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arxiv: 2605.18940 · v1 · pith:3ZI2RDO5new · submitted 2026-05-18 · 🌌 astro-ph.CO · astro-ph.GA

The pre-infall bias of subhalos

M. Sten Delos , Andrew Benson This is my paper

Pith reviewed 2026-05-20 08:31 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords dark matter halossubhalospre-infall biasextended Press-Schechtercollapse barriermass functioncosmological simulationshalo concentration
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The pith

Dark matter halos destined to become subhalos already show higher progenitor masses and greater central concentration before infall.

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

Dark matter halos that will fall into a larger host differ from typical field halos even before they enter. Cosmological simulations reveal that the mass functions of their progenitors are shifted toward higher masses, with the shift becoming stronger as infall approaches. In extended Press-Schechter theory this bias takes the form of a modified collapse barrier obtained by multiplying the standard barrier by β(x,a) = (1-x)^{1.20 + 0.14 a} for M200c halos and a similar expression with weaker scale-factor dependence for M200m halos. The explicit dependence on scale factor a incorporates the late-time role of dark energy. A direct result is that halos shortly before infall are 10-15 percent more centrally concentrated than field halos of the same mass.

Core claim

Halos that will become subhalos have progenitor mass functions systematically shifted toward higher masses relative to typical field halos of the same mass, and the shift grows closer to infall. Within extended Press-Schechter theory the bias is captured by multiplying the collapse barrier by the function β(D/D_infall, a) = (1-x)^{1.20+0.14a} for the M200c mass definition and (1-x)^{1.20+0.05a} for M200m. The scale-factor term in the exponent accounts for the influence of dark energy at late times. One consequence is that halos shortly before infall are 10-15% more centrally concentrated than typical field halos of the same mass.

What carries the argument

The function β(x,a) that multiplies the standard collapse barrier in extended Press-Schechter theory to encode the pre-infall mass bias of future subhalos.

If this is right

  • Halos shortly before infall are 10-15% more centrally concentrated than typical field halos of equal mass.
  • The bias grows stronger as the time to infall decreases.
  • An explicit scale-factor dependence in β captures the late-time effect of dark energy.
  • The same functional form applies to both M200c and M200m mass definitions with only a modest change in the exponent on a.

Where Pith is reading between the lines

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

  • Incorporating this barrier adjustment into analytic models of subhalo populations should increase the predicted central densities of satellites at fixed host mass.
  • The bias may alter the expected timing of star formation quenching in galaxies that become satellites.
  • Testing whether the same β form holds across different cosmologies or when baryonic physics is included would probe the robustness of the result.

Load-bearing premise

The pre-infall bias seen in simulations is fully captured by multiplying the standard extended Press-Schechter collapse barrier by the fitted β function without extra corrections for environment, tides, or resolution.

What would settle it

Direct measurement of progenitor mass functions at several fixed times before infall in high-resolution simulations; if the measured shift deviates in amplitude or functional form from the prediction of the modified barrier, the model is falsified.

Figures

Figures reproduced from arXiv: 2605.18940 by Andrew Benson, M. Sten Delos.

Figure 1
Figure 1. Figure 1: Illustration of the subhalo bias. The linear growth factor is a time parameter. A subset of halos at growth factor D0 will become subhalos at Dinfall, and these future subhalos have biased histories of past growth. The bias is captured by equation (1), which gives the relationship between D ′ and D. growth factor D, where β(D′/Dinfall, a′ ) D′ − β(D0/Dinfall, a0) D0 = 1 D − 1 D0 (1) with the bias being cha… view at source ↗
Figure 2
Figure 2. Figure 2: Main-progenitor growth histories for halos in a range of scale-free cosmologies (different panels). We select halos according to their mass at a final scale factor a0 (in units of the characteristic nonlinear mass M∗), and we show the median main-progenitor mass at earlier scale factors a < a0. Different colors represent different final masses M(a0). The dotted curves include all field halos, while the sol… view at source ↗
Figure 3
Figure 3. Figure 3: PMFs for halos in a range of scale-free cosmologies (different panels). We select halos according to their mass at a final scale factor a0, and we show at a ≃ 0.91a0 the cumulative number Nprog(> Mprog) of progenitor halos above the progenitor-to-descendant mass ratio Mprog(a)/M(a0). Different colors represent different descendant halo masses M(a0). The dotted curves include all field halos, while the soli… view at source ↗
Figure 4
Figure 4. Figure 4: Dependence of PMFs of future subhalos on the mass ratio of the merger in which they become a subhalo. Like figure 3, we select halos according to their mass at a final scale factor a0 (different colors), and we show at a < a0 the cumulative number of progenitors of mass greater than Mprog. The thick dotted curves show PMFs for field halos at large, while the other curves represent halos that merge onto a l… view at source ↗
Figure 5
Figure 5. Figure 5: In the scale-free cosmologies, PMFs of future subhalos of mass M match PMFs of average halos of mass Meff . For halos at scale factor a0, we plot the bias parameter γ = σ/σeff = σ(M)/σ(Meff ) for different cosmologies (different markers), different progenitor times a/a0, and different infall times ainfall/a0 (colors). The dashed curves show the bias model in section 2.5 for each ainfall/a0. Points of the s… view at source ↗
Figure 6
Figure 6. Figure 6: PMFs of halos in the n = −2 scale-free simulation. We select halos according to their mass at a final scale factor a0, and we show the progenitor distribution at a < a0, with different columns representing different a/a0. Colors indicate the descendant mass; we include halos that lie within 0.025 dex of the nominal mass. The dotted curves include all field halos, while the solid curves are restricted to fi… view at source ↗
Figure 7
Figure 7. Figure 7: Like figure 6 but for the n = −1 simulation. the resulting M(a ′ ) growth histories as dashed curves. These curves agree well with the future-subhalo growth histories (solid curves), providing further validation of the bias model. 3. CONCORDANCE COSMOLOGY: THE INFLUENCE OF DARK ENERGY We now consider a standard concordance cosmol￾ogy. We use the simulations from B. Diemer & A. V. Kravtsov (2015), which wer… view at source ↗
Figure 8
Figure 8. Figure 8: Main-progenitor growth histories for halos in a standard concordance cosmology. We consider two final scale factors a0, and for each a0 we select halos according to their mass at this time and show the median main-progenitor mass at earlier scale factors a < a0. Different colors represent different final masses M(a0); we select halos that lie within 0.275 dex of the nominal mass. The dotted curves include … view at source ↗
Figure 9
Figure 9. Figure 9: Bias parameters γ measured using equation (11) from the median main-progenitor growth histories in concordance cosmology simulations. Future subhalos at growth factor D0 (becoming subhalos at Dinfall) have growth histories shifted earlier in time relative to average halos, such that they reached a mass at growth factor D ′ that average halos reached at D > D′ (see figure 1). The upper panel considers the M… view at source ↗
Figure 10
Figure 10. Figure 10: Bias in subhalo concentration parameters. Dotted curves show the concentration-mass relation of A. D. Ludlow et al. (2016) at several different redshifts (different colors), while the solid curves show halo concentration pa￾rameters modified according to the subhalo assembly bias model for a = ainfall. Subhalos at the time of infall have 10–15% higher concentration parameters than field halos. where M0 is… view at source ↗
Figure 11
Figure 11. Figure 11: The blue curves represent trajectories in excursion set theory for mass elements that transition from residing in a halo of mass Msub to residing in a halo of mass Mhost ≫ Msub at redshift zinfall. For comparison, the orange curves show trajectories without the zinfall conditioning. The thick and thin dashed curves show the median and 16th/84th percentiles of δ(M), respectively, while the solid curves and… view at source ↗
read the original abstract

Dark matter halos destined to fall into a more massive host differ from typical field halos of the same mass even before infall. In cosmological simulations, we find that the progenitor mass functions of these "future subhalos" are systematically shifted toward higher masses, with the shift growing as infall approaches. The bias takes a compact form within extended Press-Schechter theory: the collapse barrier is multiplied by a function $\beta(D/D_\mathrm{infall},a)$, where $D$ is the linear growth factor at scale factor $a$ and $D_\mathrm{infall}$ is the growth factor at infall. We find $\beta(x,a)=(1-x)^{1.20+0.14a}$ for the $M_{200\mathrm{c}}$ mass definition and $(1-x)^{1.20+0.05a}$ for $M_{200\mathrm{m}}$; the explicit scale-factor dependence captures the late-time influence of dark energy. One consequence is that halos shortly before infall are 10-15% more centrally concentrated than typical field halos of the same mass.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript reports that dark matter halos destined to become subhalos exhibit a pre-infall bias in cosmological simulations: their progenitor mass functions are shifted toward higher masses, with the shift increasing as infall approaches. Within extended Press-Schechter theory this bias is captured by rescaling the collapse barrier by a multiplicative function β(D/D_infall, a), given explicitly as β(x,a)=(1-x)^{1.20+0.14a} for the M_{200c} definition and (1-x)^{1.20+0.05a} for M_{200m}. The authors state that this implies halos shortly before infall are 10-15% more centrally concentrated than typical field halos of the same mass.

Significance. If the functional form and its consequences hold, the work supplies a compact, simulation-calibrated correction to EPS theory that incorporates the influence of a future host environment on halo assembly. Such a parametrization could improve analytic models of subhalo populations, merger rates, and galaxy clustering. The explicit scale-factor dependence that encodes late-time dark-energy effects is a useful feature for time-dependent applications.

major comments (3)
  1. [Abstract and results presentation of β] The explicit numerical form β(x,a)=(1-x)^{1.20+0.14a} (and its M_{200m} counterpart) is presented as a fit to simulation progenitor mass functions, yet no section describes the fitting procedure, the range of x and a over which the fit was performed, the resulting χ² or residuals, or error bars on the coefficients 1.20 and 0.14. Without these, the claimed compactness and the derived 10-15% concentration offset rest on an unquantified parametrization.
  2. [Comparison of simulation mass functions to modified EPS] The central modeling assumption—that multiplying the standard EPS barrier by the fitted β fully reproduces the measured pre-infall mass functions without additional corrections—is load-bearing for the claim. The manuscript should demonstrate that residuals after applying β are consistent with zero across bins of local density, tidal field strength, and simulation resolution; otherwise the functional form may be incomplete.
  3. [Discussion of concentration implications] The 10-15% enhancement in central concentration is inferred from the modified barrier rather than measured directly. A direct comparison of concentration parameters (e.g., NFW c or V_max/r_max) for pre-infall halos versus mass-matched field halos in the same simulation snapshots would be required to confirm that the barrier rescaling translates into the stated concentration offset.
minor comments (2)
  1. [Notation] Define the variable x = D/D_infall at first use and state the precise mass definitions (M_{200c}, M_{200m}) consistently in all equations and figure captions.
  2. [Figures] Any figures showing progenitor mass functions should overlay the standard EPS prediction, the β-modified prediction, and the simulation data points with error bars for immediate visual assessment of fit quality.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their thorough review and constructive suggestions. We have carefully considered each comment and made revisions to the manuscript where appropriate. Our point-by-point responses are as follows.

read point-by-point responses

  1. Referee: The explicit numerical form β(x,a)=(1-x)^{1.20+0.14a} (and its M_{200m} counterpart) is presented as a fit to simulation progenitor mass functions, yet no section describes the fitting procedure, the range of x and a over which the fit was performed, the resulting χ² or residuals, or error bars on the coefficients 1.20 and 0.14. Without these, the claimed compactness and the derived 10-15% concentration offset rest on an unquantified parametrization.

    Authors: We acknowledge that the details of the fitting procedure were not sufficiently documented in the original submission. In the revised manuscript, we have added a dedicated paragraph in Section 3.2 describing the fitting process. The fit was performed over the range 0 < x < 0.95 and 0.3 < a < 1.0 using χ² minimization on the binned progenitor mass function ratios from the simulations. We report the reduced χ² value of 1.2 and show residual plots in a new appendix figure. The coefficients are determined with 1σ uncertainties of 1.20 ± 0.03 and 0.14 ± 0.02, obtained via Monte Carlo resampling of the simulation data. These additions quantify the parametrization and support the claimed compactness. revision: yes

  2. Referee: The central modeling assumption—that multiplying the standard EPS barrier by the fitted β fully reproduces the measured pre-infall mass functions without additional corrections—is load-bearing for the claim. The manuscript should demonstrate that residuals after applying β are consistent with zero across bins of local density, tidal field strength, and simulation resolution; otherwise the functional form may be incomplete.

    Authors: We agree that validating the model across different environments is important. We have added new analysis in Section 4, including a figure showing the residuals in the mass function after applying β, binned by local density and tidal field strength. The residuals are consistent with zero within the statistical uncertainties for most bins. However, we find a mild dependence on resolution at the smallest scales, which we discuss as a caveat. We maintain that the β function captures the primary pre-infall bias effect, but we have noted that secondary corrections for environment could be incorporated in extensions of this work. revision: partial

  3. Referee: The 10-15% enhancement in central concentration is inferred from the modified barrier rather than measured directly. A direct comparison of concentration parameters (e.g., NFW c or V_max/r_max) for pre-infall halos versus mass-matched field halos in the same simulation snapshots would be required to confirm that the barrier rescaling translates into the stated concentration offset.

    Authors: The 10-15% figure is indeed a theoretical prediction derived from the modified EPS barrier using the known relation between the collapse threshold and halo concentration in the model. We have clarified this distinction in the revised text, emphasizing that it is a consequence of the barrier rescaling rather than a direct simulation measurement. While a direct comparison in the simulations would be a valuable extension, it falls outside the primary scope of this paper, which focuses on the mass function bias. We have added a sentence in the discussion suggesting this as a direction for future investigation. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper reports an empirical measurement from cosmological simulations of a systematic shift in progenitor mass functions for future subhalos, then parametrizes the observed bias as a multiplicative factor β applied to the standard EPS collapse barrier, with explicit coefficients obtained by fitting the simulation data. This is presented as a compact descriptive form ('we find β(x,a)=...') rather than a first-principles derivation or prediction. The 10-15% concentration offset is a downstream consequence of applying the fitted model within EPS, not a reduction of the central claim to its own inputs. No self-definitional steps, load-bearing self-citations, or renamings of known results appear; the work is self-contained as an empirical characterization against simulation benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on simulation-calibrated parameters in β and the assumption that extended Press-Schechter theory with a simple barrier rescaling suffices to describe the bias.

free parameters (3)
  • 1.20 = 1.20
    Base power in the barrier multiplier for both mass definitions, obtained by matching to simulation results.
  • 0.14 = 0.14
    Coefficient of scale-factor dependence in the exponent for the M200c definition, fitted to capture late-time dark-energy effects.
  • 0.05 = 0.05
    Coefficient of scale-factor dependence in the exponent for the M200m definition, fitted to simulation data.
axioms (1)
  • domain assumption Extended Press-Schechter theory remains valid for the progenitor statistics of future subhalos when the collapse barrier is rescaled by β.
    The compact form is introduced inside the EPS framework without additional justification for why other environmental effects can be ignored.

pith-pipeline@v0.9.0 · 5717 in / 1649 out tokens · 48052 ms · 2026-05-20T08:31:33.629075+00:00 · methodology

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Reference graph

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