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While a few methods for the determination of depth-resolved strain distributions each with inherent limitations are available, tomographic reconstruction has been applied to this problem in only a limited sense. One of the challenges was the potential impact of geometric parallax, which constitutes a non-negligible lateral offset of diffraction information arising from different sample depths at the detector. Here, the effect of parallax was investigated and two main results have emerged. First, the impact of parallax was found to be additive to other offset contributions, which implies a straightforward correction. Second, for tomographic scans utilizing a full 360° rotation parallax has been found to have no impact on reconstructions of angular information.

With Cosmicflows-4, distances are compiled for 55,877 galaxies gathered into 38,065 groups. Eight methodologies are employed, with the largest numbers coming from the correlations between the photometric and kinematic properties of spiral galaxies (TF) and elliptical galaxies (FP). Supernovae that arise from degenerate progenitors (type Ia SNe) are an important overlapping component. Smaller contributions come from distance estimates from the surface brightness fluctuations of elliptical galaxies and the luminosities and expansion rates of core-collapse supernovae (SNe II). Cepheid period–luminosity relation and tip of the red giant branch observations founded on local stellar parallax measurements along with the geometric maser distance to NGC 4258 provide the absolute scaling of distances. The assembly of galaxies into groups is an important feature of the study in facilitating overlaps between methodologies. Merging between multiple contributions within a methodology and between methodologies is carried out with Bayesian Markov chain Monte Carlo procedures. The final assembly of distances is compatible with a value of the Hubble constant of H 0 = 74.6 km s−1 Mpc−1 with the small statistical error of ±0.8 km s−1 Mpc−1 but a large potential systematic error of ∼3 km s−1 Mpc−1. Peculiar velocities can be inferred from the measured distances. The interpretation of the field of peculiar velocities is complex because of large errors on individual components and invites analyses beyond the scope of this study.

A complete accounting of nearby objects—from the highest-mass white dwarf progenitors down to low-mass brown dwarfs—is now possible, thanks to an almost complete set of trigonometric parallax determinations from Gaia, ground-based surveys, and Spitzer follow-up. We create a census of objects within a Sun-centered sphere of 20 pc radius and check published literature to decompose each binary or higher-order system into its separate components. The result is a volume-limited census of ∼3600 individual star formation products useful in measuring the initial mass function across the stellar (<8M ⊙) and substellar (≳5M Jup) regimes. Comparing our resulting initial mass function to previous measurements shows good agreement above 0.8M ⊙ and a divergence at lower masses. Our 20 pc space densities are best fit with a quadripartite power law, ξ(M)=dN/dM∝M−α , with long-established values of α = 2.3 at high masses (0.55 < M < 8.00M ⊙), and α = 1.3 at intermediate masses (0.22 < M < 0.55M ⊙), but at lower masses, we find α = 0.25 for 0.05 < M < 0.22M ⊙, and α = 0.6 for 0.01 < M < 0.05M ⊙. This implies that the rate of production as a function of decreasing mass diminishes in the low-mass star/high-mass brown dwarf regime before increasing again in the low-mass brown dwarf regime. Correcting for completeness, we find a star to brown dwarf number ratio of, currently, 4:1, and an average mass per object of 0.41 M ⊙.

One of the most important applications of microlensing observations is the detection of free-floating planets (FFPs). The timescale of microlensing due to FFPs (t E) is short (a few days). Discerning the annual parallax effect in observations of these short-duration events due to FFPs by one observer is barely possible, though their parallax amplitude is larger than that in common events. In microlensing events due to FFPs, the lens–source relative trajectory alters because of the observer’s motion by δ u . This deviation is a straight line as long as t E ≪ P ⊕, and its size is δ u ∝ π rel (P ⊕ is the observer’s orbital period). So, most observed microlensing events due to close FFPs have simple Paczyńsky light curves with indiscernible but important parallax. To evaluate the destructive effects of invisible parallax in such events, we simulate ∼9650 microlensing events due to FFPs with t E < 10 days that are observed only by the Nancy Grace Roman Space Telescope (Roman). We conclude that in half of these microlensing events the missing parallax alters the real light curves, changing their shape and derived properties (by Δχ 2 ≳ 100). By fitting Paczyński light curves to these affected events we evaluate the relative and dimensionless deviations in the lensing parameters from their real values (δ t E, δ ρ ⋆, ...). We conclude that around 46 FFPs that are discovered by Roman have light curves highly affected by invisible parallax with δ t E > 0.1 and δ ρ ⋆ > 0.1. Our study reveals the importance of simultaneous and dense observations of the same microlensing events viewed by Roman by other observers circling the Sun in different orbits.

In the pursuit of understanding the population of stellar remnants within the Milky Way, we analyze the sample of ∼950 microlensing events observed by the Spitzer Space Telescope between 2014 and 2019. In this study we focus on a subsample of nine microlensing events, selected based on their long timescales, small microlensing parallaxes, and joint observations by the Gaia mission, to increase the probability that the chosen lenses are massive and the mass is measurable. Among the selected events we identify lensing black holes and neutron star candidates, with potential confirmation through forthcoming release of the Gaia time-series astrometry in 2026. Utilizing Bayesian analysis and Galactic models, along with the Gaia Data Release 3 proper-motion data, four good candidates for dark remnants were identified: OGLE-2016-BLG-0293, OGLE-2018-BLG-0483, OGLE-2018-BLG-0662, and OGLE-2015-BLG-0149, with lens masses of 3.0−1.3+1.8M⊙ , 4.7−2.1+3.2M⊙ , 3.15−0.64+0.66M⊙ and 1.40−0.55+0.75M⊙ , respectively. Notably, the first two candidates are expected to exhibit astrometric microlensing signals detectable by Gaia, offering the prospect of validating the lens masses. The methodologies developed in this work will be applied to the full Spitzer microlensing sample, populating and analyzing the timescale (t E) versus parallax (π E) diagram to derive constraints on the population of lenses in general and massive remnants in particular.

Depth information is important for postural stability and is generated by two visual systems: binocular and motion parallax. The effect of each type of parallax on postural stability remains unclear. We investigated the effects of binocular and motion parallax loss on static postural stability using a virtual reality (VR) system with a head-mounted display (HMD). A total of 24 healthy young adults were asked to stand still on a foam surface fixed on a force plate. They wore an HMD and faced a visual background in the VR system under four visual test conditions: normal vision (Control), absence of motion parallax (Non-MP)/binocular parallax (Non-BP), and absence of both motion and binocular parallax (Non-P). The sway area and velocity in the anteroposterior and mediolateral directions of the center-of-pressure displacements were measured. All postural stability measurements were significantly higher under the Non-MP and Non-P conditions than those under the Control and Non-BP conditions, with no significant differences in the postural stability measurements between the Control and Non-BP conditions. In conclusion, motion parallax has a more prominent effect on static postural stability than binocular parallax, which clarifies the underlying mechanisms of postural instability and informs the development of rehabilitation methods for people with visual impairments.

We present a Bayesian inference methodology for the estimation of orbital parameters on single-line spectroscopic binaries with astrometric data, based on the No-U-Turn sampler Markov chain Monte Carlo algorithm. Our approach is designed to provide a precise and efficient estimation of the joint posterior distribution of the orbital parameters in the presence of partial and heterogeneous observations. This scheme allows us to directly incorporate prior information about the system—in the form of a trigonometric parallax, and an estimation of the mass of the primary component from its spectral type—to constrain the range of solutions, and to estimate orbital parameters that cannot be usually determined (e.g., the individual component masses), due to the lack of observations or imprecise measurements. Our methodology is tested by analyzing the posterior distributions of well-studied double-line spectroscopic binaries treated as single-line binaries by omitting the radial velocity data of the secondary object. Our results show that the system’s mass ratio can be estimated with an uncertainty smaller than 10% using our approach. As a proof of concept, the proposed methodology is applied to 12 single-line spectroscopic binaries with astrometric data that lacked a joint astrometric–spectroscopic solution, for which we provide full orbital elements. Our sample-based methodology allows us also to study the impact of different posterior distributions in the corresponding observations space. This novel analysis provides a better understanding of the effect of the different sources of information on the shape and uncertainty in the orbit and radial velocity curve.

We report Very Long Baseline Array observations of 22 GHz H2O and 43 GHz SiO masers toward the Mira variable RR Aql. By fitting the SiO maser emission to a circular ring, we estimate the absolute stellar position of RR Aql and find agreement with Gaia astrometry to within the joint uncertainty of ≈1 mas. Using the maser astrometry we measure a stellar parallax of 2.44 ± 0.07 mas, corresponding to a distance of 410−11+12 pc. The maser parallax deviates significantly from the Gaia EDR3 parallax of 1.95 ± 0.11 mas, indicating a 3.8σ tension between radio and optical measurements. This tension is most likely caused by optical photocenter variations limiting the Gaia astrometric accuracy for this Mira variable. Combining infrared magnitudes with parallaxes for RR Aql and other Miras, we fit a period–luminosity relation using a Bayesian approach with Markov Chain Monte Carlo sampling and a strong prior for the slope of −3.60 ± 0.30 from the Large Magellanic Cloud. We find a K-band zero-point (defined at logP(days) = 2.30) of −6.79 ± 0.15 mag using very long baseline interferometry (VLBI) parallaxes and −7.08 ± 0.29 mag using Gaia parallaxes. The Gaia zero-point is statistically consistent with the more accurate VLBI value.

We investigate the underlying distribution of orbital eccentricities for planets around early-to-mid M dwarf host stars. We employ a sample of 163 planets around early- to mid-M dwarfs across 101 systems detected by NASA’s Kepler Mission. We constrain the orbital eccentricity for each planet by leveraging the Kepler lightcurve together with a stellar density prior, constructed using metallicity from spectroscopy, Ks magnitude from 2MASS, and stellar parallax from Gaia. Within a Bayesian hierarchical framework, we extract the underlying eccentricity distribution, assuming alternately Rayleigh, half-Gaussian, and Beta functions for both single- and multi-transit systems. We described the eccentricity distribution for apparently single-transiting planetary systems with a Rayleigh distribution with σ = 0.19 − 0.03 + 0.04 , and for multitransit systems with σ = 0.03 − 0.01 + 0.02 . The data suggest the possibility of distinct dynamically warmer and cooler subpopulations within the single-transit distribution: The single-transit data prefer a mixture model composed of two distinct Rayleigh distributions with σ 1 = 0.02 − 0.00 + 0.11 and σ 2 = 0.24 − 0.03 + 0.20 over a single Rayleigh distribution, with 7:1 odds. We contextualize our findings within a planet formation framework, by comparing them to analogous results in the literature for planets orbiting FGK stars. By combining our derived eccentricity distribution with other M dwarf demographic constraints, we estimate the underlying eccentricity distribution for the population of early- to mid-M dwarf planets in the local neighborhood.

We derive and publish data-driven estimates of stellar metallicity [M/H] for ∼175 million stars with low-resolution XP spectra published in Gaia DR3. The [M/H] values, along with T eff and logg , are derived using the XGBoost algorithm, trained on stellar parameters from APOGEE, augmented by a set of very-metal-poor stars. XGBoost draws on a number of data features: the full set of XP spectral coefficients, narrowband fluxes derived from XP spectra, and broadband magnitudes. In particular, we include CatWISE magnitudes, as they reduce the degeneracy of T eff and dust reddening. We also include the parallax as a data feature, which helps constrain logg and [M/H]. The resulting mean stellar parameter precision is 0.1 dex in [M/H], 50 K in T eff, and 0.08 dex in logg . This all-sky [M/H] sample is substantially larger than published samples of comparable fidelity across −3 ≲ [M/H] ≲ +0.5. Additionally, we provide a catalog of over 17 million bright (G < 16) red giants whose [M/H] values are vetted to be precise and pure. We present all-sky maps of the Milky Way in different [M/H] regimes that illustrate the purity of the data set, and demonstrate the power of this unprecedented sample to reveal the Milky Way’s structure from its heart to its disk.