Population Synthesis of Accreting Neutron Stars Emitting Gravitational Waves

The fastest-spinning neutron stars in low-mass X-ray binaries, despite having undergone millions of years of accretion, have been observed to spin well below the Keplerian break-up frequency. We simulate the spin evolution of synthetic populations of accreting neutron stars in order to assess whether gravitational waves can explain this behaviour and provide the distribution of spins that is observed. We model both persistent and transient accretion and consider two gravitational-wave-production mechanisms that could be present in these systems: thermal mountains and unstable $r$-modes. We consider the case of no gravitational-wave emission and observe that this does not match well with observation. We find evidence for gravitational waves being able to provide the observed spin distribution; the most promising mechanisms being a permanent quadrupole, thermal mountains and unstable $r$-modes. However, based on the resultant distributions alone it is difficult to distinguish between the competing mechanisms.Comment: 12 pages, 12 figures. Accepted for publication in MNRA

The intimate relation between the low T/W instability and the co-rotation point

We study the low T/W instability associated with the f-mode of differentially rotating stars. Our stellar models are described by a polytropic equation of state and the rotation profile is given by the standard j-constant law. The properties of the relevant oscillation modes, including the instability growth time, are determined from time evolutions of the linearised dynamical equations in Newtonian gravity. In order to analyse the instability we monitor also the canonical energy and angular momentum. Our results demonstrate that the l=m=2 f-mode becomes unstable as soon as a co-rotation point develops inside the star (i.e. whenever there is a point where the mode's pattern speed matches the bulk angular velocity). Considering various degrees of differential rotation, we show that the instability grows faster deep inside the co-rotation region and deduce an empirical relation that correlates the mode frequency and the star's parameters, which captures the main features of the l=m=2 f-mode growth time. This function is proportional to the product of the kinetic to gravitational energy ratio and the gradient of the star's spin, strengthening further the relationship between the co-rotation point and the low T/W instability. We briefly consider also the l=m=2 r-mode and demonstrate that it never moves far inside the co-rotation region even for significant differential rotation.Comment: 12 pages, 8 figures, 2 tables. Submitted to MNRA

A new mechanism for saturating unstable r-modes in neutron stars

We consider a new mechanism for damping the oscillations of a mature neutron star. The new dissipation channel arises if superfluid vortices are forced to cut through superconducting fluxtubes. This mechanism is interesting because the oscillation modes need to exceed a critical amplitude in order for it to operate. Once it acts the effect is very strong (and nonlinear) leading to efficient damping. The upshot of this is that modes are unlikely to ever evolve far beyond the critical amplitude. We consider the effect of this new dissipation channel on the r-modes, that may be driven unstable by the emission of gravitational waves. Our estimates show that the fluxtube cutting leads to a saturation threshold for the instability that can be smaller than that of other proposed mechanisms. This suggests that the idea may be of direct astrophysical relevance

ON THE OSCILLATION SPECTRA OF ULTRA COMPACT STARS

Quasinormal modes of ultra compact stars with uniform energy density have been calculated. For less compact stars, there is only one very slowly damped polar mode (corresponding to the Kelvin f-mode) for each spherical harmonic index $l$. Further long-lived modes become possible for a sufficiently compact star (roughly when $M/R \ge 1/3$). We compare the characteristic frequencies of these resonant polar modes to the axial modes first found by Chandrasekhar and Ferrari [{\em Proc. Roy. Soc. London A} {\bf 434} 449 (1991)]. We find that the two spectra approach each other as the star is made more compact. The oscillation frequencies of the corresponding polar and axial modes agree to within a percent for stars more compact than $M/R = 0.42$. At the same time, the damping times are slightly different. The results illustrate that there is no real difference between the origin of these axial and polar modes: They are essentially spacetime modes.Comment: 13 pages, LATEX format, 25Kb, 2 postscript figures, Proc. Roy. Soc. London in pres

International Contracts in European Courts: Jurisdiction Under Article 5(1) of the Brussels Convention

Background: Internet-based cognitive behavior therapy (ICBT) has shown promising effects in the treatment of irritable bowel syndrome (IBS). However, to date no study has used a design where participants have been sampled solely from a clinical population. We aimed to investigate the acceptability, effectiveness, and cost-effectiveness of ICBT for IBS using a consecutively recruited sample from a gastroenterological clinic. less thanbrgreater than less thanbrgreater thanMethods: Sixty-one patients were randomized to 10 weeks of ICBT (n = 30) or a waiting list control (n = 31). The ICBT was guided by an online therapist and emphasized acceptance of symptoms through exposure and mindfulness training. Severity of IBS symptoms was measured with the Gastrointestinal symptom rating scale - IBS version (GSRS-IBS). Patients in both groups were assessed at pre- and post-treatment while only the ICBT group was assessed 12 months after treatment completion. Health economic data were also gathered at all assessment points and analyzed using bootstrap sampling. less thanbrgreater than less thanbrgreater thanResults: Fifty of 61 patients (82%) completed the post-treatment assessment and 20 of 30 patients (67%) in the ICBT group were assessed at 12-month follow-up. The ICBT group demonstrated significantly (p andlt; .001) larger improvements on the IBS-related outcome scales than the waiting list group. The between group effect size on GSRS-IBS was Cohens d = 0.77 (95% CI: 0.19-1.34). Similar effects were noted on measures of quality of life and IBS-related fear and avoidance behaviors. Improvements in the ICBT group were maintained at 12-month follow-up. The ICBT condition was found to be more cost-effective than the waiting list, with an 87% chance of leading to reduced societal costs combined with clinical effectiveness. The cost-effectiveness was sustained over the 12-month period. less thanbrgreater than less thanbrgreater thanConclusions: ICBT proved to be a cost-effective treatment when delivered to a sample recruited from a gastroenterological clinic. However, many of the included patients dropped out of the study and the overall treatment effects were smaller than previous studies with referred and self-referred samples. ICBT may therefore be acceptable and effective for only a subset of clinical patients. Study dropout seemed to be associated with severe symptoms and large impairment. Objective and empirically validated criteria to select which patients to offer ICBT should be developed.Funding Agencies|Stockholm City Council||Stockholm Centre for Psychiatry Research, Linkoping University||Soderstrom-Konigska Foundation||Bror Gadelius Foundation|

Long-term Government Bond Yields and Macroeconomic Variables

This article investigates the relationship between the economic influences a country has and how the market has observed by 10-year government bond yields through a set of macroeconomic variables. It examines a set of OECD countries between 1980 and 2013 dividing them into two groups namely the G7 group and small countries, even though the specific effect of the USA is investigated as well. The Panel data regressions are estimated with OLS and with GMM. We find that there are distinguishable differences between larger and smaller countries and evidence for USA having a special position in the world economy, although the results are somewhat distorted by the latest financial crisis. Smaller countries are harsher judged on their unemployment rate and budget balance whereas larger countries can get boosts from increased net lending. USA has a higher correlation between its GDP growth and yield and has apart from the other large countries also a positive effect of running a deficit in the current account. The effect from government debt does not seem to be much different between the groups but is slightly stronger among larger countries.This article investigates the relationship between the economic influences a country has and how the market has observed by 10-year government bond yields through a set of macroeconomic variables. It examines a set of OECD countries between 1980 and 2013 dividing them into two groups namely the G7 group and small countries, even though the specific effect of the USA is investigated as well. The Panel data regressions are estimated with OLS and with GMM. We find that there are distinguishable differences between larger and smaller countries and evidence for USA having a special position in the world economy, although the results are somewhat distorted by the latest financial crisis. Smaller countries are harsher judged on their unemployment rate and budget balance whereas larger countries can get boosts from increased net lending. USA has a higher correlation between its GDP growth and yield and has apart from the other large countries also a positive effect of running a deficit in the current account. The effect from government debt does not seem to be much different between the groups but is slightly stronger among larger countries

Formulating the r-mode problem for slowly rotating neutron stars

We revisit the problem of inertial r-modes in stratified stars, drawing on a more precise description of the composition stratification in a mature neutron star. The results highlight issues with the traditional approach to the problem, leading us to rethink the computational strategy for r-modes of non-barotropic neutron stars. We outline two strategies for dealing with the problem. For moderate to slowly rotating neutron stars the only viable alternative may be to approach the problem numerically from the outset, while a meaningful slow-rotation calculation can be carried out for the fastest known spinning stars (which may be close to being driven unstable by the emission of gravitational waves). We demonstrate that the latter approach leads to a problem close, but not identical, to that for barotropic inertial modes. We also suggest that these reformulations of the problem likely resolve the long-standing problem of singular behaviour associated with a co-rotation point in rotating relativistic neutron stars. This issue needs to be resolved in order to guide future gravitational-wave searches.Comment: 22 pages, 1 figur

The r-modes of slowly rotating, stratified neutron stars

The only r-modes that exist in a globally barotropic, rotating, Newtonian star are the fundamental $l = |m|$ solutions, where $l$ and $m$ are the indices of the spherical harmonic $Y_l^m$ that describe the mode's angular dependence. This is in stark contrast to a stellar model that is non-barotropic throughout its interior, which hosts all the $l \geq |m|$ perturbations including radial overtones. In reality, neutron stars are stratified with locally barotropic regions. Therefore, we explore how stratification alters a star's ability to support r-modes. We consider the globally stratified case and examine the behaviour of the modes as the star gets close to barotropicity. In this limit, we find that all but the fundamental $l = |m|$ perturbations change character and become generic inertial modes. Restricting the analysis to $l = |m|$ perturbations, we develop the r-mode equations in order to consider stellar models that exhibit local barotropicity. Our results for such models show that the r-mode overtones diverge and join the inertial modes. This suggests that neutron stars can only support the fundamental $l = |m|$ r-modes.Comment: 15 pages, 8 figure