Subdwarf B Research Articles

Tidal Spin-up of Subdwarf B Stars

Hot subdwarf B (sdB) stars are stripped helium-burning stars that are often found in close binaries, where they experience strong tidal interactions. The dissipation of tidally excited gravity waves alters their rotational evolution throughout the sdB lifetime. While many sdB binaries have well-measured rotational and orbital frequencies, there have been few theoretical efforts to accurately calculate the tidal torque produced by gravity waves. In this work, we directly calculate the tidal excitation of internal gravity waves in realistic sdB stellar models and integrate the coupled spin–orbit evolution of sdB binaries. We find that for canonical sdB (M sdB = 0.47 M ⊙) binaries, the transitional orbital period below which they could reach tidal synchronization in the sdB lifetime is ∼0.2 day, with weak dependence on the companion masses. For low-mass sdBs (M sdB = 0.37 M ⊙) formed from more massive progenitor stars, the transitional orbital period becomes ∼0.15 day. These values are very similar to the tidal synchronization boundary (∼0.2 day) evident from observations. We discuss the dependence of tidal torques on stellar radii, and we make predictions for the rapidly rotating white dwarfs formed from synchronized sdB binaries.

TIC 441725813: A new bright hybrid hot B subdwarf pulsator with differential core versus envelope rotation

Context. The Transiting Exoplanet Survey Satellite (TESS) performs high-precision photometry over almost the whole sky primarily in search of exoplanet transits. It also provides exquisite data to study stellar variability, in particular for pulsating hot B subdwarf (sdB) stars. Aims. We present a detailed analysis of a new hybrid (p- and g-mode) sdB pulsator, TIC 441725813 (TYC 4427-1021-1), discovered and monitored by TESS for 670 days. Methods. The TESS light curves available for this star were analysed using prewhitening techniques to extract mode frequencies accurately. The pulsation spectrum was then interpreted through methods that include asymptotic period spacing relationships and the identification of rotational multiplets. We also exploited a high signal-to-noise ratio (S/N), low-resolution spectrum of TIC 441725813 using grids of non-local thermodynamic equilibrium (NLTE) model atmospheres to derive its atmospheric parameters. Results. The light curve analysis reveals that frequencies are mostly found in the g-mode region, but several p-modes are also detected, indicating that TIC 441725813 is a hybrid sdB pulsator. We identify 25 frequencies that can be associated with ℓ = 1 g-modes, 15 frequencies corresponding to ℓ = 2 g-modes, and six frequencies characteristic of p-modes. Interestingly, several frequency multiplets interpreted as rotational splittings of deep-probing g-modes indicate a slow rotation period of at least 85.3 ± 3.6 day, while splittings of mostly envelope-probing p-modes suggest a significantly shorter rotation period of 17.9 ± 0.7 day, which implies the core (mainly the helium mantle with possibly the deeper partially mixed helium-burning core that it surrounds) rotates at least 4.7 times slower than the envelope. The radial velocity curves indicate that TIC 441725813 is in a close binary system with a low-luminosity companion, possibly a white dwarf. While elusive in the available TESS photometry, a low-frequency signal that would correspond to a period of ∼6.7 h is found, albeit at a low S/N. Furthermore, we estimate the inclination angle to be ∼60° by two independent means. Conclusions. TIC 441725813 is a particularly interesting sdB star whose envelope rotates faster than the core. We hypothesise that this might be caused by the effects of a tidal interaction with a companion, although in the present case, the presence of such a companion will have to be further investigated. This analysis paves the way towards a more detailed seismic probing of TIC 441725813 using optimisation techniques, which will be presented in a second paper.

Hot subdwarfs in close binaries observed from space

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 by lcurve, 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.

A comprehensive search for hot subdwarf stars using Gaia and TESS

Hot subdwarf B (sdB) stars are evolved, subluminous, helium-burning stars that most likely form when red giant stars loose their hydrogen envelope via interactions with close companions. They play an important role in our understanding of binary evolution, stellar atmospheres, and interiors. Only a small fraction of the sdB population is known to exhibit pulsations. Pulsating sdBs have typically been discovered serendipitously in various photometric surveys because specific selection criteria for the sample are lacking. Consequently, while individual properties of these stars are well known, a comprehensive understanding of the entire population remains elusive, and many related questions remain unanswered. The Gaia mission has presented an exceptional chance to create an unbiased sample by employing precise criteria and ensuring a high degree of completeness. The progression of high-precision and high-duty cycle photometric monitoring facilitated by space missions such as Kepler/K2 and the Transiting Exoplanet Survey Satellite (TESS) has yielded an unparalleled wealth of data for pulsating sdBs. We created a dataset of confirmed pulsating sdB stars by combining information from various ground- and space-based photometric surveys. With this dataset, we present a thorough approach to search for pulsating sdB stars based on the current Gaia DR3 sample. Based on TESS photometry, we discovered 61 new pulsating sdB stars and 20 variable sdBs whose source of variability remains to be determined through future spectroscopic follow-up observations.

The mass range of hot subdwarf B stars from MESA simulations

ABSTRACT Hot subdwarf B (sdB) stars are helium core burning stars that have lost almost their entire hydrogen envelope due to binary interaction. Their assumed canonical mass of ${M_{\mathrm{sdB}}}\sim 0.47$ M⊙ has recently been debated given a broad range found both from observations as well as from the simulations. Here, we revise and refine the mass range for sdBs derived two decades ago with the Eggleton code, using the stellar evolution code mesa, and discuss the effects of metallicity and the inclusion of core overshooting during the main sequence. We find an excellent agreement for low-mass progenitors, up to ∼2.0 M⊙. For stars more massive than ∼2.5 M⊙, we obtain a wider range of sdB masses compared to the simulations from the literature. Our mesa models for the lower metallicity predict, on average, slightly more massive sdBs. Finally, we show the results for the sdB lifetime as a function of sdB mass and discuss the effect this might have in the comparison between simulations and observational samples. This study paves the way for reproducing the observed Galactic mass distribution of sdB binaries.

Pulsational Velocity Variations of the Radial Mode sdBV Star BPM 36430

Hot subdwarf B stars are core-helium burning objects that were once red giants stripped of their outer H envelopes due to binary interactions. Many exhibit pulsations that can be used to determine fundamental stellar parameters like mass and radius. High-cadence TESS photometry of the sdB star BPM 36430 revealed it to be a hybrid-mode pulsator showing several g-mode pulsations and a single strong p-mode oscillation. The latter is likely a radial mode oscillation, given its period (342 s) and high photometric amplitude (2%). Using time-series spectroscopy from the Goodman spectrograph on the 4.1 m SOAR telescope, we detect a sinusoidal radial velocity variation with a semi-amplitude of 4.4 ± 0.4 km s−1 and period consistent with photometry of the p-mode oscillation. This detection provides further evidence the 342 s mode is radial in nature, and that the Baade–Wesselink method can be used with additional observations to constrain the stellar mass and radius.

Stellar variability in Gaia DR3

Context. The unparalleled characteristics of Gaia photometry in terms of calibration, stability, time span, dynamic range, full-sky coverage, and complementary information make it an excellent choice to study stellar variability. Aims. We aim to measure the photometric dispersion in the G, GBP, and GRP bands of the 145 677 450 third Gaia data release (DR3) five-parameter sources with G ≤ 17 mag and GBP – GRP between −1.0 and 8.0 mag. We will use that unbiased sample to analyze stellar variability in the Milky Way (MW), Large Magellanic Cloud (LMC), and Small Magellanic Cloud (SMC). Methods. For each band we convert from magnitude uncertainties to observed photometric dispersions, calculate the instrumental component as a function of apparent magnitude and color, and use it to transform the observed dispersions into the astrophysical ones: sG, SGBP, and SGRP. We give variability indices in the three bands for the whole sample indicating whether the objects are non-variable, marginally variable, or clearly so. We use the subsample established by Rimoldini and collaborators with light curves and variability types to calibrate our results and establish their limitations. Results. The position of an object in the dispersion-dispersion planes can be used to constrain its variability type, a direct application of these results. We use information from the MW, LMC, and SMC color-absolute magnitude diagrams (CAMDs) to discuss variability across the Hertzsprung-Russell diagram. White dwarfs and B-type subdwarfs are more variable than main sequence (MS) or red clump (RC) stars, with a flat distribution in sG up to 10 mmag and with variability decreasing for the former with age. The MS region in the Gaia CAMD includes a mixture of populations from the MS itself and from other evolutionary phases. Its sG distribution peaks at low values (~1–2 mmag) but it has a large tail dominated by eclipsing binaries, RR Lyrae stars, and young stellar objects. RC stars are characterized by little variability, with their sG distribution peaking at 1 mmag or less. The stars in the pre-main-sequence (PMS) region are highly variable, with a power law distribution in sG with slope 2.75 and a cutoff for values lower than 7 mmag. The luminous red stars region of the Gaia CAMD has the highest variability, with its extreme dominated by AGB stars and with a power law in sG with slope ~2.2 that extends from there to a cutoff of 7 mmag. We show that our method can be used to search for LMC Cepheids. We analyze four stellar clusters with O stars (Villafranca O-016, O-021, O-024, and O-026) and detect a strong difference in sG between stars that are already in the MS and those that are still in the PMS.

The first massive compact companion in a wide orbit around a hot subdwarf star

We report the discovery of the first hot subdwarf B (sdB) star with a massive compact companion in a wide (P = 892.5 ± 60.2 d) binary system. It was discovered based on an astrometric binary solution provided by the Gaia mission Data Release 3. We performed detailed analyses of the spectral energy distribution (SED) as well as spectroscopic follow-up observations and confirm the nature of the visible component as a sdB star. The companion is invisible despite of its high mass of Mcomp = 1.50−0.45+0.37 M⊙. A main sequence star of this mass would significantly contribute to the SED and can be excluded. The companion must be a compact object, either a massive white dwarf or a neutron star. Stable Roche lobe overflow to the companion likely led to the stripping of a red giant and the formation of the sdB, the hot and exposed helium core of the giant. Based on very preliminary data, we estimate that ∼9% of the sdBs might be formed through this new channel. This binary might also be the prototype for a new progenitor class of supernovae type Ia, which has been predicted by theory.

Multifilter Time-series Observations of Eleven Blue Short-period ATLAS Variable Stars

Eleven periodic variable stars were observed photometrically through two to four filters from the set UBVR C I C . Phase-folded data for each star cover full cycles of variation. Spectral energy distributions, based on absolute photometry extracted from the literature, are used to inform models of the stars. The stars include four eclipsing systems with hot subdwarfs of spectral type O or B (sdO/B). Periods are in the range 1.8–2.2 hr. Four reflection-effect binaries, with amplitudes as large as 0.5 mag in the R C filter were observed; periods range from 1.6 to 2.4 hr. In two of these latter systems, the primary stars are also sdB stars, while two have white-dwarf components. In all eight of these binaries the companion stars are probably M dwarfs. The remaining three stars are pulsators: one large-amplitude δ Scuti star previously misclassified as an eclipsing system; one field SX Phe star near the Galactic plane; and one multiperiodic high-luminosity star of unknown type. The amplitude is usually a strong function of the wavelength in pulsating stars, but this is not the case for the high-luminosity variable. One possible explanation is that the luminous star has a pulsating companion. The SX Phe and high-luminosity star are both heavily reddened (A V > 5 mag).

The search for transiting planets around hot subdwarfs

The main goal of this project is to investigate star-planet interactions during the Red Giant Branch (RGB) phase. In particular, we focus on what happens to planetary systems once their host stars leave the main sequence and engulf close-in planets, presumably, perturbing the dy-namical architecture of the system. In this context, we wonder if close-in planets may survive this evolutionary phase, evolving towards a new stable configuration, or on the contrary, if these planets are destroyed and the entire system collapses. Whatever the outcome, how will this interaction alter the star and affect its subsequent evolution? Here, we search for observational evidence of transiting planets orbiting hot subdwarfs (sdBs) stars, which are direct post-RGB objects that have lost most of their envelopes. To this end, we analyze light curves from the space missions Kepler/K2, TESS, and CHEOPS to search for shallow periodic transits of close-in, previously engulfed planets or their remnants, such as the rocky cores of giant gas planets. By determining the occurrence of planets or remnants around sdB stars, we will place strong constraints on the evolution of planetary systems after the RGB phase of their host stars. This summary describes the methods, tools, and strategies used to explore the available photometric data in the search for transiting planets and establish detection limits that allow us to build planet occurrence rates around these stars.

Kepler, K2, and TESS observations: ensemble and comparative asteroseismology

The original Kepler mission detected 18 pulsating subdwarf B (sdBV) stars, K2 observed 161 of our proposed targets with 41 sdB stars found to show p- or g-mode pulsations, and TESS has observed about 1,000 of our proposed targets. All these data should provide ∼300 sdBV stars, from which asteroseismology will provide a host of measurables. Combined with temperatures and gravities (and radii and masses from GAIA parallaxes!), we have a powerful set of observations with which to compare models. Here we review our seismology progress with sdBV stars.

Hot Subdwarf Stars Identified in LAMOST DR8 with Single-lined and Composite Spectra

A total of 222 hot subdwarf stars were identified with LAMOST DR8 spectra, among which 131 stars show composite spectra and have been decomposed, while 91 stars present single-lined spectra. Atmospheric parameters of all sample stars were obtained by fitting hydrogen (H) and helium (He) line profiles with synthetic spectra. Two long-period composite sdB binaries were newly discovered by combining our sample with the non-single-star data from Gaia DR3. One of the new systems presents the highest eccentricity (i.e., 0.5 ± 0.09) among known wide sdB binaries, which is beyond model predictions. A total of 15 composite sdB stars fall in the high-probability binary region of the RUWE−AEN plane and deserve priority follow-up observations to further study their binary nature. A distinct gap is clearly presented among temperatures of cool companions for our composite-spectrum sample, but we could not come to a conclusion as to whether this feature is connected to the formation history of hot subdwarf stars before their binary natures are confirmed.

The fastest hot subdwarfs revisited

Hyper-velocity stars (HVS) are enigmatic objects because they are travelling so fast that they escape from the Galaxy. Among hot subdwarfs, only one such star is known, the He-sdO US 708. The Hyper-MUCHFUSS collaboration provided additional HVS candidates. Here we revisit the fastest candidates including US 708 by analysing optical spectra and spectral energy distributions using a new grid of tailored model atmospheres and report preliminary results. The sample is dominated by H-rich subdwarfs and their distribution in the Kiel diagram appears to be bimodal for the sdB stars but otherwise fits canonical evolutionary models well. Gaia’s proper motion measurements allowed a precise kinematic investigation to be made. It turns out that all previously proposed HVS candidates are actually bound to the Galaxy, except US 708. The original candidate sample turns out to belong to an extreme halo population. The scarcity of available observations of US 708 calls for space-based UV and IR photometry as well as high precision radial velocity measurements.

Short-period pulsating hot-subdwarf stars observed by TESS

We present results of a Transiting Exoplanet Survey Satellite (TESS) search for short-period pulsations in compact stellar objects observed in years 1 and 3 of the TESS mission, during which the southern ecliptic hemisphere was targeted. We describe the TESS data used and the details of the search method. For many of the targets, we use unpublished spectroscopic observations to classify the objects. From the TESS photometry, we clearly identify 43 short-period hot-subdwarf pulsators, including 32 sdB stars, eight sdOB stars, two sdO stars, and, significantly, one He-sdOB star, which is the first of this kind to show short-period pulsations. Eight stars show signals at both low and high frequencies, and are therefore “hybrid” pulsators. We report the list of prewhitened frequencies and we show the amplitude spectra calculated from the TESS data. We make an attempt to identify possible multiplets caused by stellar rotation, and we select four candidates with rotation periods between 1 and 12.9 days. The most interesting targets discovered in this survey should be observed throughout the remainder of the TESS mission and from the ground. Asteroseismic investigations of these data sets will be invaluable in revealing the interior structure of these stars and will boost our understanding of their evolutionary history. We find three additional new variable stars but their spectral and variability types remain to be constrained.

Volume-limited sample of low-mass red giant stars, the progenitors of hot subdwarf stars

Context. Current theory predicts that hot subdwarf binaries are produced from evolved low-mass binaries that have undergone mass transfer and drastic mass loss during either a common-envelope phase or a stable Roche-lobe overflow while on the red giant branch (RGB). Aims. We perform a spectroscopic survey to find binary systems that include low-mass red giants near the tip of the RGB, which are predicted to be the direct progenitors of subdwarf B (sdB) stars. We aim to obtain a homogeneous sample to search for the observational evidence of correlations between the key parameters governing the formation of sdB stars and constrain the physics of stable mass transfer. Methods. Based on data from the Gaia mission and several ground-based, multiband photometry surveys, we compiled a sample of low-mass red giant branch (RGB) candidates. The candidates were selected according to their Gaia data release 2 (DR2) color, absolute magnitude, and proper motion cuts. In this work, we concentrated on the southern hemisphere targets and conducted a spectroscopic survey of 88 red giant stars to search for the long-period RGB plus main-sequence binary systems within 200 pc. Combining radial velocity (RV) measurements from ground-based observations with CORALIE and RV measurements from Gaia DR2 and from the early data release 3 (eDR3) as well as the astrometric excess noise and renormalized unit weight error measurements from Gaia DR3, we defined a robust binary classification method. In addition, we searched for known binary systems in the literature and in Gaia DR3. Results. We select a total of 211 RGB candidates in the southern hemisphere within 200 pc based on the Gaia DR2 color-magnitude diagram. Among them, a total of 33 red giants were reported as binary systems with orbital periods between 100 and 900 days, some of which are expected to be the direct progenitors of wide binary sdB stars. In addition, we classified 37 new main-sequence plus RGB binary candidates, whose orbital parameters will be measured with future spectroscopic follow-up. Conclusions. Using high-quality astrometric measurements provided by the Gaia mission coupled with high-resolution spectroscopy from the ground, we provide a powerful method for searching for low-mass red giant stars in long-period binary systems.

Dynamical Masses of the Primary Be Star and Secondary sdB Star in the Single-lined Binary κ Dra (B6 IIIe)

Because many classical Be stars may owe their nature to mass and angular-momentum transfer in a close binary, the present masses, temperatures, and radii of their components are of high interest for comparison to stellar evolution models. Object κ Dra is a 61.5 day single-lined binary with a B6 IIIe primary. With the CHARA Array instruments MIRC/MIRC-X and MYSTIC, we detected the secondary at (approximately photospheric) flux ratios of 1.49% ± 0.10% and 1.63% ± 0.09% in the H and K band, respectively. From a large and diverse optical spectroscopic database, only the radial velocity curve of the Be star could be extracted. However, employing the parallaxes from Hipparcos and Gaia, which agree within their nominal 1σ errors, we could derive the total mass and found component masses of 3.65 ± 0.48 and 0.426 ± 0.043 M ⊙ for the Be star and the companion, respectively. Previous cross-correlation of the observed FUV spectrum with O-type subdwarf (sdO) spectral model templates had not detected a companion belonging to the hot sdO population known from ∼20 earlier-type Be stars. Guided by our full 3D orbital solution, we found a strong cross-correlation signal for a stripped subdwarf B-type companion (FUV flux ratio of 2.3% ± 0.5%), enabling the first firm characterization of such a star and making κ Dra the first mid- to late-type Be star with a directly observed subdwarf companion.

TIC 5724661: A Long-period Binary with a Pulsating sdB Star and δ Scuti Variable

Using TESS 20 s cadence data, we have discovered an unusual combination of pulsating stars in what we infer to be a binary system. The binary consists of a standard δ Scuti star with pulsations over the range 32–41 day−1; this is in a likely wide orbit with a hot subdwarf-B (sdB) star, which itself has a large-amplitude p-mode pulsation at 524 day−1. We establish constraints on the period of the putative binary by using radial velocity measurements of the δ Scuti star and show that any sdB companion star must orbit with a period greater than approximately thirty days. Our identification of this sdB binary serves as an important addition to the relatively small number of sdB binaries known to have orbital periods longer than a few days. We model such a binary using MESA and find that this system could be formed through stable, nonconservative mass transfer from either a low-mass or an intermediate-mass progenitor, without undergoing a common-envelope phase.

Probing TYC 3315-1807-1, An sdB+dM Binary Displaying Strong Period Variation and Reflection Effect

Subdwarf (sdB) stars include core helium-burning stars with a very thin hydrogen envelope that lies at the blue end of the horizontal branch (or extreme horizontal branch). Among them, short-period sdB binaries especially with cool companions are significant to test and constrain binary evolution. We discuss one such sdB+dM type binary, TYC 3315-1807-1 (V1), which was first reported by Kawka. Results of the photometric analysis on Transiting Exoplanet Survey Satellite data are being reported. Light variation in the light curve suggests that the system displays a large reflection effect with no eclipses. Spectroscopic observations of the object were also carried out to probe into the nature of secondary companion as well as to understand the post-common-envelope evolution of such objects. The variability in Balmer, He, and Na line profiles as a function of phase, probably caused by observed reflection effect was identified and studied. Period variation study of the object was done using times of minima obtained from the literature and the O − C plot was produced, which points to a decrease in the period (dp/dt = −1.36315 × 10−7 day yr−1), and the possible scenario of evolution is discussed. From the evolutionary models, we constrain the possible mass of the sdB to be 0.274 M ⊙ and that of the secondary is 0.113 M ⊙, and we conclude that V1 may evolve directly as a helium-core white dwarf.

Tidally Tilted Pulsations in HD 265435, a Subdwarf B Star with a Close White Dwarf Companion

Abstract Tidally tilted pulsators (TTPs) are an intriguing new class of oscillating stars in binary systems; in such stars, the pulsation axis coincides with the line of apsides, or tidal axis, of the binary. All three TTPs discovered so far have been δ Scuti stars. In this Letter, we report the first conclusive discovery of tidally tilted pulsations in a subdwarf B (sdB) star. HD 265435 is an sdB–white dwarf binary with a 1.65 hr period that has been identified and characterized as the nearest potential Type Ia supernova progenitor. Using TESS 20 s cadence data from Sectors 44 and 45, we show that the pulsation axis of the sdB star has been tidally tilted into the orbital plane and aligned with the tidal axis of the binary. We identify 31 independent pulsation frequencies, 27 of which have between 1 and 7 sidebands separated by the orbital frequency (ν orb) or multiples thereof. Using the observed amplitude and phase variability due to tidal tilting, we assign ℓ and m values to most of the observed oscillation modes and use these mode identifications to generate preliminary asteroseismic constraints. Our work significantly expands our understanding of TTPs, as we now know that (i) they can be found in stars other than δ Scuti pulsators, especially highly evolved stars that have lost their H-rich envelopes, and (ii) tidally tilted pulsations can be used to probe the interiors of stars in very tight binaries.

Physical Properties of 29 sdB+dM Eclipsing Binaries in Zwicky Transient Facility

The development of large-scale time-domain surveys provides an opportunity to study the physical properties as well as the evolutionary scenario of B-type subdwarfs (sdBs) and M-type dwarfs (dMs). Here, we obtained 33 sdB+dM eclipsing binaries based on the Zwicky Transient Facility (ZTF) light curves and Gaia Early Data Release 3 (EDR3) parallaxes. By using the PHOEBE code for light curve analysis, we obtain probability distributions for parameters of 29 sdB+dMs. R 1, R 2 and i are well determined, and the average uncertainty of mass ratio q is 0.08. Our parameters are in good agreement with previous works if a typical mass of sdB is assumed. Based on parameters of 29 sdB+dMs, we find that both the mass ratio q and the companion’s radius R 2 decrease with the shortening of the orbital period. For the three sdB+dMs with orbital periods less than 0.075 days, their companions are all brown dwarfs. The masses and radii of the companions satisfy the mass–radius relation for low-mass stars and brown dwarfs. Companions with radii between 0.12 R ⊙ and 0.15 R ⊙ seem to be missing in the observations. As more short-period sdB+dM eclipsing binaries are discovered and classified in the future with ZTF and Gaia, we will have more information to constrain the evolutionary ending of sdB+dMs.