Welcome to the 10th International LISA Symposium

Pulsar timing arrays, such as the North American Nanohertz Observatory for Gravitational Waves, are probing the gravitational wave universe at nanohertz frequencies, where we expect to detect and study binary supermassive black holes. This technique utilizes radio telescope observations of dozens of ultra-high precision millisecond pulsars, creating a galactic scale gravitational wave detector. Timing arrays provide complementary frequency coverage to laser interferometers operating at higher frequencies, and CMB polarization experiments sensitive to waves with even lower frequencies. In this talk, I will introduce the key methods used by timing arrays to search for a stochastic background and bright individual sources. I will also touch upon some of the challenges to detecting gravitational waves using pulsars and how these are being overcome by the NANOGrav and International Pulsar Timing Array collaborations.

To successfully detect gravitational waves with pulsar timing arrays, we need to have a comprehensive understanding of the source and characteristic of the noise in the pulse arrival times, and identify mitigation methods to reduce the noise. In this talk, we will review the noise budget for the pulsar timing array and show various methods and experiments used to quantify, characterize and reduce the timing residuals. We will discuss how we merge complementary results as an overall assessment of the components and physical causes of the timing residuals for each millisecond pulsar in the array.

The interstellar medium has both dispersive and scattering effects on the radio emission from a pulsar. These effects introduce time variable delays of the pulses on their way to Earth, and cause significant errors in the timing analysis of a pulsar, if not properly corrected for. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) uses an array of millisecond pulsars in an effort to directly detect gravitational waves. For this purpose, high precision timing of the pulsars is essential and ultimately a precision of the order of ~100 ns is required. This talk will review the effects of the interstellar medium on pulse arrival times and present some of the techniques used to mitigate the associated time delays from the pulsar signal. Correcting for these delays is essential to providing a higher timing precision and hence to increasing the array’s sensitivity to gravitational waves.

The sensitivity curve of a canonical pulsar timing array is calculated for two types of source: a monochromatic wave and a stochastic background. These calculations are performed in both a Bayesian and frequentist framework, using both analytical and numerical methods. These calculations are used to illustrate the often overlooked fact that sensitivity curves depend not only on the properties of the pulse time-of-arrival data set but also on the properties of the source being observed.