Signals and noise in Pulsar Timing Arrays

Pulsar timing arrays (PTA) are experiments that perform monitoring of pulse arrival times from an ensemble of galactic millisecond pulsars, in order to search for the stochastic gravitational-wave background from supermassive binary black holes. One of the most exciting features of pulsar timing arrays is that most sources of noise are environmental, not just instrumental. This allows studying pulsar magnetospheres, interstellar medium, and more.

This is a short note about noise and signals in PTA.

Useful dimensional relations and acronyms

Model for signals and noise

Data is modeled using a multivariate Gaussian likelihood function, which describes a probability distribution for the data (timing residuals), given the parameters of signals and noise. Each dimension of a multivariate likelihood distribution is related to the observation time.

There are two kinds of signals: deterministic and stochastic. Deterministic signals affect the values of timing residuals as a function of time, while stochastic signals affect the covariance matrix of the multivariate likelihood. Stochastic signals can be uncorrelated in time (white), which are described by the diagonal of a covariance matrix, and time-correlated (red), which generally manifest as a random wandering of pulse arrival times.

White noise

Measured "white" noise parameters of pulsars Phenomenological "white" noise parameters
  • EFAC - measurement noise multiplier
  • EQUAD - quadrature-added noise
  • ECORR - jitter-like epoch-correlated noise
  • Radiometer noise - instrumental noise of the telescope
  • Jitter noise - variability of pulse shape
  • Scintillation noise - variability of pulse amplitude
The above are factors that should be applied to uncertainty of arrival times (sigma_toa) in order to obtain a total white noise. The above factors are physical sources of noise in PTA experiments.

Red noise

Uncorrelated between pulsars Correlated between pulsars
Pulsar spin noise - irregularities in pulse ToA due to neutron star physics Stochastic gravitational-wave background from supermassive binary black holes
DM variations - they influence ToA due to interaction of radio-waves with electrons from interstellar medium. Noise PSD depends on radio-frequency. Solar system ephemeris errors - errors in knowing positions and masses of celestial bodies in the Solar System. This noise can also be modelled as a deterministic process.
Jumps, or phase jumps - errors arising from switching observing backends. Clock errors

Recent Work