Artist's sketch of accreting neutron star, a possible source of gravitational waves. Image: NASA.
Millisecond pulsars are old neutron stars that has been spun up to a rotation period on the order of a millisecond. It is assumed that the spin-up mechanism can be an accretion of matter. Another fact is that millisecond pulsars are not spinning down very much, comparing to other pulsars, according to p-pdot diagram. Timing of radio-pulsars from these neutron stars is very precice. Pulsar Timing Arrays are setups of radio-observatories recording residuals from timing models of millisecond pulars. Cross-correlated timing residuals may indicate a presense of a stochastic gravitaitonal-wave background in the nHz band, and should include the gravitational-wave background from merging galaxies in the observable Universe.
This is short note about noise properties of PTA, and it will probably expand in the future.
Useful dimensional relations and acronyms
- PSD - strain or noise power spectral density. Units:
- PTA - pulsar timing arrays
- ToA - pulse times of arrival
- DM - dispersion measure
Model for signals and noise
Likelihood function L(τ | θ) is a probability distribution of measured values (i.e. timing residuals τ) when noise and signals are present in the data. Their effect on a likelihood is described by parameters θ. In pulsar timing Likelihood is modelled as a multi-dimensional Gaussian distribution, where dimensions are related to residuals in each ToA measurement.
There are two kinds of signals: deterministic and stochastic. Deterministic signals affect the mean of L(τ|θ), while stochastic signals affect the standard deviation of our Gaussian distribution L(τ|θ).
|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 signal||Stochastic gravitational-wave background from supermassive binary black holes :) - stochastic signal|
|DM variations - they influence ToA due to interaction of radio-waves with electrons from interstellar medium. Noise PSD depends on radio-frequency, and can have a time-varying semi-periodic component (DM1 and DM2). In principle, can be subtracted. - stochastic signal||Solar system ephemeris errors - errors in knowing positions and masses of celestial bodies in our Solar system - deterministic signal|
|Jumps, or phase jumps - errors arising from switching observing backends. This noise can be subtracted.||Clock errors|
Artist's representation of a GRB jets (NASA), and a 3D model of the Lomonosov satellite (MSU).