Understanding the gravitational-wave Hellings and Downs curve for pulsar timing arrays in terms of sound and electromagnetic waves

Searches for stochastic gravitational-wave backgrounds using pulsar timing arrays look for correlations in the timing residuals induced by the background across the pulsars in the array. The correlation signature of an isotropic, unpolarized gravitational-wave background predicted by general relativity follows the so-called Hellings and Downs curve, which is a relatively simple function of the angle between a pair of Earth-pulsar baselines. In this paper, we give a pedagogical discussion of the Hellings and Downs curve for pulsar timing arrays, considering simpler analogous scenarios involving sound and electromagnetic waves. We calculate Hellings-and-Downs-type functions for these two scenarios and develop a framework suitable for doing more general correlation calculations.

Detecting massive gravitons using pulsar timing arrays

Massive gravitons are features of some alternatives to general relativity. This has motivated experiments and observations that, so far, have been consistent with the zero mass graviton of general relativity, but further tests will be valuable. A basis for new tests may be the high sensitivity gravitational wave experiments that are now being performed, and the higher sensitivity experiments that are being planned. In these experiments it should be feasible to detect low levels of dispersion due to nonzero graviton mass. One of the most promising techniques for such a detection may be the pulsar timing program that is sensitive to nano-Hertz gravitational waves. Here we present some details of such a detection scheme. The pulsar timing response to a gravitational wave background with the massive graviton is calculated, and the algorithm to detect the massive graviton is presented. We conclude that, with 90% probability, massles gravitons can be distinguished from gravitons heavier than $3times 10^{-22}$ eV (Compton wave length $lambda_{rm g}=4.1 times 10^{12}$ km), if biweekly observation of 60 pulsars are performed for 5 years with pulsar RMS timing accuracy of 100 ns. If 60 pulsars are observed for 10 years with the same accuracy, the detectable graviton mass is reduced to $5times 10^{-23}$ eV ($lambda_{rm g}=2.5 times 10^{13}$ km); for 5-year observations of 100 or 300 pulsars, the sensitivity is respectively $2.5times 10^{-22}$ ($lambda_{rm g}=5.0times 10^{12}$ km) and $10^{-22}$ eV ($lambda_{rm g}=1.2times 10^{13}$ km). Finally, a 10-year observation of 300 pulsars with 100 ns timing accuracy would probe graviton masses down to $3times 10^{-23}$ eV ($lambda_{rm g}=4.1times 10^{13}$ km).