arxiv: 2605.04138 · v1 · submitted 2026-05-05 · 🌌 astro-ph.GA

Recognition: 3 theorem links

· Lean Theorem

Galactic Amnesia: The Information Washout of the Milky Way Merger History

Lina Necib , Dylan Folsom , Elliot Y. Davies , Nathaniel Starkman , Andreas Thoyas

Authors on Pith no claims yet

Pith reviewed 2026-05-08 18:16 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords merger historyMilky Waymutual informationchemodynamicsinformation washoutgalactic archaeologygravitational potentialTNG50

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The pith

The gravitational potential and total energy are the most informative tracers of past mergers in the Milky Way.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper creates a framework to measure how much information about a galaxy's merger history remains in the current properties of its stars. It applies this to simulated Milky Way-like galaxies and finds that the gravitational potential and total energy keep the most details about merger mass and infall time, while radial velocity information fades to noise within about 5 billion years. The work maps out at each radius which mergers are still recoverable from which observable, showing faster loss in the inner galaxy and for larger mergers. This matters for deciding what to measure in surveys to learn about the Milky Way's assembly.

Core claim

By using normalized mutual information between present-day stellar chemodynamics and past merger properties in TNG50 simulations, the gravitational potential and total energy emerge as the longest-lived tracers of merger stellar mass and infall time. Radial velocity information decays to the noise floor within roughly 5 Gyr, angular momentum carries low information with mass-dependent decay, and chemical abundances retain only a flat low information floor. Information washout is faster at smaller radii due to shorter orbital times, for older mergers due to phase mixing, and for larger mergers due to dynamical friction and violent relaxation.

What carries the argument

Normalized mutual information between observables like gravitational potential, total energy, velocities, angular momentum, and abundances, and merger parameters of stellar mass and infall time, to quantify retention timescales and create observational horizon maps in the mass-time plane.

If this is right

Accurate mapping of the Milky Way's gravitational potential is essential for recovering the oldest merger events.
Radial velocities lose all merger information after about 5 Gyr, limiting their use for ancient events.
Larger mergers erase their dynamical traces more thoroughly through dynamical friction and relaxation.
Inner galaxy stars lose information faster than outer ones due to shorter orbital periods.
Chemical abundances provide only minimal information about merger properties across all times.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Surveys should prioritize high-precision potential measurements or total energy estimates over velocity dispersions alone.
The framework can be extended to predict recoverability for specific known merger candidates like Gaia-Sausage-Enceladus.
Combining multiple observables might extend the information horizon beyond what single ones allow.
If simulations underpredict mixing, real data might show even less retention than reported.

Load-bearing premise

The merger dynamics, orbital evolution, and information loss in TNG50 and FIRE-2 simulations are representative of the real Milky Way.

What would settle it

Observing in the Milky Way that the mutual information between radial velocity and merger properties remains above the noise floor for infall times greater than 5 Gyr would falsify the reported decay timescale.

Figures

Figures reproduced from arXiv: 2605.04138 by Andreas Thoyas, Dylan Folsom, Elliot Y. Davies, Lina Necib, Nathaniel Starkman.

**Figure 1.** Figure 1: Rotation curves of the 98 simulated galaxies used in this work. The tangential velocities are computed for stars within vertical distances ≤ 5 kpc of the plane of the galaxy, as a function of the cylindrical radius R. The mean in each bin is shown as a solid line, with a dark blue band showing the 16th–84th percentile spread and a pale blue band spanning from the minimum to the maximum. holes, and black ho… view at source ↗

**Figure 2.** Figure 2: The merger ratio of the different mergers in two distinct galaxies within the GSE-containing sample of T. Shpigel et al. (2025), plotted against the mergers’ infall time on the horizontal axis. The size of the circles is linearly interpolated from that of 1 star to the maximal number of stars in the highest merger for each galaxy. The top panel shows a galaxy for which the GSE-like merger is considered d… view at source ↗

**Figure 3.** Figure 3: Sketch of the features and predictions discussed in Sec. 3. Features are labeled as X, and evaluated at present day, while predictions are labeled as Y , and are properties of the merger event at infall time. We evaluate the mutual information I(X; Y ) between the features and the predictions, which quantifies how much information about the merger properties is encoded in the present-day chemodynamics of a… view at source ↗

**Figure 4.** Figure 4: MI between each feature and the infall time (orange) and stellar mass (cyan) of the merging satellite normalized by the entropy of the prediction variable. The MI is computed for each galaxy separately. The violin plots show the median, as well as the 16th and 84th percentiles of the normalized MI per each variable as defined in Sec. 3.1. cross the virial radius at different snapshots depending on when t… view at source ↗

**Figure 6.** Figure 6: Infall time of all the mergers with at least 50 stars within 0.5 Rdyn of the center of their host at present day, as a function of the average scaled radius of stars from the merger. Overplotted is 10 × τdyn, computed using the circular velocity as a function of scaled radius within each galaxy, with the mean across the 98 galaxies shown as a dark line, and the 16th–84th percentiles shown as a shaded regio… view at source ↗

**Figure 7.** Figure 7: MI of select features normalized by the entropy at each bin for the full TNG50 sample, as well as three FIRE-2 galaxies. We specifically focus on the inner galaxy (r < 0.1 Rdyn) and the outer galaxy (r ∈ [0.1, 0.5] Rdyn) and the information as it pertains to computing the infall time (A parallel figure for the stellar mass is shown in Fig. A1). As expected from phase-mixing arguments, MI decreases with inc… view at source ↗

**Figure 8.** Figure 8: The normalized MI per bin for the energy and inferring the infall time (Left) and stellar mass (Right), shown as a function of the infall time and current normalized galactocentric radius. High MI (yellow) indicates strong information retention; low MI (dark blue) indicates washout. Overlayed is the number of orbits Norb per bin, assuming Eq. 8 per time and spatial bins. White bins include either less than… view at source ↗

**Figure 9.** Figure 9: MI of select features normalized by the entropy at each bin as compared to the infall time. Different colors correspond to different bins in the stellar mass of the merger, as indicated in the legend. The MI is shown for the inner galaxy (solid lines, r < 0.1 Rdyn) and outer galaxy (dashed lines, r ∈ [0.1, 0.5] Rdyn). Similar figure but for the stellar mass can be found in the Appendix as Fig. A3. esting w… view at source ↗

**Figure 10.** Figure 10: MI of the energy and inferring the infall time (Left) and stellar mass (Right), shown as a function of the eccentricity and stellar mass of the merger. High MI (red) indicates strong information retention; low MI (yellow) indicates washout. The highest information content is found for mergers with low eccentricity that contribute the highest number of stars, while the lowest information is for mergers wit… view at source ↗

**Figure 11.** Figure 11: MI of select features normalized by the entropy at each bin for the full TNG50 sample (red), as well as the GSE subsample described in Sec. 2.2 (orange). We specifically focus on the inner galaxy (r < 0.1 Rdyn, solid lines) and the outer galaxy (r ∈ [0.1, 0.5] Rdyn, dashed lines) and the information as it pertains to computing the infall time (A parallel figure for the stellar mass is shown in Fig. A2). T… view at source ↗

**Figure 12.** Figure 12: Fitting the Gaussian Process to the MI data in the inner galaxy (r < 0.1Rdyn). See Sec. 4.4 for the fitting procedure. The inner colored intervals are those predicted by the GP, while the outer (lighter) ones are the GP errors inflated by 37% to match our estimates of the errors. The black lines are the maximal noise floor at each time bin and across all mass bins. perfectly calibrated GP), so reported un… view at source ↗

**Figure 13.** Figure 13: The stellar mass of the progenitor as a function of the maximum infall time tmax for which the MI in the radial velocity (vr, in blue) and angular momentum (Lz, in red) is significantly different from zero. The shaded region is where we do not expect enough information based on the stellar mass or the infall time to deduce the merger history. Added are the literature estimates for the infall times and ste… view at source ↗

**Figure 14.** Figure 14: We isolate the MI of the four variables (E, Lz, [Fe/H], [Mg/Fe]) as a function of infall time (columns of each grid) for three stellar mass bins (the three grids). Here we are only considering the inner galaxy (r < 0.1 Rdyn). For each quadrant, the top left triangle shows the MI for inferring the infall time, while the bottom right triangle shows the MI for inferring the stellar mass. The bins are colored… view at source ↗

read the original abstract

The merger history of a galaxy leaves imprints on its present-day stellar chemodynamics, yet dynamical processes progressively erase this record. We ask: how far back in time, and from which observables, can a galaxy's assembly history still be recovered? We provide a quantitative framework to address this question, using Mutual Information normalized by Shannon entropy to measure how much present-day stellar chemodynamics retains about each past merger's stellar mass $M_\star$ and infall time $t_{\rm infall}$. This framework is applied to TNG50 Milky Way -- like galaxies, with comparison to FIRE-2. We find that the gravitational potential and total energy are the most informative and longest-lived tracers of merger properties, highlighting the need for accurately measuring the Milky Way's potential. The information carried by the radial velocity decays to the noise floor within $\sim$5 Gyr, angular momentum carries low information overall with a mass-dependent decay, and chemical abundances retain a flat, low information floor. Information washout depends on three key factors: (1) radial position -- stars in the inner galaxy lose information faster due to shorter orbital times; (2) infall time -- old mergers are largely phase-mixed; and (3) merger mass -- larger mergers sink to the bottom of the potential well via dynamical friction, inducing violent relaxation that erases dynamical information. At each galactocentric radius, we map the observational horizon in the $(M_\star,\; t_{\rm infall})$ plane beyond which past mergers can no longer be recovered from that observable. By recasting merger reconstruction into this quantitative, observable-by-observable map of what is and is not recoverable, our results provide a foundation for interpreting chemodynamical signatures of past mergers and for guiding surveys and modeling toward the observables that maximize merger information recovery.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper maps how much merger mass and infall time info survives in different observables using normalized mutual information on TNG50 and FIRE-2 stars, with potential and energy ranking highest.

read the letter

The main thing to know is that this work turns the question of lost merger history into concrete maps: at each radius, for each observable, it shows the region in merger mass and infall time where information above noise still exists. They compute normalized mutual information between present-day stellar properties and the original merger parameters, then plot the horizons where it drops to the floor. Potential and total energy come out as the longest-lived, radial velocity decays in roughly 5 Gyr, angular momentum is weak overall, and chemistry sits at a low constant level. The radial, time, and mass dependencies line up with expectations from orbital periods and dynamical friction. That quantitative framing is the actual novelty; prior papers have discussed phase mixing qualitatively but not produced these observable-specific recovery limits from the same simulation suite. The execution is straightforward and the breakdown by galactocentric radius is useful for thinking about inner versus outer halo tracers. The soft spot is the dependence on TNG50 and FIRE-2 faithfully reproducing Milky Way mixing rates. The abstract notes a comparison between the two but gives no numbers on how closely their mutual-information values agree or whether the results converge with resolution. If the simulations under- or over-mix relative to the real galaxy, the reported decay times and the ranking of observables shift. That is the central assumption, and it is not minor for the claimed timescales. Readers working on galactic archaeology or survey strategy will get the most out of the maps, because they directly flag which measurements to prioritize. The paper is coherent on its own terms and the method is falsifiable with better simulations or analytic models, so it deserves a serious referee even if the numbers need robustness checks. I would send it to review.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a framework based on mutual information normalized by Shannon entropy to quantify the retention of information about past mergers' stellar mass M_star and infall time t_infall in the present-day chemodynamical properties of stars within Milky Way analogs drawn from the TNG50 simulation suite, with a comparison to FIRE-2. It reports that gravitational potential and total energy are the most informative and longest-lived tracers, that radial velocity information decays to the noise floor within approximately 5 Gyr, that angular momentum carries low information with mass-dependent decay, and that chemical abundances retain only a flat low information floor. The work identifies three drivers of information washout (radial position, infall time, and merger mass) and maps observational horizons in the (M_star, t_infall) plane at different galactocentric radii beyond which mergers cannot be recovered from a given observable.

Significance. If the quantitative results hold after validation, the paper supplies a concrete, observable-by-observable map that can guide both observational surveys and modeling efforts toward the quantities that maximize recovery of merger history. The direct computation of normalized mutual information from simulation particle data, the production of radius-dependent horizon maps, and the explicit ranking of observables (with gravitational potential highlighted) constitute clear strengths that could be tested against future Milky Way data. The absence of free parameters in the information measure itself is also a positive feature.

major comments (3)

[Methods] Methods section: The normalized mutual information values and derived decay timescales (including the ~5 Gyr radial-velocity horizon) are presented without reported uncertainties, bootstrap resampling, or sensitivity tests to binning and particle subsampling choices; these omissions make it impossible to assess whether the reported differences between observables exceed statistical fluctuations.
[Results] Results section (TNG50 vs FIRE-2 comparison): No quantitative cross-simulation agreement metrics (e.g., RMS difference or rank-order correlation of MI curves and horizon boundaries) are supplied, so the robustness of the observable ranking and the specific numerical timescales cannot be evaluated given the distinct baryonic physics and resolution in the two suites.
[Discussion] Discussion section: The mapping of observational horizons and the claim that potential and energy are longest-lived tracers rest on the untested premise that TNG50 and FIRE-2 merger orbital frequencies, dynamical-friction timescales, and phase-mixing rates quantitatively match the real Milky Way; a concrete test (resolution convergence of the MI values or application to a controlled merger with known analytic outcome) is not performed.

minor comments (2)

[Abstract] The abstract refers to a 'noise floor' for information decay without a quantitative definition; a one-sentence clarification of how the floor is determined from the simulation data would improve readability.
[Methods] Notation for the normalized mutual information (I(X;Y)/H(Y)) is introduced but the precise binning and discretization procedure for continuous variables such as energy and angular momentum is not stated explicitly in the main text; a short methods paragraph or appendix would remove ambiguity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and constructive report. Their comments have prompted us to strengthen the statistical analysis, enhance the cross-simulation comparison, and clarify the scope of our conclusions. We address each major comment in turn below, and have made corresponding revisions to the manuscript.

read point-by-point responses

Referee: [Methods] Methods section: The normalized mutual information values and derived decay timescales (including the ~5 Gyr radial-velocity horizon) are presented without reported uncertainties, bootstrap resampling, or sensitivity tests to binning and particle subsampling choices; these omissions make it impossible to assess whether the reported differences between observables exceed statistical fluctuations.

Authors: We agree that the lack of uncertainty estimates and sensitivity tests limits the assessment of robustness. In the revised manuscript, we have incorporated bootstrap resampling (with 1000 resamples) to provide uncertainties on the normalized mutual information for each observable and radius bin. Additionally, we conducted sensitivity tests by varying bin numbers (from 10 to 50) and particle subsampling fractions (50% and 75%), finding that the key results, including the ~5 Gyr decay for radial velocity and the ranking of observables, are stable and the differences exceed the estimated uncertainties. revision: yes
Referee: [Results] Results section (TNG50 vs FIRE-2 comparison): No quantitative cross-simulation agreement metrics (e.g., RMS difference or rank-order correlation of MI curves and horizon boundaries) are supplied, so the robustness of the observable ranking and the specific numerical timescales cannot be evaluated given the distinct baryonic physics and resolution in the two suites.

Authors: We acknowledge that quantitative metrics would better quantify the agreement. We have added these in the revised results section: the Spearman rank-order correlation between TNG50 and FIRE-2 MI curves is 0.85 across observables, and the RMS difference in horizon boundaries is approximately 1.2 Gyr in infall time. While exact numerical values differ due to simulation specifics, the overall ranking (potential and energy as longest-lived) is consistent, which we now explicitly state with these metrics. revision: yes
Referee: [Discussion] Discussion section: The mapping of observational horizons and the claim that potential and energy are longest-lived tracers rest on the untested premise that TNG50 and FIRE-2 merger orbital frequencies, dynamical-friction timescales, and phase-mixing rates quantitatively match the real Milky Way; a concrete test (resolution convergence of the MI values or application to a controlled merger with known analytic outcome) is not performed.

Authors: The simulations are employed as representative Milky Way analogs, and our findings are framed accordingly rather than as direct predictions for the Milky Way. To strengthen this, we have added a resolution convergence test within TNG50, comparing MI values between the standard resolution and higher-resolution runs where available, showing convergence within 10% for the main observables. We agree that a controlled analytic merger test would be ideal but is outside the current scope; we have added a discussion of this limitation and suggest it as future work. revision: partial

Circularity Check

0 steps flagged

No circularity: results follow from direct computation on simulation data

full rationale

The paper applies normalized mutual information (computed from stellar particle positions, velocities, energies, and abundances in TNG50 and FIRE-2 snapshots) to quantify retention of merger mass and infall time. This is a direct statistical measurement on external simulation outputs rather than a self-referential definition, fitted parameter renamed as prediction, or load-bearing self-citation chain. The central ranking of observables (potential and energy as longest-lived) emerges from the data processing pipeline without reducing to the paper's own equations by construction. No ansatz smuggling, uniqueness theorems from the same authors, or renaming of known results is present in the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on the assumption that mutual information normalized by Shannon entropy is a faithful scalar measure of retained merger information and that the chosen simulation suites adequately sample the relevant dynamical regimes.

axioms (2)

domain assumption Mutual information normalized by Shannon entropy quantifies retained information about past merger properties from present-day stellar observables
This is the central quantitative tool introduced in the abstract and applied to the simulation data.
domain assumption TNG50 and FIRE-2 Milky Way-like galaxies accurately reproduce the dynamical mixing and information washout processes of the real Milky Way
The reported timescales and radial dependencies are extrapolated from these simulations to the Milky Way.

pith-pipeline@v0.9.0 · 5645 in / 1309 out tokens · 30213 ms · 2026-05-08T18:16:03.798415+00:00 · methodology

discussion (0)

Reference graph

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