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Paolo Saracco

Publications and source records attributed to Paolo Saracco.

At least 37 records · Page 2Linked to original sources

Correspondence theorems for Hopf algebroids with applications to affine groupoids

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional conditions, this correspondence becomes bijective for Hopf algebroids. As an application, we investigate normal Hopf ideals in commutative Hopf algebroids (affine groupoid schemes) in connection with the study of normal affine subgroupoids.

math.RA↗

Unveiling the population of dual- and lensed- AGNs at sub-arcsec separations

All cosmological models of structure formation predict the existence of a widespread population of dual supermassive black holes in-spiralling inside their common host galaxy, eventually merging and giving rise to intense gravitational waves. These systems can be identified as dual AGNs at kilo parsec separations, but only very few have been confirmed at z>0.5. The appearance of multiple AGNs at small angular separations can also be due to gravitational lensing of single AGNs, which are themselves very important systems for many astrophysical topics. Here we present a novel technique, dubbed the Gaia Multipeak (GMP) method, to obtain large and reliable samples of dual/lensed AGN candidates with sub-arcsec separations by looking for AGNs showing multiple peaks in the light profiles observed by the Gaia satellite. All the GMP-selected sources with high resolution images (26 from the HST archive and 5 from dedicated adaptive-optics assisted imaging at the Large Binocular Telescope) show multiple components with sub-arcsec separation pointing toward a very high reliability of the method. By sampling separations down to ~2 kpc at z>1, this method allows us to probe the physical processes that drive the inspiralling of a pair of SMBHs inside a single galaxy.

astro-ph.GA↗

MAGAZ3NE: High Stellar Velocity Dispersions for Ultra-Massive Quiescent Galaxies at $z\gtrsim3$

In this work we publish stellar velocity dispersions, sizes, and dynamical masses for 8 ultra-massive galaxies (UMGs; log($M$/M$_\odot>11$, $z\gtrsim3$) from the Massive Ancient Galaxies At $z>3$ NEar-infrared (MAGAZ3NE) Survey, more than doubling the number of such galaxies with velocity dispersion measurements at this epoch. Using the deep Keck/MOSFIRE and Keck/NIRES spectroscopy of these objects in the $H$- and $K$-bandpasses, we obtain large velocity dispersions of $\sim400$ km s$^{-1}$ for most of the objects, which are some of the highest stellar velocity dispersions measured, and $\sim40$\% larger than those measured for galaxies of similar mass at $z\sim1.7$. The sizes of these objects are also smaller by a factor of 1.5-3 compared to this same $z\sim1.7$ sample. We combine these large velocity dispersions and small sizes to obtain dynamical masses. The dynamical masses are similar to the stellar masses of these galaxies, consistent with a Chabrier initial mass function (IMF). Considered alongside previous studies of massive quiescent galaxies across $0.2<z<4.0$, there is evidence for an evolution in the relation between the dynamical mass - stellar mass ratio and velocity dispersion as a function of redshift. This implies an IMF with fewer low mass stars (e.g., Chabrier IMF) for massive quiescent galaxies at higher redshifts in conflict with the bottom-heavy IMF (e.g., Salpeter IMF) found in their likely $z\sim0$ descendants, though a number of alternative explanations such as a different dynamical structure or significant rotation are not ruled out. Similar to data at lower redshifts, we see evidence for an increase of IMF normalization with velocity dispersion, though the $z\gtrsim3$ trend is steeper than that for $z\sim0.2$ early-type galaxies and offset to lower dynamical-to-stellar mass ratios.

astro-ph.GA↗

Universal enveloping algebras of Lie-Rinehart algebras: crossed products, connections, and curvature

We extend a theorem, originally formulated by Blattner-Cohen-Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of left Hopf algebroids. Our main motivation is an application to universal enveloping algebras of projective Lie-Rinehart algebras: for any given curved (resp. flat) connection, that is, a linear (resp. Lie-Rinehart) splitting of a Lie-Rinehart algebra extension, we provide a crossed (resp. smash) product decomposition of the associated universal enveloping algebra, and vice versa. As a geometric example, we describe the associative algebra generated by the invariant vector fields on the total space of a principal bundle as a crossed product of the algebra generated by the vertical ones and the algebra of differential operators on the base.

math.RA↗

Globalization for geometric partial comodules

We discuss globalization for geometric partial comodules in a monoidal category with pushouts and we provide a concrete procedure to construct it, whenever it exists. The mild assumptions required by our approach make it possible to apply it in a number of contexts of interests, recovering and extending numerous ad hoc globalization constructions from the literature in some cases and providing obstruction for globalization in some other cases.

math.RA↗

Hopf modules, Frobenius functors and (one-sided) Hopf algebras

We investigate the property of being Frobenius for some functors strictly related with Hopf modules over a bialgebra and how this property reflects on the latter. In particular, we characterize one-sided Hopf algebras with anti-(co)multiplicative one-sided antipode as those for which the free Hopf module functor is Frobenius. As a by-product, this leads us to relate the property of being an FH-algebra (in the sense of Pareigis) for a given bialgebra with the property of being Frobenius for certain naturally associated functors.

math.RA↗

On functors between categories of modules over trusses

Categorical aspects of the theory of modules over trusses are studied. Tensor product of modules over trusses is defined and its existence established. In particular, it is shown that bimodules over trusses form a monoidal category. Truss versions of the Eilenberg-Watts theorem and Morita equivalence are formulated. Projective and small-projective modules over trusses are defined and their properties studied.

math.RA↗

Antipodes, preantipodes and Frobenius functors

We prove that a quasi-bialgebra admits a preantipode if and only if the associated free quasi-Hopf bimodule functor is Frobenius, if and only if the relative (opmonoidal) monad is a Hopf monad. The same results hold in particular for a bialgebra, tightening the connection between Hopf and Frobenius properties.

math.RA↗

Heaps of modules and affine spaces

A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine spaces) and algebraic topology (chain contractions) are presented. Relationships between heaps of modules and modules over a ring and affine spaces are revealed and analysed.

math.RA↗

Validation of e$^+$e$^-$ Pair Production Total Cross Sections for Monte Carlo Particle Transport

Several sources of total cross sections for e$^+$e$^-$ pair production by photon interaction with matter, used by major Monte Carlo codes for particle transport, are quantitatively evaluated with respect to experimental measurements collected from the literature. They include data libraries deriving from theoretical calculations and analytical formulae representing empirical fits to tabulations. Although most of these sources of cross sections are based on one theoretical reference, the statistical data analysis documented in the paper highlights differences in their compatibility with experiment. The cross sections collected in the 1997 version of the Evaluated Photon Data Library (EPDL) exhibit the lowest incompatibility with experiment; the paper details the validation results for all the examined cross section sources. The scarcity of experimental data does not allow the validation process to discern pair production in the field of the nucleus and in the field of atomic electrons; nevertheless, the paper documents relevant clues regarding the contribution of the latter to reproduce experimental measurements.

physics.comp-ph↗

Spectroscopic Confirmation of a Protocluster at $z=3.37$ with a High Fraction of Quiescent Galaxies

We report the discovery of MAGAZ3NE J095924+022537, a spectroscopically-confirmed protocluster at $z = 3.3665^{+0.0009}_{-0.0012}$ around a spectroscopically-confirmed $UVJ$-quiescent ultra-massive galaxy (UMG; $M_{\star}=2.34^{+0.23}_{-0.34}\times10^{11} {\rm M}_\odot$) in the COSMOS UltraVISTA field. We present a total of 38 protocluster members (14 spectroscopic and 24 photometric), including the UMG. Notably, and in marked contrast to protoclusters previously reported at this epoch which have been found to contain predominantly star-forming members, we measure an elevated fraction of quiescent galaxies relative to the coeval field ($73.3^{+26.7}_{-16.9}\%$ versus $11.6^{+7.1}_{-4.9}\%$ for galaxies with stellar mass $M_{\star} \geq 10^{11} {\rm M}_\odot$). This high quenched fraction provides a striking and important counterexample to the seeming ubiquitousness of star-forming galaxies in protoclusters at $z>2$ and suggests, rather, that protoclusters exist in a diversity of evolutionary states in the early Universe. We discuss the possibility that we might be observing either "early mass quenching" or non-classical "environmental quenching." We also present the discovery of MAGAZ3NE J100028+023349, a second spectroscopically-confirmed protocluster, at a very similar redshift of $z = 3.3801^{+0.0213}_{-0.0281}$. We present a total of 20 protocluster members, 12 of which are photometric and 8 spectroscopic including a post-starburst UMG ($M_{\star}=2.95^{+0.21}_{-0.20}\times10^{11} {\rm M}_\odot$). Protoclusters MAGAZ3NE J0959 and MAGAZ3NE J1000 are separated by 18 arcminutes on the sky (35 comoving Mpc), in good agreement with predictions from simulations for the size of "Coma"-type cluster progenitors at this epoch. It is highly likely that the two UMGs are the progenitors of Brightest Cluster Galaxies (BCGs) seen in massive virialized clusters at lower redshift.

astro-ph.GA↗

Geometric partial comodules over flat coalgebras in Abelian categories are globalizable

The aim of this paper is to prove the statement in the title. As a by-product, we obtain new globalization results in cases never considered before, such as partial corepresentations of Hopf algebras. Moreover, we show that for partial representations of groups and Hopf algebras, our globalization coincides with those described earlier in literature. Finally, we introduce Hopf partial comodules over a bialgebra as geometric partial comodules in the monoidal category of (global) modules. By applying our globalization theorem we obtain an analogue of the fundamental theorem for Hopf modules in this partial setting.

math.RA↗

On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras

We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We show that this approach does not only allow to recover all known results in these settings, but it allows to treat new cases of interest, too.

math.RA↗

MAORY: A Multi-conjugate Adaptive Optics RelaY for ELT

MAORY is the adaptive optics module for ELT providing two gravity invariant ports with the same optical quality for two different client instruments. It enable high angular resolution observations in the near infrared over a large field of view (~1 arcmin2 ) by real time compensation of the wavefront distortions due to atmospheric turbulence. Wavefront sensing is performed by laser and natural guide stars while the wavefront sensor compensation is performed by an adaptive deformable mirror in MAORY which works together with the telescope's adaptive and tip tilt mirrors M4 and M5 respectively.

astro-ph.IM↗

Universal enveloping algebras of Lie-Rinehart algebras as a left adjoint functor

We prove how the universal enveloping algebra constructions for Lie-Rinehart algebras and anchored Lie algebras are naturally left adjoint functors. This provides a conceptual motivation for the universal properties these constructions satisfy. As a supplement, the categorical approach offers new insights into the definitions of Lie-Rinehart algebra morphisms, of modules over Lie-Rinehart algebras and of the infinitesimal gauge algebra of a module.

math.RA↗

The Rapid Build-up of Massive Early-type Galaxies. Supersolar Metallicity, High Velocity Dispersion and Young Age for an ETG at z=3.35

Thanks to very deep spectroscopic observations carried out at the Large Binocular Telescope, we measured simultaneously stellar age, metallicity and velocity dispersion for C1-23152, an ETG at redshift $z$=3.352, corresponding to an epoch when the Universe was $\sim$1.8 Gyr old. The analysis of its spectrum shows that this galaxy, hosting an AGN, formed and assembled $\sim$2$\times$10$^{11}$ M$_\odot$ shaping its morphology within the $\sim$600 Myr preceding the observations, since $z$$\sim$4.6. The stellar population has a mean mass-weighted age 400$^{+30}_{-70}$ Myr and it is formed between $\sim$600 Myr and $\sim$150 Myr before the observed epoch, this latter being the time since quenching. Its high stellar velocity dispersion, $σ_e$=409$\pm$60 km s$^{-1}$, confirms the high mass (M$_{dyn}$=$2.2(\pm0.4)$$\times$10$^{11}$ M$_\odot$) and the high mass density ($Σ_e^{M^*}$=$Σ_{1kpc}=3.2(\pm0.7)\times10^{10}$ M$_\odot$ kpc$^{-2}$), suggesting a fast dissipative process at its origin. The analysis points toward a supersolar metallicity, [Z/H]=0.25$^{+0.006}_{-0.10}$, in agreement with the above picture, suggesting a star formation efficiency much higher than the replenishment time. However, sub-solar metallicity values cannot be firmly ruled out by our analysis. Quenching must have been extremely efficient to reduce the star formation to SFR$<$6.5 M$_\odot$ yr$^{-1}$ in less than 150 Myr. This could be explained by the presence of the AGN, even if a causal relation cannot be established from the data. C1-23152 has the same stellar and physical properties of the densest ETGs in the local Universe of comparable mass, suggesting that they are C1-23152-like galaxies which evolved to $z=0$ unperturbed.

astro-ph.GA↗

The Massive Ancient Galaxies At $z>3$ NEar-infrared (MAGAZ3NE) Survey: Confirmation of Extremely Rapid Star-Formation and Quenching Timescales for Massive Galaxies in the Early Universe

We present near-infrared spectroscopic confirmations of a sample of 16 photometrically-selected galaxies with stellar masses log(M_star/M_sun) > 11 at redshift z > 3 from the XMM-VIDEO and COSMOS-UltraVISTA fields using Keck/MOSFIRE as part of the MAGAZ3NE survey. Eight of the ultra-massive galaxies (UMGs) have specific star formation rates (sSFR) < 0.03 Gyr-1, with negligible emission lines. Another seven UMGs show emission lines consistent with active galactic nuclei and/or star formation, while only one UMG has sSFR > 1 Gyr-1. Model star formation histories of these galaxies describe systems that formed the majority of their stars in vigorous bursts of several hundred Myr duration around 4 < z < 6during which hundreds to thousands of solar masses were formed per year. These formation ages of < 1 Gyr prior to observation are consistent with ages derived from measurements of Dn(4000) and EW0(Hδ). Rapid quenching followed these bursty star-forming periods, generally occurring less than 350 Myr before observation, resulting in post-starburst SEDs and spectra for half the sample. The rapid formation timescales are consistent with the extreme star formation rates observed in 4 < z < 7 dusty starbursts observed with ALMA, suggesting that such dusty galaxies are progenitors of these UMGs. While such formation histories have been suggested in previous studies, the large sample introduced here presents the most compelling evidence yet that vigorous star formation followed by rapid quenching is almost certainly the norm for high mass galaxies in the early universe. The UMGs presented here were selected to be brighter than Ks = 21.7 raising the intriguing possibility that even (fainter) older quiescent UMGs could exist at this epoch.

astro-ph.GA↗