Recovering the infall mass for Milky Way satellite galaxy Sextans

Using tailored N-body simulations across various Milky Way mass models, this study reconstructs the infall mass of the Sextans dwarf spheroidal galaxy to range between $1.22$and$3.14\times10^9\rm\,M_\odot$, demonstrating that its current stellar kinematics provide robust dynamical constraints while its dark matter tidal loss is primarily driven by the host galaxy's mass.

The Gist

Imagine the Milky Way as a giant, invisible whirlpool in space. Orbiting this whirlpool are hundreds of tiny, faint islands of stars called "satellite galaxies." One of these islands is Sextans, a dim, ghostly dwarf galaxy that is mostly made of invisible "dark matter" rather than visible stars.

For a long time, astronomers have been trying to answer a simple but tricky question: How heavy was Sextans when it first fell into the Milky Way's whirlpool?

This paper is like a cosmic detective story. The authors, Tian and colleagues, used supercomputers to run thousands of "time-travel" simulations to figure out Sextans' history. Here is the story of their findings, explained simply.

1. The Mystery: A Ghostly Visitor

Sextans is a bit of a puzzle. It's very faint, very spread out, and it seems to be dominated by dark matter (the invisible stuff that holds galaxies together). Because it's so faint, we can't see its history written in its stars easily.

The team wanted to know: Was Sextans a heavyweight champion when it arrived, or was it always a lightweight?

2. The Method: The Cosmic Tug-of-War

To solve this, the scientists built a digital model of the Milky Way. They knew the Milky Way's gravity acts like a giant hand, pulling on Sextans and stretching it out. This is called tidal stripping.

• The Analogy: Imagine holding a piece of soft dough (Sextans) and spinning it around a giant fan (the Milky Way). The wind (gravity) tries to pull bits of the dough off.
• The Twist: The dough has two layers. The outer layer is the Dark Matter (very stretchy and easy to pull off), and the inner core is the Stars (stiff and hard to pull off).

The team ran simulations with three different sizes of Milky Ways:

1. Light: A smaller, lighter galaxy.
2. Medium: Our best guess of the real Milky Way.
3. Heavy: A massive, heavy galaxy.

They also tested two theories about the "texture" of Sextans' dark matter:

• The "Cuspy" Theory: The dark matter is dense and pointy in the center (like a sharp mountain peak).
• The "Core" Theory: The dark matter is fluffy and spread out in the center (like a soft marshmallow), likely because the explosion of ancient stars pushed the dark matter outward.

3. The Discovery: What Happened to the Dough?

The simulations revealed some fascinating things:

• The Stars are Tough: Just like the stiff dough, the stars in Sextans didn't get pulled apart much. They stayed safe in the center. This means the way the stars are moving right now gives us a very reliable clue about how much mass is still there.
• The Dark Matter is Fragile: The invisible dark matter, however, got stripped away significantly. How much was lost depended entirely on how heavy the Milky Way was.
  • If the Milky Way is Heavy, Sextans lost about 85% of its original dark matter.
  • If the Milky Way is Light, Sextans only lost about 30%.

4. The Verdict: How Heavy Was It?

By working backward from what Sextans looks like today, the team calculated its "infall mass" (how heavy it was when it first arrived).

• If the Milky Way is heavy: Sextans was a fairly massive galaxy, weighing in at about 3 billion times the mass of our Sun.
• If the Milky Way is light: Sextans was a bit lighter, around 1.2 billion solar masses.
• The "Marshmallow" Factor: If Sextans had that fluffy, "cored" dark matter center (caused by star explosions), it could have been quite massive. But, if it had the sharp, "cuspy" center (like a standard physics prediction), it would have had to be twice as light to survive the trip without being completely shredded.

5. Why Does This Matter?

This isn't just about one galaxy. It helps us understand the rules of the universe:

• The "Too Big to Fail" Problem: There's a theory that says the Milky Way should have many heavy satellite galaxies, but we don't see them. This study suggests that maybe Sextans was heavy, but the Milky Way's gravity stripped it down so much that it looks small now. This helps solve the mystery of why we don't see the heavyweights we expected.
• Star Formation: The results suggest that Sextans was surprisingly efficient at making stars for its size, or that the dark matter inside it was shaped by star explosions in a way we are just starting to understand.

The Bottom Line

Think of Sextans as a survivor of a cosmic storm. The storm (the Milky Way) tore away most of its invisible armor (dark matter), but its heart (the stars) remained intact. By studying how much armor was lost, the scientists figured out that Sextans was likely a much bigger, more powerful galaxy in its youth than it appears today.

This paper tells us that to understand the history of our galaxy's neighbors, we have to look not just at what they are now, but to simulate the violent journey they took to get here.

Technical Summary

Here is a detailed technical summary of the paper "Recovering the infall mass for Milky Way satellite galaxy Sextans" by Tian et al. (2026).

1. Problem Statement

Understanding the formation and evolution of the Milky Way (MW) requires precise knowledge of its satellite galaxies, particularly their dark matter (DM) content and orbital histories. While Gaia data has provided precise 3D positions and velocities for many satellites, reconstructing their infall properties (specifically the initial DM halo mass and density profile prior to entering the MW) remains challenging due to:

• Uncertainties in MW Mass: The total mass of the MW is poorly constrained ($0.5 \text{--} 2 \times 10^{12} M_\odot$), significantly affecting tidal stripping calculations.
• Orbital Uncertainties: The number of pericenter passages and the specific orbital path of a satellite introduce large variances in mass loss estimates.
• Baryonic Effects: The impact of stellar feedback on the inner DM density profile (creating "cores" vs. "cusps") is uncertain, particularly for faint dwarfs like Sextans.
• The "Too-Big-to-Fail" (TBTF) Problem: Determining if low-mass satellites like Sextans reside in halos consistent with $\Lambda$CDM predictions or if they require stochastic galaxy formation scenarios.

The specific focus is on Sextans, a faint, diffuse dwarf spheroidal (dSph) galaxy ($L_V \sim 10^5 L_\odot$), to recover its progenitor DM halo mass and test the consistency of its properties with the Stellar Mass-Halo Mass (SMHM) relation.

2. Methodology

The authors employed tailored $N$-body simulations to reconstruct the evolutionary history of Sextans. The methodology involved:

• Observational Constraints:

  • Adopted current best estimates for Sextans: Stellar mass ($m_* \approx 5.9 \times 10^5 M_\odot$), projected half-light radius ($R_{1/2} \approx 20.3$ arcmin), and line-of-sight (LOS) velocity dispersion ($\sigma_{los} \approx 8.4$ km/s).
  • Used Gaia EDR3 proper motions (Li et al. 2021) combined with distance and LOS velocity to perform Orbital Integration (OI).
  • Conducted 10,000 Monte Carlo realizations to account for observational uncertainties, selecting three representative orbits (small, medium, large pericenter) for each MW mass model.

• Milky Way Models:

  • Simulated three distinct MW mass models: Light ($0.8 \times 10^{12} M_\odot$), **Fiducial** ($1.39 \times 10^{12} M_\odot$), and **Heavy** ($2.0 \times 10^{12} M_\odot$).
  • Modeled MW mass evolution over time using a quadratic function derived from the TNG50 cosmological simulation, scaling the potential and stellar components accordingly.

• Satellite Modeling & Iterative Approach:

  • Stellar Component: Modeled as a Plummer profile.
  • DM Component: Tested two initial density profiles at infall:
    1. $\alpha\beta\gamma$-model (DC14): Incorporates baryonic feedback effects (cored profile) based on the stellar-to-halo mass ratio.
    2. NFW Model: Standard cuspy profile without baryonic modification.
  • Iterative Tuning: An iterative loop adjusted the progenitor's initial virial mass ($m_{200}$), stellar mass, and scale radius until the simulated present-day properties (LOS velocity dispersion, half-light radius, and stellar mass) matched observations within error margins.
  • Dynamical Friction: Neglected in orbital integration but an empirical friction term was added to the OI to match the simulated orbit's decay.

• Simulation Code: Used AGAMA for initial condition generation and GADGET-4 for $N$-body evolution in an external MW potential.

3. Key Contributions

• First Detailed Recovery of Sextans' Infall Mass: Provided a comprehensive reconstruction of Sextans' progenitor properties across a range of MW masses and orbital histories.
• Quantification of Baryonic vs. Tidal Effects: Explicitly separated the impact of galactic tides from baryonic feedback on the DM halo structure.
• Orbital Dependence Analysis: Demonstrated how the uncertainty in MW mass dominates the uncertainty in tidal stripping, whereas orbital pericenter distance plays a secondary role.
• SMHM Constraint: Placed Sextans on the low-mass end of the Stellar Mass-Halo Mass relation, comparing results with TNG50 and abundance matching predictions.

4. Key Results

A. Tidal Evolution and Mass Loss

• Stellar Component: Stars in Sextans are mildly affected by galactic tides. The maximum tidal mass loss for the stellar component is $<5\%$, and the surface density profile remains largely unchanged.
• Dark Matter Component: Tidal stripping is significant and highly dependent on the MW mass.
  • Light MW: $\sim33\%$ mass loss.
  • Heavy MW: $\sim85\%$ mass loss.
  • The uncertainty in MW mass ($0.8 \text{--} 2 \times 10^{12} M_\odot$) introduces a$\sim46%$ uncertainty in the DM mass loss fraction.

B. Recovered Infall Mass

The recovered infall virial mass ($m_{200}$) of Sextans depends critically on the assumed DM density profile and MW mass:

• With Baryonic Effects ($\alpha\beta\gamma$-model):
  • Infall mass ranges from $1.22 \times 10^9 M_\odot$** (Light MW) to **$3.14 \times 10^9 M_\odot$ (Heavy MW).
  • These values are consistent with the SMHM relation in TNG50 and abundance matching results.
• Without Baryonic Effects (NFW profile):
  • The recovered infall mass is smaller by a factor of $\sim2$.
  • For a Light MW, the mass drops below $10^9 M_\odot$(specifically$\sim6.5 \times 10^8 M_\odot$).
  • Such low masses would place Sextans as a rare object, potentially indicating stochastic galaxy formation at the dwarf scale.

C. Density Profile and Kinematics

• Velocity Dispersion: The observed increasing LOS velocity dispersion profile (out to $1.6^\circ$) is better reproduced by the **cored$\alpha\beta\gamma$-model**. The cuspy NFW model naturally produces a declining profile unless a strong tangential anisotropy ($\beta_a \approx -0.5$) is artificially imposed.
• Inner Density: Baryonic effects create a shallow core (logarithmic slope $\approx -0.5$) in the inner region, reducing the circular velocity at $r_{1/2}$ by $\sim3$ km/s compared to a pure NFW halo.
• Globular Clusters: The survival of potential star cluster remnants in Sextans (kinematically cold substructures) favors cored profiles, as cuspy halos would likely disrupt them within $\sim5$ Gyr.

5. Significance and Implications

• SMHM Relation: The results suggest that if Sextans has a cored halo (baryonic feedback active), its infall mass fits well within the standard SMHM relation. If it retains a cuspy NFW profile, it represents a low-mass outlier, highlighting the large scatter in galaxy formation efficiency at the dwarf scale.
• MW Mass Constraints: The study reinforces that accurate knowledge of the MW's total mass is crucial for determining the formation history of its satellites.
• Nature of Dark Matter: While the current data cannot definitively rule out a cuspy profile (due to anisotropy degeneracy), the combination of kinematic profiles and the potential survival of globular clusters leans toward a cored density profile for Sextans.
• Future Directions: The structural parameters derived provide a baseline for future studies. The authors suggest that reliable infall mass constraints for a larger sample of MW satellites are necessary to fully resolve the scatter in the low-mass SMHM relation and the TBTF problem.