Variations in Millisecond Pulsar Pulse Profiles

Image: Pulsars are known to have different pulse shapes as a function of radio frequency. This variation has been well known for decades and is accounted for in our timing of millisecond pulsars. In this paper, we test how those pulse shapes vary in time (Data from: Dolch et al. 2014).

  • 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 requires extremely sensitive measurements of millisecond-pulsar pulse profiles in order to reach its goal of characterizing the low-frequency gravitational wave universe. We use some of the largest radio telescopes in the world to obtain our measurements.
  • The emission from pulsars on the timescale of a rotation (observed as a "single pulse") varies greatly. However, the average pulse profile is highly stable. This is somewhat like the difference between weather and climate. However, while the average pulse profile for most pulsars is very stable, we require them to be absolutely stable for precision timing, or to be able to account for any variations.
  • Understanding the effects of pulse profile variability is a focus of NANOGrav's Noise Budget 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. In this work, we only examined 38 of the pulsars where the observations had a high enough signal-to-noise ratio to perform the analysis.

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

Quantifying Variability

Image: The method for aligning a model pulse profile (red) with an observed profile (blue) with a simulated deviation. Rather than a simple cross correlation (panel A) with maximizes the overlap of the model with the data, we iteratively normalize the heights of the observed profile and find the best "alignment". Panel D shows that we have successfully aligned the model with the known "true" profile.

  • When we try to determine when a pulse arrives at our telescope, we fit a model template shape to each pulse profile we observe. When there is a deviation in the pulse shape, our estimate of the arrival time will be skewed if not corrected for.
  • The usual method for fitting the template shape to the data profile is to cross correlate one with the other, which finds the maximum overlap between the two. However, we developed a new method to maximize the "alignment" of the model with the data, thus allowing us to identify deviations automatically.
  • We used six different metrics to quantify the variability seen in each pulsar, each of which was sensitive to different types of variability across our observations.
  • Our method was insensitive to true shifts in the pulse emission. That is, if the pulse was actually delayed but its shape was not distorted, since we automatically try to maximize the alignment, we are unable to quantify this effect in this specific analysis. However, other methods are able to capture both effects.

Results on Profile Stability

  • Most of the 38 pulsars analyzed here show no evidence for profile variability, to the level of the sensitivity of our measurements.
  • Four pulsars show some type of variability. In some cases, the variations change randomly between each observations, and in other cases the variations persist over longer timescales covering several observations.
  • Of those four pulsars, we see two broad types of variability. In one case, there is a lot of scatter during the times of the pulsar rotation in which we see the pulsar "on" as compared to the times when the pulsar is "off", but there is no evident structure. In the other case, we see clear structure over time
  • We analyzed these four pulsars in depth, trying to figure out the causes of the different types of variability and shape changes we see.

Image: Observations of the pulsar J1713+0747. On the days highlighted in the red, we suspect there is a calibration problem rather than an astrophysical variation (see next section).

The Causes of Profile Variability

Image: A dynamic spectrum showing pulse intensity (darker = brighter) as a function of time (horizontal axis) and radio frequency (vertical axis). The darker patches show when the pulsar is brighter and is a result of scintillation. (Adapted from: Dolch et al. 2014).

  • Much of the variability we see is caused by scintillation, the same type of effect as stars twinkling in the atmosphere though for radio waves moving through the interstellar medium (see figure). This causes certain frequencies of the pulse to be brighter randomly. Since profiles vary as a function of frequency, the average pulse shape will then be slightly different due to this random weighting.
  • Some variability is due to other interstellar medium propagation effects. Scattering in the interstellar medium causes some parts of the intrinsic pulse to arrive later by a very slight amount, causing a long tail in the arriving pulse emission. Variations in the amount of scattering causes variations in the length of this tail.
  • Uncorrected instrumental effects also cause profile variability. Bad calibration of the data will cause distortions in the pulse shape, as will radio frequency interference or errors in the hardware when the data were taken.
  • For some of the variability seen, we cannot provide definite explanations but have ruled out possible candidates.

Future Directions

  • Future NANOGrav data sets will begin to incorporate this analysis into identifying observations with incorrect calibrations, allowing us to remove known bad data.
  • We can combine our profile variability analyses with our time-of-arrival estimates in a method known as Profile Domain Pulsar Timing (see Lentati et al. 2016).
  • Many propagation effects due to radio waves traveling through the interstellar medium are time variable. Disentangling the effects of the interstellar medium on our data is the prime focus of NANOGrav's Interstellar Medium Mitigation working group.
  • As our pulsar timing array grows, and with more sensitive observations, we will need to look more carefully into quantifying, understanding, and correcting any variability we identify.

Image: 10,000 unique observations of 48 pulsars in the preliminary NANOGrav 12.5-year data set.


  • Members of the NANOGrav Collaboration: P. R. Brook, A. Karastergiou*, M. A. McLaughlin, M. T. Lam, Z. Arzoumanian, S. Chatterjee, J. M. Cordes, K. Crowter, M. E. DeCesar, P. B. Demorest, T. Dolch, J. A. Ellis, R. D. Ferdman, E. C. Ferrara, E. Fonseca, P. A. Gentile, G. Jones, M. L. Jones, T. J. W. Lazio, L. Levin, D. R. Lorimer, R. S. Lynch, C. Ng, D. J. Nice, T. T. Pennucci, S. M. Ransom, P. S. Ray, R. Spiewak, I. H. Stairs, D. R. Stinebring, K. Stovall, J. K. Swiggum, W. W. Zhu
    * Not a member
  • Contact: Dr. Paul R. Brook (corresponding author), Prof. Maura McLaughlin (NANOGrav chair).

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