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Ancient star clusters were born far denser than today's young ones

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2026-07-09 21:40 UTC pith:E3IBTFHR

load-bearing objection Novel coupling of fast evolution + equilibrium models to infer GC initial conditions; headline density result is real but degenerate with uncertain BH kick physics the 1 major comments →

arxiv 2607.07010 v1 pith:E3IBTFHR submitted 2026-07-08 astro-ph.GA

Fast Dynamical Modelling of Milky Way Globular Clusters -- I. Implications for Initial Cluster Densities

Nolan Dickson , Vincent H\'enault-Brunet , Fotios Fronimos Pouliasis , Mark Gieles , Peter J. Smith This is my paper
classification astro-ph.GA
keywords globular clustersinitial conditionsstellar dynamicsblack holesinitial mass functioncluster evolutionMilky Waynatal kicks
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.

The paper's central contribution is a methodological coupling — joining fast semi-analytical evolutionary models that track how a cluster's mass, radius, and black hole content change over ~12 Gyr with multimass equilibrium models fitted to present-day observations of stellar kinematics and mass functions. This coupling lets the authors work backwards from what we see today to infer the birth conditions of Milky Way globular clusters. Applied to 35 clusters, the method reveals that these ancient systems were born with half-mass densities centered on 10^6.4 solar masses per cubic parsec — roughly an order of magnitude or more above young massive clusters in the local Universe, and consistent with the densities of proto-cluster candidates now being observed at high redshift with JWST. The high densities are driven by very compact initial half-mass radii (typically under 0.7 parsecs). The same framework yields a stellar initial mass function that is deficient in low-mass stars relative to standard prescriptions, and small present-day black hole mass fractions (under ~1.5%). The authors validate the method by recovering known initial conditions from mock observations of star-by-star simulations, and they demonstrate a key degeneracy: a roughly 40% change in assumed black hole natal kick strength can compensate an order-of-magnitude change in inferred initial density, meaning the high-density result is entangled with uncertain black hole formation physics.

Core claim

By coupling fast cluster evolution models with present-day equilibrium models fitted to observed kinematic and mass-function data, the authors infer that Milky Way globular clusters were born with half-mass densities around 10^6.4 solar masses per cubic parsec — far above local young massive clusters and consistent with high-redshift proto-globular clusters observed by JWST. The high densities arise from very compact initial radii (typically under 0.7 parsecs), and the same framework independently yields a bottom-light stellar initial mass function and small present-day black hole mass fractions (under ~1.5%).

What carries the argument

The coupling of two models: clusterBH, a semi-analytical code that evolves bulk cluster properties (total mass, half-mass radius, black hole mass fraction) from birth to the present using prescriptions for two-body relaxation, stellar evolution mass loss, tidal evaporation, and black-hole burning; and limepy, a multimass distribution-function-based equilibrium model that describes the present-day phase-space structure of stars and remnants. The free parameters of present-day mass and radius are replaced by their initial counterparts, so that present-day observations constrain birth conditions through the evolutionary bridge.

Load-bearing premise

The black hole natal kick prescription — a fallback-modulated Maxwellian with dispersion 265 km/s — is uncertain and shared with the simulation grid used for validation, so the high-density inference cannot be tested against models with different kick physics, and a roughly 40% change in kick strength could shift the inferred densities by an order of magnitude.

What would settle it

If a Milky Way globular cluster with well-constrained present-day properties were shown, through independent star-by-star modelling with different black hole kick prescriptions, to be consistent with significantly lower initial densities (e.g., below 10^5 solar masses per cubic parsec), the central high-density inference would be undermined.

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

If this is right

  • If Milky Way globular clusters were born at ~10^6.4 solar masses per cubic parsec, the formation conditions of ancient clusters differ systematically from those of young massive clusters forming today, raising the question of whether cluster formation itself has evolved over cosmic time.
  • The bottom-light IMF (~25% more black hole progenitors per unit mass than a canonical IMF) would shift predicted gravitational-wave merger rates and the expected mass distribution of merging black holes from globular cluster channels.
  • The combination of high initial black hole fractions and small present-day fractions implies very efficient dynamical ejection of black holes over cluster lifetimes, constraining the internal dynamical processing that must have occurred.
  • The consistency with high-redshift proto-GC densities suggests that JWST observations of lensed proto-clusters may be directly probing the birth environments of present-day globular clusters.
  • The demonstrated degeneracy between kick strength and initial density means that tighter observational constraints on black hole natal kicks would directly tighten constraints on cluster birth densities.

Where Pith is reading between the lines

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

  • If future electromagnetic or gravitational-wave observations tighten constraints on black hole natal kicks, the inferred initial densities could shift by up to an order of magnitude — potentially reconciling them with local young massive cluster densities if kicks turn out to be stronger than assumed.
  • The bottom-light IMF, if universal among ancient globular clusters, would imply that stellar population synthesis models assuming a canonical IMF systematically overestimate low-mass stellar content and underestimate black hole formation rates in metal-poor environments.
  • The method could be extended to globular clusters in other Local Group galaxies to test whether the high initial density is a universal feature of ancient clusters or specific to the Milky Way's formation environment.
  • A hierarchical Bayesian treatment of the full surviving and dissolved cluster population could reveal whether the individual-cluster densities reported here trace a coherent parent distribution shaped by galaxy-scale formation conditions.

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

1 major / 9 minor

Summary. This paper presents a novel framework for inferring the initial conditions of Milky Way globular clusters (GCs) by coupling the fast semi-analytical evolutionary models (clusterBH, updated in Fronimos Pouliasis et al. 2026) with multimass limepy equilibrium models. The method is validated against mock observations extracted from a grid of star-by-star Monte Carlo (CMC) simulations, demonstrating recovery of initial and present-day cluster properties (mass, half-mass radius, density, BH mass fraction) within quantified uncertainties. Applied to a sample of 35 MW GCs (from an initial 40, with 5 removed for various quality reasons), the authors infer a distribution of initial half-mass densities peaking at rho_h,0 ~ 10^{6.4} M_sun/pc^3, a bottom-light stellar IMF, and small present-day BH mass fractions (<1.5%). The implications for high-redshift proto-GC observations, IMBH formation, and gravitational-wave source rates are discussed. The paper is well-structured, the methodology is clearly described, and the validation effort is substantial.

Significance. The coupling of fast evolutionary models with equilibrium DF-based models to infer initial conditions from present-day observations is a genuine methodological advance. The validation against CMC mock observations (Section 3) is thorough and demonstrates the method's recovery power across a large parameter space. The transparency regarding the BH-kick degeneracy (Section 5.6, Figure 13) is commendable and strengthens the paper's credibility. The finding that inferred initial densities are consistent with high-redshift proto-GC observations (Section 5.1, Figure 12) provides a tangible cross-epoch link. The open-source software (GCfit, clusterBH) and the availability of fit results for all clusters enhance reproducibility.

major comments (1)
  1. Section 3 and Section 5.6: The validation in Section 3 fits mock observations from the CMC grid (Kremer et al. 2020b), but clusterBH was itself calibrated against the same CMC grid (F26). The CMC models share the same BH natal kick prescription (fallback-modulated Maxwellian, sigma=265 km/s, Fryer et al. 2012 rapid engine) and BH IFMR (Banerjee et al. 2020) as clusterBH. Therefore, the validation confirms that the method recovers initial conditions *given* a specific BH physics prescription, but cannot test whether that prescription is correct for real clusters. The authors acknowledge this in Section 5.6 and demonstrate a clear degeneracy: a ~40% change in kick strength can compensate an order-of-magnitude change in initial density (Figure 13). This means the headline quantitative result (rho_h,0 ~ 10^{6.4} M_sun/pc^3) is conditional on the assumed BH physics. The paper would be Strengt
minor comments (9)
  1. Abstract: states 'a sample of 40 MW GCs' but the final sample used is 35 (Section 4.1). The abstract should reflect the final sample size or clarify the reduction.
  2. Table 1: the prior on alpha_2 is listed as U(-1.0, alpha_1), but alpha_1 is the slope for lower masses (0.1-0.5 M_sun) and alpha_2 for higher masses (0.5-1.0 M_sun). Typically alpha_2 > alpha_1 for a bottom-light IMF. Please clarify whether the upper bound should be alpha_1 or if this is a typo.
  3. Section 2.2.1, Eq. (1): the limiting mass m_lim = 3 M_sun is chosen to 'capture only the BHs.' However, some stellar remnants (e.g., massive NSs or massive WDs) could exceed this threshold. Please justify this specific choice or note its limitations.
  4. Section 4.1: NGC 6624 is removed from the sample due to inability to fit, but no detail is given on why the models fail. A brief explanation would help readers understand whether other clusters with similar properties might encounter similar issues.
  5. Figure 9: the y-axis label for the lower panel reads 'MBH [M_sun]' but the values appear to be in units of 10^3 or 10^4 M_sun. Please verify the axis labels and units.
  6. Section 5.4: the claim that inferred initial surface densities 'clearly exceed' proposed maximum limits (~10^5 M_sun/pc^2) is significant but is stated without quantification. Providing the actual inferred surface density values or a comparison figure would strengthen this point.
  7. Section 5.2: the discussion of IMBH formation via runaway collisions references Vergara et al. (2026) and Rantala et al. (2026), but the uncertainties in the collision prescriptions (e.g., mass stripping vs. growth) are only briefly mentioned. A slightly more nuanced discussion of these uncertainties would be valuable.
  8. The reference to 'J. M. D. Kruijssen 2026' in the Introduction appears to be an encyclopedia entry. Please verify this is the intended citation and format.
  9. Throughout the paper, the notation for the effective galactocentric radius switches between R'_G and R'G. Please standardize.

Circularity Check

1 steps flagged

Validation is partially circular (clusterBH calibrated against CMC, then validated against CMC mocks), but central claims about real MW clusters are independently derived from observational data; the BH-physics degeneracy is explicitly acknowledged, not hidden.

specific steps
  1. fitted input called prediction [Section 3 (Validation) and Section 2.1 (clusterBH description)]
    "These semi-analytical models were calibrated against a large grid of CMC cluster models (K. Kremer et al. 2020b), covering a range of initial conditions, and were able to reproduce the evolution of these star-by-star models to within about 10 per cent... We then fit the cBH+limepy models to these mock observations using the same priors as for the real clusters"

    The clusterBH evolutionary models were calibrated against the CMC grid (F26). The validation in Section 3 then fits clusterBH+limepy to mock observations extracted from the same CMC grid. Recovering CMC initial conditions from CMC mock observations is partly expected by construction, since clusterBH was tuned to reproduce CMC evolution. However, this is only partial circularity: the validation tests the full inverse pipeline (including limepy equilibrium fitting and SSPtools mass function evolution, which were not part of the clusterBH calibration), and the mock observations are generated independently via cmctoolkit. The paper is transparent about the limitation: 'since the CMC models share the same underlying BH assumptions (e.g. IFMR and natal kick prescriptions), this validation cannot

full rationale

The paper's central quantitative claims (initial densities ~10^6.4 M_sun/pc^3, bottom-light IMF, small present-day BH fractions) are derived from fitting free parameters (M0, rh,0, alpha1, alpha2) to independent observational data (proper motions, LOS velocities, number densities, stellar mass functions) for 35 real MW GCs. No equation-level circularity exists where a prediction reduces to its input by construction. The BH retention fraction (Eq. 2) depends on v_esc,0 (Eq. 3), which depends on the free parameters M0 and rho_h,0 — these are inferred from data, not self-defined. The mass function evolution (Eqs. 4-6) uses clusterBH escape rates to connect IMF to PDMF, with IMF slopes as free parameters. The partial circularity is confined to the validation step: clusterBH was calibrated against CMC (F26), and Section 3 validates the fitting pipeline against CMC mocks. This tests the inverse problem (can you recover initial conditions from present-day observations?) but cannot test whether the BH physics prescriptions are correct, since CMC shares the same assumptions. The authors explicitly acknowledge this: 'this validation cannot be used to say whether those assumptions are valid for real clusters.' The degeneracy between initial density and BH natal kick strength (Section 5.6, Figure 13) is a parameter degeneracy transparently quantified and flagged for future work, not a circular derivation. Self-citations (F26, D23, D24) are methodological — describing tools used — not load-bearing for the central claims via unverified theorems.

Axiom & Free-Parameter Ledger

14 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities or particles. The free parameters are either standard limepy structural parameters, initial conditions fitted to data, or nuisance parameters for observational systematics. The new parameters zeta and eta are model modifications to the equipartition and anisotropy prescriptions, not new physics. The key axioms are standard domain assumptions in cluster dynamics (virial equilibrium, tidal field modeling) plus the BH formation prescriptions whose uncertainty the paper itself flags as critical.

free parameters (14)
  • phi_0_hat = varies per cluster
    Central potential of limepy model, fitted to observations (Table A1)
  • g = varies per cluster
    Truncation parameter, fitted to observations (Table A1)
  • log(r_a_hat) = varies per cluster
    Anisotropy radius, fitted to observations (Table A1)
  • delta = varies per cluster
    Velocity-scale mass dependence, fitted to observations (Table A1)
  • zeta = varies per cluster
    Velocity-scale high-mass scaling, new parameter introduced in this work, fitted to data (Table A1)
  • eta = varies per cluster
    Anisotropy-scale mass dependence, allowed to vary freely (new in this work vs D23), fitted to data (Table A1)
  • M_0 = 0.01-6.81 x 10^6 M_sun
    Initial total cluster mass, fitted parameter (Table A1)
  • r_h,0 = 0.05-1.7 pc
    Initial half-mass radius, fitted parameter (Table A1)
  • alpha_1 = ~0.82 median
    IMF slope below 0.5 M_sun, fitted freely (Table A1)
  • alpha_2 = ~1.47 median
    IMF slope 0.5-1 M_sun, fitted freely (Table A1)
  • F = varies per cluster
    Mass function nuisance parameter for systematic uncertainties (Table A1)
  • s2 = varies per cluster
    Number density nuisance parameter (Table A1)
  • d = varies per cluster
    Heliocentric distance, Gaussian prior from literature (Table A1)
  • 7 clusterBH model parameters = default/median values from F26
    Parameters controlling two-body relaxation, stellar evolution, tidal evaporation, BH ejection efficiency; set to default calibrated values from F26 Table 2, not re-fitted here
axioms (6)
  • domain assumption Clusters remain in virial equilibrium throughout their evolution
    The coupling of clusterBH (which assumes virial equilibrium to track r_h) with limepy (an equilibrium model) requires this. Invoked in Section 2.1 and 2.3.
  • domain assumption BH natal kicks follow a fallback-modulated Maxwellian distribution with sigma = 265 km/s
    Section 2.3, Equation 2. The canonical prescription is commonly used but uncertain; the paper demonstrates sensitivity to this in Section 5.6.
  • domain assumption The MW potential is well-approximated by a static singular isothermal sphere with v_circ = 220 km/s
    Section 2.1. Clusters are placed on circular orbits in this potential. Real orbits are eccentric and the potential evolves over 12 Gyr.
  • domain assumption The BH IFMR from SSE models (Banerjee et al. 2020) and rapid supernova scheme (Fryer et al. 2012) are valid
    Section 2.3. These prescriptions determine the initial BH mass function and are shared with the CMC validation grid.
  • ad hoc to paper clusterBH prescriptions extrapolate correctly to density regimes beyond the CMC calibration grid
    Section 4.2 acknowledges that inferred initial densities exceed the densest CMC models, so the models cannot be directly tested in this regime.
  • domain assumption The r_c - f_BH relationship from CMC models applies to real clusters
    Section 2.4.2. A regularization prior on core radius vs BH mass fraction is imposed from CMC models, though the authors note it has limited impact.

pith-pipeline@v1.1.0-glm · 51309 in / 3433 out tokens · 290747 ms · 2026-07-09T21:40:57.478944+00:00 · methodology

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read the original abstract

We infer the initial conditions of Milky Way (MW) globular clusters (GCs) from present-day observations, through the coupling of recently updated rapid cluster evolution models with multimass equilibrium models. This novel method is validated by fitting to simulated observations of a large grid of star-by-star Monte Carlo models, demonstrating that we are able to recover cluster properties like the total mass, half-mass radius/density and black hole (BH) mass fraction, both initially and at the present day, across a large region of parameter space. We apply this framework to a sample of 40 MW GCs, fitting to a suite of observed radial profiles of number densities, proper motions, line-of-sight velocities and stellar mass functions. From these fits we infer a distribution of initial half-mass densities with a median and $1\sigma$ width, across our sample, of $\rho_{h,0} = 10^{6.4\pm0.9}\,{M_\odot pc^{-3}}$, higher than what is found for young massive clusters in the Local Universe and in line with young clusters at high redshift. We also find stellar initial mass functions that are bottom-light in comparison to canonical prescriptions, and relatively small present-day BH mass fractions ($\lesssim 1.5\%$). We discuss the implications of these initial cluster densities for observations of high-redshift proto-GCs, binary BH merger rates and intermediate-mass BHs (IMBHs) in GCs. Finally, we quantify how these densities may depend on assumptions typically made surrounding BH formation and natal kicks.

Figures

Figures reproduced from arXiv: 2607.07010 by Fotios Fronimos Pouliasis, Mark Gieles, Nolan Dickson, Peter J. Smith, Vincent H\'enault-Brunet.

Figure 1
Figure 1. Figure 1: Model radial profiles (blue contours) of surface number density (Σ), line-of-sight velocity dispersions (𝜎LOS), radial (𝜎PM,R) and tangential (𝜎PM,T) proper motion dispersions, for the fit of the mock observations of the CMC simulation with initial conditions 𝑁0 = 8 × 105 , 𝑟v,0 = 2 pc, 𝑅G = 2 kpc and 𝑍 = 0.0002. The dark and light shaded regions represent the 1𝜎 and 2𝜎 credible intervals of the model fits… view at source ↗
Figure 2
Figure 2. Figure 2: Model present-day local stellar mass functions (blue contours) for the fit of the mock observations of the CMC simulation with initial conditions 𝑁0 = 8 × 105 , 𝑟v,0 = 2 pc, 𝑅G = 2 kpc and 𝑍 = 0.0002. Each panel shows the number of stars per unit mass as a function of stellar mass, for different projected distance ranges from the cluster centre. The dark and light shaded regions represent the 1𝜎 and 2𝜎 cre… view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of the model total mass, half-mass radius, half-mass density and BH mass fraction over time (blue contours) for the fit of the mock observations of the CMC simulation with initial conditions 𝑁0 = 8 × 105 , 𝑟v,0 = 2 pc, 𝑅G = 2 kpc and 𝑍 = 0.0002. The dark and light shaded regions represent the 1𝜎 and 2𝜎 credible intervals of the model fits, respectively. The true values from the CMC snapshots are … view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the initial (top row) and present-day (bottom row) values of the total mass, half-mass radius, half-mass density and mass fraction in BHs inferred by our best-fitting models (on the y-axis), against the true values from the CMC models (on the x-axis). The points are coloured based on their true initial radii, and shown by a diamond, circle or triangle based on their initial number of stars (𝑁… view at source ↗
Figure 5
Figure 5. Figure 5: Model radial profiles (blue contours) of surface number density (Σ), line-of-sight velocity dispersions (𝜎LOS), radial (𝜎PM,R) and tangential (𝜎PM,T) proper motion dispersions, for the fit of NGC 1851. The dark and light shaded regions represent the 1𝜎 and 2𝜎 credible intervals of the model fits, respectively. The ob￾servational datasets used to constrain the models are shown along￾side their 1𝜎 uncertaint… view at source ↗
Figure 6
Figure 6. Figure 6: Model present-day local stellar mass functions for the fit of NGC 1851. Each panel shows the number of stars per unit mass as a function of stellar mass, for different projected distance ranges from the cluster centre. The dark and light shaded regions represent the 1𝜎 and 2𝜎 credible intervals of the model fits, respectively. The measurements used to constrain the models are shown alongside their 1𝜎 uncer… view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of cluster total mass, half-mass radius, half– mass density and BH mass fraction over time for the fit of NGC 1851. The dark and light shaded regions represent the 1𝜎 and 2𝜎 credible intervals of the model fits, respectively. The inset panels show the posterior distributions from our fit of the initial and present-day val￾ues of each quantity. It is worth highlighting the differences in approach … view at source ↗
Figure 8
Figure 8. Figure 8: Gaussian kernel density estimates showing the overall distributions of the initial (top row) and final (bottom row) total mass, half-mass radius, half-mass density and BH mass fractions across the fits to all clusters in our sample. Median and 1𝜎 intervals are shown by the black lines. Above each panel the corresponding values for all of the CMC models included in our validation sample (Section 3) are show… view at source ↗
Figure 9
Figure 9. Figure 9: Violin plots (in blue) of the posterior probability distribution of the mass fraction in BHs ( 𝑓BH; upper panel) and the total mass in BHs (lower panel) for all clusters in our sample, except for NGC 5139 (𝜔 Cen), which has 𝑓BH ∼ 8.3 per cent, and is excluded in order to better highlight the distributions of the other clusters. The median and 1𝜎 intervals are denoted by the horizontal blue ticks within eac… view at source ↗
Figure 10
Figure 10. Figure 10: The median values and 1𝜎 uncertainties of the inferred stellar IMF power-law slopes 𝛼1 and 𝛼2 for all clusters in our sample. Gaussian kernel density estimates showing the overall distributions of each parameter are shown above and to the right. The median val￾ues of the corresponding IMF slopes from P. Kroupa (2001) (green) and H. Baumgardt et al. (2023) (red) are shown by the horizontal and vertical lin… view at source ↗
Figure 11
Figure 11. Figure 11: Tracks of the evolution of each cluster in our sample, from initial total cluster mass and half-mass radius (square markers) over their lifetimes to the present conditions (triangle markers). Only the median inferred values of each quantity are shown. All colours are assigned randomly, to differentiate the tracks. Lines of constant half-mass density and central escape velocity are shown in grey. The initi… view at source ↗
Figure 13
Figure 13. Figure 13: Evolution of cluster total mass, half-mass radius, half-mass density and BH mass fraction over time for a fidu￾cial clusterBH model with initial conditions 𝑀0 = 1 × 106 M⊙, 𝜌h,0 = 1×106 M⊙ pc−3 , [Fe/H] = −2, 𝑅 ′ G = 5 kpc, 𝛼1 = −0.82 and 𝛼2 = −1.45 (green line), as well as a set of models evolved from a grid of initial densities and corresponding BH natal kick strengths ( 𝑓k) which result in similar pres… view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of the present-day local stellar mass functions between our fit to NGC 3201 and the CMC model best matching the velocity dispersion and surface brightness profile of the cluster (𝑁0 = 8 × 105 , 𝑟𝑣,0 = 2 pc, 𝑅𝑔 = 8 kpc and 𝑍 = 0.0002) (K. Kremer et al. 2019; N. Z. Rui et al. 2021a). Each panel shows the number of stars per unit mass as a function of stellar mass, for different projected distance… view at source ↗

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Works this paper leans on

149 extracted references · 149 canonical work pages · 5 internal anchors

  1. [1]

    1961 , month = feb, journal =

    work page 1961

  2. [2]

    Michie, R. W. , year =. On the. Monthly Notices of the Royal Astronomical Society , volume =

    work page

  3. [3]

    1965 , month = feb, journal =

    work page 1965

  4. [4]

    , year =

    King, Ivan R. , year =. The Structure of Star Clusters. The Astronomical Journal , publisher =. doi:10.1086/109857 , annotation =

    work page doi:10.1086/109857

  5. [5]

    H. Monte. 1971 , month = oct, journal =. doi:10.1007/BF00649159 , annotation =

    work page doi:10.1007/bf00649159 1971

  6. [6]

    H. The. 1971 , month = nov, journal =. doi:10.1007/BF00649201 , annotation =

    work page doi:10.1007/bf00649201 1971

  7. [7]

    H. Two. 1975 , month = jan, booktitle =

    work page 1975

  8. [8]

    and Hut, P

    Casertano, S. and Hut, P. , year =. Core Radius and Density Measurements in. The Astrophysical Journal , publisher =. doi:10.1086/163589 , keywords =

    work page doi:10.1086/163589

  9. [9]

    1987 , publisher =

    Dynamical Evolution of Globular Clusters , author =. 1987 , publisher =

    work page 1987

  10. [10]

    doi:10.1086/117268 , keywords =

    1995 , month = jan, volume =. doi:10.1086/117268 , keywords =

    work page doi:10.1086/117268 1995

  11. [11]

    1996 , month = oct, volume =

    work page 1996

  12. [12]

    doi:10.1086/316869 , keywords =

    2000 , month = dec, volume =. doi:10.1086/316869 , keywords =

    work page doi:10.1086/316869 2000

  13. [13]

    2001 , month = apr, volume =

    work page 2001

  14. [14]

    2002 , month = jul, volume =

    work page 2002

  15. [15]

    and McMillan, Stephen L

    2002 , month = sep, volume =. doi:10.1086/341798 , keywords =

    work page doi:10.1086/341798 2002

  16. [16]

    doi:10.1046/j.1365-8711.2003.06504.x , keywords =

    Dynamical Evolution of Star Clusters in Tidal Fields , author =. 2003 , month = mar, journal =. doi:10.1046/j.1365-8711.2003.06286.x , keywords =

    work page doi:10.1046/j.1365-8711.2003.06286.x 2003

  17. [17]

    , year =

    2003 , month = dec, volume =. doi:10.1046/j.1365-2966.2003.07275.x , keywords =

    work page doi:10.1046/j.1365-2966.2003.07275.x 2003

  18. [18]

    doi:10.1111/j.1365-2966.2004.07942.x , journal=

    2004 , month = jul, volume =. doi:10.1111/j.1365-2966.2004.07914.x , keywords =

    work page doi:10.1111/j.1365-2966.2004.07914.x 2004

  19. [19]

    doi:10.1038/nature02448 , keywords =

    2004 , month = apr, volume =. doi:10.1038/nature02448 , keywords =

    work page doi:10.1038/nature02448 2004

  20. [20]

    doi:10.1086/430723 , keywords =

    2005 , month = jul, volume =. doi:10.1086/430723 , keywords =

    work page doi:10.1086/430723 2005

  21. [21]

    2005 , month = jul, volume =

    work page 2005

  22. [22]

    2005 , month = may, volume =

    work page 2005

  23. [23]

    2007 , month = jul, volume =

    work page 2007

  24. [24]

    2007 , month = may, journal =

    work page 2007

  25. [25]

    2007 , month = apr, volume =

    work page 2007

  26. [26]

    2008 , month = sep, volume =

    work page 2008

  27. [27]

    and Vecchio, A

    2008 , month = oct, volume =. doi:10.1111/j.1365-2966.2008.13702.x , keywords =

    work page doi:10.1111/j.1365-2966.2008.13702.x 2008

  28. [28]

    2009 , month = may, volume =

    work page 2009

  29. [29]

    doi:10.1088/0004-637X/694/2/1498 , keywords =

    2009 , month = apr, volume =. doi:10.1088/0004-637X/694/2/1498 , keywords =

    work page doi:10.1088/0004-637x/694/2/1498 2009

  30. [30]

    , archivePrefix = "arXiv", eprint =

    2010 , month = jan, volume =. doi:10.1111/j.1745-3933.2009.00777.x , keywords =

    work page doi:10.1111/j.1745-3933.2009.00777.x 2010

  31. [31]

    and McMillan, Stephen L

    Portegies Zwart, Simon F. and McMillan, Stephen L. W. and Gieles, Mark , year =. Young. Annual Review of Astronomy and Astrophysics , volume =. doi:10.1146/annurev-astro-081309-130834 , keywords =

    work page doi:10.1146/annurev-astro-081309-130834

  32. [32]

    , keywords =

    The Life Cycle of Star Clusters in a Tidal Field , author =. 2011 , month = jun, journal =. doi:10.1111/j.1365-2966.2011.18320.x , annotation =

    work page doi:10.1111/j.1365-2966.2011.18320.x 2011

  33. [33]

    Alexander, Poul E. R. and Gieles, Mark , year =. A Prescription and Fast Code for the Long-Term Evolution of Star Clusters:. Monthly Notices of the Royal Astronomical Society , volume =

    work page

  34. [34]

    doi:10.1088/0004-637X/749/1/91 , keywords =

    2012 , month = apr, volume =. doi:10.1088/0004-637X/749/1/91 , keywords =

    work page doi:10.1088/0004-637x/749/1/91 2012

  35. [35]

    doi:10.1088/0004-637X/745/2/175 , keywords =

    2012 , month = feb, volume =. doi:10.1088/0004-637X/745/2/175 , keywords =

    work page doi:10.1088/0004-637x/745/2/175 2012

  36. [36]

    2012 , month = oct, volume =

    work page 2012

  37. [37]

    2013 , month = jul, journal =

    Dynamical Evolution of Black Hole Subsystems in Idealized Star Clusters , author =. 2013 , month = jul, journal =

    work page 2013

  38. [38]

    2013 , month = mar, volume =

    work page 2013

  39. [39]

    and Hurley, Jarrod R

    Giersz, Mirek and Heggie, Douglas C. and Hurley, Jarrod R. and Hypki, Arkadiusz , year =. Monthly Notices of the Royal Astronomical Society , volume =

    work page

  40. [40]

    Mocca Code for Star Cluster Simulations --

    Hypki, Arkadiusz and Giersz, Mirek , year =. Mocca Code for Star Cluster Simulations --. Monthly Notices of the Royal Astronomical Society , volume =

    work page

  41. [41]

    Lamers, Henny J. G. L. M. and Baumgardt, Holger and Gieles, Mark , year =. The Evolution of the Global Stellar Mass Function of Star Clusters: An Analytic Description , shorttitle =. Monthly Notices of the Royal Astronomical Society , publisher =. doi:10.1093/mnras/stt808 , annotation =

    work page doi:10.1093/mnras/stt808

  42. [42]

    doi:10.1051/0004-6361/201220307 , keywords =

    2013 , month = apr, volume =. doi:10.1051/0004-6361/201220307 , keywords =

    work page doi:10.1051/0004-6361/201220307 2013

  43. [43]

    2013 , month = sep, volume =

    work page 2013

  44. [44]

    doi:10.1088/0004-637X/775/2/134 , keywords =

    2013 , month = oct, volume =. doi:10.1088/0004-637X/775/2/134 , keywords =

    work page doi:10.1088/0004-637x/775/2/134 2013

  45. [45]

    Alexander, Poul E. R. and Gieles, Mark and Lamers, Henny J. G. L. M. and Baumgardt, Holger , year =. A Prescription and Fast Code for the Long-Term Evolution of Star Clusters -. Monthly Notices of the Royal Astronomical Society , publisher =. doi:10.1093/mnras/stu899 , annotation =

    work page doi:10.1093/mnras/stu899

  46. [46]

    doi:10.1093/mnras/stt2221 , keywords =

    2014 , month = feb, volume =. doi:10.1093/mnras/stt2221 , keywords =

    work page doi:10.1093/mnras/stt2221 2014

  47. [47]

    Gieles, Mark and Alexander, Poul E. R. and Lamers, Henny J. G. L. M. and Baumgardt, Holger , year =. A Prescription and Fast Code for the Long-Term Evolution of Star Clusters --. Monthly Notices of the Royal Astronomical Society , volume =

    work page

  48. [48]

    doi:10.1051/0004-6361/201423709 , keywords =

    2014 , month = jul, volume =. doi:10.1051/0004-6361/201423709 , keywords =

    work page doi:10.1051/0004-6361/201423709 2014

  49. [49]

    doi:10.1093/mnras/stv1848 , keywords =

    2015 , month = nov, volume =. doi:10.1093/mnras/stv1848 , keywords =

    work page doi:10.1093/mnras/stv1848 2015

  50. [50]

    2015 , month = feb, volume =

    work page 2015

  51. [51]

    2015 , month = apr, volume =

    work page 2015

  52. [52]

    and Miocchi, Paolo and Vesperini, Enrico , year =

    Alessandrini, Emiliano and Lanzoni, Barbara and Ferraro, Francesco R. and Miocchi, Paolo and Vesperini, Enrico , year =. Investigating the. The Astrophysical Journal , publisher =. doi:10.3847/1538-4357/833/2/252 , keywords =

    work page doi:10.3847/1538-4357/833/2/252

  53. [53]

    doi:10.3847/0004-637X/831/2/187 , keywords =

    2016 , month = nov, volume =. doi:10.3847/0004-637X/831/2/187 , keywords =

    work page doi:10.3847/0004-637x/831/2/187 2016

  54. [54]

    2016 , month = oct, journal =

    The Effect of Pair-Instability Mass Loss on Black-Hole Mergers , author =. 2016 , month = oct, journal =. doi:10.1051/0004-6361/201628980 , keywords =

    work page doi:10.1051/0004-6361/201628980 2016

  55. [55]

    doi:10.1093/mnras/stv2325 , keywords =

    2016 , month = jan, volume =. doi:10.1093/mnras/stv2325 , keywords =

    work page doi:10.1093/mnras/stv2325 2016

  56. [56]

    2016 , month = jun, volume =

    work page 2016

  57. [57]

    2016 , month = jan, volume =

    work page 2016

  58. [58]

    doi:10.1093/mnras/stv2733 , keywords =

    2016 , month = feb, volume =. doi:10.1093/mnras/stv2733 , keywords =

    work page doi:10.1093/mnras/stv2733 2016

  59. [59]

    doi:10.1103/PhysRevD.93.084029 , keywords =

    2016 , month = apr, volume =. doi:10.1103/PhysRevD.93.084029 , keywords =

    work page doi:10.1103/physrevd.93.084029 2016

  60. [60]

    doi:10.1093/mnras/stw274 , keywords =

    2016 , month = may, volume =. doi:10.1093/mnras/stw274 , keywords =

    work page doi:10.1093/mnras/stw274 2016

  61. [61]

    doi:10.1093/mnras/stw2488 , keywords =

    2017 , month = jan, volume =. doi:10.1093/mnras/stw2488 , keywords =

    work page doi:10.1093/mnras/stw2488 2017

  62. [62]

    doi:10.1093/mnras/stx1311 , keywords =

    2017 , month = sep, volume =. doi:10.1093/mnras/stx1311 , keywords =

    work page doi:10.1093/mnras/stx1311 2017

  63. [63]

    and Nelemans, Gijs , year =

    Repetto, Serena and Igoshev, Andrei P. and Nelemans, Gijs , year =. The. Monthly Notices of the Royal Astronomical Society , publisher =. doi:10.1093/mnras/stx027 , keywords =

    work page doi:10.1093/mnras/stx027

  64. [64]

    2018 , month = oct, volume =

    work page 2018

  65. [65]

    2018 , month = aug, volume =

    work page 2018

  66. [66]

    2018 , month = sep, volume =

    work page 2018

  67. [67]

    The Devil Is in the Tails: The Role of Globular Cluster Mass Evolution on Stream Properties , shorttitle =

    Balbinot, Eduardo and Gieles, Mark , year =. The Devil Is in the Tails: The Role of Globular Cluster Mass Evolution on Stream Properties , shorttitle =. Monthly Notices of the Royal Astronomical Society , publisher =. doi:10.1093/mnras/stx2708 , keywords =

    work page doi:10.1093/mnras/stx2708

  68. [68]

    doi:10.1146/annurev-astro-081817-051839 , keywords =

    2018 , month = sep, volume =. doi:10.1146/annurev-astro-081817-051839 , keywords =

    work page doi:10.1146/annurev-astro-081817-051839 2018

  69. [69]

    doi:10.1093/mnras/sty1057 , keywords =

    2018 , month = aug, volume =. doi:10.1093/mnras/sty1057 , keywords =

    work page doi:10.1093/mnras/sty1057 2018

  70. [70]

    2018 , month = dec, journal =

    Radiation Pressure Limits on the Star Formation Efficiency and Surface Density of Compact Stellar Systems , author =. 2018 , month = dec, journal =. doi:10.1093/mnras/sty2659 , keywords =

    work page internal anchor Pith review doi:10.1093/mnras/sty2659 2018

  71. [71]

    and Bastian, Nate and Gieles, Mark and Crain, Robert A

    Forbes, Duncan A. and Bastian, Nate and Gieles, Mark and Crain, Robert A. and Kruijssen, J. M. Diederik and Larsen, S. Globular Cluster Formation and Evolution in the Context of Cosmological Galaxy Assembly: Open Questions , shorttitle =. 2018 , month = feb, journal =. doi:10.1098/rspa.2017.0616 , keywords =

    work page doi:10.1098/rspa.2017.0616 2018

  72. [72]

    2018 , month = mar, volume =

    work page 2018

  73. [73]

    2018 , month = feb, volume =

    work page 2018

  74. [74]

    doi:10.1103/PhysRevD.98.123005 , keywords =

    2018 , month = dec, volume =. doi:10.1103/PhysRevD.98.123005 , keywords =

    work page doi:10.1103/physrevd.98.123005 2018

  75. [75]

    doi:10.3847/1538-4357/aac9b9 , keywords =

    2018 , month = jul, volume =. doi:10.3847/1538-4357/aac9b9 , keywords =

    work page doi:10.3847/1538-4357/aac9b9 2018

  76. [76]

    Black Hole Growth through Hierarchical Black Hole Mergers in Dense Star Clusters: Implications for Gravitational Wave Detections , shorttitle =

    Antonini, Fabio and Gieles, Mark and Gualandris, Alessia , year =. Black Hole Growth through Hierarchical Black Hole Mergers in Dense Star Clusters: Implications for Gravitational Wave Detections , shorttitle =. Monthly Notices of the Royal Astronomical Society , publisher =. doi:10.1093/mnras/stz1149 , annotation =

    work page doi:10.1093/mnras/stz1149

  77. [77]

    Atri, P. and. Potential Kick Velocity Distribution of Black Hole. 2019 , month = nov, journal =. doi:10.1093/mnras/stz2335 , keywords =

    work page doi:10.1093/mnras/stz2335 2019

  78. [78]

    2019 , month = feb, volume =

    work page 2019

  79. [79]

    2019 , month = jun, volume =

    work page 2019

  80. [80]

    2019 , month = dec, volume =

    work page 2019

Showing first 80 references.