The physical properties of post-mass-transfer binaries

TL;DR

The paper investigates six binaries initially flagged as potential star–black hole systems using high-resolution, multi-epoch FEROS spectroscopy and spectral disentangling to measure $T_{\mathrm{eff}}$, $R_*$, and $v\sin{i}$ for both components, along with the mass ratio $q$ and flux ratios. Through spectral disentangling, TODCOR, SED fitting, and orbital analysis, the authors establish that all systems are post-mass-transfer binaries with an A-type, rapidly rotating accretor and a cool, overluminous donor of about $0.25\,M_\odot$; five show no current mass transfer, and the mass-transfer history is broadly consistent with stable, case AB transfer with $\beta \lesssim 0.7$. The accretors, while rapidly rotating, remain well below the critical velocity $v_{\mathrm{crit}}$, suggesting efficient spin-down after mass transfer that is not fully explained by tides or magnetic braking, possibly pointing to disk interactions or other angular-momentum transport processes. The work provides crucial empirical constraints on mass-transfer efficiency and angular-momentum evolution in binaries, refining the interpretation of Gaia BH-impostor candidates and informing binary-evolution models such as MESA tracks and SOBERMAN-based analyses.

Abstract

Aims. We present and analyse the detailed physical properties of six binary stellar systems, originally proposed as possible star-black hole binaries on the basis of radial velocities from Gaia's third data release, but soon recognised as likely post-mass-transfer binary systems with stripped companions. Methods. We used multi-epoch high-resolution FEROS spectra and spectral disentangling paired with stellar templates to derive effective temperatures, $T_\mathrm{eff}$; stellar radii, R*; and projected rotational velocities, v$\sin{i}$ for both components in all systems along with the mass ratio, q = $M_\mathrm{accretor}/M_\mathrm{donor}$ and the components' flux ratio as a function of wavelength. Results. Our analysis directly confirms that all systems are post-mass-transfer binaries with two luminous stars, i.e. no black hole companions. Each system contains an A-type accretor component that is rapidly rotating and a cooler very low-mass donor (~ 0.25M$\odot$) that is overluminous. Five of the systems show no trace of any emission lines, implying that there is no current mass transfer, consistent with our inferred radii, in all cases within the Roche volume. The data are generally consistent with stable case AB mass transfer with $β$ (the fraction of mass lost from the accretor) less than 0.7. While the accretor components rotate rapidly, they rotate well below the critical rotation rate, $v_\mathrm{crit}$, even though there must have been enough mass transfer to spin them up to a significant fraction of $v_\mathrm{crit}$, according to theoretical models of angular momentum transfer. As neither magnetic braking nor tidal synchronisation should have been effective in spinning down the stars, our results suggest that either mass accretion does not increase the angular momentum of the accretors to their critical values or the systems never reached these values in the first place.

Figures (12)

• Figure 1: Observed spectra for one epoch (black line, top row), the two disentangled components (magenta and cyan lines, middle row, shown in the rest frame), their sum (grey line, top row, computed by shifting and co-adding), and the residual (bottom row) for the six targets of this study, centered around the Mg ii line as seen clearly in the accretor spectrum. We also show the best-fit template spectra for each disentangled component in the middle rows (dotted lines). In this and following figures, plots showing results for target G-5536 have a light grey background to differentiate them from the other targets, due to the difficulties with the analysis encountered for this object.
• Figure 2: Observed spectra for one epoch (black line, top row), the two disentangled components (magenta and cyan lines, middle rows), their sum (grey line, top row), and the residual (bottom row) for a number of different wavelength ranges. We also show the best-fit template spectra for each disentangled component in the middle rows (dotted lines). The windows here show the Balmer series and Mg ii in the accretor, which is hot and has few lines. Here, we only show the spectra for one object (G-2966), the rest can be found in Figures \ref{['fig:regions1']} and \ref{['fig:regions2']} in the Appendix.
• Figure 3: Results of the TODCOR algorithm applied to two objects. Top panels: RV of the donor and accretor shown on the x- and y-axes, respectively. Markers show the RVs of both components determined for each epoch with different methods and in various wavelength windows, with each marker displaying a different epoch. The lines indicate the linear best-fit to the RVs, as the relationship between donor and accretor RVs is linear. Grey diamonds show the donor RVs from ceresbrahm_ceres_2017 on the x-axis, with corresponding accretor RVs on the y-axis. The accretor RVs were computed using the ceres donor RVs, the mass ratio from el-badry_what_2022, centre-of-mass velocity from Gaia, and equation \ref{['eq:RVB']}. Coloured squares and lines show the results from TODCOR for a number of wavelength windows centered on different lines. Black squares show the unweighted mean for each epoch velocity over the different wavelength windows, offset to higher $v_A$ by a small amount for clarity. The fit labelled 'Joint' is then performed to these mean values. From the slope and intercept of the best-fit line, the mass ratio and centre-of-mass velocity can be computed, see equation \ref{['eq:slopeintercept']}. Bottom panels: Plot of the mass ratio vs the centre-of-mass velocity as determined from each set of data in the top panel, coloured accordingly. The left panel shows target G-2966, while on the right we see object G-5536, with a grey background to highlight the difficulty of the analysis for this object. For G-5336, we see that while there is a big discrepancy between the mass ratio from TODCOR and the one found by el-badry_what_2022, the quality of the linear fit with TODCOR is not good, calling this result into question.
• Figure 4: Spectral energy distribution fits and light ratio as a function of wavelength for each target. In the top plot of each set, we see the donor's (magenta line) and accretor's (cyan line) model SED, as well as sum of the two component models (black line). Solid lines use stellar parameters from this work, and dotted lines the parameters derived in el-badry_what_2022. We also overplot the observed photometry (lime dots), as well as the mock photometry from this work (black squares) and el-badry_what_2022 (grey crosses). Subsection \ref{['subsec:sedfit']} describes how each of these were obtained/computed. The bottom panel shows the contribution of the donor to the total flux as a function of wavelength. Again, solid indicates this work, dotted el-badry_what_2022. The red line shows the spectroscopic light ratio derived in this work, providing an additional constraint in the SED fitting process. Target G-5536 is shown with a grey background to highlight the difficutlies with its analysis.
• Figure 5: Parameters of both components of each system as determined in this work (S+25) and el-badry_what_2022. Findings from S+25 are shown with filled symbols in magenta (donor) and cyan (accretor), while those from el-badry_what_2022 are empty, outlined in red (donor) and blue (accretor). Different symbols have been chosen to represent the six different systems, with the problematic system (G-5536) shown as more transparent than the rest. The top left panel shows a Hertzsprung-Russel diagram, including PARSEC isochrones spanning a range of ages bressan_parsec_2012a. The top right panel shows the same parameter space, but with possible MESA evolutionary paths for the donor (dashed line) and accretor (dotted line) included, as computed by el-badry_what_2022. The bottom two panels show $\log{g}$ vs. $T_\mathrm{ eff}$ and $\log{R}$ vs $T_\mathrm{ eff}$ respectively, as well as including the aforementioned MESA tracks. The grey shading behind each line indicates the amount of mass transfer in the MESA model at that evolutionary stage.