Looking into the cradle of the grave:
J22564-5910, a young post-merger hot subdwarf?

As multiple spectra are available, we can check if there is any change in the spectral features over time. In Fig. 2 the He i lines at 4471 and 5875 Å are shown together with H_α, H_β, Ca k and the O i $\lambda$ 7774 line. The change in the H_α line is clearly visible. The emission core of the line varies between a single-peaked structure and a double-peaked structure. The He i 5875 shows a similar but much weaker change; an emission peak that shifts from a double peak or flat-topped structure to a sharper single peak. The Ca k doesn’t show clear variations. But the the O i $\lambda$ 7774 line does show variations, with the strongest absorption peak moves from blue to red shifted and back. Interesting about these latter two lines is that they are typically not visible in sdB spectra as they require lower temperatures. These could be produced in the circumstellar matter.

The He i $\lambda$ 4471 line is a somewhat different feature. It can be interpreted as a triple absorption line that is shifted strongly from its central wavelength. Such a wavelength shift could be caused by the presence of a magnetic field (see Section 6.1). Another possible interpretation is that the line is a broad absorption line with an emission core centred on the rest wavelength of the line similar to the other two lines and that the rightmost absorption peak is caused by a different element (see Section 6.2).

The actual periodicity of the line changes can not be determined from these spectra, but it is estimated to be on the order of several days to potentially even weeks. Another limiting factor to this analysis is that, if the observed period is in fact due to rotation, the spectra should be affected by rotational smearing, given the long exposure times (up to a third of the period). This implies that we might not be sampling the spectral variability completely. An important notice is that the different lines vary with different periodicity. When comparing the H_α with the O i $\lambda$ 7774 line, at time 0 both are central peaked. At time 33 days they have opposite absorption peaks with H_α blue shifted and O i red shifted. At time 75 they are both red shifted. This would indicate that they have different origins or originate on different locations in the disk.

Given the spectra taken at different time intervals, it makes sense to attempt to check for radial velocity variations. However, this is complicated by the broad lines and varying line shapes. As the line cores of the hydrogen and helium lines vary strongly over time, they cannot be used to derive radial velocities. There are no clear, sharp lines visible in the spectrum belonging to the system, so the only remaining approach is to use the wings of the hydrogen lines. Different approaches were attempted, using cross-correlation with a template spectrum and the best-observed spectra, as well as fitting Gaussian functions to the wings. The most successful approach was Gaussian fitting, as it resulted in the least difference between radial velocities determined for different lines in the same spectrum.

To derive the radial velocities, hydrogen lines from H_β to H_η and H₁₀ have been used. For these lines, the line centres have been removed. The wavelength region that is excluded is determined by eye, by selecting the line part that varies the most in between the six spectra. Afterwards, a Gaussian is fitted to the wings of the same hydrogen line in all spectra, and the average value for its FWHM is used as a fixed value for the FWHM in the final fit. This way, all hydrogen lines are fitted, and the final radial velocity is the average of the RV of the different hydrogen lines. The error is calculated as the standard deviation between the different lines.

The resulting radial velocities are shown in Fig. 4, and are given in Table 3. As can be seen from that figure, almost all RVs are consistent with no significant RV variation. One spectrum, the first of the X-SHOOTER spectra, shows a possible deviation. However, from these observations, it is not possible to conclude whether the system is RV variable or not.

The triplet structure that is clearly visible in several hydrogen and helium lines immediately brings magnetic fields and Zeeman splitting to mind. This interpretation fits in with the expected evolution history of this system. As a single sdB formed by a merger, it is expected that J22564-5910 would acquire a strong magnetic field, generated through a dynamo process during the common-envelope evolution or the subsequent merger (e.g. Tout et al., 2008; García-Berro et al., 2012).

We have applied a method similar to that of Kepler et al. (2013) to estimate the field strength necessary to produce the observed line splitting. The method relies on the fact that, for magnetic fields in the range $10\,{\rm kG}-2\,{\rm MG}$, the observed line shift $\Delta\lambda$ caused by a field $B$ to the hydrogen lines can be approximated in the first order by

where the wavelength is measured in $\AA$ and the magnetic field in MG. To account for contributions of higher-order terms, we have utilised the models of Schimeczek & Wunner (2014) (see their figure 5) to estimate the averaged component separation predicted by the models. To calculate the observed separation for our obtained spectra, Gaussian lines were fitted to each Zeeman component. We only used the lines H_β, H_γ and H_δ, as for higher-order lines the triplet structure is not apparent even for low fields (see, e.g. figure 5 of Kepler et al., 2013), and H_α is seen in emission. Moreover, we only applied this method to the spectra in which the three components could be identified for these lines. Depending on field structure and orientation, one or more components can be suppressed. Our method is illustrated in Fig. 7. For each spectrum, we searched for the field strength whose predicted separation could better explain the observed spectrum by minimising the difference between observed and predicted separation for the three lines simultaneously. To estimate uncertainties, we drew flux values a thousand times, assuming a 10% uncertainty on the observed values, and repeated the estimate for each of the simulated spectra. The results are shown in Table 5. Assuming that the field does not change significantly over time, which seems to be suggested by our consistent estimates, the average field is $656\pm 51$ kG.

But how can we now understand the H $\alpha$ line profile in view of this high magnetic field strength? Emission in H $\alpha$ is not an atypical phenomenon amongst magnetic stars. Magnetically active (sub-)giants, for example, show chromospheric emission lines in H $\alpha$, but at the same time also in the cores of the Ca ii H and K lines, as well as sometimes other lines in the optical or ultraviolet (Wilson, 1963, 1968; Gray & Corbally, 2009). For some of these stars, time-variability in the chromospheric H $\alpha$ emission, that is not correlated to the rotation period, has also been reported, though, the exact origin of the variability is not yet understood (e.g., Dorren et al. 1984; Vida et al. 2015; Kővári et al. 2019; Werner et al. 2020).

There is also a small group of three cool (effective temperatures between 7500 K and 7865 K), magnetic and apparently single white dwarfs known that exhibit Zeeman-split Balmer emission lines (Greenstein & McCarthy, 1985; Reding et al., 2020; Gänsicke et al., 2020). It is thought that a conductive planet in a close orbit around these stars could result in the generation of electric currents that heat the regions near the magnetic poles of the white dwarf. The planet, in this case, would have formed in a metal-rich debris disc that was left over by a double white dwarf merger that could have produced the magnetic white dwarf (Li et al., 1998; Wickramasinghe et al., 2010). However, in contrast to our star, the emission lines in these white dwarfs are not only seen in H $\alpha$ but also H $\beta$ and are triple-peaked instead of single/double-peaked.

Last but not least, for magnetic O- and B- type main sequences stars that host a wind-fed, co-rotating, circumstellar magnetosphere, emission in H$\alpha$ is the primary visible magnetospheric diagnostic. In Fig. 6, we show such model applied to our system. In slowly rotating stars, the material persists within the magnetosphere only over the free-fall timescale, and is pulled back onto the star by gravity (so-call dynamical magnetosphere, Landstreet & Borra 1978; Ud-Doula & Owocki 2002; Petit et al. 2013). However, if the star is rapidly rotating or the magnetic field strength is high enough, the co-rotating material in the magnetosphere can reach high enough rotational velocities so that the gravitational infall can be prevented. This is the case when the Alfvén radius $R_{A}$, which characterises the maximum height of closed magnetic loops, exceeds the Keplerian co-rotation radius, $R_{K}$ (point of balance between gravitational and centrifugal force). While below $R_{K}$, the star retains a dynamical magnetosphere, above $R_{K}$ and extending to $R_{A}$, a so-called centrifugal magnetosphere forms. Herein, the trapped wind material accumulates into a relatively dense, stable and long-lived “rigidly rotating magnetosphere” (RRM, Townsend & Owocki 2005; Townsend et al. 2007). According to the RRM model, the distribution of the material then depends on the tilt, $\beta$, of the magnetic axis with respect to the rotational axis of the star. While for $\beta=0$° a continuous torus in the magnetic equatorial plane forms, two distinct plasma clouds are expected near the intersections of the magnetic and rotational equatorial planes for $\beta=90$°. The typical RRM geometry, thus, produces a double-humped emission profile, when the circumstellar magnetosphere is seen face on. Since close to $R_{K}$, the magnetosphere has its highest density, also the H$\alpha$ emission is found to peak close to $R_{K}$ (typically around $1.25\times R_{K}$, Shultz et al. 2020). The remaining shape of the H$\alpha$ emission then depends on the geometry of the RRM. Non-eclipsing stars with small $\beta$ show emission at all velocities across the line profile, whereas non-eclipsing stars with large $\beta$ will display emission only outside of $\pm R_{K}$ at maximum emission. The emission line profile is modulated by the rotation of the object. As the projected distance of the clouds from the star decreases, and – at the same time – the projected area of the clouds becomes smaller when changing from face-on to edge-on, the H $\alpha$ emission bumps decrease in strength (Shultz et al., 2020).

Since also in our star, we detect this time-variable, double-humped H$\alpha$ emission profile, the RRM model appears attractive. The multi-component absorption features seen for the CaII and OI originating in the circumstellar material (Fig. 3) could also be explained by the distribution of the material in the magnetosphere. Magneto-hydrodynamic simulation studies (e.g., Ud-Doula & Owocki 2002; Ud-Doula et al. 2008) show that in case of a large-scale, dipole magnetic field, a magnetosphere forms when the wind magnetic confinement parameter ($\eta_{\mathrm{\star}}$) is larger than one:

Here $B_{\mathrm{eq}}=B_{d}/2$ is the field strength at the magnetic equatorial surface radius, $R_{\mathrm{\star}}$, and $\dot{M}$_B=0 and $v_{\infty}$ are the fiducial mass-loss rate and terminal wind speed that the star would have in the absence of any magnetic field (all in cgs units). Assuming a typical mass loss rate for an sdB star of $10^{-11.5}$$M_{\odot}$/yr (Vink & Cassisi, 2002), $v_{\infty}=v_{esc}=1338$km/s (assuming $M=0.47$ $M_{\odot}$, and $R=0.1$ $R_{\odot}$, Hamann et al. 1981; Howarth 1987), and $R=0.1$ $R_{\odot}$, we find that in case of J22564-5910 a magnetosphere can already form for $B_{eq}\gtrapprox 24$ G. This is many orders of magnitude below of what we find above, thus, the requirement for a centrifugal magnetosphere ($R_{A}>R_{K}$) can be easily fulfilled. Assuming $M=0.47$ $M_{\odot}$, and $R=0.1$ $R_{\odot}$, we find $R_{K}=5.5\,R_{\mathrm{\star}}$ assuming the $0.07$ d period observed in the TESS light curve is the rotational period of the star. The Alfvén radius, $R_{A}$, can be estimated from the wind magnetic confinement parameter, $\eta_{*}$, via $R_{A}/R_{\mathrm{\star}}\approx 0.3\,(\eta_{*}+0.4)^{1/4}$ (Ud-Doula et al., 2008). Here, we find $R_{A}=118.6\,R_{\mathrm{\star}}$, but it should be noted that the exact value depends on the mass loss rate and terminal wind velocity, which we can only estimate. Moreover, additional circumstellar material might be present as a result of the possible merger, which we do not take into account here. What can, however, be taken away from this is that a centrifugal magnetosphere can be expected³³3Observationally, centrifugal magnetospheres are detected in stars with $\log(R_{A}/R_{K})>0.7$ (Shultz et al., 2020).

Since the rigid-body rotation of the circumstellar magnetosphere implies, that the line of sight velocity, v, is directly proportional to the projected distance from the star ($v/(v_{rot}\,sin\,i)=r/R_{\mathrm{\star}}$), one can in principle test the circumstellar magnetosphere scenario with the H$\alpha$ line profile directly (Shultz et al., 2020), as the emission peaks should occur around $R_{K}$ (see above). We find that the observed emission peaks of the H $\alpha$ line in J22564-5910 would be located at $R_{K}$ if we assume for the 0.07 d period an inclination angle of $i\approx 20$° (blue dashed-dotted lines in Fig.2). Unfortunately, due to the lack of any photospheric metal lines and the high magnetic field, it is not possible to measure $v_{rot}\,sin\,i$, plus the lack of the knowledge of the stellar mass adds another uncertainty when calculating $R_{K}$. In addition, we note that if the 0.07 d period is indeed the rotational period, then the spectra should suffer considerably from rotational smearing due to the long exposure time (one quarter of the period). Hence the line profile shapes may not be considered as reliable. Thus, based on the current data, it is not possible to entirely confirm the RRM model.

Complicated spectral line profiles may also have another explanation that does not require magnetic fields. In this section, we investigate the idea that the spectral lines are shaped by circumstellar material (CM). Such material is often present in interacting binaries or hot stars and might be present in our system too. It gives rise to emission lines of quite complicated shape which may be superposed on the absorption lines originating from the stellar atmosphere. The result would be even more complicated spectral line profiles. In this scenario double absorption like in the H_α line would not be composed of two absorption lines but from a single broad absorption line (from the stellar atmosphere) filled up by more narrow central emission from the CM. Lines with triple absorption could be understood as a single broad absorption from the photosphere filled in by a double peak emission from CM.

The most natural form of circumstellar material in a binary system or in a merger of two stars is probably an accretion disk. Typically such a disk gives rises to a double-peaked emission (unless seen pole-on). Thus an inclined disk might explain triple absorption profile seen best in H$\beta$. To demonstrate the idea that such line profiles may be due to CM, we performed a synthetic spectra calculation. As this analysis aims to be a qualitative one and not a quantitative fit to the spectra, we use a master spectrum for the comparison of the models with the observations. This master spectrum is obtained by summing all three X-SHOOTER spectra without any RV corrections for stellar motion. The spectra were then normalised.

As a first step we calculated the stellar atmosphere model using the TLUSTY code (Hubeny & Lanz, 1995). These are 1D Non-Local-Thermodynamic-Equilibrium (NLTE) atmosphere models. The spectra emerging from these atmosphere models were calculated using the code synspec (Hubeny & Lanz, 2017). We assumed T${}_{\rm eff}=26000$ K, $\log{g}=6.1$ [cgs], and solar chemical composition. Such synthetic spectra of H_β line are shown in Fig. 8. One can see very strong, deep and relatively sharp absorption originating from the stellar atmosphere. The major challenge of this model is filling this profile with emission. This intrinsic spectrum of the star was used as a boundary condition to calculate the spectra of the star and CM, for which we used the shellspec code (Budaj & Richards, 2004). It is designed to calculate light curves and spectra of interacting binaries embedded in a 3D moving CM, assuming local thermodynamic equilibrium (LTE) and optically thin scattering. The assumed stellar mass, radius, and projected equatorial rotation velocity are M = 0.47 M_⊙, R = 0.1 R_⊙, and $v\sin{i}=70$ km/s, respectively. Quadratic limb darkening coefficients for the star from Claret (2000) were assumed. The chemical composition of the CM was identical to that of the star. CM had a form of an accretion disk. Synthetic spectra of the most interesting and most complicated H$\beta$ line are also shown in Fig. 8. One can clearly see a double peak emission from the disk filling in the central part of the absorption from the photosphere. The result might look like a triple absorption.

The properties of the CM are described below. The disk was modelled using an object called NEBULA in the shellspec code. It is a flared disk characterised by its inner, $R_{in}$, and outer, $R_{out}$, radius, and an inclination $i$. Its density is decreasing in the radial direction as a power law, $\rho(r)=\rho_{\rm in}(r/r_{\rm in})^{\rho_{exp}}$, and in the vertical direction as a Gaussian. It is characterised by the density at the inner radius $\rho_{in}$ and exponent $\rho_{exp}$. We assumed $\rho_{exp}=-1$ based on Budaj et al. (2005). The temperature, similarly, has a radial power-law dependence characterised by $T_{in}$ and exponent $T_{exp}$. The velocity field is Keplerian. In reality, it may be much more complicated. The disk may have a radial inflow component and is also often accompanied by winds, jets, or other outflows. That is why we also introduce a simple parameter called ’turbulence’, $v_{T}$. Electron number densities are calculated from the density, temperature, and chemical composition assuming LTE. Values of all these parameters are summarised in Table 6.

We can conclude that CM material might explain the complicated shapes of spectral lines we observe in this star. However, these calculations should be understood only as a demonstration of the effect and disk parameters (mainly densities) represent rather a lower limit. In reality, the geometry, velocity field and behaviour of state quantities of the CM may be much more complicated than our simple disk model. Their effect will be mainly to smooth the ideal theoretical line profile. We experimented with dozens of other models of CM like shells, disks, temperature inversions, and many of them produce a similar outcome, i.e. triple absorption profiles. The most difficult problem is to fill in the sharp central absorption peak.

The advantage of this model is that it has the potential also to explain the IR excess observed in the SED, as well as the emission seen in other H and He lines in the spectra. The change in the line profiles that is shown in Fig. 2 might be explained by the disk model as well. Accretion structures are not necessarily stable and can change over time, causing changes in the line profiles. If a magnetic field is present, this can also affect the structure and cause variability. Furthermore, if there would be a secondary body present in the system, it can cause precession of the disk which would cause changes in the emission cores of the H and He lines. This body would have to be much closer than the nearby companion described in Appendix B.

The three formation channels for hot subdwarf stars are stable RLOF, CE ejection and a merger. Based on the observations we can exclude two of these channels with a very high likelihood.

All known wide sdB binaries formed through the stable RLOF channel have FGK type companions (e.g. Vos et al., 2017). These companions can be clearly seen in high-resolution spectroscopy. There is no sign of such a companion in J22564-5910, and thus this scenario can be excluded. There are then two possibilities left. J22564-5910 can be a close binary with a dM or WD companion, or it can be a single merger product.

In the case that J22564-5910 would be an sdB+dM binary, we can compare it to the known population of sdB+dM binaries. These systems have all short orbits, with their period distribution peaking at less than a day. Using the lcurve package (Copperwheat et al., 2010, App A.), we have computed the expected amplitude for the reflection effect in sdB+dM binaries for a typical dM companion at different orbital periods and inclinations angles (see Fig. 9). From this figure, it is clear that such a binary would be detected in the TESS light curve for orbital periods up to $\sim 8$ days. Since these systems are nearly never found at orbital periods larger than a few days, we can conclude that the sdB+dM possibility is very unlikely.

The above considerations leave the sdB+WD possibility. Such systems do not show a significant reflection effect in the light curves but can show ellipsoidal modulations. lcurve models show that such effects would be detectable for typical WD companions for orbital periods up to $\sim 0.3$ days. As sdB+WD binaries are observed on longer orbital periods than that, the light curve alone is not sufficient to exclude this possibility.

To further judge the sdB+WD option, the RVs derived from the spectra can be used. Known sdB+WD systems have short orbital periods and thus high RV variations. The RVs that are derived in Sect. 3.2 show possible variations of up to $\sim 30$ km/s. This would correspond to sdB+WD systems on orbital period $>5$ days, which is very exceptional for sdB+WD systems (Kupfer et al., 2015; Prince et al., 2019). The RV analysis used the wings of the H lines, which originate from the central star, and are likely not significantly influenced by the disk.

Based on the limits obtained from the light curve and the spectra, we can with high certainty say that J22564-5910 is a single sdB and thus a merger product. The derived properties suggest that the object is in a core-He burning phase. For typical double-degenerate mergers, this phase is only reached long after the merger ($\sim 10^{6}$ yr), at which point all the circumstellar material resulting from the merger should have been lost. Additionally, He-core burning products of double degenerate mergers are expected to show higher temperatures and be H-deficient, which is not the case here (Dan et al., 2014; Schwab, 2018). Therefore, a WD+MS merger is a more likely scenario for the formation of J22564-5910  as in this case the He-core burning phase can occur at lower effective temperature, and high amounts of hydrogen are still expected (Zhang et al., 2017).

In case that J22564-5910 would indeed be a magnetic system there is an extra argument to be made against the CE formalism. While the dynamo actions arising during the CE phase can indeed cause magnetic fields, models show that these fields are weak and don’t last long after the CE ejection (see e.g. Potter & Tout, 2010).