Fractional Brownian motions ruled by nonlinear equations

In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville time-derivative. Our main contribution is to highlight the link between these generalised equations and fractional Brownian motion (fBm). In particular, we investigate the governing equation of fBm and show that its diffusion coefficient must satisfy an additive evolutive fractional equation. We derive in a similar way the governing equation of the iterated fractional Brownian motion.Comment: 7 page

Polarized thermal emission from X-ray Dim Isolated Neutron Stars: the case of RX J1856.5-3754

The observed polarization properties of thermal radiation from isolated, cooling neutron stars depend on both the emission processes at the surface and the effects of the magnetized vacuum which surrounds the star. Here we investigate the polarized thermal emission from X-ray Dim Isolated Neutron Stars, taking RX J1856.5-3754 as a representative case. The physical conditions of the star outermost layers in these sources is still debated, and so we consider emission from a magnetized atmosphere and a condensed surface, accounting for the effects of vacuum polarization as the radiation propagates in the star magnetosphere. We have found that, for a significant range of viewing geometries, measurement of the phase-averaged polarization fraction and phase-averaged polarization angle at both optical and X-ray wavelengths allow us to determine whether this neutron star has an atmosphere or a condensed surface. Our results may therefore be relevant in view of future developments of soft X-ray polarimeters.Comment: 12 pages, 12 figures, accepted for publication in MNRA

Analisi Modale Sperimentale delle Appendici Aerodinamiche di una Monoposto da competizione DALLARA

In this Master of Science thesis, resulting from the cooperation between the Department of Mechanical, Nuclear and Production Engineering of the University of Pisa and Dallara Automobili s.p.a., the target was the design of a graphical user interface, in Matlab, for signal processing. The signals to be processed were acquired during modal tests aimed at detecting natural frequencies of wings of a high-performance single-seater sports car produced by Dallara. Afterward, these frequencies were compared with the frequencies of forcing functions due to the motion of the vehicle, in order to avoid the dangerous occurrence of resonances

Probing magnetars magnetosphere through X-ray polarization measurements

The study of magnetars is of particular relevance since these objects are the only laboratories where the physics in ultra-strong magnetic fields can be directly tested. Until now, spectroscopic and timing measurements at X-ray energies in soft gamma-repeaters (SGRs) and anomalous X-ray pulsar (AXPs) have been the main source of information about the physical properties of a magnetar and of its magnetosphere. Spectral fitting in the ~ 0.5-10 keV range allowed to validate the "twisted magnetosphere" model, probing the structure of the external field and estimating the density and velocity of the magnetospheric currents. Spectroscopy alone, however, may fail in disambiguating the two key parameters governing magnetospheric scattering (the charge velocity and the twist angle) and is quite insensitive to the source geometry. X-ray polarimetry, on the other hand, can provide a quantum leap in the field by adding two extra observables, the linear polarization degree and the polarization angle. Using the bright AXP 1RXS J170849.0-400910 as a template, we show that phase-resolved polarimetric measurements can unambiguously determine the model parameters, even with a small X-ray polarimetry mission carrying modern photoelectric detectors and existing X-ray optics. We also show that polarimetric measurements can pinpoint vacuum polarization effects and thus provide an indirect evidence for ultra-strong magnetic fields.Comment: 12 pages, 8 figures, accepted for publication in MNRA

Thermal emission and magnetic beaming in the radio and X-ray mode-switching PSR B0943+10

PSR B0943+10 is a mode-switching radio pulsar characterized by two emission modes with different radio and X-ray properties. Previous studies, based on simple combinations of blackbody and power law models, showed that its X-ray flux can be decomposed in a pulsed thermal plus an unpulsed non-thermal components. However, if PSR B0943+10 is a nearly aligned rotator seen pole-on, as suggested by the radio data, it is difficult to reproduce the high observed pulsed fraction unless magnetic beaming is included. In this work we reanalyze all the available X-ray observations of PSR B0943+10 with simultaneous radio coverage, modeling its thermal emission with polar caps covered by a magnetized hydrogen atmosphere or with a condensed iron surface. The condensed surface model provides good fits to the spectra of both pulsar modes, but, similarly to the blackbody, it can not reproduce the observed pulse profiles, unless an additional power law with an ad hoc modulation is added. Instead, the pulse profiles and phase-resolved spectra are well described using the hydrogen atmosphere model to describe the polar cap emission, plus an unpulsed power law. For the X-ray brighter state (Q-mode) we obtain a best fit with a temperature kT~0.09 keV, an emitting radius R~260 m, a magnetic field consistent with the value of the dipole field of 4x10^12 G inferred from the timing parameters, and a small angle between the magnetic and spin axis, $\xi$=5. The corresponding parameters for the X-ray fainter state (B-mode) are kT~0.08 keV and R~170 m.Comment: 16 pages, 10 figures, accepted for publication in Ap

Polarized emission from highly-magnetized neutron stars

The study of magnetars, the anomalous X-ray pulsars (AXPs) and the soft gamma repeaters (SGRs), and of X-ray Dim Isolated Neutron Stars (XDINSs) is of particular relevance, since these objects exhibit the strongest magnetic fields ever observed in the universe (10^13-10^15 G) and represent the only laboratories where physics in the presence of such strong magnetic fields can be tested. Until now, these peculiar neutron stars have been investigated through spectroscopic and timing measurements, which led to validate the theoretical models developed to explain their phenomenology, as in the case of the "twisted magnetosphere'' model for magnetars or the different surface emission models for XDINSs. Nevertheless, this kind of analysis alone is far from providing complete information. In this respect, X-ray polarimetry may disclose an entirely new approach in the study of highly magnetized neutron stars. Radiation emitted in the presence of strong magnetic fields, in fact, is expected to be highly polarized; polarization measurements provide two additional observables, the linear polarization fraction and the polarization angle, that can unambiguously determine the model parameters also when spectral analysis alone fails. The polarization signal that an observer at infinity would collect, however, do not necessary coincide with model predictions for the polarization at the surface, due to the effects of quantum electrodynamics in the highly magnetized vacuum around the star, coupled with the rotation of the Stokes parameters in the plane perpendicular to the line of sight, induced by the non-uniform magnetic field. In this thesis I present the results of the numerical codes I developed to simulate the polarization pattern, both at the surface and as observed at infinity, of the radiation emitted from highly magnetized, isolated neutron stars, using as templates the bright AXP 1RXS J170849.0-400910 and the XDINS RX J1856.5-3754. I demonstrate that polarization measurements can indeed provide key information about the physical and geometrical properties of these sources, allowing to directly test theoretical models. This work is also relevant in view of the launch of new-generation X-ray polarimeters, currently under development, like the X-ray Imaging Polarimeter Explorer (XIPE). For this reason, I also compare theoretical models with XIPE simulated observations, in order to show how polarization measurements can be used to extract the values of magnetospheric parameters and viewing angles

Strongly pulsed thermal X-rays from a single extended hot spot on PSR J2021+4026

The radio-quiet pulsar PSR J2021+4026 is mostly known because it is the only rotation-powered pulsar that shows variability in its {\gamma}-ray emission. Using XMM-Newton archival data, we first confirmed that its flux is steady in the X-ray band, and then we showed that both the spectral and timing X-ray properties, i.e. the narrow pulse profile, the high pulsed fraction of 80-90% and its dependence on the energy, can be better reproduced using a magnetized atmosphere model instead of a simply blackbody. With a maximum likelihood analysis in the energy-phase space, we inferred that the pulsar has, in correspondence of one magnetic pole, a hot spot of temperature T~1 MK and colatitude extension {\theta}~20{\deg}. For the pulsar distance of 1.5 kpc, this corresponds to a cap of R~5-6 km, greater than the standard dimension of the dipolar polar caps. The large pulsed fraction further argues against emission from the entire star surface, as it would be expected in the case of secular cooling. An unpulsed (<40% pulsed fraction), non-thermal component, probably originating in a wind nebula, is also detected. The pulsar geometry derived with our spectral fits in the X-ray is relatively well constrained ({\chi}=90{\deg} and {\xi}=20-25{\deg}) and consistent with that deduced from {\gamma}-ray observations, provided that only one of the two hemispheres is active. The evidence for an extended hot spot in PSR J2021+4026, found also in other pulsars of similar age but not in older objects, suggests a possible age dependence of the emitting size of thermal X-rays.Comment: Accepted for publication in A&A, 10 pages, 3 figures, 3 table

Thermal and non-thermal X-ray emission from the rotation-powered radio/γ-ray pulsar PSR J1740+1000

We report the results of new XMM-Newton observations of the middle-aged (τc = 1.1 × 105 yr) radio pulsar PSR J1740+1000 carried out in 2017–2018. These long pointings (∼530 ks) show that the non-thermal emission, well described by a power-law spectrum with photon index Γ = 1.80 ± 0.17, is pulsed with a ∼30 per cent pulsed fraction above 2 keV. The thermal emission can be well-fit with the sum of two blackbodies of temperatures kT1 = 70 ± 4 eV and kT2 = 137 ± 7 eV, and emitting radii R1=5.4+1.3−0.9 km and R2=0.70+0.15−0.13 km (for a distance of 1.2 kpc). We found no evidence for absorption lines as those observed in the shorter XMM-Newton observations (∼67 ks) of this pulsar carried out in 2006. The X-ray thermal and non-thermal components peak in antiphase and none of them is seen to coincide in phase with the radio pulse. This, coupled with the small difference in the emission radii of the two thermal components, disfavours an interpretation in which the dipolar polar cap is heated by magnetospheric backward-accelerated particles. Comparison with the other thermally emitting isolated neutron stars with spectra well described by the sum of two components at different temperatures shows that the ratios T2/T1 and R2/R1 are similar for objects of different classes. The observed values cannot be reproduced with simple temperature distributions, such as those caused by a dipolar field, indicating the presence of more complicated thermal maps

Evidence for vacuum birefringence from the first optical-polarimetry measurement of the isolated neutron star RX J1856.5-3754

The "Magnificent Seven" (M7) are a group of radio-quiet Isolated Neutron Stars (INSs) discovered in the soft X-rays through their purely thermal surface emission. Owing to the large inferred magnetic fields ($B\approx 10^{13}$ G), radiation from these sources is expected to be substantially polarised, independently on the mechanism actually responsible for the thermal emission. A large observed polarisation degree is, however, expected only if quantum-electrodynamics (QED) polarisation effects are present in the magnetised vacuum around the star. The detection of a strongly linearly polarised signal would therefore provide the first observational evidence of QED effects in the strong-field regime. While polarisation measurements in the soft X-rays are not feasible yet, optical polarisation measurements are within reach also for quite faint targets, like the M7 which have optical counterparts with magnitudes $\approx 26$--$28$. Here, we report on the measurement of optical linear polarisation for the prototype, and brightest member, of the class, RX\, J1856.5$-$3754 ($V\sim 25.5$), the first ever for one of the M7, obtained with the Very Large Telescope. We measured a polarisation degree $\mathrm{P.D.} =16.43\% \pm5.26\%$ and a polarisation position angle \mathrm{P.A.}=145\fdg39\pm9\fdg44, computed east of the North Celestial Meridian. The $\mathrm{P.D.}$ that we derive is large enough to support the presence of vacuum birefringence, as predicted by QED.Comment: 9 pages, 7 figures, accepted for publication on MNRA

Two decades of X-ray observations of the isolated neutron star RX J1856.5-3754: detection of thermal and non-thermal hard X-rays and refined spin-down measurement

The soft X-ray pulsar RX J1856.5-3754 is the brightest member of a small class of thermally-emitting, radio-silent, isolated neutron stars. Its X-ray spectrum is almost indistinguishable from a blackbody with $kT^\infty\approx 60$ eV, but evidence of harder emission above $\sim 1$ keV has been recently found. We report on a spectral and timing analysis of RX J1856.5-3754 based on the large amount of data collected by XMM-Newton in 2002--2022, complemented by a dense monitoring campaign carried out by NICER in 2019. Through a phase-coherent timing analysis we obtained an improved value of the spin-down rate $\dot{\nu}=-6.042(4)\times10^{-16}$ Hz s$^{-1}$, reducing by more than one order magnitude the uncertainty of the previous measurement, and yielding a characteristic spin-down field of $1.47\times10^{13}$ G. We also detect two spectral components above $\sim1$ keV: a blackbody-like one with $kT^\infty=138\pm13$ eV and emitting radius $31_{-16}^{+8}$ m, and a power law with photon index $\Gamma=1.4_{-0.4}^{+0.5}$. The power-law 2--8\,keV flux, $(2.5_{-0.6}^{+0.7})\times10{-15}$ erg cm$^{-2}$ s$^{-1}$, corresponds to an efficiency of $10^{-3}$, in line with that seen in other pulsars. We also reveal a small difference between the $0.1$--$0.3$ keV and $0.3$--$1.2$ keV pulse profiles, as well as some evidence for a modulation above $1.2$ keV. These results show that, notwithstanding its simple spectrum, \eighteen still has a non-trivial thermal surface distribution and features non-thermal emission as seen in other pulsars with higher spin-down power.Comment: 10 pages, 7 figures, 5 tables, accepted for publication in MNRA