Pulsars and neutron stars/Modelling timing residuals

Glitch events

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

${\varphi }_g=\mathrm{\Delta }\varphi +\mathrm{\Delta }{\nu }_p(t-t_g)+\frac{1}{2}\mathrm{\Delta }{\dot{\nu }}_p(t-t_g{)}^2+[1-e^{-(t-t_g)/{\tau }_d}]\mathrm{\Delta }{\nu }_d{\tau }_d$

where $t_g$ is the glitch epoch and $t$ is the current time.