Apsidal motion and proximity effects in the massive binary BD+60 497

TL;DR

This work uses two decades of spectroscopy and four sectors of TESS photometry to measure apsidal motion in the massive, non-eclipsing binary BD+60 497. The authors model the RVs with explicit apsidal motion, obtain a rate $\dot{\omega}=(6.15^{+1.05}_{-1.65})^{\circ}$ yr$^{-1}$, and infer an age of $4.13^{+0.42}_{-1.37}$ Myr, consistent with IC 1805. They also detect epoch-dependent changes in the reconstructed spectra of the secondary and a 6 mmag-level photometric variability whose origin likely involves a mix of proximity effects and tidally excited oscillations, rather than a single mechanism. The results highlight challenges in modeling proximity effects in massive binaries and motivate further spectroscopic monitoring and detailed light-curve modeling to fully understand BD+60 497.

Abstract

The eccentric short-period O-star binary BD+60 497 is an interesting laboratory in which to study tidal interactions in massive binary systems, notably via the detection and characterisation of apsidal motion. The rate of apsidal motion in such systems can help constrain their age and provide insight into the degree of mass concentration in the interior of massive stars. We used spectroscopic data collected over two decades to reconstruct the individual spectra of the stars and to establish their epoch-dependent radial velocities. An orbital solution, explicitly accounting for apsidal motion was adjusted to the data. Space-borne photometric time series were analysed with Fourier methods and with binary models. We derived a rate of apsidal motion of $6.15^{+1.05}_{-1.65}$ degree/yr, which suggests an age of $4.13^{+0.42}_{-1.37}$ Myr. The disentangled spectra unveiled a curious change in the spectral properties of the secondary star between the epochs 2002-2003 and 2018-2022 with the secondary spectrum appearing to be of an earlier spectral type over recent years. Photometric data show variability at the 6 mmag level on the period of the binary system, which is hard to explain in terms of proximity effects. Whilst the rate of apsidal motion agrees well with theoretical expectations, the changes in the reconstructed secondary spectrum hint at a highly non-uniform surface temperature distribution for this star. Different effects are discussed that could contribute to the photometric variations. The current most-likely explanation is a mix of proximity effects and tidally excited oscillations

Figures (14)

• Figure 1: Disentangled Aurélie spectra of BD+60$^{\circ}$ 497. Reconstructed spectra from the 2002-2003 epoch are shown by the blue continuous line for the primary, and the red continuous line for the secondary (shifted vertically by 0.2 units). The black dashed lines represent the result of the disentangling for the 2018-2022 data. The spectra are displayed normalised to the global continuum of the system. The broad double-minimum features around 4502, 4726, 4763, and 4780Å are artefacts due to the disentangling of the stationary diffuse interstellar bands at those wavelengths.
• Figure 2: Comparison between the strongest lines in the Aurélie spectra as observed in 2002-2003 (blue) and 2018-2022 (red). The lines are, from left to right He i$\lambda$ 4471, He ii$\lambda$ 4542, He ii$\lambda$ 4686, and H$\beta$. The top panel illustrates the spectra observed close to the quadrature with the primary moving towards the observer, whilst the bottom panel illustrates the comparison for phases near the opposite quadrature. Spectra in the top panel were taken on HJD 2452928.641 (blue) and HJD 2459853.5509 (red), that is respectively at phases 0.99 ($\omega = 150^{\circ}$, position angle $236^{\circ}$) and 0.78 ($\omega = 261^{\circ}$, position angle $254^{\circ}$) according to our 'RV dataset 2' ephemerides in the forthcoming Table \ref{['omegadotfit']}. Spectra in the bottom panel were obtained on HJD 2452527.555 (blue) and HJD 2458719.6140 (red), that is respectively phases 0.70 ($\omega = 144^{\circ}$, position angle $111^{\circ}$) and 0.42 ($\omega = 243^{\circ}$, position angle $130^{\circ}$) according to the same ephemerides.
• Figure 3: Comparison between the best-fit model for the primary RVs (black solid curve) computed with relation \ref{['RVomegadot']} for dataset 2. Cyan, blue, and violet filled symbols stand respectively for primary RVs from Hil06 and our disentangling of the Aurélie and HEROS spectra. The orange, red, and maroon open symbols show the secondary RVs (not used in the fit) respectively from Hil06, our Aurélie and HEROS data, whilst the dashed line illustrates the secondary RV solution inferred from the primary RV curve for a mass ratio $q = m_p/m_s = 1.28 \pm 0.03$.
• Figure 4: Evolution of the total $\dot{\omega}$ (Newtonian plus general relativity) as a function of age. The red curve displays this evolution for solar-metallicity stars of 26.2 M$_{\odot}$ and 20.4 M$_{\odot}$ in a binary with $e = 0.15$ and $P_{\rm anom} = 3.95984$ d according to the models of Cla19. The solid blue line shows our best estimate of $\dot{\omega}$ for BD+60$^{\circ}$ 497, and the hatched area provides the associated uncertainty. The brown and orange curves correspond to systems respectively with stars of masses 30.3 M$_{\odot}$ + 23.7 M$_{\odot}$ and 21.9 M$_{\odot}$ + 17.1 M$_{\odot}$.
• Figure 5: Surface temperature distribution for the stars of the BD+60$^{\circ}$ 497 binary system as computed with CoMBiSpeC at periastron (top) and apastron (bottom). The primary and secondary input radii were taken to be respectively 9.8 R$_{\odot}$ and 7.3 R$_{\odot}$, and their effective temperatures are respectively 37.5 kK and 35 kK.