a cross-correlation approach and the iraf task fxcor (Fitzpatrick, 1994). The correlation template was a normalized $R=20\,000$ model spectrum from Munari et al. (2005), specifically the model in their grid closest to our derived parameters. The resulting instantaneous RV values range from $-28.5$ to $7.2\,$km s^-1 and are listed in Table 6. Fitting the RV curve with a pure sine wave and assuming zero eccentricity, we find $K_{\rm RV}=(13.72\pm 0.63)\,$km s^-1.

TESS has observed HD 235349 (TOI $1356.01$) in sectors 15 and 16, where two exoplanet transit-like events were discovered. The depth of those events is $\approx 7.5$ ppt. The photometric data from the TESS data portal has strong systematic effects, therefore we measured target and several surrounding comparison stars from cuts of TESS calibrated full-field images using traditional aperture photometry methods. Remaining residuals in the lightcurve were removed by fitting with a low order cubic spline.

The ExoFOP-TESS database reports a period of $24.28546\pm 0.00102$ days for these transits. Phase folding our extraction of the TESS photometry with this period, we find a good agreement in the timing of the eclipses, thus we confirm the period reported in ExoFOP-TESS. Figure 5 shows the phase-folded TESS lightcurve and our radial velocity time-series for HD 235349. The offset of the radial velocity curve from the transit phase curve suggests an eccentric orbit, though we caution that due to possible systematics in our long-slit spectra, stable higher S/N follow-up is necessary to test this.

The spectroscopically determined best-fit parameters of HD 235349 are summarized in Table 5. We adopt here the values determined from the hydrogen Balmer lines: $T_{\rm eff}$ $=14\,757\pm 264\,$K and $\log\,{g}$ $=3.34\pm 0.11$.

The current mass and age of HD 235349 were determined by comparing its position in an effective temperature ($T_{\rm eff}$) – surface gravity ($\log\,{g}$) diagram with stellar evolution models without rotation at solar metallicity ($Z=0.014$; Ekström et al., 2012), as shown in Fig. 6, and interpolating between models in log mass. From this, we find a stellar mass $M_{\star}$ $=6.7^{+0.9}_{-0.8}\,M_{\sun}$, radius $R_{\star}$ $=9.2^{+1.8}_{-1.5}\,R_{\sun}$, and luminosity $\log(L_{\star}/L_{\sun})=3.55\pm 0.19$. We adopt these as our final values. As a consistency check, empirical calibrations of $M_{\star}$ and $R_{\star}$ as polynomial functions of $T_{\rm eff}$, $\log\,{g}$ and [Fe/H] (Torres et al., 2010) give consistent results with the above numbers.

The distance to HD 235349 was recently determined to be $d=1901\pm 180\,$pc using the Gaia EDR3 parallax (Bailer-Jones et al., 2021). However, the current value may not be entirely reliable, since the Renormalised Unit Weight Error (RUWE) is 2.842, while ‘good’ solutions should have a RUWE near 1.0 (or ¡ 1.4), and the “Goodness of fit statistic of model wrt along-scan observations” parameter is 38.3435, while good fits to the data should be $<3$. The EDR3 parallax ($0.5051\pm 0.0498$ mas) is also statistically incompatible with the DR2 value ($0.1530\pm 0.0834$ mas). The newer EDR3 value is likely more reliable (the older value has similar quality warnings), but we consider the possibility that there is a significant systematic error in the value. Relying on the spectroscopic stellar parameters and apparent magnitude, we can compare the Gaia distance with a luminosity-based distance. We use the previously calculated $\log(L/L_{\sun})=3.55\pm 0.19$ to obtain the stellar bolometric magnitude. Adopting a solar bolometric luminosity $L_{\sun}=3.828\times 10^{26}\,$W and an absolute bolometric magnitude $M_{\mathrm{bol}}=0\,$mag for a luminosity $L_{0}=3.0128\times 10^{28}\,$W (Resolution B2 of the XXIXth International Astronomical Union General Assembly in 2015), we obtain

Applying a bolometric correction $BC_{\rm V}=-1.19\pm 0.04$ (Pedersen et al., 2020), we find an absolute magnitude of $M_{\rm V}=-2.95\pm 0.52\,$mag. The apparent magnitude is $m_{V}=9.043\pm 0.003\,$mag and the reddening $E(B-V)=0.263\pm 0.050$ (Stassun et al., 2019). Assuming $R(V)=3.1$, we find an extinction of $A_{V}=0.817\pm 0.156$.

Using the standard relation

where $d$ is in parsecs, we then find that HD 235349 is $d=1721\pm 543$ pc away, consistent within errorbars with the distance from Gaia EDR3 determined by Bailer-Jones et al. (2021).

We further use the theoretical isochrones from Ekström et al. (2012) to determine an age $\log\tau\approx 7.68\pm 0.10\,$yr. This is also illustrated in Fig. 6. Using the corresponding evolutionary tracks, we find that on the zero-age main sequence, HD 235349 would have had $T_{\rm eff}$ $\approx 21\,000$ K and $\log\,{g}$$\,\sim 4.35$.

The best fit chemical abundances (see Table 5) and plotted relative to solar abundances in Fig. 7 (in $\log(\mathrm{X}/\mathrm{H})$ units). We find a strong overabundance of P by $1.48\pm 0.20$ dex relative to solar, and significant overabundances of Ne by $0.65\pm 0.23$ dex, and of Ti by $0.66\pm 0.20$ dex. Nd also appears to be strongly overabundant, although this is less certain as it is based on a few marginally detected lines. Mn and Ni are marginally enhanced (by $0.54\pm 0.27$ and $0.38\pm 0.14$ dex, respectively). C, O, Mg, Al, and Fe are all consistent with solar abundances (within $2\sigma$). He appears to be weakly depleted ($-0.25\pm 0.10$ dex), although this abundance is particularly sensitive to $T_{\rm eff}$. Si also appears to be slightly depleted ($-0.34\pm 0.16$ dex). Thus HD 235349 is clearly chemically peculiar, although it does not display the peculiarities typical of an HgMn star, and is only a very mild, marginally He-weak star (although it does have the enhanced P common to the He-weak PGa stars).

The He abundance is particularly temperature sensitive, if our $T_{\rm eff}$ were overestimated by $\sim$500 K the He abundance would be within uncertainty of solar (see Appendix B). Alternately, if our $T_{\rm eff}$ was underestimated, that could lead to a larger He underabundance. Ne I lines may show some weak non-local thermodynamic equilibrium (NLTE) effects in B-type stars (Alexeeva et al., 2020) (for Ne II NLTE corrections appear to be negligible). NLTE corrections for Ne I at a $T_{\rm eff}$ near 14 000 K appear to reduce the Ne abundance by a few 0.1 dex (Alexeeva et al., 2020), possibly exceeding our error bar, but unlikely to produce an abundance consistent with solar, or chemically normal B-type stars.

From analyzing individual P lines (Sect. 3.1.3) we find that lines formed mostly at smaller optical depths require significantly larger abundances of P to match the observations than lines formed deeper in the atmosphere. The individual abundances and depths where $\tau_{\ell}=1$ are plotted in Fig. 4, and we interpret this as evidence for stratification of P in the stellar atmosphere. From simultaneously fitting P lines with synthetic spectra in an MCMC analysis, we find a clear negative slope in abundance with $\log\tau_{5000}$ ($-0.52\pm 0.08$), and an abundance at $\tau_{5000}=1$ that is still enhanced relative to solar ($-5.76^{+0.13}_{-0.14}$ dex), with an important covariance between these two parameters. This P distribution is better constrained in the range of $\log\tau_{5000}$ between -1 and -2, and becomes poorly constrained above $\log\tau_{5000}$ -3 or below 0. A set of model P distributions from the final Markov chain are presented in Fig. 4 as overlapping gray lines, thus darker regions correspond to a higher density of models and a higher probability of the parameters. The posterior probability densities of the parameters are shown in Fig. 8. From the combination of the single line analysis and the parametric MCMC model, we find good evidence for stratification of P, with larger abundances higher in the atmosphere. However, since many lines of P are only marginally detected in our observations, higher precision data is needed before more details of the P distribution can be confidently constrained.

The mass of the secondary star can be constrained in two ways. Firstly, using the observed transit depth (7.5 ppt) and our radius estimate for the primary, we obtain the radius of the secondary, $R_{2}=0.79^{+0.16}_{-0.13}R_{\sun}$. In this radius estimate we assume the secondary is fully projected on the disk of the primary during photometric minimum, which is supported by the flat bottomed transits, and that the secondary contributes negligibly to the flux in the TESS band, which is supported by the small transit depth (suggesting a small cool object). In that case the ratio $R_{2}/R_{1}$ is the square root of the transit depth, and the uncertainty on $R_{2}$ is dominated by the uncertainty on $R_{1}$. Using a main sequence mass-radius relation for low-mass stars ( ${\leq}\,1.5\,M_{\sun}$, Eker et al., 2018), we find a secondary mass $M_{2}=0.80^{+0.13}_{-0.12}\,M_{\sun}$. Secondly, we can obtain $M_{2}$ from the radial velocity perturbation amplitude of the primary, given by

where $P_{\rm orb}$ is the orbital period, $e$ the orbital eccentricity, here assumed to be zero, $i$ is the inclination of the orbit, here assumed to be $90^{\circ}$, and $K_{\rm RV}=13.72\pm 0.63\,$km s^-1 (Sect. 3.2). This leads to a mass of $0.71^{+0.10}_{-0.09}$ $M_{\odot}$. If we instead assumed $i=80^{\circ}$, $M_{2}$ would increase by only $\sim$0.01 $M_{\odot}$. If we assumed $e=0.2$, that would decrease the mass by $\sim$0.02 $M_{\odot}$, and $e>0.45$ would be needed to exceed our formal error bar. We summarize these constraints on $M_{2}$ in Fig. 9. The results from both constraints are consistent, and point to $M_{2}$ in the range 0.7 – 0.8 $M_{\odot}$.

Using a Balmer line analysis, we determined an effective temperature $T_{\rm eff}$ $=14\,757\pm 264\,$K and $\log\,{g}$ $=3.34\pm 0.11$ for HD 235349. This yields a spectral type B6 III (Pecaut & Mamajek, 2013). These results are consistent with the highest $T_{\rm eff}$ and earliest spectral types from the wide range of past estimates. As noted earlier, the ExoFOP database lists two conflicting effective temperature values for HD 235349. The latest value, from the TESS project, is $T_{\rm eff}$ $=8381\pm 409\,$K. In the databases listed on ViZieR⁷⁷7http://simbad.u-strasbg.fr/simbad/sim-fid, a wider range of $T_{\rm eff}$ estimates can be found, corresponding to a spectral type range from mid-A to mid-B. Spectral type classifications spanning nearly 100 years have typically been B8 or B5 (Cannon, 1927; Hill & Lynas-Gray, 1977).

The composition of HD 235349 is clearly peculiar, with a strong overabundance of phosphorus (P, $+1.48$ dex), neon (Ne, +0.65 dex), and neodymium (Nd, +1.44 dex). The upper limits for gallium and praseodymium also allow for enhancements of up to 2 dex. Furthermore, Ti, Mn, and Ni may be slightly (a factor of $0.3$ to $0.6\,$dex) enhanced, while Si, and S appear underabundant by a similar factor and He appears to be weakly underabundant at 0.25 dex (although the He abundance is sensitive to $T_{\rm eff}$).

The star is not an obvious member of the mercury-manganese (HgMn) group of chemically peculiar stars, which extends up to temperatures similar to HD 235349 (up to $\sim$14 000 K, e.g. Ghazaryan et al., 2018). Mn is not strongly overabundant in HD 235349, and Hg (particularly the Hg II 3984 Å line) is not detected (see Fig. 2; although the upper limit is only $<3.3$ dex enhanced). Thus the star cannot be confidently classified as an HgMn star. We compare chemical abundances for a few elements of interest, for different samples of peculiar stars⁸⁸8 We have divided the sample of helium weak stars from Ghazaryan et al. (2019) into those with good evidence for strong magnetic fields in the literature (‘mag. He-w’) and those lacking evidence for a magnetic field (‘He weak’), since the presence of a strong magnetic field modifies atomic diffusion. , as a function of $T_{\rm eff}$ in Fig. 10. The strongest similarity between HD 235349 and HgMn-type stars is that HgMn stars are typically overabundant in P. Smith & Dworetsky (1993) and Ghazaryan et al. (2018) note a population of hot (¿13 000 K) HgMn stars with mild Mn overabundances (Fig. 10), which is closer to HD 235349.

While the He abundance is only mildly below solar, the P- and potentially Ga-rich pattern is consistent with the rare class of He-weak PGa chemically peculiar stars. These are weakly- or non-magnetic stars which may represent the high temperature end of HgMn stars (Borra et al., 1983). There are a few stars that have been classified as He-weak, despite apparently very modest He underabundances (e.g. Glagolevskij et al., 2007, see Fig. 10). Thus HD 235349 has similarities to the He-weak PGa stars, although given the mild He underabundance (and sensitivity of the He abundance to $T_{\rm eff}$) we do not give it this classification with a high level of confidence.

We propose that HD 235349 represents an intermediate case between HgMn and He-weak PGa stars, perhaps with some chemical peculiarities weakened by mixing from the relatively rapid rotation of the star. There is significant evidence to support the idea that He-weak PGa stars represent a continuation of HgMn stars to higher temperatures (e.g. Borra et al., 1983; Rachkovskaya et al., 2006; Hubrig et al., 2014; Monier & Khalack, 2021), with the differences in abundances due to differences in atomic diffusion with increasing temperature and perhaps an increasingly important stellar wind. HD 235349 sits near the border in $T_{\rm eff}$ between these classes of objects (Ghazaryan et al., 2018, 2019), supporting the idea that it is intermediate between these classes.

Theoretical atomic diffusion calculations support this general picture. Early work by Alecian & Michaud (1981) on diffusion suggested that the overabundance of Mn in HgMn stars should fall off with increasing $T_{\rm eff}$ somewhere in the $T_{\rm eff}$ $\sim 15000$ to 18000 K range. HD 235349 falls on the edge of this range, and this trend is generally consistent with other observations of Mn abundances (see Fig. 10). More recent work by Alecian & Stift (2019) consider time dependent diffusion including mass-loss, with a focus on HgMn stars. They consider stratification of P, finding overabundances higher in the atmosphere, and finding that these overabundances can be greatly enhanced by a weak magnetic field.

We find clear evidence for vertical stratification in the abundance of P, with larger abundances higher in the atmosphere. This can be adequately modeled with a linear distribution of P in $\log\tau_{5000}$, although higher S/N observations are needed to provide better constraints on the vertical distribution of P. Stratification of P, as well as some other elements, has been detected in a few HgMn stars (in HD 53929 and HD 63975 by Ndiaye et al. 2018, and in HD 161660 by Catanzaro et al. 2020), and also in HD 213781 which may be a blue horizontal branch star or an evolved HgMn star (Kafando et al., 2016). We find qualitatively consistent results with an apparently gradual increase in P abundance to shallower optical depths. This is also qualitatively consistent with the atomic diffusion models of P by Alecian & Stift (2019).

HD 235349 has a higher $v\sin i$ than is typical for an HgMn star or a He-weak PGa star. However, we are likely seeing the full equatorial rotation velocity (with $i$ close to $90^{\circ}$), since the system is an eclipsing binary, and with the relatively short period the orbital and rotational axes are likely aligned. The recent survey of HgMn stars by Chojnowski et al. (2020) found an average $v\sin i$ of 28 km s^-1, but also 13 stars with $v\sin i$ above 60 km s^-1. González et al. (2021) report a HgMn star with $v\sin i$ $=124$ km s^-1 as the highest $v\sin i$ HgMn star yet discovered. The high $v\sin i$ of HD 235349 likely enhances mixing in the star through meridional circulation, which may reduce the amount of chemical stratification and the strength of the observed peculiarities of some elements.

We find a low $\log\,{g}$ $=3.34\pm 0.11$ for HD 235349, which implies the star has likely evolved off the main sequence. However, that $\log\,{g}$ is not unprecedented among chemically peculiar stars in this temperature range, e.g. the HgMn star HD 63975 ($\log\,{g}$ = 3.27, Ndiaye et al., 2018), the He-weak PGa star HD 23408 ($\log\,{g}$ = 3.3, Mon et al., 1981; Monier & Khalack, 2021), and the He-weak (probably not of the PGa type) HD 5737 ($\log\,{g}$ = 3.2, Leone & Manfre, 1997; Saffe & Levato, 2014). The low $\log\,{g}$ may influence atomic diffusion, and contribute to the atypical pattern of chemical abundances observed, although the impact of $\log\,{g}$ on atomic diffusion is not well studied.

The large radius of HD 235349 rules out a planetary explanation for the transits in the TESS lightcurve, instead strongly favoring a slightly sub-solar mass main sequence star. Recently, it was found from speckle interferometry that HD 235349 has a close fainter ($\Delta m=4.1^{m}$ at 832 nm) companion at the angular distance of 0.263 arcseconds (Howell et al., 2021). It is probable that HD 235349 and this close companion form a true bound stellar system, the distance determined in current work implies the separation between two stars is at least $452\pm 143$ AU (for a distance of $1721\pm 543$ pc), but this is too distant to be the transiting object. We rule out contamination of the photometry from a different source blended within a TESS pixel (e.g. an eclipsing binary projected near HD 235349). There is no sign of another bright star within a $21^{\prime\prime}$ diameter area, and our optical spectra also contain no indications of another blended bright star. If the ${\sim}0.8\,$% dip in the summed lightcurve were from a different object it would require a faint binary where one component is completely covered, but this would produce a triangular transit whereas the TESS data clearly show a flat bottom. We conclude that the transiting companion must be bound to HD 235349, this assumption leads to a companion mass ${\approx}0.75\,$$M_{\odot}$(Sect. 4.3).

There are very few known eclipsing binaries among HgMn and He-weak stars, although new data from TESS is helping to change this. Binarity is often thought to be important for generating these chemically peculiar stars, by slowing rotation rates through tidal interactions, thereby allowing atomic diffusion to proceed efficiently. Despite this there are only ten known eclipsing binaries among HgMn stars: AR Aur (HD 34364, Nordstrom & Johansen, 1994; Hubrig et al., 2006; Folsom et al., 2010), TYC 455-791-1 (Strassmeier et al., 2017), V772 Cas (HD 10260, Kochukhov et al., 2021a), V680 Mon (HD 267564, Paunzen et al., 2021), HD 72208 (Wraight et al., 2011; Kochukhov et al., 2021c), and TYC 4047-570-1, HD 36892, HD 50984, HD 55776, HD 53004 (Kochukhov et al., 2021c). Possible eclipses have been reported in HD 161701 (Wraight et al., 2011, see also González et al. 2014), and single eclipse-like events in TESS data have been reported for HD 34923 and HD 99803 (Kochukhov et al., 2021b), but more observations are needed to confirm these. The eclipsing binary HD 66051 is of interest (Niemczura et al., 2017) although it appears to contain a magnetic Bp star (Kochukhov et al., 2018), and HD 62658 was also recently discovered to contain an eclipsing magnetic Bp star (Shultz et al., 2019). We are not aware of any eclipsing binaries among the He-weak PGa stars, perhaps due to their rarity and the difficulty in firmly establishing this classification. In this context, the eclipsing binary nature of HD 235349 is an important addition to the known hot chemically peculiar stars.