Rational Decisions, Random Matrices and Spin Glasses

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of ``optimal'' solutions is generically exponentially large: rationality is thus de facto of limited use. In addition, this problem is related to spin glasses with L\'evy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate

Noise Dressing of Financial Correlation Matrices

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). In particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.Comment: Latex (Revtex) 3 pp + 2 postscript figures (in-text

Gaia GraL: Gaia DR2 Gravitational Lens Systems. VII. XMM-Newton Observations of Lensed Quasars

© 2022. The Author(s). Published by the American Astronomical Society. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.3847/1538-4357/ac4476We present XMM-Newton X-ray observations of nine confirmed lensed quasars at 1 ≲ z ≲ 3 identified by the Gaia Gravitational Lens program. Eight systems are strongly detected, with 0.3-8.0 keV fluxes F 0.3-8.0 ≳ 5 ×10-14 erg cm-2 s-1. Modeling the X-ray spectra with an absorbed power law, we derive power-law photon indices and 2-10 keV luminosities for the eight detected quasars. In addition to presenting sample properties for larger quasar population studies and for use in planning for future caustic-crossing events, we also identify three quasars of interest: a quasar that shows evidence of flux variability from previous ROSAT observations, the most closely separated individual lensed sources resolved by XMM-Newton, and one of the X-ray brightest quasars known at z > 3. These sources represent the tip of the discoveries that will be enabled by SRG/eROSITA.Peer reviewe

Gaia GraL: Gaia DR2 gravitational lens systems – VIII. A radio census of lensed systems

© 2024 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/We present radio observations of 24 confirmed and candidate strongly lensed quasars identified by the Gaia Gravitational Lenses working group. We detect radio emission from eight systems in 5.5 and 9 GHz observations with the Australia Telescope Compact Array (ATCA), and 12 systems in 6 GHz observations with the Karl G. Jansky Very Large Array (VLA). The resolution of our ATCA observations is insufficient to resolve the radio emission into multiple lensed images, but we do detect multiple images from 11 VLA targets. We have analysed these systems using our observations in conjunction with existing optical measurements, including measuring offsets between the radio and optical positions for each image and building updated lens models. These observations significantly expand the existing sample of lensed radio quasars, suggest that most lensed systems are detectable at radio wavelengths with targeted observations, and demonstrate the feasibility of population studies with high-resolution radio imaging.Peer reviewe

Gaia GraL: Gaia DR2 Gravitational Lens Systems. VIII. A radio census of lensed systems

We present radio observations of 24 confirmed and candidate strongly lensed quasars identified by the Gaia Gravitational Lenses (GraL) working group. We detect radio emission from 8 systems in 5.5 and 9 GHz observations with the Australia Telescope Compact Array (ATCA), and 12 systems in 6 GHz observations with the Karl G. Jansky Very Large Array (VLA). The resolution of our ATCA observations is insufficient to resolve the radio emission into multiple lensed images, but we do detect multiple images from 11 VLA targets. We have analysed these systems using our observations in conjunction with existing optical measurements, including measuring offsets between the radio and optical positions, for each image and building updated lens models. These observations significantly expand the existing sample of lensed radio quasars, suggest that most lensed systems are detectable at radio wavelengths with targeted observations, and demonstrate the feasibility of population studies with high resolution radio imaging

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

Gaia GraL: Gaia DR2 Gravitational Lens Systems. VII. XMM-Newton Observations of Lensed Quasars

Abstract We present XMM-Newton X-ray observations of nine confirmed lensed quasars at 1 ≲ z ≲ 3 identified by the Gaia Gravitational Lens program. Eight systems are strongly detected, with 0.3–8.0 keV fluxes F 0.3−8.0 ≳ 5 ×10−14 erg cm−2 s−1. Modeling the X-ray spectra with an absorbed power law, we derive power-law photon indices and 2–10 keV luminosities for the eight detected quasars. In addition to presenting sample properties for larger quasar population studies and for use in planning for future caustic-crossing events, we also identify three quasars of interest: a quasar that shows evidence of flux variability from previous ROSAT observations, the most closely separated individual lensed sources resolved by XMM-Newton, and one of the X-ray brightest quasars known at z &gt; 3. These sources represent the tip of the discoveries that will be enabled by SRG/eROSITA.</jats:p

Gaia Early Data Release 3: The Gaia Catalogue of Nearby Stars

Aims. We produce a clean and well-characterised catalogue of objects within 100 pc of the Sun from the Gaia Early Data Release 3. We characterise the catalogue through comparisons to the full data release, external catalogues, and simulations. We carry out a first analysis of the science that is possible with this sample to demonstrate its potential and best practices for its use. Methods. Theselection of objects within 100 pc from the full catalogue used selected training sets, machine-learning procedures, astrometric quantities, and solution quality indicators to determine a probability that the astrometric solution is reliable. The training set construction exploited the astrometric data, quality flags, and external photometry. For all candidates we calculated distance posterior probability densities using Bayesian procedures and mock catalogues to define priors. Any object with reliable astrometry and a non-zero probability of being within 100 pc is included in the catalogue. Results. We have produced a catalogue of 331 312 objects that we estimate contains at least 92% of stars of stellar type M9 within 100 pc of the Sun. We estimate that 9% of the stars in this catalogue probably lie outside 100 pc, but when the distance probability function is used, a correct treatment of this contamination is possible. We produced luminosity functions with a high signal-to-noise ratio for the main-sequence stars, giants, and white dwarfs. We examined in detail the Hyades cluster, the white dwarf population, and wide-binary systems and produced candidate lists for all three samples. We detected local manifestations of several streams, superclusters, and halo objects, in which we identified 12 members of Gaia Enceladus. We present the first direct parallaxes of five objects in multiple systems within 10 pc of the Sun. Conclusions. We provide the community with a large, well-characterised catalogue of objects in the solar neighbourhood. This is a primary benchmark for measuring and understanding fundamental parameters and descriptive functions in astronomy.</jats:p

Observational hertzsprung-russell diagrams

We highlight the power of the Gaia DR2 in studying many fine structures of the Hertzsprung-Russell diagram (HRD). Gaia allows us to present many different HRDs, depending in particular on stellar population selections. We do not aim here for completeness in terms of types of stars or stellar evolutionary aspects. Instead, we have chosen several illustrative examples. We describe some of the selections that can be made in Gaia DR2 to highlight the main structures of the Gaia HRDs. We select both field and cluster (open and globular) stars, compare the observations with previous classifications and with stellar evolutionary tracks, and we present variations of the Gaia HRD with age, metallicity, and kinematics. Late stages of stellar evolution such as hot subdwarfs, post-AGB stars, planetary nebulae, and white dwarfs are also analysed, as well as low-mass brown dwarf objects. The Gaia HRDs are unprecedented in both precision and coverage of the various Milky Way stellar populations and stellar evolutionary phases. Many fine structures of the HRDs are presented. The clear split of the white dwarf sequence into hydrogen and helium white dwarfs is presented for the first time in an HRD. The relation between kinematics and the HRD is nicely illustrated. Two different populations in a classical kinematic selection of the halo are unambiguously identified in the HRD. Membership and mean parameters for a selected list of open clusters are provided. They allow drawing very detailed cluster sequences, highlighting fine structures, and providing extremely precise empirical isochrones that will lead to more insight in stellar physics. Gaia DR2 demonstrates the potential of combining precise astrometry and photometry for large samples for studies in stellar evolution and stellar population and opens an entire new area for HRD-based studies