Gravitational signals due to tidal interactions between white dwarfs and black holes

In this paper we compute the gravitational signal emitted when a white dwarf moves around a black hole on a closed or open orbit using the affine model approach. We compare the orbital and the tidal contributions to the signal, assuming that the star moves in a safe region where, although very close to the black hole, the strength of the tidal interaction is insufficient to provoque the stellar disruption. We show that for all considered orbits the tidal signal presents sharp peaks corresponding to the excitation of the star non radial oscillation modes, the amplitude of which depends on how deep the star penetrates the black hole tidal radius and on the type of orbit. Further structure is added to the emitted signal by the coupling between the orbital and the tidal motion.Comment: 21 pages, 8 figres. Submitted to MNRA

Evolution equations for the perturbations of slowly rotating relativistic stars

We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of linearizing the Einstein field equations leads to perturbation equations which as such cannot be used to perform numerical time evolutions. It is only through the tedious process of combining and rearranging the perturbation variables in a clever way that the system can be cast into a set of hyperbolic first order equations, which is then well suited for the numerical integration. The equations remain quite lengthy, and we therefore rederive the perturbation equations in a different gauge, which has been first proposed by Battiston et al. (1970). Using the ADM formalism, one is immediately lead to a first order hyperbolic evolution system, which is remarkably simple and can be numerically integrated without many further manipulations. Moreover, the symmetry between the polar and the axial equations becomes directly apparent.Comment: 13 pages, no figures, MSRAS typesetting, cleaning of the inadvertently disfigured equation

Gravitational Waves from Rotating Proto-Neutron Stars

We study the effects of rotation on the quasi normal modes (QNMs) of a newly born proto neutron star (PNS) at different evolutionary stages, until it becomes a cold neutron star (NS). We use the Cowling approximation, neglecting spacetime perturbations, and consider different models of evolving PNS. The frequencies of the modes of a PNS are considerably lower than those of a cold NS, and are further lowered by rotation; consequently, if QNMs were excited in a sufficiently energetic process, they would radiate waves that could be more easily detectable by resonant-mass and interferometric detectors than those emitted by a cold NS. We find that for high rotation rates, some of the g-modes become unstable via the CFS instability; however, this instability is likely to be suppressed by competing mechanisms before emitting a significant amount of gravitational waves.Comment: 5 pages, proceedings of the 5th Edoardo Amaldi Conference On Gravitational Wave

Oscillations and instabilities of fast and differentially rotating relativistic stars

We study non-axisymmetric oscillations of rapidly and differentially rotating relativistic stars in the Cowling approximation. Our equilibrium models are sequences of relativistic polytropes, where the differential rotation is described by the relativistic $j$-constant law. We show that a small degree of differential rotation raises the critical rotation value for which the quadrupolar f-mode becomes prone to the CFS instability, while the critical value of $T/|W|$ at the mass-shedding limit is raised even more. For softer equations of state these effects are even more pronounced. When increasing differential rotation further to a high degree, the neutral point of the CFS instability first reaches a local maximum and is lowered afterwards. For stars with a rather high compactness we find that for a high degree of differential rotation the absolute value of the critical $T/|W|$ is below the corresponding value for rigid rotation. We conclude that the parameter space where the CFS instability is able to drive the neutron star unstable is increased for a small degree of differential rotation and for a large degree at least in stars with a higher compactness.Comment: 16 pages, 11 figures; paper accepted for publication in Phys. Rev. D (81.084019

Crustal Oscillations of Slowly Rotating Relativistic Stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.Comment: 15 page

Determination of Helicoverpa armigera (Lepidoptera: Noctuidae) larval instars and age based on head capsule width and larval weight

Προνύμφες του Helicoverpa armigera (Lepidoptera: Noctuidae) εκτράφηκαν σε χώρο με 26°C, φωτόφαση 16 ωρών και σχετική υγρασία 60-75%. Μετρήθηκαν, ανά προνυμφικό στάδιο, το πλάτος της κεφαλικής κάψας και το βάρος κάθε προνύμφης 2-3 ημέρες μετά την έκδυση, με σκοπό τον προσδιορισμό του προνυμφικού σταδίου και της ηλικίας. Χρησιμοποιήθηκε επί πλέον το βάρος της προνύμφης γιατί δεν είναι ασφαλής ο προσδιορισμός των προνυμφικών σταδίων μόνο από το πλάτος της κεφαλικής κάψας, καθόσον υπάρχει αλληλεπικάλυψη μεταξύ πλάτους ενός σταδίου και του προηγούμενου και επόμενου του, και ακόμη παρατηρείται διαφορετικός αριθμός σταδίων μεταξύ των προνυμφών. Η ανάπτυξη συμπληρώνεται σε 5 προνυμφικά στάδια στο 75% των προνυμφών, σε 6 στο 24% και σε 7 στο1%. Το πλάτος της κεφαλικής κάψας ήταν αρκετό για τη διάκριση των προνυμφών της Ιου σταδίου μόνο και το μέγιστο πλάτος ήταν 0,4mm. Το βάρος της προνύμφης ήταν ικανό μόνο του να προσδιορίσει προνύμφες 1ης και 2ης ηλικίας. Η διαφορά μεταξύ Ιου και 2ου σταδίου ήταν lmg και μεταξύ 2ου και 3ου σταδίου 5,5mg. Συσχέτιση και ανάλυση παραλλακτικότητας των δύο παραμέτρων μας δίνει τη δυνατότητα προσδιορισμού όλων των προνυμφικών σταδίων μιας προνύμφης με πιθανότητα 96,9%,.καθώς και την ηλικία της σε ημέρες από την εκκόλαψη.Larνae of Helicoverpa armigera (Hubner) (Lepidoptera: Noctuidae) were reared in laboratory conditions (26°C, 16:8 L:D) and measurements of larval head capsule width, and body weight, were used in order to determine the boundaries of larval instars. Larvae of Η. armigera completed development in 5 to 7 instars. Head capsule width could predict the larval instar only for Ll. The upper boundary of head width for L1 was 0.4mm. Body weight could predict both L1 and L2 larval instars. Boundaries between L1-L2 instars were found to be 1 mg and for L2-L3 5,5 mg. Correlation and regression analysis suggest that a combination of head capsule width and body weight can predict both larval instars and chronological age under constant conditions in the laboratory

Evolution equations for slowly rotating stars

We present a hyperbolic formulation of the evolution equations describing non-radial perturbations of slowly rotating relativistic stars in the Regge--Wheeler gauge. We demonstrate the stability preperties of the new evolution set of equations and compute the polar w-modes for slowly rotating stars.Comment: 27 pages, 2 figure