Clock-jitter reduction in LISA time-delay interferometry combinations

The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. The three-spacecraft constellation forms a nearly-equilateral triangle, which experiences flexing along its orbit around the Sun. These time-varying and unequal armlengths require to process measurements with time-delay interferometry (TDI) to synthesize virtual equal-arm interferometers, and reduce the otherwise overwhelming laser frequency noise. Algorithms compatible with such TDI combinations have recently been proposed in order to suppress the phase fluctuations of the onboard ultra-stable oscillators (USO) used as reference clocks. In this paper, we propose a new method to cancel USO noise in TDI combinations. This method has comparable performance to existing algorithms, but is more general as it can be applied to most TDI combinations found in the literature. We compute analytical expressions for the residual clock noise before and after correction, accounting for the effect of time-varying beatnote frequencies, previously neglected. We present results of numerical simulations that are in agreement with our models, and show that clock noise can be suppressed below required levels. The suppression algorithm introduces a new modulation noise, for which we propose a partial mitigation. This modulation noise remains the limiting effect for clock-noise suppression, setting strict timing requirements on the sideband generation.Comment: 12 pages, 4 figure

A unified model for the LISA measurements and instrument simulations

LISA is a space-based mHz gravitational-wave observatory, with a planned launch in 2034. It is expected to be the first detector of its kind, and will present unique challenges in instrumentation and data analysis. An accurate pre-flight simulation of LISA data is a vital part of the development of both the instrument and the analysis methods. The simulation must include a detailed model of the full measurement and analysis chain, capturing the main features that affect the instrument performance and processing algorithms. Here, we propose a new model that includes, for the first time, proper relativistic treatment of reference frames with realistic orbits; a model for onboard clocks and clock synchronization measurements; proper modeling of total laser frequencies, including laser locking, frequency planning and Doppler shifts; better treatment of onboard processing and updated noise models. We then introduce two implementations of this model, LISANode and LISA Instrument. We demonstrate that TDI processing successfully recovers gravitational-wave signals from the significantly more realistic and complex simulated data. LISANode and LISA Instrument are already widely used by the LISA community and, for example, currently provide the mock data for the LISA Data Challenges.Comment: 27 pages, 16 figures, 3 table

LISAmax: Improving the Low-Frequency Gravitational-Wave Sensitivity by Two Orders of Magnitude

Within its Voyage 2050 planning cycle, the European Space Agency (ESA) is considering long-term large class science mission themes. Gravitational-wave astronomy is among the topics under study. Building on previous work by other authors, this paper studies a gravitational-wave interferometer concept, dubbed "LISAmax", consisting of three spacecraft, each located close to one of the Sun-Earth libration points L3, L4 and L5, forming a triangular constellation with an arm length of 259 million kilometers (to be compared to LISA's 2.5 million kilometer arms). We argue that this is the largest triangular formation that can be reached from Earth without a major leap in mission complexity and cost (hence the name). The sensitivity curve of such a detector is at least two orders of magnitude lower in amplitude than that of LISA, at frequencies below 1 mHz. This makes the observatory sensitive to gravitational waves in the {\mu}Hz range and opens a new window for gravitational-wave astronomy, not covered by any other planned detector concept. We analyze in detail the constellation stability for a 10-year mission in the full numerical model including insertion, dispersion, and self-gravity-induced accelerations. We compute the orbit transfers using a European launcher and chemical propulsion. Different orbit options, such as precessing, inclined orbits, the use of flybys for the transfer, and the launch strategy, are discussed. The payload design parameters are assessed, and the expected sensitivity curve is compared with a number of potential gravitational-wave sources. No show stoppers are identified at this point of the analysis.Comment: 20 pages, 11 figures, 3 table

Adapting time-delay interferometry for LISA data in frequency

Time-delay interferometry (TDI) is a post-processing technique used to reduce laser noise in heterodyne interferometric measurements with unequal armlengths, a situation characteristic of space gravitational detectors such as Laser Interferometer Space Antenna (LISA). This technique consists in properly time-shifting and linearly combining the interferometric measurements in order to reduce the laser noise by several orders of magnitude and to detect gravitational waves. In this communication, we show that the Doppler shift due to the time evolution of the armlengths leads to an unacceptably large residual noise when using interferometric measurements expressed in units of frequency and standard expressions of the TDI variables. We also present a technique to mitigate this effect by including a scaling of the interferometric measurements in addition to the usual time-shifting operation when constructing the TDI variables. We demonstrate analytically and using numerical simulations that this technique allows one to recover standard laser noise suppression which is necessary to measure gravitational waves.Comment: 7 pages, 4 figure

Assessing the data-analysis impact of LISA orbit approximations using a GPU-accelerated response model

The analysis of gravitational wave (GW) datasets is based on the comparison of measured time series with theoretical templates of the detector's response to a variety of source parameters. For LISA, the main scientific observables will be the so-called time-delay interferometry (TDI) combinations, which suppress the otherwise overwhelming laser noise. Computing the TDI response to GW involves projecting the GW polarizations onto the LISA constellation arms, and then combining projections delayed by a multiple of the light propagation time along the arms. Both computations are difficult to perform efficiently for generic LISA orbits and GW signals. Various approximations are currently used in practice, e.g., assuming constant and equal armlengths, which yields analytical TDI expressions. In this article, we present 'fastlisaresponse', a new efficient GPU-accelerated code that implements the generic TDI response to GWs in the time domain. We use it to characterize the parameter-estimation bias incurred by analyzing loud Galactic-binary signals using the equal-armlength approximation. We conclude that equal-armlength parameter-estimation codes should be upgraded to the generic response if they are to achieve optimal accuracy for high (but reasonable) SNR sources within the actual LISA data.Comment: 15 pages, 7 figures, 2 table

TDI noises transfer functions for LISA

The LISA mission is the future space-based gravitational wave (GW) observatory of the European Space Agency. It is formed by 3 spacecraft exchanging laser beams in order to form multiple real and virtual interferometers. The data streams to be used in order to extract the large number and variety of GW sources are Time-Delay Interferometry (TDI) data. One important processing to produce these data is the TDI on-ground processing which recombines multiple interferometric on-board measurements to remove certain noise sources from the data such as laser frequency noise or spacecraft jitter. The LISA noise budget is therefore expressed at the TDI level in order to account for the different TDI transfer functions applied for each noise source and thus estimate their real weight on mission performance. In order to derive a usable form of these transfer functions, a model of the beams, the measurements, and TDI have been developed, and several approximation have been made. A methodology for such a derivation has been established, as well as verification procedures. It results in a set of transfer functions, which are now used by the LISA project, in particular in its performance model. Using these transfer functions, realistic noise curves for various instrumental configurations are provided to data analysis algorithms and used for instrument design.Comment: 15 pages, 7 figure

Uncovering gravitational-wave backgrounds from noises of unknown shape with LISA

Detecting stochastic background radiation of cosmological origin is an exciting possibility for current and future gravitational-wave (GW) detectors. However, distinguishing it from other stochastic processes, such as instrumental noise and astrophysical backgrounds, is challenging. It is even more delicate for the space-based GW observatory LISA since it cannot correlate its observations with other detectors, unlike today's terrestrial network. Nonetheless, with multiple measurements across the constellation and high accuracy in the noise level, detection is still possible. In the context of GW background detection, previous studies have assumed that instrumental noise has a known, possibly parameterized, spectral shape. To make our analysis robust against imperfect knowledge of the instrumental noise, we challenge this crucial assumption and assume that the single-link interferometric noises have an arbitrary and unknown spectrum. We investigate possible ways of separating instrumental and GW contributions by using realistic LISA data simulations with time-varying arms and second-generation time-delay interferometry. By fitting a generic spline model to the interferometer noise and a power-law template to the signal, we can detect GW stochastic backgrounds up to energy density levels comparable with fixed-shape models. We also demonstrate that we can probe a region of the GW background parameter space that today's detectors cannot access

Ranging Sensor Fusion in LISA Data Processing: Treatment of Ambiguities, Noise, and On-Board Delays in LISA Ranging Observables

Interspacecraft ranging is crucial for the suppression of laser frequency noise via time-delay interferometry (TDI). So far, the effect of on-board delays and ambiguities in the LISA ranging observables was neglected in LISA modelling and data processing investigations. In reality, on-board delays cause offsets and timestamping delays in the LISA measurements, and PRN ranging is ambiguous, as it only determines the range up to an integer multiple of the pseudo-random noise (PRN) code length. In this article, we identify the four LISA ranging observables: PRN ranging, the sideband beatnotes at the interspacecraft interferometer, TDI ranging, and ground-based observations. We derive their observation equations in the presence of on-board delays, noise, and ambiguities. We then propose a three-stage ranging sensor fusion to combine these observables in order to gain optimal ranging estimates. We propose to calibrate the on-board delays on ground and to compensate the associated offsets and timestamping delays in an initial data treatment (stage 1). We identify the ranging-related routines, which need to run continuously during operation (stage 2), and implement them numerically. Essentially, this involves the reduction of ranging noise, for which we develop a Kalman filter combining the PRN ranging and the sideband beatnotes. We further implement crosschecks for the PRN ranging ambiguities and offsets (stage 3). We show that both ground-based observations and TDI ranging can be used to resolve the PRN ranging ambiguities. Moreover, we apply TDI ranging to estimate the PRN ranging offsets

Workshop on Gravitational-Wave Astrophysics for Early Career Scientists

Gravitational-wave science is rapidly growing in maturity as a research area; in May 2021 the next generation of gravitational-wave scientists gathered together to create a vision of the future of the field.Non peer reviewe