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Prestellar cores undergoing quasi-equilibrium collapse spend most of their collapse on a timescale of about twice the freefall time, and the longer lifetimes inferred from survey counts are artifacts of beam smoothing and unsteady star form

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2026-08-04 22:51 UTC pith:4IATAZ25

load-bearing objection The internal simulation results are solid and the beam-smearing explanation for the steep lifetime trend is genuinely new, but the headline discrepancy with observed 6-14 t_ff lifetimes rests on a steady-state assumption the authors themselves think is false. the 2 major comments →

arxiv 2509.07083 v1 pith:4IATAZ25 submitted 2025-09-08 astro-ph.GA astro-ph.SR

Prestellar Cores in Turbulent Clouds: Observational Perspectives on Structure, Kinematics, and Lifetime

Sanghyuk Moon , Eve C. Ostriker This is my paper
classification astro-ph.GA astro-ph.SR
keywords prestellar corescore lifetimefreefall timeturbulent equilibrium spherecoherent coreslinewidth–size relationbeam smoothingstar formation rate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that the structure, kinematics, and apparent lifetimes of prestellar cores in turbulent clouds can be explained by quasi-equilibrium collapse plus observational projection, without invoking special core states. Using simulated cores backed by the turbulent equilibrium sphere model, the authors find that once collapse begins, a core's remaining lifetime tracks about twice its freefall time through most of its evolution. They argue that the steep decrease of observed core lifetime with density is produced by finite telescope beams, which smear the densest cores and bias the density estimator, and that the flat linewidths of 'coherent cores' are line-of-sight projection effects masking a power-law velocity structure. The measured prestellar-to-infall duration ratio matches observed prestellar-to-Class 0+I source counts, but absolute lifetimes inferred from Class II counts (6–14 tff) exceed simulation lifetimes (~2 tff); the authors conclude accelerated star formation is the most likely resolution. If right, this reframes statistical core surveys: their lifetime curves encode resolution and star formation history as much as core physics, and the characteristic density for star formation is environmental rather than universal.

Core claim

At the paper's core is a claim about what observers actually see. In the simulated ensemble, prestellar cores evolve through a core-building phase dominated by converging turbulent flows and then a collapse phase in which the net inward force is only about 20% of gravity. Because the collapse is quasi-equilibrium, the remaining lifetime of a core is roughly twice the freefall time at its central density over most of its life, not the freefall time itself. When the same cores are viewed as an observer would view them, two apparent patterns emerge that are not intrinsic: beam smoothing lowers the inferred central densities of evolved cores and makes lifetimes look much shorter than the freefal

What carries the argument

The paper's load-bearing theoretical object is the turbulent equilibrium sphere (TES), a generalization of the Bonnor-Ebert sphere in which pressure includes thermal plus turbulent contributions, with the turbulent velocity dispersion growing as a power law with radius. The TES provides a critical radius rcrit where stability is lost; a core begins runaway collapse when rcrit falls below the local tidal radius set by the surrounding gravitational potential. On the observational side, the argument runs through two constructs: the density estimator nobs_H,c = NH,c/RFWHM (central column density over full-width-half-maximum radius), which is unbiased only if the central column-density plateau is

Load-bearing premise

The load-bearing premise is that prestellar cores form at a constant rate, so the observed ratio of prestellar cores to Class II sources equals the ratio of their average lifetimes; the authors themselves conclude this premise is probably false, with accelerated star formation the most likely resolution.

What would settle it

A decisive test would independently date the star formation history of a set of Gould Belt clouds and check whether the prestellar-to-Class II number ratio stays near the simulation ratio (~2 tff) in clouds with demonstrably steady star formation; if it remains about seven times higher, the discrepancy is real. A second test is angular resolution: at resolution that resolves the central column-density plateau (<~0.01 pc at 250 pc), the apparent lifetime-density curve should flatten toward ~2 tff if beam smoothing is the cause.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Survey-based prestellar core lifetimes should be corrected for beam smearing: the apparent steep decrease of lifetime with density is a resolution artifact, not evidence for faster evolution at higher density.
  • The ratio of prestellar duration to envelope infall time from the simulations matches observed prestellar-to-Class 0+I counts, so the simulations do not underproduce the prestellar phase; the discrepancy with Class II-based counts requires a different explanation.
  • The gap between simulated (~2 tff) and observed (6–14 tff) absolute lifetimes is most plausibly closed by accelerated (non-steady) core/star formation; in that case number-count ratios overestimate prestellar lifetimes.
  • Observed coherent cores do not require a special kinematic state: line-of-sight projection of a power-law turbulent velocity field flattens the apparent velocity dispersion profile.
  • The characteristic density at which cores become unstable is predicted to vary with environmental conditions (mean density, Mach number, virial parameter), so 'density thresholds' for star formation should not be treated as a universal constant.

Where Pith is reading between the lines

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

  • If the accelerated-star-formation explanation is right, the prestellar-to-Class II ratio should correlate with independently measured cloud star formation histories: clouds that have just begun forming stars should show systematically longer apparent core lifetimes.
  • The beam-smoothing interpretation predicts that higher-resolution observations (sub-0.01 pc at Gould Belt distances) should flatten the observed lifetime-density curve toward ~2 tff, while coarser-beam catalogs should show steeper apparent trends.
  • The leff,obs proxy offers a path to recovering the intrinsic linewidth-size slope from tracer pairs with different critical densities; applying it to pairs such as N2H+ and C18O could test whether the ~0.5 exponent extends below sonic scales.
  • Because the characteristic collapse density scales with mean density, Mach number, and virial parameter, apparent 'star formation thresholds' inferred from column-density maps should vary between clouds; a fixed threshold would only be an environment-averaged value.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper re-analyzes a simulated ensemble of prestellar cores from the authors' earlier work (Papers II/III) from an observer's perspective. It introduces observational proxies for central volume density and freefall time, defines and measures a 'remaining lifetime' and cumulative residence-time statistics, and reports that after the critical time cores collapse on a timescale of ~2 tff. It predicts a characteristic critical core density that scales with GMC properties (Eq. 38), argues that finite beam smoothing steepens the apparent lifetime-density relation, compares the simulated residence times to HGBS number counts, and shows that line-of-sight projection and tracer-density weighting flatten the projected velocity dispersion, producing apparent 'coherent cores.'

Significance. If the results hold, they materially reframe observational interpretation: the turnover in the core density histogram can be used to infer a collapse threshold, the observed steep decline of core lifetime with density may be a resolution artifact, and coherent cores need not indicate a special kinematic state. The core internal result is well supported: the ~2tff collapse timescale is tied to a directly measured force imbalance (F_imb = -0.2) in the simulations, and Figs. 4 and 5(c) show ~2tff behavior over a wide density range. Eq. (38) gives a falsifiable environmental scaling, and the public TES implementation is a useful reproducibility feature. The main weakness is in the observational-lifetime normalization step, discussed below.

major comments (2)
  1. [§4.1, Eq. (42), Fig. 9(b)] The factor ~7 discrepancy between simulated and empirical lifetimes ('6–14 tff') rests entirely on Eq. (42), which assumes a constant core formation rate. At the end of §4.1 the authors state that accelerated star formation 'is most likely based on the currently available information.' If star formation is accelerating, Eq. (42) overestimates the prestellar lifetime and the normalization gap in Fig. 9(b) no longer provides a meaningful constraint on the simulated ~2tff lifetimes. The abstract and Section 5 item 4 nevertheless present the simulated lifetime as 'significantly shorter' than empirical estimates. Please either present this comparison strictly as conditional on steady-state formation, or model the acceleration/selection correction and show how Fig. 9(b) changes. Figure 10 should also be labeled as sharing the steady-state assumption, even though it is less sensitive because th
  2. [§3.4, Eqs. (24)–(26), Fig. 11(b)] The demonstration that line-of-sight velocity dispersions flatten, producing apparent coherent cores, uses the top-hat tracer window Θ_thr with nmin ≤ nH < 10 nmin (Eq. 25), which the authors themselves call 'highly simplified.' Section 4.2 shows that replacing this with a step function changes the σlos–size relation qualitatively (Fig. 11b). The paper should test whether the central flattening in Figs. 7(b)–(d) survives for the step-function or other plausible tracer weighting before concluding that coherence is purely a projection effect; alternatively, the conclusion should be explicitly restricted to the adopted window and presented as a proof-of-concept rather than a general observational claim.
minor comments (6)
  1. [§2.2, §5] Typos: 'physicial' (§2.2), 'apprarently' and 'succesfully' (§5). The title also contains a spurious space in 'T urbulent.'
  2. [Appendix A, Fig. 14 caption] The caption says 'Similar to Figure 14' but should refer to Figure 13.
  3. [§3.3, after Eq. (35)] The sentence 'taking 9 rs = rs,box' contains a stray numeral; it should read 'taking rs = rs,box.'
  4. [Fig. 9(b)] The thin blue line is scaled by an arbitrary factor 6.7. The caption should state explicitly that this scaling is for shape comparison only and carries no statistical weight.
  5. [Fig. 11(a)] For the Fuller & Myers (1992) data, please specify which lines/tracers are plotted and whether error bars are omitted for readability.
  6. [§4.1, Eq. (42)] The derivation of Eq. (42) also assumes that stage B follows stage A and that all cores complete both stages; stating this alongside the constant-rate assumption would improve clarity.

Circularity Check

0 steps flagged

No significant circularity: the 2 tff collapse timescale is measured from simulation force balance, not defined into existence, and observational comparisons use independent HGBS data with openly flagged assumptions.

full rationale

The paper's central claims do not reduce to their inputs by construction. The quasi-equilibrium collapse timescale of ~2 tff is presented as a measurement from the authors' own Paper II force balance (Fimb = -0.2) and is also directly visible in this paper's Figure 4 trajectories; it is not defined as 2 tff via Equation (31) or any fitting. The TES model is adopted from the authors' prior work, but this is an explicit theoretical framework whose assumptions are stated (power-law turbulence, Equation (7)) and whose structural predictions are compared to the simulations in Figure 1, rather than being smuggled in as an unexamined ansatz. The characteristic-density estimate (Equation (38)) is a scalings-based prediction with an explicitly posited rcrit ~ rtidal ~ rs; this is self-referential in the sense that it uses the authors' own simulation-derived ratios, but it is not equivalent to the target result by definition and is presented as a testable environmental scaling. The observational lifetime comparison (Figure 9b) uses the standard constant-formation-rate conversion, Equation (42), and the authors explicitly and repeatedly flag that accelerated star formation is 'most likely based on the currently available information,' which would remove the normalization discrepancy. This is a transparent limitation and an assumption, not a fitted input renamed as a prediction. The beam-smoothing and projection explanations for the apparent lifetime slope and 'coherent cores' are forward-model demonstrations compared against external HGBS data and prior synthetic-observation work (Offner et al. 2008), so they are not circular. The paper is heavily self-referential in that it analyzes the authors' own simulations through the authors' own model, but the citations are to code-reproduced, published results and the key comparisons are to independent observational catalogs; this does not rise to circularity under the stated rules.

Axiom & Free-Parameter Ledger

6 free parameters · 7 axioms · 0 invented entities

Everything load-bearing is quantified above. No new physical entities are introduced. The governing equation of motion (Eq 1) and freefall time (Eq 29) are standard; the nontrivial inputs are the power-law turbulence ansatz (Eq 7), the simplified tracer window (Eq 25), the steady-state counting assumption (Eq 42), the posited rcrit ~ rtidal ~ rs, and the fiducial T = 10 K, n0 = 200 cm-3 mapping. flos is a tunable normalization, not an entity.

free parameters (6)
  • flos path-length fudge factor = 0.2
    Explicitly called a fudge factor. Chosen as 0.2 because the TES average-to-edge density ratio is 2-2.5; converts Nd,avg/nmin into a line-of-sight half-thickness. Calibrates the leff,obs proxy, and the recovered linewidth-size slopes (0.28-0.49) in Figure 12 shift with this choice and with Theta_thr.
  • tracer threshold densities nmin = 2e3, 6e3, 2e4 cm-3
    Hand-selected density thresholds in the top-hat selection function (Eq 25) meant to mimic dense-gas tracers such as N2H+ and 13CO. The flatness of the projected velocity dispersion profiles (Figure 7), the sigma_los-leff relation (Figure 8), and the proxy results (Figures 11-12) all depend on these values.
  • smoothing beam FWHM = 0.045 pc (36.3 arcsec)
    Gaussian convolution width matching Herschel 500 um resolution at the 254 pc mass-weighted distance of the nine HGBS clouds. The systematic underestimate of evolved core densities, and hence the artificial steepening of the lifetime curve in Figure 9b, is produced by this choice.
  • Class II lifetime Delta t_II = 2 Myr
    Assumed Class II lifetime from Evans et al. 2009 and Dunham et al. 2015, used with Eq 42 to convert Npre/NII into absolute prestellar lifetimes. The entire factor-of-7 normalization discrepancy of Figure 9b scales linearly with this value.
  • pencil-beam aperture radius Rap = 0.05 pc
    Fixed aperture for sigma_los and leff measurements in Figures 8 and 12; the authors state that adopting 0.02 pc leaves the results unchanged.
  • TES fit parameters for the example core = rs = 0.062 pc, p = 0.69, xi_s = 6.44
    Best-fit sonic radius and turbulence power-law index for the single example core in Figures 1-2, used to construct the matching TES density profile. Illustrative only.
axioms (7)
  • domain assumption Isothermal equation of state at T = 10 K, mapped to physical units with n_H,0 = 200 cm-3; all results scale with these fiducial choices.
    Section 2.2 states the simulations are dimensionless and rescaled using T = 10 K and n_H,0 = 200 cm-3. Lifetime and density comparisons to HGBS data inherit these choices; magnetic fields, chemistry, and radiation transfer are absent.
  • domain assumption Turbulent velocity dispersion increases with radius as a power law (Eq 7), with statistically isotropic turbulence.
    Adopted from Paper I and stated as verified in Papers II and III. This underpins the TES interpretation used to define tcrit, rcrit, and the example-core comparison in Section 3.1.
  • domain assumption The simplified top-hat tracer selection function Theta_thr (Eq 25) approximates molecular-line excitation and freeze-out.
    Section 3.1: line-of-sight velocity dispersions and the entire coherent-core and linewidth-size analysis (Figures 7-12) are computed with this window. The authors call it 'highly simplified' and show that a step-function window materially changes the results (Figure 11b).
  • domain assumption Steady-state core formation: cores form at a constant rate, so number-count ratios equal lifetime ratios (Eq 42).
    Section 4.1: the conversion Npre/NII times Delta t_II = 2 Myr into prestellar lifetimes, which produces the 6-14 tff estimates, requires constant formation rate. The authors state that accelerated star formation would invalidate this and judge that scenario 'most likely' given current information.
  • ad hoc to paper Posit: neighboring density structures develop at separations ~ r_s, so rcrit ~ rtidal ~ r_s for critical cores.
    Section 3.3, footnote 9: needed to convert the TES relation and box-scale sonic radius into the characteristic density estimates (Eqs 34-38). The paper verifies median values rcrit/rtidal = 0.93 and rtidal/rs = 1.13 in its own simulations.
  • standard math Standard Bonnor-Ebert and TES stability analysis, and the freefall timescale definition (Eq 29), apply to the simulated cores.
    Section 2.1: the Emden-Chandrasekhar equation, the critical radius xi_crit, and frell-fall time are standard analytic results used to identify tcrit, interpret lifetimes, and translate densities into timescales.
  • domain assumption Magnetic fields and chemistry/radiation transfer do not alter the lifetime and kinematic conclusions.
    Section 4.1: the authors argue supercritical cores collapse unimpeded by magnetic fields, citing Chen & Ostriker 2015 and Offner et al. 2025, and defer chemistry and radiative transfer to future work. These absences are acknowledged limitations for the tracer modeling.

pith-pipeline@v1.3.0-alltime-deepseek · 25773 in / 20233 out tokens · 188470 ms · 2026-08-04T22:51:35.467835+00:00 · methodology

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read the original abstract

We analyze an ensemble of simulated prestellar cores to facilitate interpretation of structure, kinematics, and lifetime of observed cores. While our theory predicts a "characteristic" density for star formation, it also predicts that the individual critical density varies among cores; any observed sample thus contains cores at various evolutionary stages within a given density bin. By analyzing the remaining lifetime, we find cores undergoing quasi-equilibrium collapse evolve on a timescale of twice the freefall time throughout most of their life. Our analysis shows that the central column density and the associated full-width half maximum provide a reasonably accurate observational estimator of the central volume density, and therefore the freefall time; this does, however require resolving the central column density plateau. Observations with a finite beam size tend to underestimate densities of evolved cores, and this makes observed lifetimes appear to decrease more steeply than the apparent freefall time. We measure from our simulations the ratio of prestellar duration to envelope infall time, and find this is consistent with the observed relative number of prestellar cores and embedded protostars. Yet, the absolute core lifetime in our simulations is significantly shorter than would be expected from empirical measurements of the relative numbers of prestellar cores and Class II sources; we discuss several possible reasons for this discrepancy. Finally, our simulated cores have nearly constant line-of-sight velocity dispersion within the emitting region in the sky plane, resembling observed "coherent cores." We show that this "coherence" is a consequence of projection effects, which mask the intrinsic power-law velocity structure function. We discuss possible ways to estimate line-of-sight path lengths.

Figures

Figures reproduced from arXiv: 2509.07083 by Eve C. Ostriker, Sanghyuk Moon.

Figure 1
Figure 1. Figure 1: Density and velocity structures of a representative core at tcrit. (a) The measured volume density profile (black) and the semianalytic solutions for the BE sphere (purple) and the TES (cyan) with matching ρc, rs, and p. The circles mark the critical radius for each model. The inset shows the column density map made by projecting the (0.3 pc) 3 cubic region around this core along the z-axis. (b) The radial… view at source ↗
Figure 2
Figure 2. Figure 2: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Ensemble of column density profiles of cores, normalized to each core’s central column density and color-coded by τevol. (b) The true central volume density vs. its observational proxy n obs H,c ≡ NH,c/RFWHM, also color-coded by τevol; the dotted diagonal line indicates identical values. Note that the radius at which NH/NH,c = 0.5 in panel (a) defines RFWHM/2 (see Equation (28)). as an observational pr… view at source ↗
Figure 4
Figure 4. Figure 4: Selected trajectories of the “remaining lifetime” (Equation (31)) as a function of n obs H,c. Plus symbols mark the loci of t = tcrit (at this point the hue changes from blue to red) for the entire core sample, with those corresponding to the selected trajectories boldfaced. Dotted diagonal lines indicate tff and 2tff . dius becomes negative (see Equation 18 and Paper II). In observations, much less detail… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Time evolution of the observational central volume density, with each line representing an individual core. The x-axis is shifted with respect to the critical time of each core. For comparison, we also plot the theoretical trajectory of freefall collapse starting from a central density of 105 cm−3 by the red line. (b) Histogram of the time spent in each density bin (Equation (32)). (c) Cumulative histo… view at source ↗
Figure 6
Figure 6. Figure 6: Distribution of the sonic radius (relative to cloud-scale LJ,0) and the average density (relative to mean cloud density ρ0) of cores measured at their individual tcrit. Red and blue circles correspond to individual cores formed in Mach 5 and Mach 10 models, respectively, with a hue rep￾resenting the ratio rcrit/rs. The red and blue horizontal lines show rs,box for Mach 5 and Mach 10 models, respectively. T… view at source ↗
Figure 7
Figure 7. Figure 7: (a) Radial profiles of the three-dimensional rms velocity dispersion (Equation (39)) for all critical cores. Circles mark each core’s critical radius. (b) Projected radial profiles of the line-of-sight velocity dispersion (see Equations (24)–(26) for the relevant definitions), using the threshold density nmin = 2×104 cm−3 . Thin lines represent individual cores projected along x-, y-, and z-axes, and Panel… view at source ↗
Figure 8
Figure 8. Figure 8: The line-of-sight velocity dispersion σlos (Equa￾tion (41)) versus the effective line-of-sight path length leff (Equation (40)), for all critical cores seen in x-, y-, and z-projections. Both quantities are obtained by taking av￾erage over a pencil beam with fixed aperture Rap = 0.05 pc around each core center. Red, orange, and blue points cor￾respond to the results with nmin = 2×104 cm−3 , 6×103 cm−3 , an… view at source ↗
Figure 9
Figure 9. Figure 9: (a) Similar to [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The ratio of the average starless (i.e., prior to introduction of a sink particle) duration above each central density bin to the average infall time measured for simulated cores (black line with markers). Here, similar to [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The line-of-sight velocity dispersion averaged within a circular aperture Rap = RFWHM,d, vs. the plane-of-sky core radius RFWHM,d. Both quantities are computed after applying the density selection function Θthr to the data, where panels (a) and (b) show the results using a top-hat and a step function, respectively. For comparison, we plot the best-fit intrinsic linewidth–size relation shown in [PITH_FULL… view at source ↗
Figure 12
Figure 12. Figure 12: Similar to [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: The average duration that prestellar cores spend above each central density bin, obtained by taking the ratio of the number of prestellar cores above each bin to the number of Class II YSOs, multiplied by the reference timescale of ∆tII = 2Myr. The individual cloud names are annotated on top of each panel. Two dashed lines mark tff and 10tff . In this section, we construct so called “JWT” plots (N. E. Jes… view at source ↗
Figure 14
Figure 14. Figure 14: Similar to [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗

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