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Abstract Emission lines from Rydberg transitions are detected for the first time from a region close to the surface of Betelgeuse. The H30αline is observed at 231.905 GHz, with an FWHM ∼42 km s−1and extended wings. A second line at 232.025 GHz (FWHM ∼21 km s−1), is modeled as a combination of Rydberg transitions of abundant low first ionization potential metals. Both H30αand the Rydberg combined line X30αare fitted by Voigt profiles, and collisional broadening with electrons may be partly responsible for the Lorentzian contribution, indicating electron densities of a few 108cm−3. X30αis located in a relatively smooth ring at a projected radius of 0.9× the optical photospheric radiusR⋆, whereas H30αis more clumpy, reaching a peak at ∼1.4R⋆. We use a semiempirical thermodynamic atmospheric model of Betelgeuse to compute the 232 GHz (1.29 mm) continuum and line profiles making simple assumptions. Photoionized abundant metals dominate the electron density, and the predicted surface of continuum optical depth unity at 232 GHz occurs at ∼1.3R⋆, in good agreement with observations. Assuming a Saha–Boltzmann distribution for the level populations of Mg, Si, and Fe, the model predicts that the X30αemission arises in a region of radially increasing temperature and turbulence. Inclusion of ionized C and non-LTE effects could modify the integrated fluxes and location of emission. These simulations confirm the identity of the Rydberg transition lines observed toward Betelgeuse and reveal that such diagnostics can improve future atmospheric models.more » « less
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Aims.We aim to accurately measure the dynamical mass and distance of Cepheids by combining radial velocity measurements with interferometric observations. Cepheid mass measurements are particularly necessary for solving the Cepheid mass discrepancy, while independent distance determinations provide a crucial test of the period–luminosity relation andGaiaparallaxes. Methods.We used the multi-telescope interferometric combiner, the Michigan InfraRed Combiner (MIRC) of the Center for High Angular Resolution Astronomy (CHARA) Array, to detect and measure the astrometric positions of the high-contrast companion orbiting the Galactic Cepheid SU Cygni. We also present new radial velocity measurements from ultraviolet spectra taken with theHubbleSpace Telescope. The combination of interferometric astrometry with optical and ultraviolet spectroscopy provided the full orbital elements of the system, in addition to component masses and the distance to the Cepheid system. Results.We measured the mass of the Cepheid,MA = 4.859 ± 0.058 M⊙, and its two companions,MBa = 3.595 ± 0.033 M⊙andMBb = 1.546 ± 0.009 M⊙. This is the most accurate existing measurement of the mass of a Galactic Cepheid (1.2%). Comparing with stellar evolution models, we show that the mass predicted by the tracks is higher than the measured mass of the Cepheid, which is similar to the conclusions of our previous work. We also measured the distance to the system to be 926.3 ± 5.0 pc, obtaining an unprecedented parallax precision of 6 μas (0.5%), which is the most precise and accurate distance for a Cepheid. This precision is similar to what is expected byGaiafor its last data release (DR5 in ∼2030) for single stars fainter thanG = 13, but is not guaranteed for stars as bright as SU Cyg. Conclusions.We demonstrate that evolutionary models remain incapable of accurately reproducing the measured mass of Cepheids, often predicting higher masses for the expected metallicity, even when factors such as rotation or convective core overshooting are taken into account. Our precise distance measurement allowed us to compare predictions from some period–luminosity relations. We find a disagreement of 0.2–0.5 mag with relations calibrated from photometry, while relations calibrated from a direct distance measurement are in better agreement.more » « lessFree, publicly-accessible full text available January 1, 2026
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Context. As primary anchors of the distance scale, Cepheid stars play a crucial role in our understanding of the distance scale of the Universe because of their period-luminosity relation. Determining precise and consistent parameters (radius, temperature, color excess, and projection factor) of Cepheid pulsating stars is therefore very important. Aims. With the high-precision parallaxes delivered by the early third Gaia data release (EDR3), we aim to derive various parameters of Cepheid stars in order to calibrate the period-luminosity and period-radius relations and to investigate the relation of period to p -factor. Methods. We applied an implementation of the parallax-of-pulsation method through the algorithm called spectro-photo-interferometry of pulsating stars (SPIPS), which combines all types of available data for a variable star (multiband and multicolor photometry, radial velocity, effective temperature, and interferometry measurements) in a global modeling of its pulsation. Results. We present the SPIPS modeling of a sample of 63 Galactic Cepheids. Adopting Gaia EDR3 parallaxes as an input associated with the best available dataset, we derive consistent values of parameters for these stars such as the radius, multiband apparent magnitudes, effective temperatures, color excesses, period changes, Fourier parameters, and the projection factor. Conclusions. Using the best set of data and the most precise distances for Milky Way Cepheids, we derive new calibrations of the period-luminosity and period-radius relations: M K S = −5.529 ±0.015 − 3.141 ±0.050 (log P − 0.9) and log R = 1.763 ±0.003 + 0.653 ±0.012 (log P − 0.9). After investigating the dependences of the projection factor on the parameters of the stars, we find a high dispersion of its values and no evidence of its correlation with the period or with any other parameters such as radial velocity, temperature, or metallicity. Statistically, the p -factor has an average value of p = 1.26 ± 0.07, but with an unsatisfactory agreement ( σ = 0.15). In absence of any clear correlation between the p -factor and other quantities, the best agreement is obtained under the assumption that the p -factor can take any value in a band with a width of 0.15. This result highlights the need for a further examination of the physics behind the p -factor.more » « less
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Context. A low-mass companion potentially in the brown dwarf mass regime was discovered on a ~12 yr orbit (~5.5 au) around HD 167665 using radial velocity (RV) monitoring. Joint RV–astrometry analyses confirmed that HD 167665B is a brown dwarf with precisions on the measured mass of ~4–9%. Brown dwarf companions with measured mass and luminosity are valuable for testing formation and evolutionary models. However, its atmospheric properties and luminosity are still unconstrained, preventing detailed tests of evolutionary models. Aims. We further characterize the HD 167665 system by measuring the luminosity and refining the mass of its companion and reassessing the stellar age. Methods. We present new high-contrast imaging data of the star and of its close-in environment from SPHERE and GRAVITY, which we combined with RV data from CORALIE and HIRES and astrometry from HIPPARCOSandGaia. Results. The analysis of the host star properties indicates an age of 6.20 ± 1.13 Gyr. GRAVITY reveals a point source near the position predicted from a joint fit of RV data and HIPPARCOS–Gaiaproper motion anomalies. Subsequent SPHERE imaging confirms the detection and reveals a faint point source of contrast of ∆H2= 10.95 ± 0.33 mag at a projected angular separation of ~180 mas. A joint fit of the high-contrast imaging, RV, and HIPPARCOSintermediate astrometric data together with theGaiaastrometric parameters constrains the mass of HD 167665B to ~1.2%, 60.3 ± 0.7MJ. The SPHERE colors and spectrum point to an early or mid-T brown dwarf of spectral type T4−2+1. Fitting the SPHERE spectrophotometry and GRAVITY spectrum with synthetic spectra suggests an effective temperature of ~1000–1150 K, a surface gravity of ~5.0–5.4 dex, and a bolometric luminosity log(L/L⊙)=−4.892−0.028+0.024dex. The mass, luminosity, and age of the companion can only be reproduced within 3σby the hybrid cloudy evolutionary models of Saumon & Marley (2008, ApJ, 689, 1327), whereas cloudless evolutionary models underpredict its luminosity.more » « lessFree, publicly-accessible full text available November 1, 2025
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Context. The surface brightness – color relationship (SBCR) is a poweful tool for determining the angular diameter of stars from photometry. It was for instance used to derive the distance of eclipsing binaries in the Large Magellanic Cloud (LMC), which led to its distance determination with an accuracy of 1%. Aims. We calibrate the SBCR for red giant stars in the 2.1 ≤ V − K ≤ 2.5 color range using homogeneous VEGA/CHARA interferometric data secured in the visible domain, and compare it to the relation based on infrared interferometric observations, which were used to derive the distance to the LMC. Methods. Observations of eight G–K giants were obtained with the VEGA/CHARA instrument. The derived limb-darkened angular diameters were combined with a homogeneous set of infrared magnitudes in order to constrain the SBCR. Results. The average precision we obtain on the limb-darkened angular diameters of the eight stars in our sample is 2.4%. For the four stars in common observed by both VEGA/CHARA and PIONIER/VLTI, we find a 1 σ agreement for the angular diameters. The SBCR we obtain in the visible has a dispersion of 0.04 magnitude and is consistent with the one derived in the infrared (0.018 magnitude). Conclusions. The consistency of the infrared and visible angular diameters and SBCR reinforces the result of 1% precision and accuracy recently achieved on the distance of the LMC using the eclipsing-binary technique. It also indicates that it is possible to combine interferometric observations at different wavelengths when the SBCR is calibrated.more » « less
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Abstract Tight relationships exist in the local Universe between the central stellar properties of galaxies and the mass of their supermassive black hole (SMBH)1–3. These suggest that galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase4–6. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to examine this relationship is at the peaks of star formation and black hole growth 8–12 billion years ago (redshifts 1–3)7. Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back in time of 11 billion years, by spatially resolving the broad-line region (BLR). We detect a 40-μas (0.31-pc) spatial offset between the red and blue photocentres of the Hα line that traces the velocity gradient of a rotating BLR. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2 × 108 solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6 × 1011 solar masses, which indicates an undermassive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the SMBH, indicating a delay between galaxy and black hole formation for some systems.more » « less
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Context.Since 2019, GRAVITY has provided direct observations of giant planets and brown dwarfs at separations of down to 95 mas from the host star. Some of these observations have provided the first direct confirmation of companions previously detected by indirect techniques (astrometry and radial velocities). Aims.We want to improve the observing strategy and data reduction in order to lower the inner working angle of GRAVITY in dual-field on-axis mode. We also want to determine the current limitations of the instrument when observing faint companions with separations in the 30–150 mas range. Methods.To improve the inner working angle, we propose a fiber off-pointing strategy during the observations to maximize the ratio of companion-light-to-star-light coupling in the science fiber. We also tested a lower-order model for speckles to decouple the companion light from the star light. We then evaluated the detection limits of GRAVITY using planet injection and retrieval in representative archival data. We compare our results to theoretical expectations. Results.We validate our observing and data-reduction strategy with on-sky observations; first in the context of brown dwarf follow-up on the auxiliary telescopes with HD 984 B, and second with the first confirmation of a substellar candidate around the starGaiaDR3 2728129004119806464. With synthetic companion injection, we demonstrate that the instrument can detect companions down to a contrast of 8 × 10−4(ΔΚ= 7.7 mag) at a separation of 35 mas, and a contrast of 3 × 10−5(ΔΚ= 11 mag) at 100 mas from a bright primary (K< 6.5), for 30 min exposure time. Conclusions.With its inner working angle and astrometric precision, GRAVITY has a unique reach in direct observation parameter space. This study demonstrates the promising synergies between GRAVITY andGaiafor the confirmation and characterization of substellar companions.more » « less
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