A Long Drive to Outer Space? Put Gravitational Waves on the Radio!

Title: Searching for gravitational waves via Doppler tracking by future missions to Uranus and Neptune

Authors: Deniz Soyuer, Lorenz Zwick,  Daniel J. D’Orazio and Prasenjit Saha

First Author’s Institution: Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland

Status: Submitted to MNRAS; Available on Arxiv

You are a planetary scientist who has just sent out a brand new space probe to explore the outer solar system. All you have to do to get exciting data from Uranus and Neptune is, um, wait for a decade for it to get there. Worry not, today’s authors revisit an idea to make this long journey more enjoyable: by turning on the radio and listening to gravitational waves!

Fig 1: It’s cold, dark, and a long way to go. Do we sit idle, or turn on the radio to catch gravitational waves? Image credit: NASA, modified by the author

The Radio

Gravitational waves are tiny ripples in space-time that are generated by the motion of massive, compact bodies like black holes. A passing gravitational wave causes extremely small fluctuations in the distance between two free bodies. The idea of using faraway spacecraft to detect gravitational waves dates back to the launch of the pioneering voyagers themselves, almost 50 years ago. All planetary probes are in constant contact with the Earth via the Deep Space Network (DSN), an array of giant radio antennas across the globe. This radio communication back-and-forth between the DSN and probes in the outer solar system, over 10 A.U. away, can be used as a giant single arm of ground-based interferometers like LIGO and Virgo used to detect gravitational waves. 

While interferometers compare relative displacements along two path lengths, changes in the distance to a single space probe can be tracked by means of doppler shifts. The DSN uses a single radio frequency for communication with the spacecraft, which can shift to a slightly higher or lower value depending on whether the probe experienced a bump towards or away from the Earth. A passing gravitational wave would jitter both the Earth and the spacecraft at different times and show up as a doppler shift in the DSN signal in two corresponding pulses, with an additional pulse being that of Earth’s jitter transponded back from the spacecraft (Figure 2). This reflected pulse comes back after exactly twice the light travel-time between the Earth and the probe, while the timing of the spacecraft jitter pulse in the middle depends on the angle between the gravitational wave propagation and the line-of-sight to the spacecraft.

Fig. 2: The ‘three pulse signal’ expected as a doppler shift in the radio communication with the spacecraft. The three pulses are generated due to a passing gravitational wave shaking, or buffeting (i) The Earth, (ii) the spacecraft and (iii) the signal due to the Earth buffeting, reflected back (from Fig. 1 in this review article).

As one can imagine, it is extraordinarily difficult to see this three pulse signal in practice because (i) the actual displacement due to gravitational waves is extremely tiny, and (ii) the Earth and the spacecraft are not perfectly stable relative to each other. A number of steps need to be taken in order to characterize the background noise and pick out any gravitational-wave doppler shift. To monitor tiny doppler shifts, the radio frequency used for communication needs to be extremely stable. The spacecraft’s trajectory relative to the Earth must be carefully accounted for and subtracted from the signal. Even then, the DSN antennas and the probe itself can face mechanical jitters that cause doppler shifts. 

Increasing the time of observation can improve our chances of detecting gravitational waves. But this also poses an interesting challenge: tracking doppler shifts with the desired level of sensitivity in the radio communications is not possible when the Sun comes in the way, due to plasma scintillation interference with radio waves. In fact, it is only conducive to observe doppler shifts when the probe is on the opposite side of the Sun with respect to the Earth, with the Sun-Earth-Probe angle greater than 150 degrees. This is possible only for a window of around 40 days at a time, and for 10 such windows over the course of a decade-long journey. Imagine going on a 10 hour drive, but only being able to turn on the music for an hour!

The Music

What kind of gravitational waves can one detect using spacecraft communication? Since the baseline or the distance to the probes is several astronomical units, this method of detection is sensitive to gravitational waves with long wavelengths, or low frequencies in the millihertz range. In contrast, LIGO and Virgo search for gravitational waves in the range of a few tens to a thousand hertz, where chirps of binary mergers involving stellar mass black holes and neutron stars can be heard.

Sources that emit low-frequency gravitational-wave rumbles include the merger of Supermassive Black Hole binaries (SMBH), and Extreme Mass Ratio Inspirals (EMRIs), where a stellar mass black hole collapses into a supermassive black hole. This is the same band of frequencies that the future space-based gravitational-wave interferometer, LISA will be sensitive to. Figure 3 shows a comparison of the sensitivity of spacecraft probes and LISA for different kinds of gravitational wave sources. While the dedicated LISA mission will be able to detect these sources quite easily, the possibility of hearing gravitational waves via radio communication with space probes will depend on improvements in tackling the various kinds of noise described above. 

Fig 3: The sensitivity (y-axis) to low-frequency (x-axis) gravitational waves of a space probe of a Cassini-like mission, compared to other gravitational wave detectors like LISA and aLIGO. If the detector curve ‘bucket’ is lower than the signal strength of gravitational waves from different sources (red: supermassive black holes, green & black: EMRIs), it is sensitive to detecting them. The yellow, blue and pink buckets below Cassini represent the increasing sensitivity that follows reducing noise to various degrees represented by sigma, the Allan deviation (From FIgure 3 in the Paper).    

With the leaps in technology made since the Pioneer and Voyager missions, it is worth going back to explore the farthest reaches of our solar system. Several missions are being proposed to study the ice giants, Uranus and Neptune, in the coming decades. While it takes a long time to achieve their science goals after launch, we can still extract gravitational-wave science out of them, almost as a side-hobby with no additional cost! In addition, these space probes will perfectly compliment LISA in detecting low-frequency gravitational waves as they ride along the same tides.

Astrobite edited by: Huei Sears

Featured image credit: SpaceX, adapted from CNBC

About Sumeet Kulkarni

I'm a third-year PhD candidate at the University of Mississippi. My research revolves around various aspects of gravitational wave astrophysics as well as noise characterization of the LIGO detectors. It involves a lot of coding, and I like to keep tapping my fingers on a keyboard even in my spare time, creating tunes instead of bugs. I run a science cafe featuring monthly public talks for the local community here in Oxford, MS, and I also love writing popular science articles. My other interests include reading, cooking, cats and coffee.

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