Gravitational-wave bursts and stochastic background from superfluid vortex avalanches during pulsar glitches

The current-quadrupole gravitational-wave signal emitted during the spin-up phase of a pulsar glitch is calculated from first principles by modeling the vortex dynamics observed in recent Gross-Pitaevskii simulations of pinned, decelerating quantum condensates. Homogeneous and inhomogeneous unpinning geometries, representing creep- and avalanche-like glitches, provide lower and upper bounds on the gravitational wave signal strength respectively. The signal arising from homogeneous glitches is found to scale with the square root of glitch size, whereas the signal from inhomogeneous glitches scales proportional to glitch size. The signal is also computed as a function of vortex travel distance and stellar angular velocity. Convenient amplitude scalings are derived as functions of these parameters. For the typical astrophysical situation, where the glitch duration (in units of the spin period) is large compared to the vortex travel distance (in units of the stellar radius), an individual glitch from an object $1\,\rm{kpc}$ from Earth generates a wave strain of $10^{-24} [(\Delta\omega/\omega) / 10^{-7}] (\omega/10^2 \rm{rad s}^{-1})^3 (\Delta r / 10^{-2} \rm{m})^{-1}$, where $\Delta r$ is the average distance travelled by a vortex during a glitch, $\Delta\omega/\omega$ is the fractional glitch size, and $\omega$ is the pulsar angular velocity. The non-detection of a signal from the 2006 Vela glitch in data from the fifth science run conducted by the Laser Interferometer Gravitational-Wave Observatory implies that the glitch duration exceeds $\sim 10^{-4}\,\rm{ms}$. This represents the first observational lower bound on glitch duration to be obtained.Comment: Accepted for publication in MNRA

A trend-preserving bias correction – The ISI-MIP approach

Statistical bias correction is commonly applied within climate impact modelling to correct climate model data for systematic deviations of the simulated historical data from observations. Methods are based on transfer functions generated to map the distribution of the simulated historical data to that of the observations. Those are subsequently applied to correct the future projections. Here, we present the bias correction method that was developed within ISI-MIP, the first Inter-Sectoral Impact Model Intercomparison Project. ISI-MIP is designed to synthesise impact projections in the agriculture, water, biome, health, and infrastructure sectors at different levels of global warming. Bias-corrected climate data that are used as input for the impact simulations could be only provided over land areas. To ensure consistency with the global (land + ocean) temperature information the bias correction method has to preserve the warming signal. Here we present the applied method that preserves the absolute changes in monthly temperature, and relative changes in monthly values of precipitation and the other variables needed for ISI-MIP. The proposed methodology represents a modification of the transfer function approach applied in the Water Model Intercomparison Project (Water-MIP). Correction of the monthly mean is followed by correction of the daily variability about the monthly mean. Besides the general idea and technical details of the ISI-MIP method, we show and discuss the potential and limitations of the applied bias correction. In particular, while the trend and the long-term mean are well represented, limitations with regards to the adjustment of the variability persist which may affect, e.g. small scale features or extremes

Stochastic simulations of conditional states of partially observed systems, quantum and classical

In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional state will be given by a state matrix $\rho_r(t)$ and if classical the conditional state will be given by a probability distribution $P_r(x,t)$ where $r$ is the result of the measurement. Thus to determine the evolution of this conditional state under continuous-in-time monitoring requires an expensive numerical calculation. In this paper we demonstrating a numerical technique based on linear measurement theory that allows us to determine the conditional state using only pure states. That is, our technique reduces the problem size by a factor of $N$, the number of basis states for the system. Furthermore we show that our method can be applied to joint classical and quantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure

The Impact of HI in Galaxies on 21-cm Intensity Fluctuations During the Reionisation Epoch

We investigate the impact of neutral hydrogen (HI) in galaxies on the statistics of 21-cm fluctuations using analytic and semi-numerical modelling. Following the reionisation of hydrogen the HI content of the Universe is dominated by damped absorption systems (DLAs), with a cosmic density in HI that is observed to be constant at a level equal to ~2% of the cosmic baryon density from z~1 to z~5. We show that extrapolation of this constant fraction into the reionisation epoch results in a reduction of 10-20% in the amplitude of 21-cm fluctuations over a range of spatial scales. The assumption of a different percentage during the reionisation era results in a proportional change in the 21-cm fluctuation amplitude. We find that consideration of HI in galaxies/DLAs reduces the prominence of the HII region induced shoulder in the 21-cm power spectrum (PS), and hence modifies the scale dependence of 21-cm fluctuations. We also estimate the 21cm-galaxy cross PS, and show that the cross PS changes sign on scales corresponding to the HII regions. From consideration of the sensitivity for forthcoming low-frequency arrays we find that the effects of HI in galaxies/DLAs on the statistics of 21-cm fluctuations will be significant with respect to the precision of a PS or cross PS measurement. In addition, since overdense regions are reionised first we demonstrate that the cross-correlation between galaxies and 21-cm emission changes sign at the end of the reionisation era, providing an alternative avenue to pinpoint the end of reionisation. The sum of our analysis indicates that the HI content of the galaxies that reionise the universe will need to be considered in detailed modelling of the 21-cm intensity PS in order to correctly interpret measurements from forthcoming low-frequency arrays.Comment: 11 pages, 6 figures. Submitted to MNRA

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.Comment: 7 pages, 2 figures. Shorter, significantly modified, updated versio

Superfluid vortex unpinning as a coherent noise process, and the scale invariance of pulsar glitches

The scale-invariant glitch statistics observed in individual pulsars (exponential waiting-time and power-law size distributions) are consistent with a critical self-organization process, wherein superfluid vortices pin metastably in macroscopic domains and unpin collectively via nearest-neighbor avalanches. Macroscopic inhomogeneity emerges naturally if pinning occurs at crustal faults. If, instead, pinning occurs at lattice sites and defects, which are macroscopically homogeneous, we show that an alternative, noncritical self-organization process operates, termed coherent noise, wherein the global Magnus force acts uniformly on vortices trapped in a range of pinning potentials and undergoing thermal creep. It is found that vortices again unpin collectively, but not via nearest-neighbor avalanches, and that, counterintuitively, the resulting glitch sizes are scale invariant, in accord with observational data. A mean-field analytic theory of the coherent noise process, supported by Monte-Carlo simulations, yields a power-law size distribution, between the smallest and largest glitch, with exponent $a$ in the range $-2\leq a \leq 0$. When the theory is fitted to data from the nine most active pulsars, including the two quasiperiodic glitchers PSR J0537$-$6910 and PSR J0835$-$4510, it directly constrains the distribution of pinning potentials in the star, leading to two conclusions: (i) the potentials are broadly distributed, with the mean comparable to the standard deviation; and (ii) the mean potential decreases with characteristic age. An observational test is proposed to discriminate between nearest-neighbor avalanches and coherent noise.Comment: 39 pages, 11 figures. Accepted for publication in Ap

Modification of the 21-cm power spectrum by X-rays during the epoch of reionisation

We incorporate a contribution to reionization from X-rays within analytic and semi-numerical simulations of the 21-cm signal arising from neutral hydrogen during the epoch of reionization. We explore the impact that X-ray ionizations have on the power spectrum (PS) of 21-cm fluctuations by varying both the average X-ray MFP and the fractional contribution of X-rays to reionization. In general, prior to the epoch when the intergalactic medium is dominated by ionized regions (H {\sevensize II} regions), X-ray-induced ionization enhances fluctuations on spatial scales smaller than the X-ray MFP, provided that X-ray heating does not strongly supress galaxy formation. Conversely, at later times when \H2 regions dominate, small-scale fluctuations in the 21-cm signal are suppressed by X-ray ionization. Our modelling also shows that the modification of the 21-cm signal due to the presence of X-rays is sensitive to the relative scales of the X-ray MFP, and the characteristic size of \H2 regions. We therefore find that X-rays imprint an epoch and scale-dependent signature on the 21-cm PS, whose prominence depends on fractional X-ray contribution. The degree of X-ray heating of the IGM also determines the extent to which these features can be discerned. We show that the MWA will have sufficient sensitivity to detect this modification of the PS, so long as the X-ray photon MFP falls within the range of scales over which the array is most sensitive ($\sim0.1$ Mpc$^{-1}$). In cases in which this MFP takes a much smaller value, an array with larger collecting area would be required.Comment: 15 pages, 6 figures, Accepted for publication in MNRAS X-ray heating contribution now adde

Adiabatic Elimination in Compound Quantum Systems with Feedback

Feedback in compound quantum systems is effected by using the output from one sub-system (``the system'') to control the evolution of a second sub-system (``the ancilla'') which is reversibly coupled to the system. In the limit where the ancilla responds to fluctuations on a much shorter time scale than does the system, we show that it can be adiabatically eliminated, yielding a master equation for the system alone. This is very significant as it decreases the necessary basis size for numerical simulation and allows the effect of the ancilla to be understood more easily. We consider two types of ancilla: a two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g. an optical mode). For each, we consider two forms of feedback: coherent (for which a quantum mechanical description of the feedback loop is required) and incoherent (for which a classical description is sufficient). We test the master equations we obtain using numerical simulation of the full dynamics of the compound system. For the system (a parametric oscillator) and feedback (intensity-dependent detuning) we choose, good agreement is found in the limit of heavy damping of the ancilla. We discuss the relation of our work to previous work on feedback in compound quantum systems, and also to previous work on adiabatic elimination in general.Comment: 18 pages, 12 figures including two subplots as jpeg attachment