
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.
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 |
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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 sketch of accreting neutron star, a possible source of gravitational waves. Image: NASA.
Artist's representation of a GRB jets (NASA), and a 3D model of the Lomonosov satellite (MSU).