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Radial redistribution of stellar orbits in FIRE simulations of Milky-Way-mass galaxies

Using FIRE-2 cosmological simulations of 11 Milky-Way-mass galaxies, this study quantifies stellar radial migration by revealing that while younger stars generally migrate inward and older stars outward, the scatter in orbital redistribution saturates at approximately 2 kpc for stars older than 3 Gyr, contradicting expectations of monotonic growth and aligning with recent observational inferences.

Original authors: Matthew A. Bellardini, Fiona McCluskey, Andrew Wetzel, Cecilia Steel, Sarah R. Loebman, Jorge Moreno

Published 2026-05-11

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CC BY 4.0

Original authors: Matthew A. Bellardini, Fiona McCluskey, Andrew Wetzel, Cecilia Steel, Sarah R. Loebman, Jorge Moreno

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a galaxy not as a static, frozen picture, but as a bustling, chaotic city where the residents (stars) are constantly moving around. For a long time, astronomers thought that once a star was "born" in a specific neighborhood, it mostly stayed there, perhaps wandering a little bit but generally keeping its address. This paper challenges that idea by asking: How much do stars actually move from their birthplaces to where we see them today?

The authors used powerful computer simulations of 11 galaxies (similar in size to our own Milky Way) to track the journeys of stars from the moment they were born until the present day. Here is what they found, explained simply:

1. The "Address" Problem

In a city, your address is usually your physical location. But in a galaxy, stars orbit in circles (or ellipses) around the center. A star might be at its closest point to the center one moment and its farthest point the next.

The researchers realized that how you define a star's "address" matters. They tested five different ways to measure a star's orbital radius (its distance from the center):

Instantaneous: Where is it right this second?
Average: Where does it spend most of its time?
Guiding Center: If the star were on a perfect circle, where would that circle be?

The Takeaway: It turns out that as long as you use the same definition of "address" to pick the stars and to measure their movement, you get consistent results. However, if you mix and match definitions, the numbers get messy.

2. The Great Migration: Who Moves Where?

The study looked at two types of movement:

The Net Shift: Did the star move generally inward or outward?
The Scatter: How much did the star wander back and forth (like a drunk walk)?

The Surprising Patterns:

Young Stars (The Newcomers): Stars born recently (in the last few billion years) tend to move inward slightly. They were born on nice, neat circular tracks, but as they interact with gas clouds and other stars, they get nudged closer to the center.
Old Stars (The Veterans): Stars born a long time ago (more than 4–5 billion years) tend to move outward. Why? Because the galaxy was much smaller and more compact when they were born. To end up in the outer neighborhoods today, they had to migrate outward significantly.
The "Spin" Factor: As stars move outward, they also tend to gain speed in their orbit (angular momentum). It's like a figure skater extending their arms to spin faster, but in reverse: as they move out, the galaxy's rotation speeds them up.

3. The "Saturation" Surprise (The Most Important Finding)

For decades, astronomers thought that the longer a star lived, the more it would wander. They imagined a "diffusion" process, like a drop of ink spreading in water: the longer you wait, the wider the spread gets.

The Paper's Discovery: This is not true for galaxies.

The First 3 Billion Years: Stars do wander more as they get older. The "scatter" (how much they move back and forth) increases.
After 3–4 Billion Years: The wandering stops increasing. It hits a "ceiling" or a saturation point. Even for stars that are 10 or 12 billion years old, they haven't wandered any further than stars that are 4 billion years old. The scatter stays flat at about 2 kiloparsecs (roughly 6,500 light-years).

The Analogy: Imagine a child running around a playground. At first, as they get older, they run further and further from the swings. But eventually, they hit the fence. No matter how much older they get, they can't run past the fence. The "fence" in a galaxy is set by the galaxy's structure; once stars have explored their maximum range, they don't keep wandering forever.

4. Why This Matters for Our Galaxy (The Milky Way)

The Milky Way is full of stars with different ages and chemical compositions. Astronomers use these clues to figure out the galaxy's history. If stars move around a lot, it scrambles the history book.

The Good News: The amount of wandering found in these simulations matches what we observe in the Milky Way. This gives us confidence that our models of galaxy evolution are on the right track.
The Bad News (for simple models): You can't just assume that an old star has wandered twice as far as a young star. Because the wandering "saturates," old stars might have stayed relatively close to their birth neighborhoods, just like middle-aged stars. This changes how we reconstruct the Milky Way's past.

5. What Drives the Movement?

The paper looked at what causes these stars to move.

Galaxy Size: Bigger galaxies seem to have stars that wander more.
Disk Formation Time: Interestingly, when the galaxy's thin disk formed didn't seem to change how much stars wandered (the scatter). However, it did affect the net direction. Galaxies that formed their disks later tended to push their stars outward more than galaxies that formed early.

Summary in a Nutshell

Stars in galaxies are not static; they migrate.

Young stars tend to drift slightly inward.
Old stars tend to drift outward because the galaxy was smaller when they were born.
The wandering stops growing after a few billion years. Stars don't keep drifting forever; they hit a limit.
This behavior matches what we see in our own Milky Way, helping us understand that the "history book" of our galaxy is scrambled, but not as chaotically as some older theories suggested.

The paper essentially tells us that the cosmic dance of stars has a rhythm and a limit, rather than being a random, endless drift.

Technical Summary: Radial Redistribution of Stellar Orbits in FIRE Simulations of Milky-Way-Mass Galaxies

Problem Statement
A central challenge in galactic archeology is determining the extent to which stellar orbits redistribute (migrate) after birth. Stars currently observed at a specific galactocentric radius ( $R$ ) may have formed at significantly different locations, scrambling the record of a galaxy's formation history and the chemical conditions of its birth interstellar medium (ISM). While previous studies have sought to quantify this "radial redistribution" (often termed radial migration), there is a lack of consensus regarding its strength, its dependence on stellar age, and its impact on present-day galactic properties. Much of the uncertainty stems from the difficulty of inferring past conditions from present-day observations, which requires assumptions about the historical state of the ISM and the dynamical evolution of the disk. Furthermore, theoretical expectations often assume radial redistribution behaves as a monotonic diffusive process increasing with age ( $\tau^{0.5}$ ), a hypothesis that requires rigorous testing in a cosmological context.

Methodology
The authors utilize cosmological zoom-in simulations from the Feedback In Realistic Environments (FIRE-2) project, analyzing a sample of 11 Milky Way (MW) and M31-mass galaxies. These simulations self-consistently model the multiphase ISM, star formation, and stellar feedback (including supernovae, winds, and radiation pressure) within a fully cosmological context, resolving individual star-forming regions and dynamical perturbations (internal and external).

Key methodological components include:

Orbital Radius Metrics: The study comprehensively compares five distinct definitions of orbital radius ( $R_{orbit}$ $R_{or bi t}$ ) to measure redistribution:
1. $R_{phys}$ : Instantaneous physical radius.
2. $R_{\langle R \rangle}$ : Spatially-averaged radius (mean of apocenter and pericenter).
3. $R_{\langle t \rangle}$ : Time-averaged radius.
4. $R_{circ}(E)$ : Radius of a circular orbit with the same energy.
5. $R_{circ}(j)$ : Radius of a circular orbit with the same specific angular momentum (guiding center radius).
Quantification: The authors measure the change in orbital radius ( $\Delta R_{orbit}$ ), specific angular momentum ( $j$ ), and azimuthal velocity ( $v_\phi$ ) from birth to the present day. They characterize both the median (net) change and the scatter ( $\sigma(\Delta R_{orbit})$ ), the latter being a standard metric for radial diffusion.
Temporal Eras: Results are analyzed across three distinct eras of disk formation identified in previous work: "pre-disk" (ages $\gtrsim 8$ Gyr, dispersion-dominated), "early-disk" (ages $\approx 4-8$ Gyr, thick disk, net rotation), and "late-disk" (ages $\lesssim 4$ Gyr, thin disk, near-circular orbits).
Selection Consistency: A critical methodological constraint is that stars are selected and redistribution is measured using the same metric of $R_{orbit}$ to ensure self-consistency.

Key Contributions and Results

Metric Consistency: The study finds that while the absolute values of different $R_{orbit}$ metrics differ (e.g., $R_{phys}$ is generally larger than $R_{circ}(j)$ for older stars), the inferred trends for radial redistribution are generally consistent provided that the same metric is used to select stars today and to measure the redistribution. Inconsistencies arise only if metrics are mixed (e.g., selecting by $R_{phys}$ but measuring $\Delta R$ via $R_{circ}(j)$ ).
Net Redistribution vs. Diffusion:
- Age Dependence: The net change in orbital radius ( $\Delta R_{orbit}$ ) and angular momentum ( $j$ ) depends strongly on stellar age and current location. Stars selected by their current radius ( $R_{now}$ ) show a bifurcation: stars younger than $\approx 5$ Gyr generally decreased in $R_{orbit}$ , $j$ , and $v_\phi$ since birth, while older stars generally increased in these quantities.
- Inside-Out Growth: This trend reflects the inside-out growth of galaxies; older stars formed when the galaxy was more compact, so those currently at large radii must have undergone significant outward redistribution.
- Birth Selection: Conversely, if stars are selected by their birth radius, they typically decreased in $R_{orbit}$ and $j$ across almost all ages, highlighting the asymmetry introduced by the declining stellar density profile.
Saturation of Radial Diffusion:
- A primary finding is that the scatter in radial redistribution, $\sigma(\Delta R_{orbit})$ , does not increase monotonically with age. Instead, it increases for stars up to $\approx 3$ Gyr old and then saturates at $\sigma(\Delta R_{orbit}) \approx 2$ kpc for older stars.
- This saturation contradicts the common expectation of a diffusive process scaling as $\tau^{0.5}$ . The authors note that for stars born in the pre-disk and early-disk eras, the primary mode of redistribution is a net shift in the median radius rather than diffusion about the birth radius.
Comparison with Observations and Other Simulations:
- Auriga Simulations: When compared to the Auriga simulations (using consistent selection criteria based on birth radius), FIRE-2 results are broadly similar, though FIRE-2 shows slightly less redistribution, potentially due to differences in ISM modeling and galaxy sizes.
- Milky Way Inferences: The FIRE-2 results align well with recent semi-empirical inferences for the MW (Ratcliffe et al. 2025) and analytic models (Frankel et al. 2020) for stars up to $\approx 4-6$ Gyr. However, FIRE-2 and Ratcliffe et al. (2025) both suggest a saturation of $\sigma(\Delta R)$ at older ages, which is inconsistent with a simple extrapolation of the monotonic increase proposed by Frankel et al. (2020).
Correlations with Galaxy Properties:
- The timing of disk formation (lookback time to disk onset) correlates with the net redistribution ( $\Delta R_{orbit}$ ) but does not correlate with the scatter ( $\sigma(\Delta R_{orbit})$ ). This implies that the total amount of radial diffusion experienced by a population is independent of the age of the thin disk.
- Larger galaxies (in terms of stellar mass and size) tend to experience more radial redistribution in terms of scatter ( $\sigma$ ).

Significance
The paper claims that its results provide a robust, cosmologically self-consistent framework for understanding stellar radial redistribution. By demonstrating that radial diffusion saturates rather than increasing indefinitely with age, the authors challenge standard diffusive models used in galactic archeology. They argue that interpreting the present-day record of the MW requires models that account for the specific dynamical history of the disk, including the transition from bursty, turbulent early phases to settled thin disks. The finding that net redistribution (coherent shifts) dominates over diffusion for older stars suggests that the "scrambling" of birth conditions is not purely random but is driven by systematic evolutionary processes like inside-out growth and feedback-driven breathing modes. The agreement with recent observational inferences (Ratcliffe et al. 2025) validates the FIRE-2 approach while highlighting the need to revise assumptions about the monotonicity of radial migration in older stellar populations.