Gravitational wave search with a Pulsar Timing Array in France – PTA-France

A pulsar is a rapidly rotating neutron star that emits a beam of electromagnetic waves like a lighthouse. Millisecond pulsars are extremely stable rotators and serve as ultra-precise «clocks« that we time with a radio telescope. Deviations in the Time of Arrival (TOA) of individual pulsars are caused by the nature of the pulsars (slowing down, relativistic effects), by the interstellar medium, instrumental noise and, most interestingly, by the propagation of the pulses in the gravitational wave tidal field. When averaged over long periods of time, many of these effects are small and allow us to search for gravitational waves with equally long periods of time. The gravitational frequency range accessible by pulsar timing is limited in its lower part by the length of the observation period: with T~10-20 years of monitoring, a frequency threshold of 1/T ~ 1.5-3.0 nanoHz is obtained. The upper limit is set by the observation rate: two measurements per week lead to an upper limit of a few microHz. The sensitivity itself is related to the temporal accuracy achieved by the instruments and the development of analytical methods. A typical accuracy dt ~100 nanoseconds on most stable pulsars gives a detection level in the amplitude of the gravitational waves dt/T~10E-16.
This technique, known as the «Pulsar Timing Array« is a (PTA), thus covers a frequency range complementary to LIGO-Virgo and LISA, and where one expects the gravitational emission from the population of super massive black hole binaries (SMBHBs) formed during the long process of galaxy aggregation.

On the instrumental part (task 1), we initiated the development with available hardware for a first prototype and sent one of the electronic engineers from Nançay Observatory (Cédric Viou) to visit the developers group of Green Bank Telescope (USA) in order to initiate the design of the first level of the backend (channel splitting, ADC performance test, calibration of gains and polarizations). Concerning the observational part and the data processing (task 2), we have acquired during the first 18 months the equivalent of 6000 hours of telescope time at the NRT on the 80 millisecond pulsars of the PTA program. We also participated in the first observations of the MeerTime program with the MeerKAT telescope (65 millisecond pulsars observed every 2-3 weeks since March 2019). Lucas Guillemot has done important work on the polarization calibration of the NRT, which has resulted in a significant improvement in the accuracy of the timing data. Concerning the gravitational wave analysis (task 3), the main advances concern : the modelling of the uncertainties on planetary ephemerides, the comparison of pulse arrival time pipelines (with or without frequency information), the testing of several probability function samplers for gravitational wave analysis, the implementation of new methods for the evaluation of the low-frequency noise component for individual pulsars, the production of new limits on the detection of individual sources and on the stochastic background from the latest generation of European data.

Thanks to the ANR PTA-France, the weight of the French group has very clearly led the European consortium to relaunch and refocus its activity on the PTA activity.

The list of ongoing projects is as follows, each of which will be published within a few months to a year:
- Artificial intelligence methods applied to sorting out interferences in pulsar data and impact on PTA sensitivity,
- new methods for analysing timing data by taking into account temporal and frequency variations in the emission profile of pulsars,
- application of new methods for analysing foreground noise based on clock comparison techniques used in metrology
- new limit on the stochastic background from the latest IPTA data,
- detection and characterization of a correlated low-frequency signal in the EPTA data,
- impact of uncertainties in INPOP planetary ephemerides on the detection of the gravitational wave background,
- detection limits on the stochastic background from individual pulsars and impact of TOAs extraction methods or likelihood exploration algorithms,
- development of new analytical methods to detect individual sources of gravitational waves, by robustly separating individual sources from the stochastic background and taking into account the eccentricity of orbits ;
- application to IPTA and EPTA DR2 data for the search for continuous sources
- timing and analysis of the relativistic binary system PSR J1528-3146 with common NRT and MeerKAT data,
- polarization calibration methods and impact on the timing accuracy of PTA data,
- study of multi-channel sampling techniques with jumps between models,
- application of Bayesian hypermodel structures for model comparison in gravitational wave analysis.

Hobbs et al 2020, A pulsar-based time-scale from the International Pulsar Timing Array, MNRAS 491, 5951

Perera et al 2019, The International Pulsar Timing Array: second data release, MNRAS 490, 4666

Ossokine et al 2020, Multipolar Effective-One-Body Waveforms for Precessing Binary Black Holes: Construction and Validation”, e-Print: 2004.09442 (PRD in press)

Toubiana et al 2020, Tests of general relativity with stellar-mass black hole binaries observed with LISA, PhRvD, 101, 4038

Chua et al 2020, Gaussian processes for the interpolation and marganalization of waveform error in extreme-mass-ratio-inspiral parameter estimation, PhRvD, 101, 4027

Sesana, Lamberts, Petiteau 2020, Finding binary black holes in the Milky Way with LISA, MNRAS 494, L75

Caputo et al 2020, Gravitational-wave Detection and Parameter Estimation for Accreting Black-hole Binaries and Their Electromagnetic Counterpart, ApJ 892, 90

Bailes et al 2020, The MeerKAT Telescope as a Pulsar Facility: System verification and early science results from MeerTime, PASA in press
Vernotte, Rubiola, Chen 2020, Responses and Degrees of Freedom of PVAR for a Continuous Power-Law PSD, e-Print: 2005.13631 (IEEE in press)

Voisin et al 2020, An improved test of the strong equivalence principle with the pulsar in a triple star system, A&A 638, 24

Bak Nielsen et al 2020, Timing stability of three black widow pulsars, MNRAS 494, 2591

Ng et al 2020, A Shapiro delay detection in the pulsar binary system PSR J1811-2405, MNRAS 493, 1261

Zhu et al 2019, Tests of gravitational symmetries with pulsar binary J1713+0747, MNRAS 482, 3249

Chen et al 2019, Constraining astrophysical observables of galaxy and supermassive black hole binary mergers using pulsar timing arrays, MNRAS 488, 401

Guillemot et al 2019, Timing of PSR J2055+3829, an eclipsing black widow pulsar discovered with the Nançay Radio Telescope, A&A 629, 92

The timing of an array of millisecond pulsars (PTA) acts as a galactic-scale detector to observe gravitational wave (GW) sources in the nHz frequency range. The goal of this project is to detect low-frequency GWs while maximizing the scientific output of the Nançay radio telescope (NRT) and participating in operations of the South African MeerKAT radio telescope. We propose new data analysis methods to detect GWs emitted by multiple supermassive black hole binaries in eccentric orbits, while modeling pulsar and noise properties. We will develop a new state-of-the-art pulsar observing backend, to achieve coherent de-dispersion over a very large frequency range (1.5 to 3.5 GHz) and substantially increase our sensitivity at these key radio frequencies. The expected results are the potential first ever detection of GWs in the nHz domain, a much improved understanding of millisecond pulsars and of the weak perturbations that affect their timing stability, and new tests of General Relativity.

This project is based on the long-term know-how of a composite team, made of radio astronomers who are specialists in pulsar timing, in Bayesian techniques and in GW data analyses. The NRT already produces high cadence pulsar data with a dedicated state-of-the-art backend enabling us to analyze data from the telescope’s L-band receiver (1.1-1.7 GHz) optimally. The new instrumentation will allow us to cover the whole band accessible with its high frequency S-band receiver, bringing a leap in sensitivity in a domain where the observed radio signal from pulsars is much less affected by interstellar medium perturbations. The support from the ANR will provide us with the resources to fully participate in the scientific exploitation of today’s best radio telescope in the Southern hemisphere, MeerKAT, and allow us to extend the sky coverage for GW searches. This involvement will also firmly install our French team in the long-term preparation of the SKA (Square Kilometer Array) project, which has just been included in the national road map. This is a unique opportunity to train future radio astronomers on one of its key science programs. We will also benefit from our engagement in the LISA project, sharing the expertise accumulated in both communities and building new GW detection algorithms at the interface between both projects, implementing more sophisticated and realistic GW models, and introducing machine learning in the trans-dimensional Bayesian analysis.

The PTA technique indeed gives us access to a frequency domain complementary to those covered by Virgo-LIGO and LISA, where one expects GW emission from sources such as super massive black hole binaries (SMBHBs) formed in the long process of galaxy aggregation, and also stochastic GWs from the cosmological background generated by inflation in the very early Universe or by a network of cosmic strings. Characterizing those individual sources (parameters, rate, sky distribution, etc...) would yield unique information about the formation and evolution of SMBHBs through cosmic history and bring original constraints on the hierarchical galaxy formation. Moreover, the detection of this GW signal will allow us to refine the prognoses for SMBHB mergers in the LISA band.

To reach these goals, we need a dedicated post-doc involved in both MeerKAT pulsar timing observations and in the combination of data from all radio telescopes involved in the International Pulsar Timing Array organization. Developing and implementing new data analysis techniques at the interface between PTA and LISA is a great project for a PhD student, who will take advantage of the APC environment and get unique skills for the future exploitation of LISA and SKA data. Finally, a strong involvement in MeerKAT and the availability of a wide-band pulsar instrumentation at NRT will clearly maintain the French radio telescope in the race up to the SKA era (>2025) and strengthen our position in the SKA Pulsar Science Working Group.