A possible precursor for the detection of nanohertz gravitational waves or unmodeled pulsar noise?
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
- PSD - power spectral density. Units:
- PTA - pulsar timing arrays
- ToA - pulse times of arrival
- DM - dispersion measure
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.
|Measured "white" noise parameters of pulsars||Phenomenological "white" noise parameters|
|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.|
|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|
We model red noise and link exponential dips in residuals with pulse shape changes