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arxiv: 2605.18665 · v1 · pith:B2NBW2A3new · submitted 2026-05-18 · 🌌 astro-ph.GA · astro-ph.SR

CCD () photometry of the open cluster NGC 6793 and its dynamical evolution

Zahra Al , Y\"uksel Karata\c{s} , Raul Michel Murillo , Charles Bonatto , Orhan G\"une\c{s} , \.Inci Akkaya Oralhan , Ey\"up Kaan \"Ulgen This is my paper

Pith reviewed 2026-05-20 08:51 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords open cluster NGC 6793CCD photometryisochrone fittingdynamical evolutiontidally filling statecluster dissolution
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The pith

New photometry shows NGC 6793 is 525 million years old at 575 parsecs and tidally filling, set to dissolve before final contraction.

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

The paper uses new CCD UBV(RI) photometry to determine the physical properties and current dynamical state of the open cluster NGC 6793. Isochrone fitting places the cluster at an intermediate age with a distance of roughly 575 parsecs from the Sun. Structural analysis reveals a shrinking core and a tidal-to-Jacobi radius ratio near unity, indicating the cluster is now filling its tidal boundary. This state implies the cluster will disperse into the galactic field before it can reach a more compact final phase. Such detailed tracking of one cluster contributes to understanding how open clusters evolve and dissolve over time in the Milky Way disk.

Core claim

Padova isochrone fitting to the V × (B-V) colour-magnitude diagram yields an intermediate age of 525 ± 51 Myr and a distance modulus of μ = 8.80 ± 0.05 mag, corresponding to a distance of d = 575 ± 58 pc. The core radius appears to be shrinking due to advanced dynamical evolution (log τ2 = 1.13), and the ratio Rt/RJ = 0.99 indicates the cluster is currently in a tidally filling state that will lead to dissolution before the final contraction phase.

What carries the argument

The ratio of tidal radius to Jacobi radius (Rt/RJ) together with core-to-half-mass and half-mass-to-Jacobi radius ratios used to diagnose the combined effects of internal relaxation and external tides.

If this is right

  • The cluster's evolution is governed by the combined effects of internal two-body relaxation, mass segregation, and external tidal perturbations.
  • NGC 6793 belongs among the relatively compact clusters with galactocentric radius less than 7.9 kpc.
  • The cluster will dissolve and disperse before entering the final contraction phase.
  • Its current parameter pairs place it in a stable compact state against two-body encounters and tidal heating.

Where Pith is reading between the lines

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

  • Clusters with similar radius ratios may commonly dissolve while still tidally filling rather than after further contraction.
  • Tracking more clusters with Rt/RJ near 1 could refine models of open-cluster lifetimes in the inner galactic disk.
  • The dissolution of such clusters would increase the supply of field stars with ages around 500 Myr.

Load-bearing premise

The stars selected for the colour-magnitude diagram are predominantly cluster members with negligible field-star contamination.

What would settle it

An independent measurement that yields a substantially different age, distance, or a tidal-to-Jacobi radius ratio clearly below 0.8 would contradict the tidally filling dissolution scenario.

read the original abstract

We present new astrophysical parameters for the open cluster NGC~6793 based on new CCD $UBV(RI)_{KC}$ photometry. We derived a reddening of $E(B-V) = 0.24 \pm 0.02$~mag and a heavy element abundance of $Z = 0.024$ ($[Fe/H] = +0.20$~dex). Padova isochrone fitting to the $V \times (B-V)$ colour-magnitude diagram yields an intermediate age of $525 \pm 51$~Myr and a distance modulus of $\mu = 8.80 \pm 0.05$~mag, corresponding to a distance of $d = 575 \pm 58$~pc from the Sun. The core radius of NGC~6793 appears to be shrinking due to advanced dynamical evolution ($\log\tau_{2} = 1.13$), driven by mass segregation and the evaporation of low-mass stars from the central region. The ratios of core to half-mass radius ($R_{c}/R_{h}$) and half-mass to Jacobi radius ($R_{h}/R_{J}$) indicate that the cluster's evolution is governed by the combined effects of internal two-body relaxation, mass segregation, and external tidal perturbations. The ratio $R_{t}/R_{J} = 0.99$ suggests that the cluster is currently in a tidally filling state. The parameter pairs ($t_{diss}/t_{rlx_{1}} = 40$, $\log R_{J}/R_{c} = 0.72$) and ($R_{h}/R_{J} = 0.38$, $\log\rho_{amb} = -0.88$) place NGC~6793 among the relatively compact clusters within $R_{GC} < 7.9$~kpc. This implies a compact internal structure that is stable against the combined effects of two-body encounters and tidal heating. Given its current state, NGC~6793 will likely dissolve and disperse before entering the final contraction phase ($R_{4}$ regime).

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

2 major / 1 minor

Summary. The manuscript presents new CCD UBV(RI) photometry of the open cluster NGC 6793. Padova isochrone fitting to the V × (B-V) CMD yields E(B-V) = 0.24 ± 0.02 mag, Z = 0.024, age 525 ± 51 Myr, and distance modulus μ = 8.80 ± 0.05 mag (d = 575 ± 58 pc). Dynamical analysis indicates a shrinking core (log τ2 = 1.13) due to mass segregation, with ratios Rc/Rh, Rh/RJ, and Rt/RJ = 0.99 placing the cluster in a tidally filling state that will lead to dissolution before the R4 contraction phase; it is classified among compact clusters with R_GC < 7.9 kpc.

Significance. If the membership selection and parameter derivations are robust, the work supplies updated astrophysical parameters for NGC 6793 together with a dynamical-evolution context that links internal relaxation, mass segregation, and external tides. Explicit uncertainties and use of standard Padova models are positive features that aid reproducibility and comparison with other clusters.

major comments (2)
  1. [Abstract] Abstract: The derived age (525 ± 51 Myr), distance modulus (μ = 8.80 ± 0.05 mag), and all downstream dynamical ratios (Rt/RJ = 0.99, log τ2 = 1.13, t_diss/t_rlx1 = 40) rest on the assumption that stars selected for the V × (B-V) CMD are predominantly cluster members. No Gaia proper-motion or radial-velocity membership probabilities, nor statistical field subtraction via a control field, are reported; field contamination could shift the turn-off morphology and bias the fitted parameters.
  2. [Abstract] Abstract: The structural radii (Rc, Rh, RJ) and relaxation times used to compute the reported ratios and the conclusion that the cluster is tidally filling are obtained from the isochrone-derived mass and radius; the manuscript does not detail the exact computation, error propagation, or correction for unresolved binaries, leaving the robustness of Rt/RJ = 0.99 and the dissolution prediction difficult to evaluate.
minor comments (1)
  1. [Title] The title contains the apparent placeholder 'CCD () photometry'; this should be corrected to specify the filters clearly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below and have revised the manuscript to improve transparency and robustness.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The derived age (525 ± 51 Myr), distance modulus (μ = 8.80 ± 0.05 mag), and all downstream dynamical ratios (Rt/RJ = 0.99, log τ2 = 1.13, t_diss/t_rlx1 = 40) rest on the assumption that stars selected for the V × (B-V) CMD are predominantly cluster members. No Gaia proper-motion or radial-velocity membership probabilities, nor statistical field subtraction via a control field, are reported; field contamination could shift the turn-off morphology and bias the fitted parameters.

    Authors: Our candidate selection was performed by restricting to stars within the apparent cluster radius and retaining those that follow the clear main-sequence and turn-off locus in the V × (B-V) diagram. We acknowledge that this photometric selection alone does not fully exclude field interlopers and that Gaia proper-motion or parallax membership probabilities would strengthen the analysis. In the revised manuscript we will add a dedicated subsection on membership, cross-match the photometric catalogue with Gaia DR3 to report the fraction of stars with high membership probability, and discuss the possible effect of residual contamination on the fitted age and distance. We will also note the absence of a control-field subtraction as a limitation of the current data set. revision: partial

  2. Referee: [Abstract] Abstract: The structural radii (Rc, Rh, RJ) and relaxation times used to compute the reported ratios and the conclusion that the cluster is tidally filling are obtained from the isochrone-derived mass and radius; the manuscript does not detail the exact computation, error propagation, or correction for unresolved binaries, leaving the robustness of Rt/RJ = 0.99 and the dissolution prediction difficult to evaluate.

    Authors: The core radius Rc was obtained from a King-model fit to the observed radial density profile. The half-mass radius Rh and Jacobi radius RJ were computed from the total cluster mass (derived by integrating the isochrone mass function down to the photometric limit) using the standard relations of Portegies Zwart et al. (2010). Relaxation times followed the Spitzer (1987) formulae. We agree that these steps were not described in sufficient detail. In the revised version we will insert an expanded methods subsection that (i) reproduces the exact equations employed, (ii) propagates the uncertainties in distance, reddening, and photometric completeness into the derived radii and relaxation times, and (iii) discusses the possible bias introduced by unresolved binaries (estimated at the 20–30 % level for a typical open-cluster binary fraction). We will also state that a spectroscopic binary correction lies outside the scope of the present photometric study. revision: yes

Circularity Check

0 steps flagged

No circularity: parameters from external isochrone fits, dynamical ratios computed downstream

full rationale

The derivation begins with standard CCD photometry reduced to a V vs (B-V) CMD, followed by fitting to independent Padova isochrones to obtain age, distance modulus, reddening and metallicity. Structural radii (Rc, Rh, RJ) and relaxation times are then calculated directly from the fitted mass, observed star counts and standard dynamical formulae; the ratios log τ2, Rt/RJ and others are simple algebraic combinations of these quantities. No equation redefines a fitted parameter as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled in. The chain is therefore self-contained against external benchmarks and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard stellar evolution models and dynamical scaling relations taken from prior literature, plus several quantities fitted directly to the new photometry.

free parameters (4)
  • Reddening E(B-V) = 0.24 ± 0.02 mag
    Fitted value used to align the observed CMD with theoretical isochrones.
  • Metallicity Z = 0.024
    Chosen or fitted to match the heavy-element abundance in the isochrone grid.
  • Age = 525 ± 51 Myr
    Primary fitted parameter from Padova isochrone matching to the CMD.
  • Distance modulus μ = 8.80 ± 0.05 mag
    Fitted to set the absolute scale of the CMD.
axioms (2)
  • domain assumption Padova isochrones provide an accurate representation of stellar evolution at the derived age and metallicity for this cluster.
    Directly invoked for CMD fitting to obtain age and distance.
  • domain assumption Structural radii and relaxation times can be reliably estimated from the observed photometry and standard dynamical formulas without large corrections for binaries or incompleteness.
    Required for the core-shrinkage and tidal-filling conclusions.

pith-pipeline@v0.9.0 · 5967 in / 1820 out tokens · 52484 ms · 2026-05-20T08:51:34.245196+00:00 · methodology

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Works this paper leans on

77 extracted references · 77 canonical work pages

  1. [1]

    2010, RMxAA, 46,

    Akkaya, Í., Schuster, W.J., Michel, R., Chavarría-K, C., Moitinho, A., Vázquez, R., Karataş, Y. 2010, RMxAA, 46,

    work page 2010

  2. [2]

    2015,New Astronomy, 34,

    Akkaya Oralhan, Í., Karataş, Y., Schuster, W.J., Michel, R., Chavarría, C. 2015,New Astronomy, 34,

    work page 2015

  3. [3]

    2019,Journal of Astrophysics and Astronomy, 40,

    Akkaya Oralhan, Í., Michel, R., Schuster, W.J., Karataş, Y., Karslı, Y., Chavarría, C. 2019,Journal of Astrophysics and Astronomy, 40,

    work page 2019

  4. [4]

    Akkaya Oralhan, I., Cakmak, H., Karataş, Y., Michel, R., Bonatto, C., 2024,MNRAS, 531,

    work page 2024

  5. [5]

    Allison, R.J., Goodwin, S.P., Parker, R.J., Portegies- Zwart, S.F., de Grijs, R., Kouwenhoven, M.B.N., 2009,MNRAS, 395,

    work page 2009

  6. [6]

    2023,MNRAS, 525, 2315 Almeida, D., Moitinho, A., Moreiral, S

    Almeida, A., Monteiro, H., Dias, W.S. 2023,MNRAS, 525, 2315 Almeida, D., Moitinho, A., Moreiral, S. 2025,A&A, 693, 305 Alvarez-Baena, N., Carrera, R., Thompson, H., et al., 2024,A&A, 687,

    work page 2023

  7. [7]

    Angelo,M.S.,SantosJr,J.F.C.,Corradi,W.J.B.,2020, MNRAS, 493,

    Andrae, R., Fouesneau, M., Creevey, O., et al., 2023, A&A, 674, A9. Angelo,M.S.,SantosJr,J.F.C.,Corradi,W.J.B.,2020, MNRAS, 493,

    work page 2023

  8. [8]

    Angelo,M.S.,Corradi,W.J.B.,SantosJr,J.F.C.,Maia, F.F.S., Ferreira, F.A., 2021,MNRAS, 500,

    work page 2021

  9. [9]

    Angelo, M.S., Santos Jr, J.F.C., Maia, F.F.S., Corradi, W.J.B., 2023,MNRAS, 522,

    work page 2023

  10. [10]

    Angelo,M.S.,SantosJr,J.F.C.,Corradi,W.J.B.,Maia, F.F.S., 2025,MNRAS, 539,

    work page 2025

  11. [11]

    Arenou,F.,Luri,X.,Babusiaux,C.,etal.,2018,A&A, 616,

    work page 2018

  12. [12]

    Astrophys

    #### Page 22 of 1J. Astrophys. Astr.(0000)000: #### Bailer-Jones, C.A.L., Rybizki, J., Fouesneau, M., Mantelet, G., Andrae, R., 2018,AJ, 156,

    work page 2018

  13. [13]

    Belwal, K., Bisht, D., Jiang, I.-G., Yadav, R. K. S., Raj, A., Rangwal, G., Dattatrey, A. K., Bisht, M. S., Durgapal, A., 2025,MNRAS, 544,

    work page 2025

  14. [14]

    Bland-Hawthorn, J., Gerhard, O., 2016,ARA&A, 54,

    Binney, J., Merrifield, M., 1998,Galactic Astronomy, Princeton University Press, Princeton. Bland-Hawthorn, J., Gerhard, O., 2016,ARA&A, 54,

    work page 1998

  15. [15]

    Bonatto, C., Bica, E., Santos Jr, J.F.C., 2005,A&A, 433,

    work page 2005

  16. [16]

    Bonatto, C., Bica, E., 2007,MNRAS, 377,

    work page 2007

  17. [17]

    Bonatto, C., Bica, E., 2010,A&A, 521,

    work page 2010

  18. [18]

    Bonatto, C., Bica, E., 2011,MNRAS, 415,

    work page 2011

  19. [19]

    Bovy, J., Rix, H.-W., Liu, C., Hogg, D

    Bossini, D., Vallenari, A., Bragaglia, A., et al., 2019, A&A, 623, A108. Bovy, J., Rix, H.-W., Liu, C., Hogg, D. W., Beers, T. C., & Lee, Y. S., 2012,ApJ, 753,

    work page 2019

  20. [20]

    Bovy, J., & Rix, H.-W., 2013,ApJ, 779,

    work page 2013

  21. [21]

    Bovy, J., 2015, galpy: A Python Library for Galactic Dynamics,ApJS, 216,

    work page 2015

  22. [22]

    Bressan, A., Marigo, P., Girardi, L., Salasnich, B., Dal Cero, C., Rubele, S., Nanni, A., 2012,MNRAS, 427,

    work page 2012

  23. [23]

    Brunthaler,A.,Reid,M.J.,Menten,K.M.,etal.,2011, AN, 332,

    work page 2011

  24. [24]

    Camargo, D., Bonatto, C., Bica, E., 2009,A&A, 508,

    work page 2009

  25. [25]

    Camargo, D., Bonatto, C., Bica, E., 2010,A&A, 521,

    work page 2010

  26. [26]

    Cantat-Gaudin,T.,Jordi,C.,Vallenari,A.,etal.,2018, A&A, 618,

    work page 2018

  27. [27]

    Cantat-Gaudin, T., Anders, F., Castro-Ginard, A., et al., 2020,A&A, 640,

    work page 2020

  28. [28]

    Carrera, R., Pasquato, M., Vallenari, A., et al., 2019, A&A, 627,

    work page 2019

  29. [29]

    Caffau, E., Ludwig, H.-G., Steffen, M., Freytag, B., Bonifacio, P., 2011,Solar Phys., 268,

    work page 2011

  30. [30]

    Chumak, Y.O., Platais, I., McLaughlin, D.E., Ras- torguev, A.S., Chumak, O.V., 2010,MNRAS, 402,

    work page 2010

  31. [31]

    Dean, J.F., Warren, P.R., Cousins, A.W.J., 1978,MN- RAS, 183,

    Cropper, M., et al., 2018,A&A, 616, A5. Dean, J.F., Warren, P.R., Cousins, A.W.J., 1978,MN- RAS, 183,

    work page 2018

  32. [32]

    J., 1998,MNRAS, 298,

    Dehnen, W., & Binney, J. J., 1998,MNRAS, 298,

    work page 1998

  33. [33]

    Dias, W.S., Monteiro, H., Moitinho, A., et al., 2021, MNRAS, 504,

    work page 2021

  34. [34]

    I., Balaguer-Núñez, L., Castro-Ginard, A., Cantat-Gaudin, T., & Casamiquela, L., 2023, A&A, 675, A89

    Donada, J., Anders, F., Jordi, C., Masana, E., Gieles, M., Perren, G. I., Balaguer-Núñez, L., Castro-Ginard, A., Cantat-Gaudin, T., & Casamiquela, L., 2023, A&A, 675, A89. Donor, J., et al., 2020,AJ, 159, 199 Fernie,J.D.,1961,Monthly Notes of the Astronomical Society of South Africa, 20,

    work page 2023

  35. [35]

    M., et al., 2013,The Astrophysical Journal Letters, 777, L1

    Frinchaboy, P. M., et al., 2013,The Astrophysical Journal Letters, 777, L1. Fukushige, T., Heggie, D.C., 1995,MNRAS,276,

    work page 2013

  36. [36]

    Gaia Collaboration, Lindegren, L., Bastian, U., Bier- mann, M., et al., 2021,A&A, 649, A4

    Gaia Collaboration, Brown, A.G.A., Vallenari, A., Prusti, T., de Bruijne, J.H.J., et al., 2016,A&A, 595, A2. Gaia Collaboration, Lindegren, L., Bastian, U., Bier- mann, M., et al., 2021,A&A, 649, A4. Gaia Collaboration, Vallenari, A., Brown, A.G.A., et al., 2023,A&A, 674, A1. Geller,A.M.,Mathieu,R.D.,Braden,E.K.,Meibom, S., Platais, I., Dolan, C. J., 2010...

    work page 2016

  37. [37]

    Gieles, M., Athanassoula, E., Portegies-Zwart, S., 2007,MNRAS, 376,

    work page 2007

  38. [38]

    Gillessen, S., Eisenhauer, F., Trippe, S., Alexander, T., Genzel, R., Martins, F., & Ott, T., 2009,ApJ, 692,

    work page 2009

  39. [39]

    M., Grundy, W

    Girard, T. M., Grundy, W. M., Lopez, C. E., van Altena, W. F., 1989,AJ, 98,

    work page 1989

  40. [40]

    Güneş,O.,Karataş,Y.,Bonatto,C.,2017,Astronomis- che Nachrichten (AN), 338,

    work page 2017

  41. [41]

    He, Z., Wang, K., Luo, Y., Li, J., Liu, X., & Jiang, Q., 2022, ApJS, 262,

    work page 2022

  42. [42]

    Press, Chapter

    Heggie, D., Hut, P., 2003,The Gravitational Million- Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics, Cambridge Univ. Press, Chapter

    work page 2003

  43. [43]

    L., & Reffert, S., 2024, A&A, 686, A42

    Hunt, E. L., & Reffert, S., 2024, A&A, 686, A42. J. Astrophys. Astr.(0000)000: #### Page 23 of 1 #### Hunt, E.L., Reffert, S., 2023,A&A, 673,

    work page 2024

  44. [44]

    L., & Reffert, S., 2024,A&A, 686, A42

    Hunt, E. L., & Reffert, S., 2024,A&A, 686, A42. Jadhav, V.V., Roy, K., Joshi, N., Annapurni Subrama- niam, A., 2021,AJ, 162,

    work page 2024

  45. [45]

    Just, A., Piskunov, A

    Johnson,D.R.H.,Soderblom,D.R.,1987,AJ,93,864. Just, A., Piskunov, A. E., Klos, J. H., Kovaleva, D. A., & Polyachenko, E. V., 2023, A&A, 672, A187. Karataş, Y., Cakmak, H., Akkaya-Oralhan, Í., et al., 2023,MNRAS, 521,

    work page 1987

  46. [46]

    Karataş, Y., Schuster, W.J., 2006,MNRAS, 371,

    work page 2006

  47. [47]

    J., & Lynden-Bell, D., 1986,MNRAS, 221,

    Kerr, F. J., & Lynden-Bell, D., 1986,MNRAS, 221,

    work page 1986

  48. [48]

    V., Piskunov, A

    Kharchenko, N. V., Piskunov, A. E., Schilbach, E., Röser, S., & Scholz, R.-D., 2016, A&A, 585, A101. King, I., 1962,AJ, 67,

    work page 2016

  49. [49]

    King, I., 1966,AJ, 71,

    work page 1966

  50. [50]

    Kroupa, P., 2001,MNRAS, 322,

    Krone-Martins, A., Moitinho, A., 2014,A&A, 561, A57. Kroupa, P., 2001,MNRAS, 322,

    work page 2014

  51. [51]

    Küpper, A. H. W., Kroupa, P., Baumgardt, H., & Heggie, D. C., 2010,MNRAS, 401,

    work page 2010

  52. [52]

    Lamers, H.J.G.L.M., Gieles, M., Portegies Zwart, S.F., 2005,A&A, 429,

    work page 2005

  53. [53]

    Lamers, H.J.G.L.M., Gieles, M., 2006,A&A, 455,

    work page 2006

  54. [54]

    Landolt, A.U., 2009,AJ, 137,

    work page 2009

  55. [55]

    Yang, C., 2003,apj, 872,

    Li, C., Zhao G. Yang, C., 2003,apj, 872,

    work page 2003

  56. [56]

    Liu, D., Xu, Y., Hao, C., Bian, S., Lin, Z., Li, Y., & Li, J., 2023, ApJS, 268,

    Lindegren, L., et al., 2021,A&A, 649, A2. Liu, D., Xu, Y., Hao, C., Bian, S., Lin, Z., Li, Y., & Li, J., 2023, ApJS, 268,

    work page 2021

  57. [57]

    Llorente de Andres, F., Morales-Durán, C., 2022, American Journal of Astronomy and Astrophysics, 9,

    work page 2022

  58. [58]

    Mackey, A.D., Gilmore, G.F., 2003,MNRAS, 338,

    work page 2003

  59. [59]

    Mackey, A.D., Wilkinson, M.I., Davies, M.B., Gilmore, G.F., 2008,MNRAS, 386,

    work page 2008

  60. [60]

    J., 2017,MNRAS, 465,

    McMillan, P. J., 2017,MNRAS, 465,

    work page 2017

  61. [61]

    1981, Galactic Astronomy: Structure and Kinematics, 2nd edition Minchev,I.,Anders,F.,Recio-Blanco,A.,etal.,2018, MNRAS, 481,

    Mihalas, G., & Binney, J. 1981, Galactic Astronomy: Structure and Kinematics, 2nd edition Minchev,I.,Anders,F.,Recio-Blanco,A.,etal.,2018, MNRAS, 481,

    work page 1981

  62. [62]

    D., 2006,MNRAS, 373,

    Naylor, T., Jeffries, R. D., 2006,MNRAS, 373,

    work page 2006

  63. [63]

    Pace, G., Pasquini, L., François, P., 2008,A&A, 489, 403–412

    Newville, M., Stensitzki, T., Allen, D.B., Ingargiola, A., 2014, LMFIT: Non-Linear Least-Square Mini- mization and Curve-Fitting for Python. Pace, G., Pasquini, L., François, P., 2008,A&A, 489, 403–412. Pancino, E., Carrera, R., Rossetti, E., Gallart, C., 2010,A&A, 511, A56. Pera, M.S., Perren, G.I., Moitinho, A., Navone, H.D., Vazquez, R.A., 2021,A&A, 650,

    work page 2014

  64. [64]

    Piatti, A.E., Angelo, M.S., Dias, W., 2019,MNRAS, 488,

    work page 2019

  65. [65]

    Pietrinferni, A., Salaris, M., Cassisi, S., Savino, A., Mucciarelli,A.,Hyder,D.,Hidalgo,S.,2024,MNRAS, 527, 2065 Piskunov, A.E., Schilbach, E., Kharchenko, N.V., Röser, S., Scholz, R.-D.,2007,A&A, 468, 151, A56. Poggio, E., Drimmel, R., Cantat-Gaudin, T., Ramos, P., Ripepi, V., Zari, E., Andrae, R., Blomme, R., Chemin, L., Clementini, G., Figueras, F., Fo...

    work page 2024

  66. [66]

    Portegies Zwart, S.F., McMillan, S.L.W., Gieles, M., 2010,ARA&A, 48,

    work page 2010

  67. [67]

    Recio-Blanco, A., Kordopatis, G., de Laverny, P., et al., 2023,A&A, 674, A38

    Paunzen, E., Netopil, M., Heiter, U., Soubiran, C., 2010,A&A, 517, A32. Recio-Blanco, A., Kordopatis, G., de Laverny, P., et al., 2023,A&A, 674, A38. Schilbach, E., Kharchenko, N.V., Piskunov, A.E., Röser, S., Scholz, R.D., 2006,A&A, 456,

    work page 2010

  68. [68]

    Schönrich, R., Binney, J., Dehnen, W., 2010,MNRAS, 403,

    work page 2010

  69. [69]

    Astrophys

    #### Page 24 of 1J. Astrophys. Astr.(0000)000: #### Schuster, W.J., Michel, R., Dias, W., Tapia-Peralta, T., Vázquez, R., Macfarland, J., Chavarría, C., Santos, C., Moitinho, A., 2007, Galaxy Evolution Across the Hubble Time, eds. F. Combes and J. Palouš, Proc. IAU Symp. 235,

    work page 2007

  70. [70]

    Soubiran, C., et al., 2019,A&A, 623,

    work page 2019

  71. [71]

    Spitzer, L., Hart, M., 1971,AJ, 164,

    work page 1971

  72. [72]

    Stetson, P.B., 1987,PASP, 99,

    work page 1987

  73. [73]

    15, Pachart Pub

    Straižys, V., 1995, Multicolor Stellar Photometry, Astronomy and Astrophysics Series, Vol. 15, Pachart Pub. House. Sung, H., Lim, B., Bessell, M.S., Kim, J.S., Hur, H., Chun, M-Y., Park, B-G., 2013,JKAS, 46,

    work page 1995

  74. [74]

    Tapia, M.T., Schuster, W.J., Michel, R., Chavarría- K, C., Dias, W.S., Vázquez, R., Moitinho, A., 2010, MNRAS, 401,

    work page 2010

  75. [75]

    Tarricq, Y., Soubiran, C., Casamiquela, L., Castro- Ginard, A., Olivares, J., Miret-Roig, N., Galli, P.A.B., 2022,A&A, 659, A59

    Tarricq, Y., et al., 2021,A&A, 647, A19. Tarricq, Y., Soubiran, C., Casamiquela, L., Castro- Ginard, A., Olivares, J., Miret-Roig, N., Galli, P.A.B., 2022,A&A, 659, A59. Taşdemir, S., 2025,İUPress PAR, 3, 1–20 Wilson C. P., 1975, AJ, 80, 175 van den Berg, S., Morbey, C., Pazder, J., 1991,ApJ, 375,

    work page 2021

  76. [76]

    Xue, X.-X., Rix, H.-W., Zhao, G., Re Fiorentin, P., Naab, T., Steinmetz, M., van den Bosch, F

    Xu, M., Fu, X., Chen, Y., Li, L., Fang, M., Zhao, H., Liu, P., & Zuo, Y., 2025, A&A, 698, A156. Xue, X.-X., Rix, H.-W., Zhao, G., Re Fiorentin, P., Naab, T., Steinmetz, M., van den Bosch, F. C., et al., 2008,ApJ, 684,

    work page 2025

  77. [77]

    Zhang, Y., Liu, J., & Zhang, F., 2013, inIAU Sympo- sium, 295, 62

    work page 2013