Image: Each individual observation in the 11-year data set. The colors represent different radio frequencies.

• Precision timing of millisecond pulsars over years and decades allows us to build models of radio-pulse arrival times of incredible accuracy. These models account for the pulsar's spin period, its evolution, the dispersion of radio pulses in the interstellar medium, and many other effects. Developing precision timing models for many pulsars allows their use as tools to test fundamental physics.
• NANOGrav's goal is the detection and characterization of the low-frequency gravitational wave universe. To achieve this, we must be able to accurately time pulses to a precision of 10s to 100s of nanoseconds as they travel across the Galaxy, for a large number of the most precise pulsars.
• Besides accounting for the intrinsic spin properties of the pulsar and dispersion, we need to determine where the Earth is in the Solar System, the pulsar's relative motion to the Solar System, the pulsar's motion if it is in an orbit with a binary companion, etc. Typically we observe pulsars once per month and are able to build our timing models from measurements of the arrival times of the different pulsars. For several pulsars, we observe about once per week.
• Building ever-increasingly advanced models for our pulse arrival times is a prime focus of NANOGrav's Timing working group.

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• NANOGrav's latest data release contains radio-pulse times of arrival (TOAs) and timing-models for 45 millisecond pulsars.
• The observations span roughly 11.4 years, from July 30, 2005, to December 31, 2015. We cover radio frequencies from 300 MHz to 2.5 GHz. The pulsar with the largest data volume is J1713+0747, with 28,000 TOAs.
• Observations were carried out using the 100-m Robert C. Byrd Green Bank Telescope (GBT) of the Green Bank Observatory, and the 305-m William E. Gordon Telescope (Arecibo) of Arecibo Observatory.
• In the sky map shown here, pulsar positions are marked by circles, with areas proportional to the number of TOAs in the dataset; the color scale indicates the timing baseline. The 34 pulsars with baselines greater than 3 years have solid red edges. We use only these 34 in our searches for a GW background.

• Read 11-yr data paper
• Download data

Image: Sky map of NANOGrav pulsars in the 11-yr data set. (Credit: Arzoumanian et al. 2018b)

Image: three types of signals we are trying to observe in our pulsar residuals: an unknown wander in the timing of our pulsars from an ensemble of supermassive black hole binaries, a merging single binary with a known pattern, and a merger event with a known pattern.

• NANOGrav's current observing strategy is driven by two science targets: the gravitational wave background and single sources. Sensitivity to the gravitational wave background is most easily obtained by observing lots of pulsars, driving NANOGrav's pulsar search and timing efforts to find and time many millisecond pulsars. For single sources, we want to observe a few pulsars with very high timing precision so that we can identify specific signals (such as a sinusoid) in our data. NANOGrav currently observes all of its pulsars for one hour per month per telescope so that we can detect and characterize the background, and for several other pulsars we observe weekly in "high cadence" campaigns so we can gain increased pulsar sensitivity, and thus sensitivity to single sources of gravitational waves
• Beyond choosing which sources are in the high cadence campaigns, NANOGrav typically does not spend more or less time on different pulsars to improve its sensitivity.
• We described the sensitivity to gravitational waves with a metric that acts like a "signal-to-noise ratio", that is, how much of the signal we want to see is greater than the uncertainty in our measurements. So far, our gravitational wave signal has been very weak, and so this ratio is much less than 1. The higher the signal-to-noise ratio is, the more confident we are in having detected a source.
• We expect our answer to depend on where pulsars lie in the sky, how "good" the pulsars are, what telescopes we are using to observe, and what types of sources we want to observe.

• Our code will shortly be open-sourced and freely available on GitHub.
• Using the positions and observing times, along with the white noise (timing precision) and red noise (timing accuracy) parameters describing the pulsars in our 11-year data set, our code will optimize how much telescope time should be given to each pulsar, again depending on the type of source to observe. We have not used any new pulsars in our optimization, and so this work will have to be repeated in the future.
• For the stochastic background, our findings agree with the notion that we want to observe as many pulsars as possible and time them roughly evenly such that the "quality" of each pulsar is the same, that is, we should time worse pulsars slightly more than better pulsars. These results depend on the positions of the pulsars and other factors. We also find that our results are robust to the presence of red noise (errors in timing accuracy) in our pulsars.
• For continuous wave sources, we find that of order 10 pulsars should be observed. However, which pulsars should be observed depends on the position of the gravitational wave source you want to study. We know of positions of possible candidates but do not know where binaries exist a priori, which is why we want to use gravitational waves to detect them in the first place.

Image: Sky map of NANOGrav pulsars in the 11-yr data set, showing pulsars in relation to possible individual detectable supermassive black hole binaries.

Image: radio telescopes of the International Pulsar Timing Array (IPTA).

• NANOGrav works in collaboration with other groups as part of the International Pulsar Timing Array (IPTA) to study as many pulsars as possible with the highest timing precisions.
• With many radio telescopes, with different sensitivities, it may be preferential for certain telescopes to observe specific pulsars rather than for multiple telescopes to spend their time observing the same sources. The IPTA needs to decide how to weight the importance of different science goals in order to determine how to allocate the time of its different radio telescopes. This work will need to be redone as new facilities come online.
• The development and deployment of wideband receivers at our current facilities can improve our arrival-time precision. While radiometer noise will typically increase with these systems compared to current receivers, the gain in overall integration time by not needing to switch frequency bands will improve our timing sensitivity by roughly √2. Current observing strategies can also implement tuning of center frequencies for immediate precision gains.
• NANOGrav is currently observing 76 pulsars rather than the 45 studied here. This work will need to be redone with all of the pulsars observed by NANOGrav, and the IPTA, and as we understand the timing properties of our pulsars better, we can make more informed decisions on how to optimize our pulsar timing array.

• Members of the NANOGrav Collaboration: M. T. Lam
• Contact: Dr. Michael T. Lam (corresponding author), Dr. Scott Ransom (NANOGrav chair).

The NANOGrav Collaboration at the 2017 Fall meeting in Lafayette College, PA