This paper documents the seventeenth data release (DR17) from the Sloan Digital Sky Surveys; the fifth and final release from the fourth phase (SDSS-IV). DR17 contains the complete release of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, which reached its goal of surveying over 10,000 nearby galaxies. The complete release of the MaNGA Stellar Library accompanies this data, providing observations of almost 30,000 stars through the MaNGA instrument during bright time. DR17 also contains the complete release of the Apache Point Observatory Galactic Evolution Experiment 2 survey that publicly releases infrared spectra of over 650,000 stars. The main sample from the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), as well as the subsurvey Time Domain Spectroscopic Survey data were fully released in DR16. New single-fiber optical spectroscopy released in DR17 is from the SPectroscipic IDentification of ERosita Survey subsurvey and the eBOSS-RM program. Along with the primary data sets, DR17 includes 25 new or updated value-added catalogs. This paper concludes the release of SDSS-IV survey data. SDSS continues into its fifth phase with observations already underway for the Milky Way Mapper, Local Volume Mapper, and Black Hole Mapper surveys.

Context. Rotation significantly impacts on the structure and life of stars. In phases of high rotation velocity (close to critical), the photospheric structure can be highly modified, and present in particular geometrical deformation (rotation flattening) and latitudinaldependent flux (gravity darkening). The fastest known rotators among the nondegenerate stars close to the main sequence, Be stars, are key targets for studying the effects of fast rotation on stellar photospheres. Aims. We seek to determine the purely photospheric parameters of Achernar based on observations recorded during an emission-free phase (normal B phase). Methods. Several recent works proved that optical/IR long-baseline interferometry is the only technique able to sufficiently spatially resolve and measure photospheric parameters of fast rotating stars. We thus analyzed ESO-VLTI (PIONIER and AMBER) interferometric observations of Achernar to measure its photospheric parameters by fitting our physical model CHARRON using a Markov chain Monte Carlo method. This analysis was also complemented by spectroscopic, polarimetric, and photometric observations to investigate the status of the circumstellar environment of Achernar during the VLTI observations and to cross-check our model-fitting results. Results. Based on VLTI observations that partially resolve Achernar, we simultaneously measured five photospheric parameters of a Be star for the first time: equatorial radius (equatorial angular diameter), equatorial rotation velocity, polar inclination, position angle of the rotation axis projected on the sky, and the gravity darkening β coefficient (effective temperature distribution). The close circumstellar environment of Achernar was also investigated based on contemporaneous polarimetry, spectroscopy, and interferometry, including image reconstruction. This analysis did not reveal any important circumstellar contribution, so that Achernar was essentially in a normal B phase at least from mid-2009 to end-2012, and the model parameters derived in this work provide a fair description of its photosphere. Finally, because Achernar is the flattest interferometrically resolved fast rotator to-date, the measured β and flattening, combined with values from previous works, provide a crucial test for a recently proposed gravity darkening model. This model offers a promising explanation to the fact that the measured β parameter decreases with flattening and shows significantly lower values than the classical prediction of von Zeipel.

We analyse interferometric data obtained for Regulus with AMBER (Astronomical Multi-BEam combineR) at high spectral resolution (λ/δλ ≈ 12000) across the Brγ spectral line. The study of the photocentre displacement allows us to constrain a large number of stellar parameters -equatorial radius R eq , equatorial velocity V eq , inclination i, rotation-axis position angle P A rot , and flattening -with an estimation of gravity-darkening coefficient β using previously published theoretical results. We use the Simulation Code of Interferometric-observations for ROtators and CirCumstellar Objects (SCIROCCO), a semi-analytical algorithm dedicated to fast rotators. We chose Regulus because it is a very well-known edge-on star, for which an alternative approach is needed to check the previously published results. Our analysis showed that a significant degeneracy of solution is present. By confronting the results obtained by differential interferometry with those obtained by conventional long-base interferometry, we obtain similar results (within the uncertainties), thereby validating our approach, where V eq and i are found separately. From the photocentre displacement, we can independently deduce P A rot . We use two minimization methods to restrict observed stellar parameters via a fast rotator model: a non-stochastic method (χ 2 fit) and a stochastic one (Markov Chain Monte Carlo method), in order to check whether the correct global minimum is achieved particularly with respect to the degeneracies of the gravity darkening parameter β, where we demonstrate, using a quantitative analysis of parameters, that the estimate of β is easier for stars with an inclination angle of around 45 • .

Context. Spectrally resolved long-baseline optical/IR interferometry of rotating stars opens perspectives to investigate their fundamental parameters and the physical mechanisms that govern their interior, photosphere, and circumstellar envelope structures. Aims. Based on the signatures of stellar rotation on observed interferometric wavelength-differential phases, we aim to measure angular diameters, rotation velocities, and orientation of stellar rotation axes. Methods. We used the AMBER focal instrument at ESO-VLTI in its high-spectral resolution mode to record interferometric data on the fast rotator Achernar. Differential phases centered on the hydrogen Br γ line (K band) were obtained during four almost consecutive nights with a continuous Earth-rotation synthesis during ∼5 h/night, corresponding to ∼60 • position angle coverage per baseline. These observations were interpreted with our numerical code dedicated to long-baseline interferometry of rotating stars. Results. By fitting our model to Achernar's differential phases from AMBER, we could measure its equatorial radius R eq = 11.6 ± 0.3 R , equatorial rotation velocity V eq = 298 ± 9 km s −1 , rotation axis inclination angle i = 101.5 ± 5.2 • , and rotation axis position angle (from North to East) PA rot = 34.9 ± 1.6 • . From these parameters and the stellar distance, the equatorial angular diameter / eq of Achernar is found to be 2.45 ± 0.09 mas, which is compatible with previous values derived from the commonly used visibility amplitude. In particular, / eq and PA rot measured in this work with VLTI/AMBER are compatible with the values previously obtained with VLTI/VINCI. Conclusions. The present paper, based on real data, demonstrates the super-resolution potential of differential interferometry for measuring sizes, rotation velocities, and orientation of rotating stars in cases where visibility amplitudes are unavailable and/or when the star is partially or poorly resolved. In particular, we showed that differential phases allow the measurement of sizes up to ∼4 times smaller than the diffraction-limited angular resolution of the interferometer.

Context. As previously demonstrated on Achernar, one can derive the angular radius, rotational velocity, axis tilt, and orientation of a fast-rotating star from the differential phases obtained by spectrally resolved long baseline interferometry using earth-rotation synthesis.Aims. We applied this method on a small sample of stars for different spectral types and classes, in order to generalize the technique to other rotating stars across the H-R diagram and determine their fundamental parameters. Methods. We used differential phase data from the AMBER/VLTI instrument obtained prior to refurbishing its spectrometer in 2010. With the exception of Fomalhaut, which has been observed in the medium-resolution mode of AMBER (λ/δλ ≈ 1500), our three other targets, Achernar, Altair, and δ Aquilae offered high-resolution (λ/δλ ≈ 12 000) spectro-interferometric data around the Brγ absorption line in K band. These data were used to constrain the input parameters of an analytical, still realistic model to interpret the observations with a systematic approach for the error budget analysis in order to robustly conclude on the physics of our 4 targets. We applied the super resolution provided by differential phases φ diff to measure the size (equatorial radius R eq and angular diameter / eq ), the equatorial rotation velocity (V eq ), the inclination angle (i), and the rotation axis position angle (PA rot ) of 4 fast-rotating stars: Achernar, Altair, δ Aquilae, and Fomalhaut. The stellar parameters of the targets were constrained using a semi-analytical algorithm dedicated to fast rotators SCIROCCO. Results. The derived parameters for each star were R eq = 11.2 ± 0.5 R , V eq sin i = 290 ± 17 km s −1 , PA rot = 35.4• ± 1.4• , for Achernar; R eq = 2.0 ± 0.2 R , V eq sin i = 226 ± 34 km s −1 , PA rot = −65.5 • ± 5.5• , for Altair; R eq = 2.2 ± 0.3 R , V eq sin i = 74 ± 35 km s −1 , PA rot = −101.2• ± 14 • , for δ Aquilae; and R eq = 1.8 ± 0.2 R , V eq sin i = 93 ± 16 km s −1 , PA rot = 65.6 • ± 5 • , for Fomalhaut. They were found to be compatible with previously published values from differential phase and visibility measurements, while we were able to determine, for the first time, the inclination angle i of Fomalhaut (i = 90• ± 9 • ) and δ Aquilae (i = 81 • ± 13 • ), and the rotation-axis position angle PA rot of δ Aquilae. Conclusions. Beyond the theoretical diffraction limit of an interferometer (ratio of the wavelength to the baseline), spatial super resolution is well suited to systematically estimating the angular diameters of rotating stars and their fundamental parameters with a few sets of baselines and the Earth-rotation synthesis provided a high enough spectral resolution.

Aims. We present a near-infrared spectro-interferometric observation of the non-Mira-type, semiregular asymptotic giant branch star SW Vir. Our aim is to probe the physical properties of the outer atmosphere with spatially resolved data in individual molecular and atomic lines. Methods. We observed SW Vir in the spectral window between 2.28 and 2.31 µm with the near-infrared interferometric instrument AMBER at ESO's Very Large Telescope Interferometer (VLTI). Results. Thanks to AMBER's high spatial resolution and high spectral resolution of 12 000, the atmosphere of SW Vir has been spatially resolved not only in strong CO first overtone lines but also in weak molecular and atomic lines of H 2 O, CN, HF, Ti, Fe, Mg, and Ca. While the uniform-disk diameter of the star is 16.23±0.20 mas in the continuum, it increases up to 22-24 mas in the CO lines. Comparison with the MARCS photospheric models reveals that the star appears larger than predicted by the hydrostatic models not only in the CO lines but also even in the weak molecular and atomic lines. We found that this is primarily due to the H 2 O lines (but also possibly due to the HF and Ti lines) originating in the extended outer atmosphere. Although the H 2 O lines manifest themselves very little in the spatially unresolved spectrum, the individual rovibrational H 2 O lines from the outer atmosphere can be identified in the spectro-interferometric data. Our modeling suggests an H 2 O column density of 10 19 -10 20 cm −2 in the outer atmosphere extending out to ∼2 R ⋆ . Conclusions. Our study has revealed that the effects of the nonphotospheric outer atmosphere are present in the spectrointerferometric data not only in the strong CO first overtone lines but also in the weak molecular and atomic lines. Therefore, analyses of spatially unresolved spectra, such as for example analyses of the chemical composition, should be carried out with care even if the lines appear to be weak.

We determine the physical parameters of the outer atmosphere of a sample of eight evolved stars, including the Red SuperGiant α Sco, the Red Giant Branch stars α Boo and γ Cru, the K giant λ Vel, the normal M-giants BK Vir and SW Vir, and the Mira star W Hya (in two different luminosity phases) by spatially resolving the stars in the individual carbon monoxide (CO) first overtone lines. We used the AM-BER (Astronomical Multi-BEam combineR) instrument at the Very Large Telescope Interferometer (VLTI), in high-resolution mode (λ/∆λ ≈ 12000) between 2.28 and 2.31 µm in K-band. The maximal angular resolution is 10 mas, obtained by triplets telescope configuration, with baselines from 7 to 48 m. By using a numerical model of a molecular atmosphere in spherical shells (MOLsphere), named PAMPERO (for Physical Approach of Molecular Photospheric Ejection at high-angular-Resolution for evOlved-stars) we add multiple extended CO layers above the photospheric MARCS model at an adequate spatial resolution. We use the differential visibilities and the spectrum to estimate the size (R) of the CO MOLsphere, its column density (N CO ) and temperature (T mol ) distributions along the stellar radius. The combining of the χ2 minimization and a fine grid approach for uncertainty analysis leads to reasonable N CO and T mol distributions along the stellar radius of the MOLsphere.

The spectacular results provided by the second generation VLTI instruments GRAVITY and MATISSE on Active Galactic Nuclei trigger and justify a strong increase in the sensitivity limit of optical interferometers. A key component of such an upgrade is off-axis fringe tracking. To evaluate its potential and limitations, we describe and analyze its error budget including fringe sensing precision and temporal, angular and chromatic perturbations of the piston. The global tracking error is computed using standard seeing parameters for different sites, seeing conditions and telescope sizes for the current GRAVITY Fringe Tracker and a new concept of Hierarchical Fringe Tracker. Then, it is combined with a large catalog of guide star candidates from Gaia to produce sky coverage maps that give the probability to find a usable off-axis guide star in any part of the observable sky. These maps can be used to set the specifications of the system, check its sensitivity to seeing conditions and evaluate the feasibility of science programs. We check the availability of guide stars and the tracking accuracy for a large set of 15799 Quasars to confirm the feasibility of a large program on BLRs in the K band with the GRAVITY Fringe Tracker and show how it can be extended to the L, M and N bands. Another set of 331 well-characterized nearby AGNs shows the high potential of MATISSE for imaging and characterization of the dust torus in the N band under off-axis tracking on both UTs and ATs.