Pulsar Timing Concepts to get across –Searching is only the beginning –By timing pulsars we extract most of the science –The principles involve some simple physics

Timing pulsars

The timing model Recall: Taylor series f(x) = f(a) + f’(a) (x-a)/1! + f”(a)(x-a) 2 /2! + …! In pulsar timing, we expand pulse phase w.r.t time For binary pulsars, we also need to add the delay as the pulsar moves around the orbit..

The timing model Maximum delay is when pulsar is farthest away. Maximum advance is when the pulsar is closest.

Timing model residuals

Timing binary pulsars We can measure five so-called Keplerian parameters: Orbital period, Semi-major axis, eccentricity, Epoch of periastron, Epoch of ascending node

Weighing binaries with Kepler’s law and the “mass function” One equation - but three unknowns! –Can place a lower limit on the companion mass –Gives us some idea of what the companion is.. –A starting point for further analyses Definition comes from Newtonian gravity…

Weighing binaries with Einstein Using general relativity there are a number of additional (post-Keplerian) parameters –Rate of advance of periastron –Rate of decay of the orbital period –Time dilation and gravitational redshift of pulsar –Delay of pulsed signal in gravitational well All of these parameters depend on the masses of the pulsar and its companion. (see eqs of Living Review) These are the topics of tomorrow night’s lecture…

Mass-Mass diagram

Pulsars as clocks

Summary Concepts to get across –Pulsars are remarkably stable clocks –We observe each pulsar regularly for > 1 yr –A wealth of parameters can be measured Motivation for doing this –Pulsar timing probes fundamental physics –Each one helps models of population –We might someday set our watches by pulsars –Gravitational waves (tonight’s lecture) –General relativity (tomorrow’s lecture)