Can you hear the (ultralow-frequency gravitational wave) music?

Title: Using Pulsar Parameter Drifts to Detect Sub-Nanohertz Gravitational Waves

Authors: William DeRocco, Jeff A. Dror

First Author’s Institution: Department of Physics, University of California Santa Cruz

Status: Published in Physical Review Letters [closed access]

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Various pulsar timing arrays (PTAs) observed evidence for a nanohertz-frequency gravitational background last year, opening a new window in gravitational wave astronomy. The “background” seen by the PTAs originates from a collection of gravitational wave signals from various sources in the universe. This signal is in the nanohertz frequency range, and supermassive black hole binaries (SMBHB) are considered as primary candidates for the sources of the gravitational wave background (GWB). Inspiraling SMBHBs across the universe emit gravitational waves and they overlap with each other creating the background “hum”.

Although we may have detected a gravitational wave background from SMBHBs, we have yet to observe gravitational waves from isolated SMBHBs. These are known as continuous gravitational waves and are challenging to distinguish from the background noise. These sources emit nanohertz (10^-9 Hz) frequency gravitational waves during the late stages of the inspiral of the SMBHB (see Figure 1), when they are very close to each other (about hundreds of astronomical units, or AU). Gravitational waves from the early stage of binary inspiral emit at ultra-low frequencies, in the picohertz (10^-12 Hz) range, which cannot be detected using the traditional methods employed by PTAs.

PTAs use pulsars, which are rapidly rotating neutron stars with very regular periods. This causes them to act like cosmic lighthouses, emitting radiation once every rotation. When the gravitational wave background passes through a pulsar, it can cause deviations in the arrival time of the pulses from the pulsar. By computing the difference between the observed pulse arrival time and the expected time of arrival (called timing residuals), we can infer information about the stretching and squeezing of space caused by the passing gravitational wave. The timing residuals of pulsars in different parts of the sky are all correlated. Strong evidence for this correlation was observed in the 15-year data set published by NANOGrav, suggesting a detection of nanohertz-frequency gravitational waves.

In today’s paper, the authors use observed data from pulsars to uncover these ultra-low frequency hums. Although they do not find significant evidence for any gravitational waves (GWs), they compute a limit to the maximum possible observable gravitational wave signal strain (which measures how the GWs stretch and squeeze spacetime) in the picohertz range.

How is the SMBH How does Pulsar-Timing work? How is this method different?

Detecting gravitational waves with frequencies less than a nanohertz is challenging for PTAs, as they are not very sensitive to signals in this frequency range. Instead, the authors suggest examining individual pulsar data and extracting “drifts” in various observed pulsar parameters caused by gravitational waves. They investigate the effect of GWs on i) the second derivative of the pulsar’s rotational time period with respect to time and ii) the rate of orbital decay in the case of pulsars in binary systems. Both of these parameters are expected to be affected by gravitational waves. For example, a passing gravitational wave can cause a relative acceleration of the pulsar, which will affect the orbital decay rate. Similarly, the second derivative of the pulsar time period contains a contribution from the jerk induced by passing GWs.

Once the properties of the pulsars in the binary are known, the orbital decay rate can be predicted. This prediction helps to isolate the contribution of GW-induced acceleration from the observed orbital decay. A similar method can be applied to the second derivative of the pulsar’s period, capturing the effects of jerks caused by passing gravitational waves. After isolating the acceleration and jerk contribution in the pulsar data, the authors check if the computed values can be explained by the presence of a continuous gravitational wave signal. While no direct evidence of a signal is observed, they compute limits on the GW strain that can be observed in the picohertz range using this analysis (see figure 2).

The authors note that the dataset used is six to seven years old, and they believe the GW strain limits calculated can be further improved with updated analysis. This work has expanded the low-frequency gravitational wave window, greatly aiding in the search for continuous gravitational waves. If the GWB is coming from binary SMBHs, then a corresponding signal should be observed in the sub-nanohertz frequency range. It will be interesting to search for these ultra-low frequency GWs in parallel to the nanohertz GWs searches by PTAs.

Astrobite edited by Lindsay Gordon

Featured image credit: Pranav Satheesh

• About the Author

About Pranav Satheesh

I am a second year graduate student in physics at the University of Florida. My research focuses on studying supermassive binary and triple black hole dynamics using cosmological simulations. In my free time, I love drawing, watching movies, cooking, and playing board games with my friends.

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