Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInterferometer responses to gravitational waves: Comparing FINESSE simulations and analytical solutions
74
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A comparison of analytic calculations and FINESSE simulations of interferometer responses to gravitational wave strain. The response to a gravitational wave is gradually built up from the effect of modulating a space by a gravitational wave to Sagnac and Michelson interferometers with and without arm cavities. This document details the steps necessary to perform such simulations in FINESSE and explicitly derives the interferometer response equations.
rate research
Read More
This document records the results of a comparison of the interferometer simulation Finesse against an analytic (MATLAB based) calculation of the alignment sensing signals of a Fabry Perot cavity. This task was started during the commissioning workshop at the LIGO Livingston site between the 28.1. and 1.02 2013 with the aim of creating a reference example for validating numerical simulation tools. The FFT based simulation OSCAR joined the battle later.
Finesse is a fast interferometer simulation program. For a given optical setup, it computes the light field amplitudes at every point in the interferometer assuming a steady state. To do so, the interferometer description is translated into a set of linear equations that are solved numerically. For convenience, a number of standard analyses can be performed automatically by the program, namely computing modulation-demodulation error signals, transfer functions, shot-noise-limited sensitivities, and beam shapes. Finesse can perform the analysis using the plane-wave approximation or Hermite-Gauss modes. The latter allows computation of the properties of optical systems like telescopes and the effects of mode matching and mirror angular positions.
We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar $Psi_4$ at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects---unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-$Psi_4$ waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-$Psi_4$ and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for $m=0$ memory modes.
Using numerical simulations of helical inflationary magnetogenesis in a low reheating temperature scenario, we show that the magnetic energy spectrum is strongly peaked at a particular wavenumber that depends on the reheating temperature. Gravitational waves (GWs) are produced at frequencies between 3 nHz and 50 mHz for reheating temperatures between 150 MeV and 3x10^5 GeV, respectively. At and below the peak frequency, the stress spectrum is always found to be that of white noise. This implies a linear increase of GW energy per logarithmic wavenumber interval, instead of a cubic one, as previously thought. Both in the helical and nonhelical cases, the GW spectrum is followed by a sharp drop for frequencies above the respective peak frequency. In this magnetogenesis scenario, the presence of a helical term extends the peak of the GW spectrum and therefore also the position of the aforementioned drop toward larger frequencies compared to the case without helicity. This might make a difference in it being detectable with space interferometers. The efficiency of GW production is found to be almost the same as in the nonhelical case, and independent of the reheating temperature, provided the electromagnetic energy at the end of reheating is fixed to be a certain fraction of the radiation energy density. Also, contrary to the case without helicity, the electric energy is now less than the magnetic energy during reheating. The fractional circular polarization is found to be nearly hundred per cent in a certain range below the peak frequency range.
The low-Reynolds number hydrodynamics of slender ribbons is accurately captured by slender-ribbon theory, an asymptotic solution to the Stokes equation which assumes that the three length scales characterising the ribbons are well separated. We show in this paper that the force distribution across the width of an isolated ribbon located in a infinite fluid can be determined analytically, irrespective of the ribbons shape. This, in turn, reduces the surface integrals in the slender-ribbon theory equations to a line integral analogous to the one arising in slender-body theory to determine the dynamics of filaments. This result is then used to derive analytical solutions to the motion of a rigid plate ellipsoid and a ribbon torus and to propose a ribbon resistive-force theory, thereby extending the resistive-force theory for slender filaments.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
