On tilted Giraud subcategories

Firstly we provide a technique to move torsion pairs in abelian categories via adjoint functors and in particular through Giraud subcategories. We apply this point in order to develop a correspondence between Giraud subcategories of an abelian category C and those of its tilt H(C) i.e., the heart of a t-structure on the derived category D(C)i nduced by a torsion pair

Overlapping inflows as catalysts of AGN activity - II. Relative importance of turbulence and inflow-disc interaction

The main challenge for understanding the fuelling of supermassive black holes in active galactic nuclei is not to account for the source of fuel, but rather to explain its delivery from the boundaries of the black hole sphere of influence (10-100 pc) down to sub-parsec scales. In this work, we report on a series of numerical experiments aimed at exploring in further depth our model of 'overlapping inflow events' as catalysts for rapid accretion, seeding a turbulent field in the infalling gas. We initially set a gaseous shell in non-equilibrium rotation around a supermassive black hole. After infall, the shell stalls in a disc-like structure. A second shell is then set in either corotation or counterrotation with respect to the first and is let to impinge on the previously formed disc. We find that combined turbulence and overlap significantly enhance accretion in counterrotating inflows, while turbulence dominates for corotating inflows. The leftovers of overlapping inflows are warped nuclear discs, whose morphology depend on the relative orientation and angular momentum of the disc and the shell. Overlapping inflows leave observational signatures in the gas rotation curves

Overlapping inflow events as catalysts for supermassive black hole growth

One of the greatest issues in modelling black hole fuelling is our lack of understanding of the processes by which gas loses angular momentum and falls from galactic scales down to the nuclear region where an accretion disc forms, subsequently guiding the inflow of gas down to the black hole horizon. It is feared that gas at larger scales might still retain enough angular momentum and settle into a larger scale disc with very low or no inflow to form or replenish the inner accretion disc (on similar to 0.01 pc scales). In this paper we report on hydrodynamical simulations of rotating infalling gas shells impacting at different angles on to a pre-existing, primitive large-scale (similar to 10 pc) disc around a supermassive black hole. The aim is to explore how the interaction between the shell and the disc redistributes the angular momentum on scales close to the black hole's sphere of influence. Angular momentum redistribution via hydrodynamical shocks leads to inflows of gas across the inner boundary, enhancing the inflow rate by more than 2-3 orders of magnitude. In all cases, the gas inflow rate across the inner parsec is higher than in the absence of the interaction, and the orientation of the angular momentum of the flow in the region changes with time due to gas mixing. Warped discs or nested misaligned rings form depending on the angular momentum content of the infalling shell relative to the disc. In the cases in which the shell falls in near counter-rotation, part of the resulting flows settle into an inner dense disc which becomes more susceptible to mass transfer

Quantum Backaction on kg-Scale Mirrors: Observation of Radiation Pressure Noise in the Advanced Virgo Detector

The quantum radiation pressure and the quantum shot noise in laser-interferometric gravitational wave detectors constitute a macroscopic manifestation of the Heisenberg inequality. If quantum shot noise can be easily observed, the observation of quantum radiation pressure noise has been elusive, so far, due to the technical noise competing with quantum effects. Here, we discuss the evidence of quantum radiation pressure noise in the Advanced Virgo gravitational wave detector. In our experiment, we inject squeezed vacuum states of light into the interferometer in order to manipulate the quantum backaction on the 42 kg mirrors and observe the corresponding quantum noise driven displacement at frequencies between 30 and 70 Hz. The experimental data, obtained in various interferometer configurations, is tested against the Advanced Virgo detector quantum noise model which confirmed the measured magnitude of quantum radiation pressure noise

The population of merging compact binaries inferred using gravitational waves through GWTC-3

We report on the population properties of 76 compact binary mergers detected with gravitational waves below a false alarm rate of 1 per year through GWTC-3. The catalog contains three classes of binary mergers: BBH, BNS, and NSBH mergers. We infer the BNS merger rate to be between 10 $\rm{Gpc^{-3} yr^{-1}}$ and 1700 $\rm{Gpc^{-3} yr^{-1}}$ and the NSBH merger rate to be between 7.8 $\rm{Gpc^{-3}\, yr^{-1}}$ and 140 $\rm{Gpc^{-3} yr^{-1}}$ , assuming a constant rate density versus comoving volume and taking the union of 90% credible intervals for methods used in this work. Accounting for the BBH merger rate to evolve with redshift, we find the BBH merger rate to be between 17.9 $\rm{Gpc^{-3}\, yr^{-1}}$ and 44 $\rm{Gpc^{-3}\, yr^{-1}}$ at a fiducial redshift (z=0.2). We obtain a broad neutron star mass distribution extending from $1.2^{+0.1}_{-0.2} M_\odot$ to $2.0^{+0.3}_{-0.3} M_\odot$. We can confidently identify a rapid decrease in merger rate versus component mass between neutron star-like masses and black-hole-like masses, but there is no evidence that the merger rate increases again before 10 $M_\odot$. We also find the BBH mass distribution has localized over- and under-densities relative to a power law distribution. While we continue to find the mass distribution of a binary's more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above $\sim 60 M_\odot$. The rate of BBH mergers is observed to increase with redshift at a rate proportional to $(1+z)^{\kappa}$ with $\kappa = 2.9^{+1.7}_{-1.8}$ for $z\lesssim 1$. Observed black hole spins are small, with half of spin magnitudes below $\chi_i \simeq 0.25$. We observe evidence of negative aligned spins in the population, and an increase in spin magnitude for systems with more unequal mass ratio

Cotilting bimodules and their dualities

A right R-module UR is said to be cotilting if Cog(UR)=⊥UR, where ⊥UR=KerExt1R(,U). So cotilting modules generalize injective cogenerators. If U is cotilting, then T=(KerHom(−,U),Cog(U)) is a torsion theory, the so-called cotilting torsion theory. A bimodule SUR is cotilting if SUR is faithfully balanced and both UR and SU are cotilting modules. So cotilting bimodules generalize Morita bimodules. The main topic of the paper is the study of dualities induced by cotilting bimodules, as a generalization of the classical theory of Morita dualities. Let SUR be a cotilting bimodule and put Δ=Hom(,U) and Γ=Ext1(,U). Denote by Y the class of all U-reflexive modules, by C the class of all modules of the form K/L where K,L∈Y, and by X the class of all T-torsion modules from C. These classes are studied in the first part of the paper, in order to prove their closure properties, and show that they are sufficiently large. For example, by Proposition 5, C contains all finitely presented modules. The main result of the paper is the following "cotilting theorem'': If U is a cotilting bimodule, then Δ and Γ realize a duality between the classes Y and X, respectively. Moreover, there is a natural morphism γM:Γ2(M)→M such that the sequence 0→Γ2(M)@>γM>>M@>δM>>Δ2(M)@>>>0 is exact for all M∈C, where δM is the evaluation map. In the case of Morita dualities, Müller proved that U-reflexive modules coincide with the linearly compact ones. Inspired by this result, the author studies U-torsionless linearly compact (U-tl.l.c.) modules in the case when U is a cotilting module. In Proposition 10, he proves that if SUR is a cotilting bimodule then any U-tl.l.c. bimodule is U-reflexive, and asks whether the converse is true. (By a recent example of D'Este, this is not true in general.) Finally, the author introduces abstract "duality conditions'' for a pair of torsion theories. These are necessary conditions for the pair to be cogenerated by a cotilting bimodule. The conditions are not sufficient in general. Nevertheless, by Proposition 13, they ensure uniqueness of the representing bimodule

Tilting modules and ∗*-modules

C. Menini and A. Orsatti [Rend. Sem. Mat. Univ. Padova 82 (1989), 203--231 (1990); MR1049594 (91h:16026)] introduced 17-modules in order to characterize equivalences between certain full subcategories of module categories over two rings. If one restricts the study to the case of finite-dimensional algebras over a field k, it was shown by G. D'Este and the reviewer [Rend. Sem. Mat. Univ. Padova 83 (1990), 77--80; MR1066430 (91i:16027)] that faithful 17-modules are tilting modules in the sense of the reviewer and C. M. Ringel [Trans. Amer. Math. Soc. 274 (1982), no. 2, 399--443; MR0675063 (84d:16027)]. The paper under review now generalizes this characterization to arbitrary rings using the natural generalizations for tilting modules in this case

Dualities induced by cotilting bimodules

This paper looks at the dualities induced by cotilting bimodules, which provide a natural generalization of Morita dualities. One of the main goals of the paper is to show that linear compactness also plays a relevant role in this situation, despite the fact that the subcategories involved in cotilting dualities are usually not as wide and do not have closure properties as good as in the Morita case. Ordinary linear compactness does not behave well in this more general context as, for example, the U-reflexive modules with respect to a cotilting bimodule SUR need not be linearly compact. This motivates the study of three generalizations of linear compactness (relative to the bimodule SUR) which are used, among other things, to characterize U-reflexive torsion-free modules. The paper ends with the construction of a cotilting bimodule as a "dual'' of a tilting one and it is shown that this construction is often well behaved from the point of view of linear compactness

Tilting in Grothendieck categories

Given any Grothendieck category G, we study the notion of a tilting object of G, proving some basic facts of tilting theory in this general setting. Our results apply, for instance, to categories of modules over arbitrary rings, as well as to the theory of sheaves in algebraic geometry