Pulsars and neutron stars/Modelling timing residuals

Glitch events

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

$\phi _{g}=\Delta \phi +\Delta \nu _{p}(t-t_{g})+{\frac {1}{2}}\Delta {\dot {\nu }}_{p}(t-t_{g})^{2}+\left[1-e^{-(t-t_{g})/\tau _{d}}\right]\Delta \nu _{d}\tau _{d}$

where $t_{g}$ is the glitch epoch and $t$ is the current time.