BitBOINC

💫 Phygas: finding where runaway stars and pulsars were born 💫

Phygas is the newest research project on bitboinc, a sibling of Nostos. It uses the same basic idea, running the clock backwards through the Milky Way, but asks a different question: not which star a visitor from interstellar space came from, but which star cluster a fast-moving star or a neutron star was born in. Here's what it computes, and why each step is there.

🌟 Stars on the run

Most stars are born in groups: clusters of tens to thousands of stars that formed together from the same gas cloud. Over time most clusters slowly dissolve and their stars drift apart at a few km/s. But some stars leave in a hurry, and there are two known ways this happens:

[*]A supernova in a binary. Most massive stars have a companion. When one of the two explodes, the pair can be torn apart: the companion flies off at roughly the speed it was orbiting with, often several tens of km/s, and becomes a runaway star. The exploded star leaves a neutron star behind, which usually gets an extra kick from the explosion itself, often hundreds of km/s. Many neutron stars are seen from Earth as pulsars.
[*]Close encounters. In the crowded core of a young cluster, three or four stars can come so close to each other that one of them is flung out at high speed.

Phygas is Greek for "fugitive". For each of these fugitives it tries to answer three questions: which cluster did it come from, when did it leave, and how fast was it thrown out?

❓ Why it matters

[*]A pulsar's birth cluster tells us where and when its supernova happened, and the speed at which it left is the kick it received. How neutron stars get these kicks is still poorly understood, and every pulsar with a known birthplace is one measurement of it.
[*]If a runaway star and a pulsar left the same cluster at the same time, they are very likely the two halves of a binary broken up by that supernova. Only a handful of such pairs are known, each found one at a time.
[*]For the clusters themselves: how many stars they lose, and how fast, tells us how they formed and how they dissolve.

Until now this has been studied one region or a few dozen stars at a time. Pulsars against open clusters were studied in 2025, but only for the pulsars with independent distance measurements. Nobody has traced every star with a known 3D motion against every young cluster in the Galaxy. That's what Phygas does.

🌌 The ingredients

[*]The stars. The same 33 million Gaia DR3 stars as Nostos: every star with a position, distance, proper motion and radial velocity, i.e. a full 3D position and 3D velocity, together with their measurement errors and the official parallax correction.
[*]The pulsars. All 702 pulsars in the ATNF pulsar catalogue that have a measured proper motion and a distance. 356 of them have a measured parallax. For the rest, the distance comes from the dispersion measure (how much the radio pulse is delayed by free electrons along the way), which is less precise, and that uncertainty goes into the calculation. A pulsar's radial velocity can't be measured at all, so it is drawn from the known spread of neutron-star velocities (Hobbs et al. 2005, about 265 km/s in each direction).
[*]The clusters. 4,087 star clusters and moving groups that can be younger than 100 million years, from the Gaia-based catalogue of Hunt & Reffert (2024), with their positions, motions, ages and sizes. Older clusters are left out: an escape more than 100 million years ago can't be traced back reliably. For the 878 clusters without a measured mean radial velocity, it is drawn around the value Galactic rotation predicts, ±10 km/s.
[*]The Milky Way's gravity. The same Galaxy model as Nostos (Allen & Santillán 1991). Each pair is followed back for as long as the cluster could have existed: the cluster's age (its upper estimate), at most 100 million years.

🔁 What a task does

There are two kinds of task.

Star tasks take 20,000 stars each and compare every one of them with all 4,087 clusters. A full Monte Carlo for 33 million × 4,087 pairs would take thousands of CPU-years, so star tasks use a faster method that gives the same answer as long as the uncertainties stay moderate:

[*]the star and the cluster are traced back along their best-estimate orbits;
[*]six slightly shifted orbits are traced alongside them, which shows how each measurement error grows over time and in which direction (an orbit stretches errors along the direction of motion much more than across it);
[*]so at every moment the code knows not only where the star most likely was, but also the size and shape of its uncertainty cloud;
[*]for every cluster it finds the moment of best match and computes the probability that the star was inside the cluster's core (its half-mass radius), and inside the cluster at all;
[*]pairs with a probability of at least 0.1% are kept; everything else is dropped.

One star against all clusters takes about 0.15 seconds, so a task runs roughly 50 minutes. The whole catalogue is about 1,660 tasks.

Pulsar tasks take one pulsar each. Pulsar distance and velocity uncertainties are far too large for the shortcut, so here it's the full Monte Carlo: 1,000 copies of the pulsar and 1,000 copies of each nearby cluster, each drawn from its own measurement errors, traced back together in steps of 50,000 years, with the closest approach refined between steps. For every cluster the result is the range of closest distances, times and relative speeds, and the fraction of copies that passed through the cluster.

🎲 The catch: chance crossings

A star can pass through a cluster by pure chance. Moving groups near the Sun cover large parts of the sky, and nearby stars cross them all the time. Our first full test task showed how strong this is: when the same 20,000 stars were run again with their velocities shuffled between them, so that no real connection could exist, about 90% as many "candidates" came out. Most raw hits are coincidences.

But not all of them. For slow pairs, with a relative speed under 20 km/s, the real run gave 758 against 454 in the shuffled run: a clear excess. Among the clusters with the largest excess was the beta Tucanae group, a known young moving group. So Phygas never treats a single hit as a birthplace: for every cluster, the real counts are compared with the chance level from shuffled control runs, and only the excess counts.

✅ Proving it works first

Before launch, the pulsar part had to reproduce published results:

[*]The pulsar B1259-63 is known to belong to the cluster UBC 525. Phygas ranks UBC 525 first out of all 4,087 clusters.
[*]For the double pulsar J0737-3039, a 2026 study found the moving group Theia 58 a more likely birthplace than the cluster OC 0450. Phygas puts Theia 58 in its top four, with OC 0450 lower.
[*]The pulsar J0826+2637 was linked to the cluster Stock 7 in 2014, using pre-Gaia distances. With Gaia's distance to Stock 7, Phygas finds that link weak: only 7.5% of the copies pass through the cluster. That's what newer data should do: confirm some older claims and weaken others.

📏 What the numbers mean, and their limits

[*]Distances are in parsecs (1 pc = 3.26 light years); times in millions of years before today; speeds in km/s, measured relative to the cluster, which for a real escape is the ejection speed.
[*]The further back, the less certain. A velocity error of 1 km/s moves a star by about 1 parsec per million years, so for distant stars the uncertainty after tens of millions of years can reach hundreds of parsecs. Such pairs come out with a low probability, as they should.
[*]Only clusters that still exist and are in the catalogue can be found. If a star's birth cluster has already dissolved, there's no match, and that is a valid answer.
[*]Pulsars without a parallax have less certain distances, so their results are broader.

🎯 What comes out of it

[*]an all-sky catalogue: for every young cluster, the stars and neutron stars that may have left it, with when and how fast;
[*]for every pulsar, its most likely birth clusters, the time of its supernova and the speed of its kick;
[*]a search for runaway stars and pulsars that left the same cluster at the same time;
[*]all results, raw data included, published openly.

Pulsar tasks go out first, then the stars. Progress and the best candidates so far are on the Phygas page. Questions are welcome below.

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Phygas is a very nice addition

Will there be more tasks? Or was that everything already?

We have processed almost all the data; more new data needs to be released for future tasks, so we will wait for the telescopes to do their work.

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