Context. Strings and other alternative theories describing the quantum properties of space-time suggest that space-time could present a foamy structure and also that, in certain cases, quantum gravity (QG) may manifest at energies much below the Planck scale. One of the observable effects could be the degradation of the diffraction images of distant sources. Aims. We searched for this degradation effect, caused by QG fluctuations, in the light of the farthest quasars (QSOs) observed by the Hubble Space Telescope with the aim of setting new limits on the fluctuations of the space-time foam and QG models. Methods. We developed a software that estimates and compares the phase variation in the interference patterns of the high-redshift QSOs, taken from the snapshot survey of HST-SDSS, with those of stars that are expected to not be affected by QG effects. We used a two-parameter function to determine, for each test star and QSO, the maximum of the diffraction pattern and to calculate the Strehl ratio. Results. Our results go far beyond those already present in the literature. By adopting the most conservative approach where the correction terms, that describe the possibility for space-time fluctuations cumulating across long distances and partially compensate for the effects of the phase variations, are taken into account. We exclude the random walk model and most of the holographic models of the space-time foam. Without considering these correction terms, all the main QG scenarios are excluded. Finally, our results show the absence of any directional dependence of QG effects and the validity of the cosmological principle with an independent method; that is, viewed on a large scale, the properties of the Universe are the same for all observers, including the effects of space-time fluctuations.

Abstract. In millisecond pulsars the existence of the Coriolis force allows the development of the so-called Rossby oscillations (r-modes) which are know to be unstable to emission of gravitational waves. These instabilities are mainly damped by the viscosity of the star or by the existence of a strong magnetic field. A fraction of the observed millisecond pulsars are known to be inside Low Mass X-ray Binaries (LMXBs), systems in which a neutron star (or a black hole) is accreting from a donor whose mass is smaller than 1 M⊙. Here we show that the r-mode instabilities can generate strong toroidal magnetic fields by inducing differential rotation. In this way we also provide an alternative scenario for the origin of the magnetars. IntroductionThe r-mode oscillations in all rotating stars are unstable for emission of gravitational waves [1]. These modes play therefore a very important role in the astrophysics of compact stars and in the search for gravitational waves. On the other hand the existence of millisecond pulsars implies the presence of damping mechanisms of the r-modes. Damping mechanisms are associated with bulk and shear viscosity and with the possible existence of the so called Ekman layer. The latter is located at the interface between the solid crust and the fluid of the inner core and in this region friction is significantely enhanced respect to friction in a purely fluid component. All these mechanisms are strongly temperature dependent. An important class of rapidly rotating neutron stars are the accreting millisecond pulsars associated with Low Mass X-ray Binaries (LMXBs). For these objects the internal temperature is estimated to be in the range 10 8 -10 8.5 K [2, 3] and their frequencies can be as large as ∼ 650 Hz. In this range of temperatures and in the case of a purely nucleonic star, bulk and shear viscosities alone cannot stabilize stars whose frequency exceeds ∼ 100 Hz. A possible explanation of the stability of stars rotating at higher frequencies is based on the Ekman layer, but recent calculations show that this explanation holds only for rather extreme values of the parameters [4]. In this contribution we propose a new damping mechanism based on the generation inside the star of strong magnetic fields produced by r-mode instabilities. This same mechanism has been proposed in the case of rapidly rotating, isolated and newly born neutron stars in [5,6]. In that paper the mechanism which generates the magnetic field is investigated only during the relatively short period in which the star remains always in the instability region. In our work we consider accreting stars and we investigate the interplay between r-modes and magnetic field on an extremely long period and we show that in this scenario a very strong magnetic field can

Differential rotation induced by the r-mode instability can generate very strong toroidal fields in the core of accreting, millisecond spinning neutron stars. We introduce explicitly the magnetic damping term in the evolution equations of the r-modes and solve them numerically in the Newtonian limit, to follow the development and growth of the internal magnetic field. We show that the strength of the latter can reach large values, B ∼ 10 14 G, in the core of the fastest accreting neutron stars. This is strong enough to induce a significant quadrupole moment of the neutron star mass distribution, corresponding to an ellipticity |ǫB| ∼ 10 −8 . If the symmetry axis of the induced magnetic field is not aligned with the spin axis, the neutron star radiates gravitational waves. We suggest that this mechanism may explain the upper limit of the spin frequencies observed in accreting neutron stars in Low Mass X-Ray Binaries. We discuss the relevance of our results for the search of gravitational waves.

We show that the r-mode instability can generate strong toroidal fields in the core of accreting millisecond quark stars by inducing differential rotation. We follow the spin frequency evolution on a long time-scale, taking into account the magnetic damping rate in the evolution equations of r-modes. The maximum spin frequency of the star is only marginally lower than without the magnetic field. The late-time evolution of the stars that enter the r-mode instability region is instead quite different if the generated magnetic fields are taken into account: they leave the millisecond pulsar region and become radio pulsars.

In rotating neutron stars the existence of the Coriolis force allows the presence of the so-called Rossby oscillations (r-modes) which are known to be unstable to emission of gravitational waves. Here, for the first time, we introduce the magnetic damping rate in the evolution equations of r-modes. We show that r-modes can generate very strong toroidal fields in the core of accreting millisecond pulsars by inducing differential rotation. We shortly discuss the instabilities of the generated magnetic field and its long time-scale evolution in order to clarify how the generated magnetic field can stabilize the star.