View source for Pulsars and neutron stars/Modelling timing residuals

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== Introduction ==

== Pulse numbering ==

== Glitch events ==

In tempo/tempo2, glitch events are modelled as an offset in pulse phase, <math>\Delta \phi</math> and the permanent increments in the pulse frequency <math>\Delta \nu_p</math> and first frequency time derivative <math>\Delta \dot{\nu}_p</math>.  In addition it is sometimes necessary to in a transient frequency increment <math>\Delta \nu_d</math> which decays exponentially to zero with a timescale of <math>\tau_d</math>.    The phase model (caused by the glitch) is therefore taken as:

<math>\phi_g = \Delta \phi + \Delta \nu_p(t-t_g) + \frac{1}{2}\Delta\dot{\nu}_p(t-t_g)^2 + \left[ 1 - e^{-(t-t_g)/\tau_d}\right]\Delta\nu_d \tau_d</math>

where <math>t_g</math> is the glitch epoch and <math>t</math> is the current time.

== Frequency-dependent and frequency-independent noise ==

== Spatially correlated timing residuals ==

== Spectral analysis of timing residuals ==

== Interpolation and extrapolation of pulsar timing residuals ==

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