Fast Simulation of Gaussian-Mode Scattering for Precision Interferometry

Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, com- missioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical simulations are indispensable tools for this task but their utility can in practice be limited by the computational cost of describing the scattering process. In this paper we present an efficient method to significantly reduce the computational cost of optical simulations that incorporate scattering. This is accomplished by constructing a near optimal representation of the complex, multi-parameter 2D overlap integrals that describe the scattering process (referred to as a reduced order quadrature). We demonstrate our technique by simulating a near-unstable Fabry-Perot cavity and its control signals using similar optics to those installed in one of the LIGO gravitational-wave detectors. We show that using reduced order quadrature reduces the computational time of the numerical simulation from days to minutes (a speed-up of $\approx 2750 \times$) whilst incurring negligible errors. This significantly increases the feasibility of modelling interferometers with realistic imperfections to overcome current limits in state-of-the-art optical systems. Whilst we focus on the Hermite-Gaussian basis for describing the scattering of the optical fields, our method is generic and could be applied with any suitable basis. An implementation of this reduced order quadrature method is provided in the open source interferometer simulation software Finesse.Comment: 15 pages, 11 figure

Long Term Study of the Double Pulsar J0737-3039 with XMM-Newton: pulsar timing

The relativistic double neutron star binary PSR J0737-3039 shows clear evidence of orbital phase-dependent wind-companion interaction, both in radio and X-rays. In this paper we present the results of timing analysis of PSR J0737-3039 performed during 2006 and 2011 XMM-Newton Large Programs that collected ~20,000 X-ray counts from the system. We detected pulsations from PSR J0737-3039A (PSR A) through the most accurate timing measurement obtained by XMM-Newton so far, the spin period error being of 2x10^-13 s. PSR A's pulse profile in X-rays is very stable despite significant relativistic spin precession that occurred within the time span of observations. This yields a constraint on the misalignment between the spin axis and the orbital momentum axis Delta_A ~6.6^{+1.3}_{-5.4} deg, consistent with estimates based on radio data. We confirmed pulsed emission from PSR J0737-3039B (PSR B) in X-rays even after its disappearance in radio. The unusual phenomenology of PSR B's X-ray emission includes orbital pulsed flux and profile variations as well as a loss of pulsar phase coherence on time scales of years. We hypothesize that this is due to the interaction of PSR A's wind with PSR B's magnetosphere and orbital-dependent penetration of the wind plasma onto PSR B closed field lines. Finally, the analysis of the full XMM-Newton dataset provided evidences of orbital flux variability (~7%) for the first time, involving a bow-shock scenario between PSR A's wind and PSR B's magnetosphere.Comment: Comments: 16 Pages, 6 Figures. Accepted for publication in Astrophysical Journal (Draft Version

X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783

We have characterized the energy-dependent X-ray variability properties of the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing Explorer data. The high-frequency fluctuation power spectral density function (PSD) slope is consistent with flattening towards higher energies. Light curve cross correlation functions yield no significant lags, but peak coefficients generally decrease as energy separation of the bands increases on both short and long timescales. We have measured the coherence between various X-ray bands over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the temporal frequency of the low-frequency power spectral density function (PSD) break tentatively detected by Markowitz et al. and includes the lowest temporal frequency over which coherence has been measured in any AGN to date. Coherence is generally near unity at these temporal frequencies, though it decreases slightly as energy separation of the bands increases. Temporal frequency-dependent phase lags are detected on short time scales; phase lags are consistent with increasing as energy separation increases or as temporal frequency decreases. All of these results are similar to those obtained previously for several Seyfert galaxies and stellar-mass black hole systems. Qualitatively, these results are consistent with the variability models of Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol. 635, p. 180; version 2 has minor grammatical changes; 23 pages; uses emulateapj