Subdwarf Research Articles

Advanced classification of hot subdwarf binaries using artificial intelligence techniques and Gaia DR3 data

Hot subdwarf stars are compact blue evolved objects, burning helium in their cores surrounded by a tiny hydrogen envelope. In the Hertzsprung-Russell Diagram they are located by the blue end of the Horizontal Branch. Most models agree on a quite probable common envelope binary evolution scenario in the Red Giant phase. However, the current binarity rate for these objects is yet unsolved, but key, question in this field. This study aims to develop a novel classification method for identifying hot subdwarf binaries within large datasets using Artificial Intelligence techniques and data from the third Gaia data release (GDR3). The results will be compared with those obtained previously using Virtual Observatory techniques on coincident samples. The methods used for hot subdwarf binary classification include supervised and unsupervised machine learning techniques. Specifically, we have used Support Vector Machines (SVM) to classify 3084 hot subdwarf stars based on their colour-magnitude properties. Among these, 2815 objects have Gaia DR3 BP/RP spectra, which were classified using Self-Organizing Maps (SOM) and Convolutional Neural Networks (CNN). In order to ensure spectral quality, previously to SOM and CNN classification, our 2815 BP/RP set were pre-analysed with two different approaches: the cosine similarity technique and the Uniform Manifold Approximation and Projection (UMAP) technique. Additional analysis onto a golden sample of 88 well-defined objects, is also presented. The findings demonstrate a high agreement level (sim 70-90<!PCT!>) with the classifications from the Virtual Observatory Sed Analyzer (VOSA) tool. This shows that the SVM, SOM, and CNN methods effectively classify sources with an accuracy comparable to human inspection or non-AI techniques. Notably, SVM in a radial basis function achieves 70.97<!PCT!> reproducibility for binary targets using photometry, and CNN reaches 84.94<!PCT!> for binary detection using spectroscopy. We also found that the single--binary differences are especially observable on the infrared flux in our Gaia DR3 BP/BR spectra, at wavelengths larger than $ sim $700 nm. We find that all the methods used are in fairly good agreement and are particularly effective to discern between single and binary systems. The agreement is also consistent with the results previously obtained with VOSA. In global terms, considering all quality metrics, CNN is the method that provides the best accuracy. The methods also appear effective for detecting peculiarities in the spectra. While promising, challenges in dealing with uncertain compositions highlight the need for caution, suggesting further research is needed to refine techniques and enhance automated classification reliability, particularly for large-scale surveys.

A spectroscopic and kinematic survey of fast hot subdwarfs

Hot subdwarfs (sdO/B) are the stripped helium cores of red giants formed via binary interactions. Close hot subdwarf binaries with massive white dwarf companions have been proposed as possible progenitors of thermonuclear supernovae type Ia (SN Ia). If the supernova is triggered by stable mass transfer from the helium star, the companion should survive the explosion and should be accelerated to high velocities. The hypervelocity star US 708 is regarded as the prototype for such an ejected companion. To find more of those objects we conducted an extensive spectroscopic survey. Candidates for such fast stars have been selected from the spectroscopic database of the Sloan Digital Sky Survey (SDSS) and several ground-based proper-motion surveys. Follow-up spectroscopy has been obtained with several 4m- to 10m-class telescopes. Combining the results from quantitative spectroscopic analyses with space-based astrometry from Gaia Early Data Release 3 (EDR3) we determined the atmospheric and kinematic parameters of 53 fast hot subdwarf stars. None of these stars is unbound to the Galaxy, although some have Galactic restframe velocities close to the Galactic escape velocity. 21 stars are apparently single objects, that crossed the Galactic disc within their lifetimes in the sdO/B stage and could be regarded as potential candidates for the SN Ia ejection scenario. However, the properties of the full sample are more consistent with a pure old Galactic halo population. We therefore conclude that the fast sdO/B stars we found are likely to be extreme halo stars.

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.

Large-scale ordered magnetic fields generated in mergers of helium white dwarfs

Stellar mergers are one important path to highly magnetised stars. Mergers of two low-mass white dwarfs may create up to every third hot subdwarf star. The merging process is usually assumed to dramatically amplify magnetic fields. However, so far only four highly magnetised hot subdwarf stars have been found, suggesting a fraction of less than $1<!PCT!>$. We present two high-resolution magnetohydrodynamical (MHD) simulations of the merger of two helium white dwarfs in a binary system with the same total mass of $0.6\,M_ We analysed an equal-mass merger with two $0.3\,M_ white dwarfs, and an unequal-mass merger with white dwarfs of $0.25\,M_ and $0.35\,M_ We simulated the inspiral, merger, and further evolution of the merger remnant for about $50$ rotations. We found efficient magnetic field amplification in both mergers via a small-scale dynamo, reproducing previous results of stellar merger simulations. The magnetic field saturates at a similar strength for both simulations. We then identified a second phase of magnetic field amplification in both merger remnants that happens on a timescale of several tens of rotational periods of the merger remnant. This phase generates a large-scale ordered azimuthal field via a large-scale dynamo driven by the magneto-rotational instability. Finally, we speculate that in the unequal-mass merger remnant, helium burning will initially start in a shell around a cold core, rather than in the centre. This forms a convection zone that coincides with the region that contains most of the magnetic energy, and likely destroys the strong, ordered field. Ohmic resistivity might then quickly erase the remaining small-scale field. Therefore, the mass ratio of the initial merger could be the selecting factor that decides if a merger remnant will stay highly magnetised long after the merger.

Shocking and Mass Loss of Compact Donor Stars in Type Ia Supernovae

Type Ia supernovae arise from thermonuclear explosions of white dwarfs accreting from a binary companion. Following the explosion, the surviving donor star leaves at roughly its orbital velocity. The discovery of the runaway helium subdwarf star US 708, and seven hypervelocity stars from Gaia data, all with spatial velocities ≳900 km s−1, strongly support a scenario in which the donor is a low-mass helium star or a white dwarf. Motivated by these discoveries, we perform three-dimensional hydrodynamical simulations with the Athena++ code, modeling the hydrodynamical interaction between a helium star or helium white dwarf and the supernova ejecta. We find that ≈0.01–0.02 M ⊙ of donor material is stripped, and explain the location of the stripped material within the expanding supernova ejecta. We continue the postexplosion evolution of the shocked donor stars with the MESA code. As a result of entropy deposition, they remain luminous and expanded for ≈105–106 yr. We show that the postexplosion properties of our helium white dwarf donor agree reasonably with one of the best-studied hypervelocity stars, D6-2.

MK-like spectral classification for hot subdwarf stars with LAMOST spectra

Abstract An MK-like spectral classification has been conducted for 1224 hot subdwarf stars with LAMOST DR9 low-resolution spectra. The whole sample was divided into four categories according to the spectral line characteristics: He-normal, He-weak, He-strong C, and He-strong. Each selected spectrum was assigned a spectral class, a luminosity class, and a helium class by comparing the line depth and width with standard spectra selected in LAMOST. Relationships between atmospheric parameters and spectral classification are also presented.

Spectral analysis of three hot subdwarf stars: EC 11481-2303, Feige 110, and PG 0909+276

Context. For the precise spectral analysis of hot stars, advanced stellar-atmosphere models that consider deviations from the local thermodynamic equilibrium are mandatory. This requires accurate atomic data to calculate all transition rates and occupation numbers for atomic levels in the considered model atoms, not only for a few prominent lines exhibited in an observation. The critical evaluation of atomic data is a challenge because it requires precise laboratory measurements. Ultraviolet spectroscopy of hot stars with high resolving power provide such “laboratory” spectra. Aims. We compare observed, isolated lines of the iron group (here calcium to nickel) with our synthetic line profiles to judge the accuracy of the respective oscillator strengths. This will verify them or yield individual correction values to improve the spectral analysis, that is the determination of, for example, effective temperature (Teff) and abundances. Methods. To minimize the error propagation from uncertainties in Teff, surface gravity (𝑔), and abundance determination, we start with a precise reanalysis of three hot subdwarf stars, namely EC 11481-2303, Feige 110, and PG0909+276. Then, we measure the abundances of the iron-group elements individually. Based on identified, isolated lines of these elements, we compare observation and models to measure their deviation in strength (equivalent width). Results. For EC 11481–2303 and Feige 110, we confirmed the previously determined Teff and log 𝑔 values within their error limits. For all three stars, we fine-tuned all metal abundances to achieve the best reproduction of the observation. For more than 450 isolated absorption lines of the iron group, we compared modeled and observed line strengths. Considering the uncertainty of the analysis and evaluation procedure, an upper limit for the uncertainty of the underlying atomic data was established. Conclusions. We selected strong, reliable isolated absorption lines, which we recommend to use as reference lines for abundance determinations in related objects.

Classification of LAMOST spectra of B-type and hot subdwarf stars using kernel support vector machine

Machine learning has emerged as a leading field in artificial intelligence, demonstrating expert-level performance in various domains. Astronomy has benefited from machine learning techniques, particularly in classifying and identifying stars based on their features. This study focuses on the spectra-based classification of 11,408 B-type and 2422 hot subdwarf stars. The study employs baseline correction using Asymmetric Least Squares (ALS) to enhance classification accuracy. It applies the Pan-Core concept to identify 500 unique patterns or ranges for both types of stars. These patterns are the foundation for creating Support Vector Machine (SVM) models, including the linear (L-SVM), polynomial (P-SVM), and radial basis (R-SVM) kernels. Parameter tuning for the SVM models is achieved through cross-validation. Evaluation of the SVM models on test data reveals that the linear kernel SVM achieves the highest accuracy (87.0%), surpassing the polynomial kernel SVM (84.1%) and radial kernel SVM (80.1%). The average calibrated accuracy falls within the range of 90–95%. These results demonstrate the potential of using spectrum-based classification to aid astronomers in improving and expanding their understanding of stars, with a specific focus on the identification of hot subdwarf stars. This study presents a valuable investigation for astronomers, as it enables the classification of stars based on their spectra, leveraging machine learning techniques to enhance their knowledge and insights in astronomy.

Short-period pulsating hot subdwarf stars observed by TESS

We present the results of an extension of our Transiting Exoplanet Survey Satellite (TESS) search for short-period pulsations in compact stellar objects observed during the second and fourth years of the TESS mission, which targeted the northern ecliptic hemisphere. For many of the targets, we exploited unpublished spectroscopic data to confirm or re-evaluate the object’s spectral classification. From the TESS photometry, we identified 50 short-period hot-subdwarf pulsators, including 35 sdB and 15 sdOB stars. The sample contains 26 pulsators that were unknown prior to the TESS mission. Nine stars show signals at both low and high frequencies and have been categorized as “hybrid” pulsators. For each pulsator, we report the list of prewhitened frequencies, along with and their amplitude spectra calculated from the TESS data. We attempt to identify possible multiplets caused by stellar rotation and we report five candidates with rotation periods between 11 and 46 d. With the search for p-mode pulsating hot subdwarfs in TESS Sectors 1–60 complete, we discuss the completeness of the study, as well as the instability strip and the evolutionary status of the stars we found. We also compare the distribution of pulsation periods as a function of effective temperature and surface gravity with theoretical predictions. We find that the percentage of undetected pulsators in the TESS mission increases with decreasing brightness measurements of stars, reaching 25% near the 15th magnitude. When comparing the distribution of hot subdwarfs in the log g − Teff plane with stellar models, we underline the importance of a proper treatment of the hydrogen-rich envelope composition (strongly affected by microscopic diffusion processes). We also emphasize that the stellar mass is a significant factor in understanding the instability strip. The p-mode instability strip is confirmed to be narrower than predicted by prior non-adiabatic calculations based on models incorporating equilibrium between gravitational settling and radiative levitation for iron. This implies that competing mixing processes ignored in these models must play a role in reducing the amount of levitating iron in the stellar envelope. Interestingly, we find that the coolest p-mode pulsators with Teff ≲ 30 000 K (including the hybrid ones) tend to cluster around the terminal age of the extreme horizontal branch of canonical mass (TAEHB at ∼0.47 M⊙). This trend is expected from the non-adiabatic pulsation calculations. Otherwise, the overall pulsation period distributions tend to reproduce the predicted trends in Teff and log g.

Mode identification and period fitting in six pulsating hot subdwarfs

Abstract We report the results of our analysis of six gravity-mode pulsating hot subdwarf stars observed in the short cadence mode by Transiting Exoplanet Survey Satellite. We detected at least 10 pulsation periods in each star, searched for multiplets, and used an asymptotic period spacing to identify modes.We used a grid of evolutionary and pulsation models calculated with the MESA and GYRE, along with spectroscopic parameters and modal degree identification, to derive the physical properties of the stars.We checked the relation between the helium content and pulsations and found that no pulsator exists among the extremely helium-rich hot subdwarfs, while the number of detected pulsators in other helium groups increases as the helium content decreases.We found p- and g-mode hot subdwarfs pulsators in all Galactic populations.

On the Surface Helium Abundance of B-type Hot Subdwarf Stars from the WD+MS Channel of Type Ia Supernovae

The origin of intermediate helium (He)-rich hot subdwarfs is still unclear. Previous studies have suggested that some surviving Type Ia supernovae (SNe Ia) companions from the white dwarf + main-sequence (WD+MS) channel may contribute to the intermediate He-rich hot subdwarfs. However, previous studies ignored the impact of atomic diffusion on the post-explosion evolution of surviving companion stars of SNe Ia, leading to the aspect that they could not explain the observed surface He abundance of intermediate He-rich hot subdwarfs. In this work, by taking the atomic diffusion and stellar wind into account, we trace the surviving companions of SNe Ia from the WD+MS channel using the one-dimensional stellar evolution code MESA until they evolve into hot subdwarfs. We find that the surface He-abundances of our surviving companion models during their core He-burning phases are in a range of −1≲log(NHe/NH)≲0 , which are consistent with those observed in intermediate He-rich hot subdwarfs. This seems to further support the notion that it is possible for surviving companions of SNe Ia in the WD+MS channel to form some intermediate He-rich hot subdwarfs.

The double low-mass white dwarf eclipsing binary system J2102–4145 and its possible evolution

In recent years, about 150 low-mass white dwarfs (WDs), typically with masses below 0.4 M⊙, have been discovered. The majority of these low-mass WDs are observed in binary systems as they cannot be formed through single-star evolution within Hubble time. In this work, we present a comprehensive analysis of the double low-mass WD eclipsing binary system J2102−4145. Our investigation encompasses an extensive observational campaign, resulting in the acquisition of approximately 28 h of high-speed photometric data across multiple nights using NTT/ULTRACAM, SOAR/Goodman, and SMARTS-1m telescopes. These observations have provided critical insights into the orbital characteristics of this system, including parameters such as inclination and orbital period. To disentangle the binary components of J2102−4145, we employed the XTGRID spectral fitting method with GMOS/Gemini-South and X-shooter data. Additionally, we used the PHOEBE package for light curve analysis on NTT/ULTRACAM high-speed time-series photometry data to constrain the binary star properties. Our analysis unveils remarkable similarities between the two components of this binary system. For the primary star, we determine Teff,1 = 13 688−72+65 K, log g1 = 7.36 ± 0.01, R1 = 0.0211 ± 0.0002 R⊙, and M1 = 0.375 ± 0.003 M⊙, while, the secondary star is characterised by Teff,2 = 12952−66+53 K, log g2 = 7.32 ± 0.01, R2 = 0.0203−0.0003+0.0002 R⊙, and M2 = 0.314 ± 0.003 M⊙. Furthermore, we found a notable discrepancy between Teff and R of the less massive WD, compared to evolutionary sequences for WDs from the literature, which has significant implications for our understanding of WD evolution. We discuss a potential formation scenario for this system which might explain this discrepancy and explore its future evolution. We predict that this system will merge in ∼800 Myr, evolving into a helium-rich hot subdwarf star and later into a hybrid He/CO WD.

Identifying hot subdwarf stars from photometric data using a Gaussian mixture model and graph neural network

Abstract Hot subdwarf stars are very important for understanding stellar evolution, stellar astrophysics, and binary star systems. Identifying more such stars can help us better understand their statistical distribution, properties, and evolution. In this paper, we present a new method to search for hot subdwarf stars in photometric data (BP, RP, G, g, r, i, z, y) using a machine-learning algorithm, a graph neural network, and a Gaussian mixture model. We use a Gaussian mixture model and Markov distance to build the graph structure, and on the graph structure we use a graph neural network to identify hot subdwarf stars from a dataset containing 31838 stars, with the recall, precision, and F1 score maximized on the original, weight, and synthetic minority oversampling technique datasets. Finally, to validate the model, we selected about 2116 hot subdwarf candidates from the Gaia Data Release 3 database and compared them with the studies by Culpan et al. (2022, A&A, 662, A40) and Geier et al. (2019, A&A, 621, A38).

Flare Hunting in Hot Subdwarf and White Dwarf Stars from Cycles 1–5 of TESS Photometry

Stellar flares are critical phenomena on stellar surfaces, which are closely tied to stellar magnetism. While extensively studied in main-sequence (MS) stars, their occurrence in evolved compact stars, specifically hot subdwarfs and white dwarfs (WDs), remains scarcely explored. Based on Cycles 1–5 of TESS photometry, we conducted a pioneering survey of flare events in ∼12,000 compact stars, corresponding to ∼38,000 light curves with a 2 minute cadence. Through dedicated techniques for detrending light curves, identifying preliminary flare candidates, and validating them via machine learning, we established a catalog of 1016 flares from 193 compact stars, including 182 from 58 sdB/sdO stars and 834 from 135 WDs, respectively. However, all flaring compact stars showed signs of contamination from nearby objects or companion stars, preventing sole attribution of the detected flares. For WDs, it is highly probable that the flares originated from their cool MS companions. In contrast, the higher luminosities of sdB/sdO stars diminish companion contributions, suggesting that detected flares originated from sdB/sdO stars themselves or through close magnetic interactions with companions. Focusing on a refined sample of 23 flares from 13 sdB/sdO stars, we found their flare frequency distributions were slightly divergent from those of cool MS stars; instead, they resemble those of hot B/A-type MS stars having radiative envelopes. This similarity implies that the flares on sdB/sdO stars, if these flares did originate from them, may share underlying mechanisms with hot MS stars, which warrants further investigation.

A 500 pc volume-limited sample of hot subluminous stars. I. Space density, scale height, and population properties

We present the first volume-limited sample of spectroscopically confirmed hot subluminous stars out to 500 pc, defined using the accurate parallax measurements from the Gaia space mission data release 3 (DR3). The sample comprises a total of 397 members, with 305 ($ 77<!PCT!>$) identified as hot subdwarf stars, including 83 newly discovered systems. Of these, we observe that 178 ($ are hydrogen-rich sdBs, 65 are sdOBs ($ 21<!PCT!>$), 32 are sdOs ($ 11<!PCT!>$), and 30 are He-sdO/Bs ($ 10<!PCT!>$). Among them, 48 ($ 16<!PCT!>$) exhibit an infrared excess in their spectral energy distribution fits, suggesting a composite binary system. The hot subdwarf population is estimated to be 90<!PCT!> complete, assuming that most missing systems are these composite binaries located within the main sequence (MS) in the Gaia colour-magnitude diagram (CMD). The remaining sources in the sample include cataclysmic variables (CVs), blue horizontal branch stars (BHBs), hot white dwarfs (WDs), and MS stars. We derived the mid-plane density $ $ and scale height $ h z $ for the non-composite hot subdwarf star population using a hyperbolic sechant profile (sech$^2$). The best-fit values are $ $ stars/pc3 and $ h z 62$ pc. When accounting for the composite-colour hot subdwarfs and their estimated completeness, the mid-plane density increases to $ $ stars/pc3. This corrected space density is an order of magnitude lower than predicted by population synthesis studies, supporting previous observational estimates.

He-rich Hot Subdwarf Stars Observed in Gaia DR3 and LAMOST DR7: Carbon and Nitrogen Abundances and Kinematics

We conducted an analysis of the abundances of He, C, and N in 210 He-rich hot subdwarfs observed within both the Gaia Data Release 3 (DR3) and LAMOST DR7 data sets. This analysis involved fitting the LAMOST spectra with Tlusty/Synspec non-LTE synthetic spectra. By examining the Galactic spatial positions, velocity vectors, and orbital parameters of these stars, we determined their Galactic population memberships utilizing LAMOST radial velocities and Gaia DR3 parallaxes along with proper motions. Our investigation revealed two positive correlations of C and one positive correlation of N with respect to the He abundance. We found a clear C abundance dichotomy where approximately 82% of the stars show N enrichment above the solar value. Moreover, we observed a bimodal distribution of C abundances, prominently evident in both the Galactic thin and thick disks but absent in the halo population. Furthermore, we found that the scenario of the merger channel of double helium white dwarfs is inadequate to explain the formation of C-deficient He-rich hot subdwarfs.

Multi-periodicity in the high gravity blue large amplitude pulsator ZTF J071329.02-152125.2

Abstract New time series photometry of the pulsating hot subdwarf star ZTF J071329.02-152125.2 is presented. Rapid (timescale of hours) changes in the amplitude of the known pulsation in the star was observed. This could be ascribed to beating between three closely spaced frequencies, but analysis of all available photometry finds a range of different frequencies, with widely different amplitudes. A new frequency of 49.66 d $^{-1}$ , suggestive of gravity-mode pulsation, was also discovered. The star may be a hybrid p-mode/g-mode hot subdwarf pulsator which sometimes exhibits extraordinarily large amplitude variability.

An observed population of intermediate-mass helium stars that have been stripped in binaries

The hydrogen-rich outer layers of massive stars can be removed by interactions with a binary companion. Theoretical models predict that this stripping produces a population of hot helium stars of ~2 to 8 solar masses ( M ☉ ), however, only one such system has been identified thus far. We used ultraviolet photometry to identify potential stripped helium stars then investigated 25 of them using optical spectroscopy. We identified stars with high temperatures (~60,000 to 100,000 kelvin), high surface gravities, and hydrogen-depleted surfaces; 16 stars also showed binary motion. These properties match expectations for stars with initial masses of 8 to 25 M ☉ that were stripped by binary interaction. Their masses fall in the gap between subdwarf helium stars and Wolf-Rayet stars. We propose that these stars could be progenitors of stripped-envelope supernovae.

Amplitude and frequency variations in PG 0101+039 from K2 photometry

Context. K2 photometry is suitable for the exploitation of mode variability on short timescales in hot B subdwarf stars and this technique is useful in constraining nonlinear quantities addressed by the stellar theory of high-order perturbation in the future. Aims. We analyzed high-quality K2 data collected for PG 0101+039 over about 80 days and we extracted the frequency content of oscillation. We determined the star’s rotational and orbital properties, in addition to characterizing the dynamics of the amplitude and frequency. Methods. The frequencies were extracted from light curves via a standard prewhitening technique. The binary information was obtained from variations both in brightness and radial velocities. The amplitude and frequency modulations (i.e., AMs and FMs) of the oscillation modes were measured by piece-wise light curves and characterized by a Markov chain Monte Carlo (MCMC) method. Results. We extracted 137 independent frequencies in PG 0101+039 and derived period spacing of ∼252 s and 144 s for the dipole and quadruple modes, respectively. We derived rotation periods of ∼8.81 ± 0.06 days and ∼8.60 ± 0.16 days based on g- and p-mode multiplets, respectively, implying a marginally differential rotation with a probability of ∼60%. We find that the rotation period is much shorter than the orbital period of ∼0.57 d, indicating that this system is not synchronized. The AMs and FMs were found to be measurable for 44 frequencies with high enough amplitude, including 12 rotational components. We characterized their modulating patterns and found a clear correlation between the amplitude and frequency variation, linked to nonlinear resonant couplings. In general, the modulating scale and timescale are on the order of a few dozen of nanohertz and a few tens of days, respectively. These values can serve as important constraints on future calculations of nonlinear amplitude equations. Conclusions. PG 0101+039 is an unsynchronized system containing a component whose amplitude and frequency variations are generally found to be on a shorter timescale than previously reported for other sdB pulsators. Those findings are essential to setting observational constraints on the nonlinear dynamics of resonant mode couplings and orbital solutions.

A self-synthesized origin for heavy metals in hot subdwarf stars

Context. A number of He-rich hot subdwarf stars present high abundances for trans-iron elements, such as Sr, Y, Zr, and Pb. Diffusion processes are important in hot subdwarf stars and it is generally believed that the high abundances of heavy elements in these peculiar stars are due to the action of radiative levitation. However, during the formation of He-rich hot subdwarf stars, hydrogen can be ingested into the convective zone driven by the He-core flash. It is known that episodes of protons being ingested into He-burning convective zones can lead to neutron-capture processes and the formation of heavy elements. Aims. In this work, we aim to explore, for the first time, whether neutron-capture processes can occur in late He-core flashes taking place in the cores of the progenitors of He-rich hot subdwarfs. We aim to explore the possibility of a self-synthesized origin for the heavy elements observed in some He-rich hot subdwarf stars. Methods. We computed a detailed evolutionary model for a stripped red-giant star using a stellar evolution code with a nuclear network comprising 32 isotopes. Then we post-processed the stellar models in the phase of helium and hydrogen burning using a post-processing nucleosynthesis code with a nuclear network of 1190 species, which allowed us to follow the neutron-capture processes in detail. Results. We find the occurrence of neutron-capture processes in our model, with neutron densities reaching a value of ∼5 × 1012 cm−3. We determined that the trans-iron elements are enhanced in the surface by 1 to 2 dex, as compared to initial compositions. Moreover, the relative abundance pattern [Xi/Fe] produced by neutron-capture processes closely resembles those observed in some He-rich hot subdwarf stars, hinting at a possible self-synthesized origin for the heavy elements in these stars. Conclusions. We conclude that intermediate neutron-capture processes can occur during a proton ingestion event in the He-core flash of stripped red-giant stars. This mechanism offers a natural channel for the production of the heavy elements observed in certain He-rich hot subdwarf stars.