Extrasolar Trojans, or exotrojans which are asteroids that share the same orbit as an exoplanet (a planet outside of our solar system), are still enigmatic to astronomers. Named for the famed heroes of the Trojan War, our solar system’s Trojans are essentially cosmic fossils from the formation of our solar system. We don’t know much about their extrasolar counterparts, but now a West Virginia University (WVU) graduate student is pioneering our understanding of these leftover space rocks that may one day give us a better understanding of how our solar system was created.
Let’s begin by going back over four billion years when our newly formed solar system consisted of trillions of tiny little rocky and icy objects. Many of these objects came together to form the planets. Most of the other objects were scattered into the distant reaches of our solar system and beyond.
Turning our attention to the monster planet Jupiter, its Trojans have been gravitationally trapped in Jupiter’s orbit around the Sun for billions of years. These leftover space rocks are mostly pristine asteroids that orbit with Jupiter in two huge swarms leading and trailing the planet. There are so many of them that they’re usually just referred to as THE Trojans. They’re quite mysterious and we think that they come from the outer solar system. They’re also special in terms of understanding the evolution of the solar system because they’ve remained gravitationally stable for over four billion years, despite Jupiter’s orbital migrations.
"To understand their stability, imagine a ball at the bottom of a valley. If you push it up the valley, it will want to come back down. Trojans do a similar thing in their shared dance around the sun with their host planet,” Taylor explains.
The abundance of Trojans in our Solar System suggests that extrasolar Trojans, or exotrojans should also be common. While almost every exotrojan search has been done around main-sequence stars, like our Sun for example, no study has looked for them around pulsar binary systems.
Until now.
A breakthrough study was recently published in the Astrophysical Journal and with WVU Dept. of Physics and Astronomy and Center for Gravitational Waves and Cosmology graduate student, Jackson Taylor, leading the first of its kind search for exotrojans in a new location.
Taylor’s study presents the first search for pulsar-bound exotrojans and places the first observational constraints on their masses in pulsar binary systems.
"A pulsar is a type of neutron star, an incredibly compact star that is the zombified remnant of a previously ordinary massive main-sequence star. What separates pulsars from other stars is that they emit extremely regular bursts of electromagnetic radiation known as pulses. In fact, the times of arrival of these pulses are so predictable that only atomic clocks are more precise timekeepers, earning pulsars the moniker 'cosmic clocks.' Astronomers use these clock-like beams to better understand our Universe,” Taylor explains.
Using accurately measured pulse times of arrival, Taylor et al. created new techniques to place upper mass constraints on potential exotrojans around eight pulsars observed in the NANOGrav 15-year data set. Of the eight pulsars used in this study, four were observed using data from the former Arecibo Observatory in Puerto Rico and four were observed using data from the Green Bank Telescope here in West Virginia. These results offer initial observational constraints, or parameters of data, on the existence of exotrojans around pulsars, specifically pulsar binary systems where the pulsar has a smaller companion.
“The long and great history of astronomy teaches us that discovery comes from looking where no one has looked before, and I see no reason to stop now.” Jackson Taylor
“We took pulsar times of arrival from known binary pulsar systems. We then adapted existing models for how exotrojans affect ordinary exoplanets to explain how a Trojan in a pulsar binary system would mark its presence in the pulse times of arrival.”
No one has performed this type of search before. Taylor led the discovery using his adapted model to perform the search. He created this model in the pulsar timing context to detect the back and forth motions of the pulsar’s companion and possible Trojan, much like how a ball would oscillate back and forth at the bottom of a valley.
In pulsar binary systems, the train of pulses will show some pulses arriving sooner than expected with others arriving later. This is due to the fact that the pulsar is orbiting the system’s “center of mass,” meaning the pulsar’s distance to the Earth will change throughout the orbit. In other words, the light travel time of the pulses to our telescopes change according to the binary orbital period. If we add a Trojan to the system, then things get even more complex. The Trojan will oscillate, like a ball at the bottom of a valley, along the orbit with a frequency called the "libration frequency.” The result is that the pulsar will speed up or slow down during its journey around the center of mass, with the rate of speed ups/slow downs matching the same libration frequency. Taylor expanded upon earlier studies to develop a model for how an oscillating Trojan shows up in the pulses times of arrival, adding to the astronomers' toolbox of knowledge when analyzing pulsars.
The publication details Taylor’s foundational model that would allow researchers to detect exotrojans in a pulsar binary system where the exotrojan shares the same orbit as a pulsar. “No one has seriously looked for pulsar Trojans until now. Even though we only place upper mass constraints, we now have the times of arrival model that can be used on pulsars not analyzed in this study,” Taylor notes. Specifically, the pulsar may have low mass and a co-orbital Trojan that shares the space within the system.
Taylor applied his model to the NANOGrav 15 year narrowband data set, looking closely at the pulsars whose companions have a low enough mass for the system to stably host Trojans. He applied the model to NANOGrav’s 70 pulsars, then pared it down to eight pulsar binary systems which satisfied the mass criteria that the pulsar must be at least 25 times more massive than its companion. “We were able to place constraints and say that if co-orbitals did exist in these systems, they can likely be no more massive than the Earth.”
Taylor further explains the connection between pulsars and exotrojans.
“There are now only about 12 exoplanets around pulsars that we know of today, depending on what you call an exoplanet. Contrast this with the over 3,000 known pulsars. Therefore, pulsar exoplanets are quite rare. This being said, because the number of pulsar exoplanets is more than zero, the pulsar environment has to occasionally be conducive to mass accumulation in the form of planets. Therefore, we suspect that the formation of pulsar Trojans may be possible, and so we perform the first rigorous search for them here in the Astrophysical Journal.”
Professor Emmanuel Fonseca, Taylor’s research advisor, substantiates the project’s results, explaining “Like Jackson stated, pulsars are known to represent extreme environments and it's hard to truly determine whether a planetary-mass object is truly an 'exoplanet' or the remnant of a companion star that's basically been shredded of its mass by the radiation from the nearby pulsar. However, we know that several planetary-mass objects indeed exist around pulsars; and Jackson's model provides an exciting way to constrain the presence of the analogs of other objects known to reside in our own Solar System."
Taylor further states, “Our study shows that pulsar Trojans are either rare, or extremely low-mass. Pulsar environments may be even more inhospitable than previously thought.”
As if that weren’t enough of a result, Taylor uncovered the twist of two false positives.
The data presented two strange potential detections, but under closer inspection, Taylor ran further calculations and concluded that they are not real; in other words, not caused by Trojans. The two false positives happen to both be from black widow pulsars. Black widow pulsars continuously collect matter from their companion. Its material gets stripped off due to its proximity to the pulsar, and eventually the pulsar consumes the smaller companion.
Taylor was the first to detect this strange, new noise. And while the inconclusive noise is new and mysterious in and of itself, it presents a new, curious question for astronomers to explore.
Future studies will benefit from his method with improved sensitivity that comes from additional data added from observations. “Maybe Trojans already exist in the dataset, but we need an extra boost to surge above the noise,” Taylor states. He continues his optimism for future work, “This study affirms and expands upon the state-of-the-art of detecting new pulsar time of arrival models. We look forward to casting our work onto the upcoming pulsar timing array datasets.”
“The long and great history of astronomy teaches us that discovery comes from looking where no one has looked before, and I see no reason to stop now.”
Jackson Taylor is a PhD student in the West Virginia University Department of Physics and Astronomy and the Center for Gravitational Waves and Cosmology. His research orbits around using pulsars as accelerometers to study not only pulsar systems, but also our solar system.
His research advisor is Prof. Emmanuel Fonseca.
Funding Acknowledgement:
eNASA West Virginia Space Grant Consortium Grant # 80NSSC25M7079,
This work has been carried out as part of the NANOGrav Collaboration, which receives support from the National Science Foundation (NSF) Physics Frontiers Center, award numbers 1430284 and 2020265.
hal/02/23/2026