Cluster Before Stack: A New Algorithm for Pulsar Timing

To measure properties of a pulsar accurately, astronomers have to stack many individual observations together to boost the signal above the noise. But what if there was a more clever, more effective way to add observations than simple stacking?

Weak Cosmic Lighthouses

Pulsars, or rapidly spinning neutron stars that emit narrow cones of radio waves, are often referred to as the galaxy’s lighthouses. Just like a sailor looking to shore might see a periodic flash when a lighthouse’s beacon sweeps over their ship, so too would radio telescopes aimed at a pulsar detect a “pulse” when its beam sweeps across Earth. However, although this comparison to lighthouses is a powerful analogy, it starts to break down when considering the speed and strength of these flashes.

While lighthouses may take several seconds to rotate their lens and lamp once around, pulsars do the same in just a few milliseconds. What’s more, while lighthouses are designed to be bright enough that sailors can notice every individual flash, pulsars are comparatively dim. To confidently measure the “pulse profile,” or how a pulsar’s radio intensity changes as a function of its rotation phase, astronomers need to stack those hundreds of thousands of pulses together into one artificial super-bright pulse. Only then can they measure the quantities they care about, like the precise spin period and average pulse arrival time.

This practice rests of the subtle assertion that every individual pulse is just a noisy variation of the same unchanging pulse profile. But is that safe to assume? And can we improve the precision of our measurements by doing something more complex than simple stacking? These are the questions recently tackled by a team of astronomers led by Sofia V. Sosa Fiscella (Rochester Institute of Technology) in research published in The Astrophysical Journal.

Squeezing the Data

The researchers focused on one particularly bright source named PSR J2145−0750 that was observed by the Green Bank Telescope for two hours in 2017. This pulsar is so bright that it’s possible to measure quantities like the pulse width, height, center, and total energy of individual pulses, not just the final stack. The team did just that for each of the more than 200,000 pulses in their dataset and assigned each one a vector of four numbers. When they next sorted the pulses into distinct groups, they found that there were indeed correlations among these variables: for example, pulses with higher maximum heights tended to arrive earlier and be narrower than the overall average.

To take advantage of this structure, they created a stacked pulse profile for each cluster, measured the center in each of them, then averaged all the cluster-specific times together into a final answer. While the standard method of stacking all of the data into one pulse profile resulted in a timing precision of 0.066 microsecond, this new method shrank the uncertainty to 0.057 microsecond, a meaningful improvement.

Though the team cautions that this new method will likely only be relevant for the pulsars for which we can measure individual pulses, they also point out that as better telescopes come online, we’ll be able to do that for more pulsars. In the meantime, astronomers can take comfort in the fact that as our technological abilities improve, so do our abilities to squeeze as much from our data as possible.

Citation

“Improving Pulsar Timing Precision with Single Pulse Fluence Clustering,” Sofia V. Sosa Fiscella et al 2025 ApJ 984 111. doi:10.3847/1538-4357/adc1c2