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Detailed studies of hot subdwarf B (sdB) stars with red dwarf (dM) or brown dwarf (BD) companions can shed light on the effects of binarity on late stellar evolution. Such systems exhibit a strong, quasi-sinusoidal reflection effect due to irradiation of the cool companion, and some even show primary and secondary eclipses. For this work, we computed Fourier transforms of TESS light curves of sdB+dM/BD binaries and investigate correlations between the relative amplitudes and phases of their harmonics and system parameters. We show that the reflection effect shape strongly depends on the orbital inclination, with nearly face-on systems having much more sinusoidal shapes than nearly edge-on systems. This information is encoded by the relative strength of the first harmonic in the Fourier transform. By comparing observations of solved systems to synthetic light curves generated bylcurve, we find that the inclination of non-eclipsing systems with high signal-to-noise light curves can be determined to within ≈10° simply by measuring their orbital periods and first harmonic strengths. We also discovered a slight asymmetry in the reflection effect shape of sdB+dM/BD binaries using the relative phase of the first harmonic. From our analysis of synthetic light curves, we conclude the asymmetry results from relativistic beaming of both stellar components. This marks the first time Doppler beaming has been detected in sdB+dM/BD systems. Although advanced modeling is necessary to quantify the effects of secondary parameters, such as limb darkening, the temperature ratio, and the radius ratio on the reflection effect shape, our pilot study demonstrates that it might be possible to extract both the inclination angle and cool companion velocity from the light curves of non-eclipsing systems. 

Context. Hot subdwarfs in close binaries with either M dwarf, brown dwarf, or white dwarf companions show unique light variations. In hot subdwarf binaries with M dwarf or brown dwarf companions, we can observe the so-called reflection effect, while in hot subdwarfs with close white dwarf companions, we find ellipsoidal modulation and/or Doppler beaming. Aims. Analyses of these light variations can be used to derive the mass and radius of the companion and determine its nature. Thereby, we can assume the most probable sdB mass and the radius of the sdB derived by the fit of the spectral energy distribution and the Gaia parallax. Methods. In the high signal-to-noise space-based light curves from the Transiting Exoplanet Survey Satellite and the K2 space mission, several reflection effect binaries and ellipsoidal modulation binaries have been observed with much better quality than with ground-based observations. The high quality of the light curves allowed us to analyze a large sample of sdB binaries with M dwarf or white dwarf companions using LCURVE . Results. For the first time, we can constrain the absolute parameters of 19 companions of reflection effect systems, covering periods from 2.5 to 19 h and with companion masses from the hydrogen-burning limit to early M dwarfs. Moreover, we were able to determine the mass of eight white dwarf companion to hot subdwarf binaries showing ellipsoidal modulations, covering the as-yet unexplored period range of 7 to 19 h. The derived masses of the white dwarf companions show that all but two of the white dwarf companions are most likely helium-core white dwarfs. Combining our results with previously measured rotation velocities allowed us to derive the rotation period of seven sdBs in short-period binaries. In four of those systems, the rotation period of the sdB agrees with a tidally locked orbit, whereas in the other three systems, the sdB rotates significantly more slowly. 

Context. About a third of the hot subdwarfs of spectral type B (sdBs), which are mostly core-helium-burning objects on the extreme horizontal branch, are found in close binaries with cool, low-mass stellar, substellar, or white dwarf companions. They can show light variations due to different phenomena. Aims. Many hot subdwarfs now have space-based light curves with a high signal-to-noise ratio available. We used light curves from the Transiting Exoplanet Survey Satellite and the K2 space mission to look for more sdB binaries. Their light curves can be used to study the hot subdwarf primaries and their companions, and obtained orbital, atmospheric, and absolute parameters for those systems, when combined with other analysis methods. Methods. By classifying the light variations and combining these with the fit of the spectral energy distribution, the distance derived by the parallaxes obtained by Gaia , and the atmospheric parameters, mainly from the literature, we could derive the nature of the primaries and secondaries in 122 (75%) of the known sdB binaries and 82 newly found reflection effect systems. We derived absolute masses, radii, and luminosities for a total of 39 hot subdwarfs with cool, low-mass companions, as well 29 known and newly found sdBs with white dwarf companions. Results. The mass distribution of hot subdwarfs with cool, low-mass stellar and substellar companions, differs from those with white dwarf companions, implying they come from different populations. By comparing the period and minimum companion mass distributions, we find that the reflection effect systems all have M dwarf or brown dwarf companions, and that there seem to be several different populations of hot subdwarfs with white dwarf binaries – one with white dwarf minimum masses around 0.4  M ⊙ , one with longer periods and minimum companion masses up to 0.6  M ⊙ , and at the shortest period, another with white dwarf minimum masses around 0.8  M ⊙ . We also derive the first orbital period distribution for hot subdwarfs with cool, low-mass stellar or substellar systems selected from light variations instead of radial velocity variations. It shows a narrower period distribution, from 1.5 h to 35 h, compared to the distribution of hot subdwarfs with white dwarfs, which ranges from 1 h to 30 days. These period distributions can be used to constrain the previous common-envelope phase. 

The hot nine-component system HD 93206, which contains a gravitationally bounded eclipsing Ac1+Ac2 binary ( P  = 5.9987 d) and a spectroscopic Aa1+Aa2 ( P  = 20.734 d) binary can provide important insights into the origin and evolution of massive stars. Using archival and new spectra, and a rich collection of ground-based and space photometric observations, we carried out a detailed study of this object. We provide a much improved description of both short orbits and a good estimate of the mutual period of both binaries of about 14 500 d (i.e. 40 years). For the first time, we detected weak lines of the fainter component of the 6.0 d eclipsing binary in the optical region of the spectrum, measured their radial velocities, and derived a mass ratio of M Ac2 / M Ac1  = 1.29, which is the opposite of what was estimated from the International Ultraviolet explorer (IUE) spectra. We confirm that the eclipsing subsystem Ac is semi-detached and is therefore in a phase of large-scale mass transfer between its components. The Roche-lobe filling and spectroscopically brighter component Ac1 is the less massive of the two and is eclipsed in the secondary minimum. We show that the bulk of the H α emission, so far believed to be associated with the eclipsing system, moves with the primary O9.7 I component Aa1 of the 20.73 d spectroscopic binary. However, the weak emission in the higher Balmer lines seems to be associated with the accretion disc around component Ac2. We demonstrate that accurate masses and other basic physical properties including the distance of this unique system can be obtained but require a more sophisticated modelling. A first step in this direction is presented in the accompanying Paper II (Brož et al.). 

Eclipsing post-common-envelope binaries are highly important for resolving the poorly understood, very short-lived common-envelope phase of stellar evolution. Most hot subdwarfs (sdO/Bs) are the bare helium-burning cores of red giants that have lost almost all of their hydrogen envelope. This mass loss is often triggered by common-envelope interactions with close stellar or even substellar companions. Cool companions to hot subdwarf stars such as late-type stars and brown dwarfs are detectable from characteristic light-curve variations – reflection effects and often eclipses. In the recently published catalog of eclipsing binaries in the Galactic Bulge and in the Asteroid Terrestrial-impact Last Alert System (ATLAS) survey, we discovered 125 new eclipsing systems showing a reflection effect seen by visual inspection of the light curves and using a machine-learning algorithm, in addition to the 36 systems previously discovered by the Optical Gravitational Lesing Experiment (OGLE) team. The Eclipsing Reflection Effect Binaries from Optical Surveys (EREBOS) project aims at analyzing all newly discovered eclipsing binaries of the HW Vir type (hot subdwarf + close, cool companion) based on a spectroscopic and photometric follow up to derive the mass distribution of the companions, constrain the fraction of substellar companions, and determine the minimum mass needed to strip off the red-giant envelope. To constrain the nature of the primary we derived the absolute magnitude and the reduced proper motion of all our targets with the help of the parallaxes and proper motions measured by the Gaia mission and compared those to the Gaia white-dwarf candidate catalog. It was possible to derive the nature of a subset of our targets, for which observed spectra are available, by measuring the atmospheric parameter of the primary, confirming that less than 10% of our systems are not sdO/Bs with cool companions but are white dwarfs or central stars of planetary nebula. This large sample of eclipsing hot subdwarfs with cool companions allowed us to derive a significant period distribution for hot subdwarfs with cool companions for the first time showing that the period distribution is much broader than previously thought and is ideally suited to finding the lowest-mass companions to hot subdwarf stars. The comparison with related binary populations shows that the period distribution of HW Vir systems is very similar to WD+dM systems and central stars of planetary nebula with cool companions. In the future, several new photometric surveys will be carried out, which will further increase the sample of this project, providing the potential to test many aspects of common-envelope theory and binary evolution.