Radio-X-ray Synergy to discover and Study Jetted Tidal Disruption Events

Observational consequences of tidal disruption of stars (TDEs) by supermassive black holes (SMBHs) can enable us to discover quiescent SMBHs, constrain their mass function, study formation and evolution of transient accretion disks and jet formation. A couple of jetted TDEs have been recently claimed in hard X-rays, challenging jet models, previously applied to $\gamma$-ray bursts and active galactic nuclei. It is therefore of paramount importance to increase the current sample. In this paper, we find that the best strategy is not to use up-coming X-ray instruments alone, which will yield between several (e-Rosita) and a couple of hundreds (Einstein Probe) events per year below redshift one. We rather claim that a more efficient TDE hunter will be the Square Kilometer Array (SKA) operating {\it in survey mode} at 1.4 GHz. It may detect up to several hundreds of events per year below $z \sim 2.5$ with a peak rate of a few tens per year at $z\approx 0.5$. Therefore, even if the jet production efficiency is {\it not } $100\%$ as assumed here, the predicted rates should be large enough to allow for statistical studies. The characteristic TDE decay of $t^{-5/3}$, however, is not seen in radio, whose flux is quite featureless. {\it Identification} therefore requires localization and prompt repointing by higher energy instruments. If radio candidates would be repointed within a day by future X-ray observatories (e.g. Athena and LOFT-like missions), it will be possible to detect up to $\approx 400$ X-ray counterparts, almost up to redshift $2$. The shortcome is that only for redshift below $\approx 0.4$ the trigger times will be less than 10 days from the explosion. In this regard the X-ray surveys are better suited to probe the beginning of the flare, and are therefore complementary to SKA.Comment: Astrophysical Journal (revised version

Hilbert Functions of Filtered Modules

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area of dynamic mathematical activity. Motivated by the ever increasing interest in this field, our goal is to gather together many new developments of this theory into one place, and to present them using a unifying approach which gives self-contained and easier proofs. In this text we shall discuss many results by different authors, following essentially the direction typified by the pioneering work of J. Sally. Our personal view of the subject is most visibly expressed by the presentation of Chapters 1 and 2 in which we discuss the use of the superficial elements and related devices. Basic techniques will be stressed with the aim of reproving recent results by using a more elementary approach. Over the past few years several papers have appeared which extend classical results on the theory of Hilbert functions to the case of filtered modules. The extension of the theory to the case of general filtrations on a module has one more important motivation. Namely, we have interesting applications to the study of graded algebras which are not associated to a filtration, in particular the Fiber cone and the Sally-module. We show here that each of these algebras fits into certain short exact sequences, together with algebras associated to filtrations. Hence one can study the Hilbert function and the depth of these algebras with the aid of the know-how we got in the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom

Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He

Defects are believed to play a fundamental role in the supersolid state of 4He. We have studied solid 4He in two dimensions (2D) as function of the number of vacancies n_v, up to 30, inserted in the initial configuration at rho = 0.0765 A^-2, close to the melting density, with the exact zero temperature Shadow Path Integral Ground State method. The crystalline order is found to be stable also in presence of many vacancies and we observe two completely different regimes. For small n_v, up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n_v, the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. In the equilibrated state it is no more possible to recognize vacancies because they mainly transform into quantum dislocations and crystalline order is found almost independent on how many vacancies have been inserted in the initial configuration. The one--body density matrix in this latter regime shows a non decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of incommensurate versus commensurate state loses meaning for solid 4He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in presence of up to 100 vacancies

Strong coupling analysis of the large-N 2-d lattice chiral models

Two dimensional large-N chiral models on the square and honeycomb lattices are investigated by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic scaling. Indeed in the strong coupling region a quite large range of beta values exists where the fundamental mass agrees, within about 5% on the square lattice and about 10% on the honeycomb lattice, with the continuum predictions in the %%energy scheme.Comment: 16 pages, Revtex, 8 uuencoded postscript figure

Exact ground state Monte Carlo method for Bosons without importance sampling

Generally ``exact'' Quantum Monte Carlo computations for the ground state of many Bosons make use of importance sampling. The importance sampling is based, either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of Path Integral Ground State (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a non zero overlap with the ground state, that gives rise to a discrete path which is sampled via a Metropolis like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid 4He with PIGS by considering as initial wave function a constant, i.e. the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e. there is no importance sampling. For both the phases we obtain results converging to those obtained by considering the best available variational wave function (the Shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function and the static structure factor, but also for off-diagonal ones, such as the one--body density matrix. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature Path Integral Monte Carlo.Comment: 11 pages, 10 figure

Afterglow lightcurves, viewing angle and the jet structure of gamma-ray bursts

Gamma ray bursts are often modelled as jet-like outflows directed towards the observer; the cone angle of the jet is then commonly inferred from the time at which there is a steepening in the power-law decay of the afterglow. We consider an alternative model in which the jet has a beam pattern where the luminosity per unit solid angle (and perhaps also the initial Lorentz factor) decreases smoothly away from the axis, rather than having a well-defined cone angle within which the flow is uniform. We show that the break in the afterglow light curve then occurs at a time that depends on the viewing angle. Instead of implying a range of intrinsically different jets - some very narrow, and others with similar power spread over a wider cone - the data on afterglow breaks could be consistent with a standardized jet, viewed from different angles. We discuss the implication of this model for the luminosity function.Comment: Corrected typo in Eq. 1

On measuring the Galactic dark matter halo with hypervelocity stars

Hypervelocity stars (HVSs) travel from the Galactic Centre across the dark matter halo of the Milky Way, where they are observed with velocities in excess of the Galactic escape speed. Because of their quasi-radial trajectories, they represent a unique probe of the still poorly constrained dark matter component of the Galactic potential. In this paper, we present a new method to produce such constraints. Our likelihood is based on the local HVS density obtained by back-propagating the observed phase space position and quantifies the ejection probability along the orbit. To showcase our method, we apply it to simulated Gaia samples of $\sim200$ stars in three realistic Galactic potentials with dark matter components parametrized by spheroidal NFW profiles. We find that individual HVSs exhibit a degeneracy in the scale mass-scale radius plane ($M_s-r_s$) and are able to measure only the combination $\alpha = M_s/r_s^2$. Likewise, a degeneracy is also present between $\alpha$ and the spheroidal axis-ratio $q$. In the absence of observational errors, we show the whole sample can nail down both parameters with {\it sub-per cent} precision (about $1\%$ and $0.1\%$ for $\alpha$ and $q$ respectively) with no systematic bias. This remarkable power to constrain deviations from a symmetric halo is a consequence of the Galactocentric origin of HVSs. To compare our results with other probes, we break the degeneracy in the scale parameters and impose a mass-concentration relation. The result is a competitive precision on the virial mass $M_{200}$ of about $10\%$.Comment: See Fig. 8 for a summar

Morphology of galaxies with quiescent recent assembly history in a Lambda-CDM universe

The standard disc formation scenario postulates that disc forms as the gas cools and flows into the centre of the dark matter halo, conserving the specific angular momentum. Major mergers have been shown to be able to destroy or highly perturb the disc components. More recently, the alignment of the material that is accreted to form the galaxy has been pointed out as a key ingredient to determine galaxy morphology. However, in a hierarchical scenario galaxy formation is a complex process that combines these processes and others in a non-linear way so that the origin of galaxy morphology remains to be fully understood. We aim at exploring the differences in the formation histories of galaxies with a variety of morphology, but quite recent merger histories, to identify which mechanisms are playing a major role. We analyse when minor mergers can be considered relevant to determine galaxy morphology. We also study the specific angular momentum content of the disc and central spheroidal components separately. We used cosmological hydrodynamical simulations that include an effective, physically motivated supernova feedback that is able to regulate the star formation in haloes of different masses. We analysed the morphology and formation history of a sample of 15 galaxies of a cosmological simulation. We performed a spheroid-disc decomposition of the selected galaxies and their progenitor systems. The angular momentum orientation of the merging systems as well as their relative masses were estimated to analyse the role played by orientation and by minor mergers in the determination of the morphology. We found the discs to be formed by conserving the specific angular momentum in accordance with the classical disc formation model. The specific angular momentum of the stellar central spheroid correlates with the dark matter halo angular momentum and determines a power law. AbridgedComment: 10 pages, 9 figures, A&A in pres

Quantized vortices in two dimensional solid 4He

Diagonal and off-diagonal properties of 2D solid 4He systems doped with a quantized vortex have been investigated via the Shadow Path Integral Ground State method using the fixed-phase approach. The chosen approximate phase induces the standard Onsager-Feynman flow field. In this approximation the vortex acts as a static external potential and the resulting Hamiltonian can be treated exactly with Quantum Monte Carlo methods. The vortex core is found to sit in an interstitial site and a very weak relaxation of the lattice positions away from the vortex core position has been observed. Also other properties like Bragg peaks in the static structure factor or the behavior of vacancies are very little affected by the presence of the vortex. We have computed also the one-body density matrix in perfect and defected 4He crystals finding that the vortex has no sensible effect on the off-diagonal long range tail of the density matrix. Within the assumed Onsager Feynman phase, we find that a quantized vortex cannot auto-sustain itself unless a condensate is already present like when dislocations are present. It remains to be investigated if backflow can change this conclusion.Comment: 4 pages, 3 figures, LT26 proceedings, accepted for publication in Journal of Physics: Conference Serie