On the Quasi-Periodic Oscillations of Magnetars

We study torsional Alfv\'en oscillations of magnetars, i.e., neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system (X,Y), where $X=\sqrt{a_1} \sin \theta$, $Y=\sqrt{a_1}\cos \theta$ and $a_1$ is the radial component of the magnetic field. In this coordinate system, the 1+2-dimensional evolution equation describing the quasi-periodic oscillations, QPOs, see Sotani et al. (2007), is reduced to a 1+1-dimensional equation, where the perturbations propagate only along the Y-axis. We solve the 1+1-dimensional equation for different boundary conditions and open magnetic field lines, i.e., magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field, as well as closed magnetic lines, i.e., magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPOs frequencies; a family of "lower" QPOs frequencies which is located near the X-axis and a family of "upper" frequencies located near the Y-axis. According to Levin (2007), the fundamental frequencies of these two families can be interpreted as the turning points of a continuous spectrum. We find that the upper frequencies are constant multiples of the lower frequencies with a constant equaling 2n+1. For the closed lines, the corresponding factor is n+1 . By these relations, we can explain both the lower and the higher observed frequencies in SGR 1806-20 and SGR 1900+14.Comment: 8 pages, 7 figure

Coupled polar-axial magnetar oscillations

We study coupled axial and polar axisymmetric oscillations of a neutron star endowed with a strong magnetic field, having both poloidal and toroidal components. The toroidal component of the magnetic field is driving the coupling between the polar and axial oscillations. The star is composed of a fluid core as well as a solid crust. Using a two dimensional general relativistic simulation and a magnetic field B = 10^16 G, we study the change in the polar and axial spectrum caused by the coupling. We find that the axial spectrum suffers a dramatic change in its nature, losing its continuum character. In fact, we find that only the 'edges' of the continua survive, generating a discrete spectrum. As a consequence the crustal frequencies, that in our previous simulation could be absorbed by the continua, if they were embedded inside it, are now long living oscillations. They may lose their energy only in the very special case that they are in resonance with the 'edges' of the continua.Comment: 12 pages, 3 figures. Revised version accepted in MNRA

Relativistic models of magnetars: structure and deformations

We find numerical solutions of the coupled system of Einstein-Maxwell's equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass M = 1.4 Msun and surface magnetic fields of the order of 10^15 G, a quadrupole ellipticity of the order of 10^(-6) - 10^(-5) should be expected. Low mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10^(-3) in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.Comment: 25 pages, 9 figures, submitted to MNRA

Relativistic models of magnetars: the twisted-torus magnetic field configuration

We find general relativistic solutions of equilibrium magnetic field configurations in magnetars, extending previous results of Colaiuda et al. (2008). Our method is based on the solution of the relativistic Grad-Shafranov equation, to which Maxwell's equations can be reduced in some limit. We obtain equilibrium solutions with the toroidal magnetic field component confined into a finite region inside the star, and the poloidal component extending to the exterior. These so-called twisted-torus configurations have been found to be the final outcome of dynamical simulations in the framework of Newtonian gravity, and appear to be more stable than other configurations. The solutions include higher order multipoles, which are coupled to the dominant dipolar field. We use arguments of minimal energy to constrain the ratio of the toroidal to the poloidal field.Comment: 13 pages, 12 figures. Minor changes to match the version published on MNRA

Gravitational wave emission from a magnetically deformed non-barotropic neutron star

A strong candidate for a source of gravitational waves is a highly magnetised, rapidly rotating neutron star (magnetar) deformed by internal magnetic stresses. We calculate the mass quadrupole moment by perturbing a zeroth-order hydrostatic equilibrium by an axisymmetric magnetic field with a \emph{linked poloidal-toroidal structure}. In this work, we do \emph{not} require the model star to obey a barotropic equation of state (as a realistic neutron star is not barotropic), allowing us to explore the hydromagnetic equilibria with fewer constraints. We derive the relation between the ratio of poloidal-to-total field energy $\Lambda$ and ellipticity $\epsilon$ and briefly compare our results to those obtained using the barotropic assumption. Then, we present some examples of how our results can be applied to astrophysical contexts. First, we show how our formulae, in conjunction with current gravitational wave (non-)detections of the Crab pulsar and the Cassiopeia A central compact object (Cas A CCO), can be used to constrain the strength of the internal toroidal fields of those objects. We find that, for the Crab pulsar (whose canonical equatorial dipole field strength, inferred from spin down, is $4\times 10^8$ T) to emit detectable gravitational radiation, the neutron star must have a strong toroidal field component, with maximum internal toroidal field strength $B_{\mathrm{tm}}=7\times 10^{12}$ T; for gravitational waves to be detected from the Cas A CCO at 300 Hz, $B_{\mathrm{tm}}\sim 10^{13}$ T, whereas detection at 100 Hz would require $B_{\mathrm{tm}}\sim 10^{14}$ T. Using our results, we also show how the gravitational wave signal emitted by a magnetar immediately after its birth (assuming it is born rapidly rotating, with $\Lambda\lesssim 0.2$) makes such a newborn magnetar a stronger candidate for gravitational wave detection than, for example, an SGR giant flare.Comment: 15 pages, 8 figures, 2 table

A meteorological–hydrological regional ensemble forecast for an early-warning system over small Apennine catchments in Central Italy

Abstract. The weather forecasts for precipitation have considerably improved in recent years thanks to the increase of computational power. This allows for the use of both a higher spatial resolution and the parameterization schemes specifically developed for representing sub-grid scale physical processes at high resolution. However, precipitation estimation is still affected by errors that can impact the response of hydrological models. To the aim of improving the hydrological forecast and the characterization of related uncertainties, a regional-scale meteorological–hydrological ensemble is presented. The uncertainties in the precipitation forecast and how they propagate in the hydrological model are also investigated. A meteorological–hydrological offline coupled ensemble is built to forecast events in a complex-orography terrain where catchments of different sizes are present. The Best Discharge-based Drainage (BDD; both deterministic and probabilistic) index, is defined with the aim of forecasting hydrological-stress conditions and related uncertainty. In this context, the meteorological–hydrological ensemble forecast is implemented and tested for a severe hydrological event which occurred over Central Italy on 15 November 2017, when a flood hit the Abruzzo region with precipitation reaching 200 mm (24 h)−1 and producing damages with a high impact on social and economic activities. The newly developed meteorological–hydrological ensemble is compared with a high-resolution deterministic forecast and with the observations (rain gauges and radar data) over the same area. The receiver operating characteristic (ROC) statistical indicator shows how skilful the ensemble precipitation forecast is with respect to both rain-gauge- and radar-retrieved precipitation. Moreover, both the deterministic and probabilistic configurations of the BDD index are compared with the alert map issued by Civil Protection Department for the event showing a very good agreement. Finally, the meteorological–hydrological ensemble allows for an estimation of both the predictability of the event a few days in advance and the uncertainty of the flood. Although the modelling framework is implemented on the basins of the Abruzzo region, it is portable and applicable to other areas

Overview of the first HyMeX Special Observation Period over Italy: observations and model results

Abstract. The Special Observation Period (SOP1), part of the HyMeX campaign (Hydrological cycle in the Mediterranean Experiments, 5 September–6 November 2012), was dedicated to heavy precipitation events and flash floods in the western Mediterranean, and three Italian hydro-meteorological monitoring sites were identified: Liguria–Tuscany, northeastern Italy and central Italy. The extraordinary deployment of advanced instrumentation, including instrumented aircrafts, and the use of several different operational weather forecast models, including hydrological models and marine models, allowed an unprecedented monitoring and analysis of high-impact weather events around the Italian hydro-meteorological sites. This activity has seen strong collaboration between the Italian scientific and operational communities. In this paper an overview of the Italian organization during SOP1 is provided, and selected Intensive Observation Periods (IOPs) are described. A significant event for each Italian target area is chosen for this analysis: IOP2 (12–13 September 2012) in northeastern Italy, IOP13 (15–16 October 2012) in central Italy and IOP19 (3–5 November 2012) in Liguria and Tuscany. For each IOP the meteorological characteristics, together with special observations and weather forecasts, are analyzed with the aim of highlighting strengths and weaknesses of the forecast modeling systems, including the hydrological impacts. The usefulness of having different weather forecast operational chains characterized by different numerical weather prediction models and/or different model set up or initial conditions is finally shown for one of the events (IOP19)

Gravitational waves from single neutron stars: an advanced detector era survey

With the doors beginning to swing open on the new gravitational wave astronomy, this review provides an up-to-date survey of the most important physical mechanisms that could lead to emission of potentially detectable gravitational radiation from isolated and accreting neutron stars. In particular we discuss the gravitational wave-driven instability and asteroseismology formalism of the f- and r-modes, the different ways that a neutron star could form and sustain a non-axisymmetric quadrupolar "mountain" deformation, the excitation of oscillations during magnetar flares and the possible gravitational wave signature of pulsar glitches. We focus on progress made in the recent years in each topic, make a fresh assessment of the gravitational wave detectability of each mechanism and, finally, highlight key problems and desiderata for future work.Comment: 39 pages, 12 figures, 2 tables. Chapter of the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action 1304. Minor corrections to match published versio

On the combined use of rain gauges and GPM IMERG satellite rainfall products for hydrological modelling: impact assessment of the cellular-automata-based methodology in the Tanaro River basin in Italy

The uncertainty of hydrological forecasts is strongly related to the uncertainty of the rainfall field due to the nonlinear relationship between the spatio-temporal pattern of rainfall and runoff. Rain gauges are typically considered to provide reference data to rebuild precipitation fields. However, due to the density and the distribution variability of the rain gauge network, the rebuilding of the precipitation field can be affected by severe errors which compromise the hydrological simulation output. On the other hand, retrievals obtained from remote sensing observations provide spatially resolved precipitation fields, improving their representativeness. In this regard, the comparison between simulated and observed river flow discharge is crucial for assessing the effectiveness of merged precipitation data in enhancing the model's performance and its ability to realistically simulate hydrological processes. This paper aims to investigate the hydrological impact of using the merged rainfall fields from the Italian rain gauge network and the NASA Global Precipitation Measurement (GPM) IMERG precipitation product. One aspect is to highlight the benefits of applying the cellular automata algorithm to pre-process input data in order to merge them and reconstruct an improved version of the precipitation field. The cellular automata approach is evaluated in the Tanaro River basin, one of the tributaries of the Po River in Italy. As this site is characterized by the coexistence of a variety of natural morphologies, from mountain to alluvial environments, as well as the presence of significant civil and industrial settlements, it makes it a suitable case study to apply the proposed approach. The latter has been applied over three different flood events that occurred from November to December 2014. The results confirm that the use of merged gauge–satellite data using the cellular automata algorithm improves the performance of the hydrological simulation, as also confirmed by the statistical analysis performed for 17 selected quality scores.</p