Greek mythology has given a name to a great many objects in our solar system. But perhaps one of the least well understood are the Trojans, named after the people of Troy featured in The Iliad. When astronomers refer to them, they are normally talking about a group of over 10,000 confirmed asteroids orbiting at the Lagrange points both in front of and behind Jupiter on its orbit around the Sun. But, more generally, astronomers can now use the term to refer to any co-orbital setup - indeed almost every planet in our solar system has Trojans, though not as many as Jupiter. Which also leads to the belief that “exotrojans” must exist around other stars. Despite our best efforts with initiatives like the TROY project, so far we have yet to find one. But a new paper published in The Astrophysical Journal by Jackson Taylor of West Virginia University and an abundance of co-authors took the hunt to one of the most extreme environments in the universe: pulsar binary systems.
A rough understanding of orbital mechanics is key to understanding where Trojans come from. Between any two bodies floating in space there is a gravitational tug of war where the gravities from each object pull on the other one. When those two bodies are massive, like a star and a planet, this creates distinct pockets of gravitational equilibrium, typically formed by an equilateral triangle with the two main bodies, leading and trailing the smaller one by 60 degrees on its orbital path. These are known as two of the Lagrange Points - specifically L4 and L5 - of the system. If a third object, like an asteroid or even a smaller planet, wanders into one of these spots, it can become trapped and orbit in tandem with the larger planet indefinitely.
Astronomers have been hunting for these objects around ordinary, main-sequence stars for a while now. But Taylor’s team turned their attention to “black widow” pulsars instead. These violent binary systems are made up of a rapidly spinning millisecond pulsar and a much smaller companion star, which is often around 1% of the mass of the Sun. The intense radiation from the pulsar slowly strips material away from its companion, effectively destroying it over time - hence the nickname “black widow”.
NASA depiction of a black widow pulsar eating its companion. Credit - NASA Goddard YouTube ChannelThis might seem like less than an ideal place to look for co-orbiting planets. However, the low mass companion actually means that the math for finding stable orbits in this system is actually more likely than that around more ordinary binary star systems.
Even so, it’s not like astronomers can directly see a Trojan exoplanet, especially not with a black widow pulsar flailing nearby. Traditional methods of exoplanet detection fail in these systems. Exoplanet detection usually watches for small gravitational pulls of a planet on its host star, but in these binary systems, that gravitational pull would be from the companion star, not from any Trojan planet, which would be even smaller.
To make up for this difficulty, Taylor and his team tried two different detection techniques. For one, which they applied to a binary system called PSR J1641+8049, they compared optical light curves with radio data. They knew that optical light peaks when the heated side of a companion star faces Earth, whereas radio pulses track the orbital center of mass of the entire system (which could be three or more bodies). If there was a mismatch between the two measurements, it would point to a third body (i.e. a Trojan) messing with the radio pulse timing.
NASA video explaining useful facts about the Trojan asteroids. Credit - NASA YouTube ChannelTheir second method, which they used on eight different black widow binary systems, uses the NANOGrav 15-year dataset, which tracks a feature known as radio pulse times of arrival (TOAs). If a system contains a Trojan, it will “librate” (or wobble) around its stable point, which causes the system’s center of mass to oscillate at the same frequency. This change is detectable by slight differences in when radio signals arrive at Earth - hence their “time of arrival” - indicating that a third object creating instability causes adjustments in radio pulse timing.
Despite using two different techniques on a total of nine different systems, the researchers were unable to definitively say that they had detected any Trojans. Two systems from the NANOGrav dataset appeared to have what the authors believe to be false positive signals, most likely caused by either random noise from the host pulsar, or by transit tracking limitations of Arecibo, one of the observatories used to collect the data. Other than that, they could definitively say that there were no objects, not even the mass of Earth, around the remaining seven binary pulsar systems, with the exception of the system tested with the optical to radio comparison, which could only limit a Trojan to the size of at most 8 Jupiters.
Given the ubiquity of these objects in our own solar system, it would seem premature to rule them out in other ones entirely. Admittedly, something the size of Earth would require a pretty gravitationally stable system to capture it, so there might even be some smaller objects in the systems they already looked at. Astronomers will have plenty more opportunities to analyze further datasets, like the upcoming NANOGrav 20-year release, to hunt for these elusive cosmic stowaways.
Learn More:
WVU - Trailblazing the Search for Pulsar-Bound Exotrojans
J.D. Taylor et al. - Searching for Exotrojans in Pulsar Systems
UT - Is This The First Exoplanet Trojan, or the Result of an Epic Collision Between Worlds?
UT - A new way to Discover Planets? Astronomers Detect an Exoplanet by Seeing its Trojan Belts