High-precision Timing of Millisecond Pulsars

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.
  • 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. We also need to understand where our sources of measurement errors come from in implementing a "noise model" along with the timing model. Each Earth-pulsar line of sight is different and therefore we need to model each one independently and in potentially different ways.
  • Building ever-increasingly advanced models for our pulse arrival times is a prime focus of NANOGrav's Timing working group.

The NANOGrav 11-year Data Set

  • 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.

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

Noise Modeling

Image: Timing residuals for the first-discovered millisecond pulsar B1937+21. Our noise modeling takes into account the long-term "wander" of the arrival times, some of which is intrinsic to the pulsar, some caused by propagation through the interstellar medium, and some due to gravitational waves.

  • To determine when a pulse arrives, we fit a template shape to each pulse profile we observe. Since our instruments are inherently noisy, we do not perfectly measure the TOA and there is uncertainty in our arrival-time estimates. Other sources of noise are also introduced, from intrinsic pulse-to-pulse variations ("jitter") to interstellar-medium propagation effects to radio-frequency-interference around the observatories.
  • For each pulsar, we use a maximum likelihood approach to model its noise properties. We included terms to describe unaccounted for "white noise" (uncorrelated in time, some uncorrelated in frequency) as well as "red noise" (long-term correlations). These noise properties can be used to quantify the "timing quality" of each pulsar. Understanding them is crucial for understanding our pulsars as a detector for gravitational waves.
  • We identified red noise in the pulse arrival times of 11 of our pulsars. Gravitational waves will cause red noise in our timing but may have different characteristics than other sources of red noise, including interstellar scattering variations, intrinsic spin noise, or gravitational interactions with other objects around the pulsar.
  • As our data sets become more complex, we are working to develop more sophisticated techniques for both understanding and modeling our noise.


  • Each pulsar traces a path across the sky relative to the Earth. We need to account for the position of the pulsar, proper motion, and parallax, in our timing models so that we avoid pulse arrival-time variations due to these effects.
  • It takes several years before we can see the sinusoidal patterns of the astrometric terms in our data, and therefore we require that we have three years of data on a pulsar before we include it in our data sets. We fit for all of the parameters, including parallax, regardless of its formal statistical significance.
  • We performed an astrometric analysis of the pulsars in our 9-year data set. We reported 12 significant distance measurements, placed both lower and upper limits on many others, and also looked at the distribution of millisecond pulsar velocities through the Galaxy.
  • In the 11-year data set, we reported 20 significant timing parallaxes, with three being the first measurements presented. We found some discrepancies with other pulsar-timing works which are likely due to differences in noise modeling. We also compared our measurements with those done via very long baseline interferometry (VLBI).

Image: Path of our pulsars through the galaxy, as seen across the sky, over the last five million years. (Credit: Matthews et al. 2016).

Binary Systems

Image: The mass/orbital-period correlation due to extended mass transfer. (Credit: Fonseca et al. 2016).

  • The majority of our millisecond pulsars have binary companions. The formation of millisecond pulsars requires material to be pulled from a companion onto the pulsar so that it is "recycled" and spun up to very rapid speeds with incredibly stable rotation, allowing them to be the most well-timed astrophysical objects.
  • Pulsars in binary systems have allowed for extremely stringent tests of gravity, including: providing the Hulse-Taylor system as the first indirect evidence for gravitational waves, searching for deviations from general relativity, and constraining variations in the gravitational constant over time.
  • We performed an analysis of the 25 binary systems in our 9-year data set. We found a wide range of binary pulsar masses and made new measurements of the relativistic "Shapiro delay". We also found long-term secular variations in orbital parameters for many of our pulsars.
  • In the 11-year data set, we analyzed 31 binary systems with a variety of models which describe the binary orbital parameters. Sixteen pulsars show significant Shapiro delays and five show a decay of the period of their orbits over time. As we obtain more data, our understanding of these systems will greatly improve over time.

Future Directions

  • We have begun data reduction on 48 pulsars for the NANOGrav 12.5-year data set. While the timing baseline has only increased by 1.5 years, we have a 50% increase in data over the 11-year data set, with roughly 10,000 unique observations.
  • The 12.5-year data set will include new methods for processing and analyzing our data, along with comparisons to previous works. We are introducing wideband timing, which will fit frequency-dependent effects simultaneously and reduce the number of arrival times by an order of magnitude, as well as use NANOGrav's newly-developed PINT timing package to independently produce timing models.
  • With a preliminary version of the data set, we have identified a second "chromatic timing event" due to a structure in the interstellar medium towards PSR J1713+0747, one of our best timed pulsars. Advanced modeling techniques are being developed to understand this event. In addition, we are working on understanding the radio-frequency-dependence of pulse-to-pulse variations ("jitter") with the data set profiles.
  • The 14-year data set, with observations up through the end of 2018, will include timing on many more new pulsars, each with more than three years of data. This data set will provide increased sky coverage and unparalleled sensitivity to low-frequency gravitational waves.

Image: A comparison of conventional timing, which produces many arrival times per observation, and wideband timing, which produces a single arrival time along with an estimate of frequency-dependent dispersion.


  • Members of the NANOGrav Collaboration: Z. Arzoumanian, A. Brazier, S. Burke-Spolaor, S. Chamberlin, S. Chatterjee, B. Christy, J. M. Cordes, N. J. Cornish, F. Crawford, H. T. Cromartie, K. Crowter, M. E. DeCesar, P. B. Demorest, T. Dolch, J. A. Ellis, R. D. Ferdman, E. C. Ferrara, E. Fonseca, N. Garver-Daniels, P. A. Gentile, D. Halmrast, E. Huerta, F. A. Jenet, C. Jessup, G. Jones, M. L. Jones, D. L. Kaplan, M. T. Lam, T. J. W. Lazio, L. Levin, A. Lommen, D. R. Lorimer, J. Luo, R. S. Lynch, D. Madison, A. M. Matthews, M. A. McLaughlin, S. T. McWilliams, C. Mingarelli, C. Ng, D. J. Nice, T. T. Pennucci, S. M. Ransom, P. S. Ray, X. Siemens, J. Simon, R. Spiewak, I. H. Stairs, D. R. Stinebring, K. Stovall, J. K. Swiggum, S. R. Taylor, M. Vallisneri, R. van Haasteren, S. J. Vigeland, W. W. Zhu
  • Contact: Prof. David. J. Nice (corresponding author), Prof. Maura McLaughlin (NANOGrav chair).

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