The mass of Albireo Aa and the nature of Albireo AB: New aspects from Gaia DR2

Aims: We aim to clarify the nature of Albireo AB and specifically to decipher whether it is an optical or physical pair. We also try to determine the mass of Albireo Aa. Methods: We scrutinize and compare the available absolute astrometric data (from Hipparcos and Gaia DR2) of Albireo A and B, and we investigate the relative orbit of the pair Albireo Aa,Ac using orbit solutions based on ground-based interferometric measurements. Results: The mass of Albireo Aa (K3 II) is surprisingly small; only an upper limit of about 0.7 solar masses could be derived. The systemic proper motion of Aa,Ac differs from that of component B by about 10 mas/year with an uncertainty of less than 2 mas/year. Albireo AB is therefore most probably an optical double. Conclusions: Specific astrometric and spectroscopic follow-up observations clarifying the surprising mass estimate for Albireo Aa are recommended.Comment: 4 pages, 3 figures, accepted by Astron. Astrophy

Expectations on the mass determination using astrometric microlensing by Gaia

Context. Astrometric gravitational microlensing can be used to determine the mass of a single star (the lens) with an accuracy of a few percent. To do so, precise measurements of the angular separations between lens and background star with an accuracy below 1 milli-arcsecond at different epochs are needed. Hence only the most accurate instruments can be used. However, since the timescale is in the order of months to years, the astrometric deflection might be detected by Gaia, even though each star is only observed on a low cadence. Aims. We want to show how accurately Gaia can determine the mass of the lensing star. Methods. Using conservative assumptions based on the results of the second Gaia Data release, we simulated the individual Gaia measurements for 501 predicted astrometric microlensing events during the Gaia era (2014.5 - 2026.5). For this purpose we use the astrometric parameters of Gaia DR2, as well as an approximative mass based on the absolute G magnitude. By fitting the motion of lens and source simultaneously we then reconstruct the 11 parameters of the lensing event. For lenses passing by multiple background sources, we also fit the motion of all background sources and the lens simultaneously. Using a Monte-Carlo simulation we determine the achievable precision of the mass determination. Results. We find that Gaia can detect the astrometric deflection for 114 events. Further, for 13 events Gaia can determine the mass of the lens with a precision better than 15% and for 13 + 21 = 34 events with a precision of 30% or better.Comment: 13 pages; 10 figures; 3 tables; accepted by A&A (April. 28th 2020) The Python-based code for our simulation is made publicly available https://github.com/jkluter/ML

Ongoing Astrometric Microlensing Events of Two Nearby Stars

Context. Astrometric microlensing is an excellent tool to determine the mass of a stellar object. By measuring the astrometric shift of a background source star in combination with precise predictions of its unlensed position and of the lens position, gravitational lensing allows to determine the mass of the lensing star with a precision of 1 percent, independent of any prior knowledge. Aims. Making use of the recently published Gaia Data Release 2 (Gaia DR2) we predict astrometric microlensing events by foreground stars of high proper motion passing by a background star in the coming years. Methods. We compile a list of ~148.000 high-proper-motion stars within Gaia DR2 with $\mu_{tot}$ > 150 mas/yr. We then search for background stars close to their paths and calculate the dates and separations of the closest approaches. Using color and absolute magnitude, we determine approximate masses of the lenses. Finally, we calculate the expected astrometric shifts and magnifications of the predicted events. Results . We detect two ongoing microlensing events by the high proper motion stars Luyten 143-23 and Ross 322 and predict closest separations of (108.5 $\pm$ 1.4) mas in July 2018 and (125.3 $\pm$ 3.4) mas in August 2018, respectively. The respective expected astrometric shifts are (1.74 $\pm$ 0.12) mas and (0.76 $\pm$ 0.06) mas. Furthermore, Luyten 143-23 will pass by another star in March 2021 with a closest separation of (280.1 $\pm$ 1.1) mas, which results in an expected shift of (0.69 $\pm$ 0.05) mas.Comment: Submitted to A&A, accepted June 14, 2018. 4 pages, 3 figures, 2 table

A conjugate gradient algorithm for the astrometric core solution of Gaia

The ESA space astrometry mission Gaia, planned to be launched in 2013, has been designed to make angular measurements on a global scale with micro-arcsecond accuracy. A key component of the data processing for Gaia is the astrometric core solution, which must implement an efficient and accurate numerical algorithm to solve the resulting, extremely large least-squares problem. The Astrometric Global Iterative Solution (AGIS) is a framework that allows to implement a range of different iterative solution schemes suitable for a scanning astrometric satellite. In order to find a computationally efficient and numerically accurate iteration scheme for the astrometric solution, compatible with the AGIS framework, we study an adaptation of the classical conjugate gradient (CG) algorithm, and compare it to the so-called simple iteration (SI) scheme that was previously known to converge for this problem, although very slowly. The different schemes are implemented within a software test bed for AGIS known as AGISLab, which allows to define, simulate and study scaled astrometric core solutions. After successful testing in AGISLab, the CG scheme has been implemented also in AGIS. The two algorithms CG and SI eventually converge to identical solutions, to within the numerical noise (of the order of 0.00001 micro-arcsec). These solutions are independent of the starting values (initial star catalogue), and we conclude that they are equivalent to a rigorous least-squares estimation of the astrometric parameters. The CG scheme converges up to a factor four faster than SI in the tested cases, and in particular spatially correlated truncation errors are much more efficiently damped out with the CG scheme.Comment: 24 pages, 16 figures. Accepted for publication in Astronomy & Astrophysic

Cluster virial expansion for nuclear matter within a quasiparticle statistical approach

Correlations in interacting many-particle systems can lead to the formation of clusters, in particular bound states and resonances. Systematic quantum statistical approaches allow to combine the nuclear statistical equilibrium description (law of mass action) with mean-field concepts. A chemical picture, which treats the clusters as distinct entities, serves as an intuitive concept to treat the low-density limit. Within a generalized Beth-Uhlenbeck approach, the quasiparticle virial expansion is extended to include arbitrary clusters, where special attention must be paid to avoid inconsistencies such as double counting. Correlations are suppressed with increasing density due to Pauli blocking. The contribution of the continuum to the virial coefficients can be reduced by considering clusters explicitly and introducing quasiparticle energies. The cluster-virial expansion for nuclear matter joins known benchmarks at low densities with those near saturation density.Comment: 18 pages, 6 figures, 2 table