adsabs/AstroCLIMB huggingface dataset:
Paper: Temporal Evolutions and Quasiperiodic Variations Present in the Sunspot Number and Group Sunspot Area Data Measured at Kodaikanal Observatory for Solar Cycles 14–24
Authors: Belur Ravindra, Partha Chowdhury, Pratap Chandra Ray, Kumaravel Pichamani
Figure caption: Wavelet plots showing the presence of the ∼22 yr Hale cycle in the hemispheric and full-disk group sunspot area data sets.
Paper: Temporal Evolutions and Quasiperiodic Variations Present in the Sunspot Number and Group Sunspot Area Data Measured at Kodaikanal Observatory for Solar Cycles 14–24
Authors: Belur Ravindra, Partha Chowdhury, Pratap Chandra Ray, Kumaravel Pichamani
Figure caption: Same as Figure 16, but for the group sunspot area data.
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: Left: the observed physical offset distribution of short GRBs, divided into the Gold, Silver, and Bronze samples; arrows from the bottom denote medians of each distribution. As expected, the bursts with the most tenuous associations (Bronze sample) are farther from their hosts than the Gold and Silver samples. Also shown are the observed offsets of long GRBs and the sampled distributions taking into account uncertainties (red; Blanchard et al. 2016). Right: the observed physical offset distribution of short GRBs (navy blue) and the sampled distributions taking into account measurement uncertainties (shaded light blue). A comparison to representative NS-NS merger models for differing metallicities (dotted and dashed–dotted green lines; Wiggins et al. 2018) shows that the observed and model distributions are overall consistent, although there is a relative dearth of observed high-offset short GRBs. Also shown is the observed distribution of globular clusters in the elliptical galaxy NGC821 (dashed–dotted black line; Spitler et al. 2008); overall, short GRBs are clearly not as extended as this population.
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: Left: the host-normalized offsets of 34 short GRBs with respect to their host galaxy centers (represented by the origin), where uncertainties on individual measurements correspond to 1σ confidence. The axes are oriented with north up and east to the left, and the scale is in the frame of the host galaxy (in which negative values correspond to east and/or south of the galaxy). Concentric dashed circles denote 1re , 5re , and 10re  offsets, while the red circle denotes the median on the full distribution of 1.5r  e . Right: the observed distribution of host-normalized offsets for short GRBs (blue solid line) and the sampled distributions with uncertainties (blue shaded region). Also shown are the corresponding distributions of long GRBs (red; Blanchard et al. 2016) and globular clusters in the elliptical galaxy NGC821 (Spitler et al. 2008; dashed–dotted black line). Overall, short GRBs are farther from their hosts than long GRBs but closer than globular clusters, even when normalized by their host galaxy sizes.
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: The fields of six short GRBs with no clear host association (﹩{P}_{\mathrm{cc},\min }\gtrsim 0.25﹩), classified as “Inconclusive” associations. Orange dashed circles are XRT positions, while solid blue circles are optical positions. Also displayed is the field of GRB 201006A, which has a high-extinction sightline of A  V  = 3.5 mag (falling in the observing constraint category), but for which we have deep K-band imaging to place limits on a redder host. These images reach 3σ depths of ≳26–28 mag on coincident host galaxies.
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: Probability of chance coincidence vs. redshift for the host associations in our sample, color coded by classification as Gold (yellow), Silver (gray), or Bronze (orange). Diamonds denote spectroscopic redshifts while squares represent photometric redshifts. Error bars correspond to a 1σ confidence. As expected, the average P cc increases with redshift, especially beyond z ≳ 1. Put another way, the robustness of association decreases with increasing redshift. We also note the larger prevalence of photometric redshifts at z ≳ 1. Not shown are host galaxies with unknown redshift (which are largely Bronze classifications and are likely to be low-luminosity hosts or at z ≳ 1).
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: Left: classification of all short GRBs in the starting sample of short GRBs primarily discovered by Swift. Of the 149 total detected Swift short GRBs, host associations exist for ≈56% of the population, while only ≈4% have inconclusive hosts. We exclude ≈40% of the total population because they have no reported afterglows, afterglow localizations too large to enable meaningful host galaxy searches, or are events that are subject to optical observing constraints. Right: classification of the 90 short GRBs in our sample for which meaningful host searches and follow-up are feasible. We report host associations for ≈93.3% of events (84); the most robust associations (﹩{P}_{\mathrm{cc},\min }\lesssim 0.02﹩) comprise over half of events (Gold sample). We cannot make conclusive host associations (﹩{P}_{\mathrm{cc},\min }\gtrsim 0.25﹩) for ≈6.7% of events.
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: Left: the locations of 84 short GRBs with respect to their host galaxy centers (represented by the origin), where uncertainties on individual measurements correspond to 1σ confidence. The axes are oriented with north up and east to the left, and the scale is in the frame of the host galaxy (in which negative values correspond to east and/or south of the galaxy). Concentric dashed circles denote 10, 30, and 50 kpc offsets, while the red circle denotes the median on the full distribution of 7.7 kpc. Right: same as left panel, but for only the inner 10 kpc from the host galaxy centers. The panels demonstrate that while most short GRBs reside at ≲10 kpc from their host galaxies, a significant fraction lie outside of this galactocentric radius.
Paper: Short GRB Host Galaxies. I. Photometric and Spectroscopic Catalogs, Host Associations, and Galactocentric Offsets
Authors: Wen-fai Fong, Anya E. Nugent, Yuxin Dong, Edo Berger, Kerry Paterson, Ryan Chornock, Andrew Levan, Peter Blanchard, Kate D. Alexander, Jennifer Andrews, Bethany E. Cobb, Antonino Cucchiara, Derek Fox, Chris L. Fryer, Alexa C. Gordon, Charles D. Kilpatrick, Ragnhild Lunnan, Raffaella Margutti, Adam Miller, Peter Milne, Matt Nicholl, Daniel Perley, Jillian Rastinejad, Alicia Rouco Escorial, Genevieve Schroeder, Nathan Smith, Nial Tanvir, Giacomo Terreran
Figure caption: Optical spectroscopy of 18 short GRB host galaxies that are newly presented in this work. In each panel, the spectral lines which enable redshift determination are denoted. Four additional new spectra have consistent results with previous works and thus are not shown.
Paper: High-energy Photon Opacity in the Twisted Magnetospheres of Magnetars
Authors: Kun Hu, Matthew G. Baring, Alice K. Harding, Zorawar Wadiasingh
Figure caption: Schematic diagram displaying the photon propagation geometry in a twisted magnetosphere. The rotation axis ﹩\,\hat{{\boldsymbol{\Omega }}}\,﹩ is depicted as a black arrow, and the magnetic dipole moment vector ﹩\,{\hat{{\boldsymbol{\mu }}}}_{{\rm{B}}}\,﹩ at one particular rotational phase is displayed as a purple arrow. The star’s magnetic inclination is ﹩\,\alpha =\arccos [{\hat{{\boldsymbol{\mu }}}}_{{\rm{B}}}\cdot \hat{{\boldsymbol{\Omega }}}]\,﹩. One photon is emitted at   r  E  (emission polar angle ﹩\,{\theta }_{{\rm{E}}}=\arccos [{\hat{{\boldsymbol{r}}}}_{{\rm{E}}}\cdot \hat{{\boldsymbol{\Omega }}}]\,﹩) and propagates through the foreground of the magnetosphere: the trajectory of the photon is represented by a green curve, lying in front of the star; ﹩\,\hat{{\boldsymbol{k}}}\,﹩ signifies the changing direction (unit momentum vector) of the photon. Twisted field loops with a  p = 0.75  (ΔΦtw = 84°) parameterization in the Schwarzschild metric ( M NS = 1.44 M ⊙) are plotted as black curves anchored at a colatitude of  30°  relative to the magnetic axis. An untwisted field loop anchored at the same magnetic colatitude is also depicted as a dashed black curve for comparison. A representative angle  ΘkB  between the photon trajectory and a local magnetic field is highlighted.
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: A mode develops between the gravity band and the pressure band (bottom) when the acoustic–buoyant frequency S (top) of Equation (3) changes sign. From left to right: toy profile that cancels in the bulk, decaying positive profile of S, polytrope with polytropic index n = 3 and a MESA solar-like profile. Physical values of the harmonic degree ℓ are integer, and plotted with large points, from 0 to 20. Noninteger values are plotted with small points for readability. Surface-gravity waves are filtered out by appropriate boundary conditions. The mode transiting between bands is highlighted in black. These values are computed by solving Equation (1) numerically using Dedalus (Burns et al. 2020).
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: Local dispersion relation of the problem, as modeled by Equations (8)–(9). The p-mode and the g-mode (solid lines) result from the coupling of acoustic and buoyant oscillations (dashed lines for k  z  = 0). Both S and k  z  pull the bands away. For any mode, including k  z  = 0, a gap exists as soon as S ≠ 0.
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: Left: spectrum of the minimal model parameterized by Equation (14). The topological mode is the n = 0 mode, and transits between the bands. Right: measure of the error a JWKB approximation of the solutions would make. The error on the n = 0 mode is not small.
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: Vector field of the Berry curvature in parameter space {k  r , L  ℓ , S}. Left:  F  (1), associated to the g band (source). Right:  F  (2), associated to the p band (sink). The red dot is the degenerated point at (0, N, 0).
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: Spectrum of the waves in a stratified medium with 2D plane-parallel geometry. The buoyancy frequency N is set as a constant. S is set according to the profile displayed on the right panel of the figure. The Lamb-like wave develops around the cancellation point of S (pink interval). The surface-gravity wave is trapped at the top surface (green interval). The two waves do not overlap significantly: the system has two modes with zero nodes.
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: Peaks of S through positive values imply the existence of two topological modes in the spectrum. The sharper the peak, the more the modes hybridize, and their branches avoid crossing in the spectrum.
Paper: Topological Modes in Stellar Oscillations
Authors: Armand Leclerc, Guillaume Laibe, Pierre Delplace, Antoine Venaille, Nicolas Perez
Figure caption: Spectrum of the same problem as presented in Figure 7, for a profile of S whose zero is closer to the surface z = z 2. The Lamb-like and surface-gravity waves overlap and hybridize. This results in one n = 0 mode: the f-mode.
Paper: Stellar Distributions around a Supermassive Black Hole: Strong-segregation Regime Revisited
Authors: Itai Linial, Re'em Sari
Figure caption: The phase-space density of stars of different mass groups, f(x, m) for a mass function that scales as ﹩{dN}/{dm}\propto {m}^{-6}﹩, as given in Equation (27). The vertical axis, m 5/2 f(x, m) represents the phase-space density of particles of mass of order m, multiplied by m 3/2. Different curves correspond to different mass groups, evenly spaced in logarithmic scale, as shown in the legend, indicating the arbitrarily normalized particle mass. Asterisks represent the energy at which each mass group locally dominates the scatterings. The dominating mass increases as the energy x is increased.
Paper: The Properties of Fast Yellow Pulsating Supergiants: FYPS Point the Way to Missing Red Supergiants
Authors: Trevor Z. Dorn-Wallenstein, Emily M. Levesque, James R. A. Davenport, Kathryn F. Neugent, Brett M. Morris, K. Azalee Bostroem
Figure caption: Amplitude in magnitudes of a companion star as a function of the companion star’s TESS magnitude that would appear as 100 ppm variability when blended with a nonvariable T = 12 primary. The red box corresponds to the typical brightness and amplitude range of a β Cepheid star in the LMC. The blue line intersects the red box, which indicates that the observed variability in this toy example is consistent with contamination by a pulsating B-type companion.
Paper: The Properties of Fast Yellow Pulsating Supergiants: FYPS Point the Way to Missing Red Supergiants
Authors: Trevor Z. Dorn-Wallenstein, Emily M. Levesque, James R. A. Davenport, Kathryn F. Neugent, Brett M. Morris, K. Azalee Bostroem
Figure caption: Example of the Gaussian process-based approach to identifying FYPS. The data in blue is a section of the TESS lightcurve of the FYPS HD 269953, with a 30 minute Gaussian smoothing applied for clarity. The orange line shows the maximum-likelihood GP fit. The individual components are shown in green (periodic mean function) and red (SLF variability), with offsets applied for clarity.
Paper: The Properties of Fast Yellow Pulsating Supergiants: FYPS Point the Way to Missing Red Supergiants
Authors: Trevor Z. Dorn-Wallenstein, Emily M. Levesque, James R. A. Davenport, Kathryn F. Neugent, Brett M. Morris, K. Azalee Bostroem
Figure caption: Hertzprung–Russel diagram showing the effective temperatures and luminosities of the 126 stars in our sample. Stars in the LMC are shown as blue circles, and stars in the SMC as purple squares. The five FYPS identified in Dorn-Wallenstein et al. (2020) are shown as red stars. Black lines show rotating evolution models at LMC metallicity (solid line; Eggenberger et al. 2021) and SMC metallicity (dashed line; Georgy et al. 2013), with their initial masses indicated.
Paper: Characterizing Compact 15–33 GHz Radio Continuum Sources in Local U/LIRGs
Authors: Y. Song, S. T. Linden, A. S. Evans, L. Barcos-Muñoz, E. J. Murphy, E. Momjian, T. Díaz-Santos, K. L. Larson, G. C. Privon, X. Huang, L. Armus, J. M. Mazzarella, V. U, H. Inami, V. Charmandaris, C. Ricci, K. L. Emig, J. McKinney, I. Yoon, D. Kunneriath, T. S.-Y. Lai, E. E. Rodas-Quito, A. Saravia, T. Gao, W. Meynardie, D. B. Sanders
Figure caption: IRAS 17208-0014. Left: HST/NICMOS F160W image, displayed in arcsinh stretch with bilinear interpolation. The yellow square outlines the field of view of the 33 GHz VLA continuum. Middle: 33 GHz VLA continuum observed with the A-configuration (beam shown on the lower left in white). Right: 15 GHz VLA continuum observed with the A-configuration.
Paper: Characterizing Compact 15–33 GHz Radio Continuum Sources in Local U/LIRGs
Authors: Y. Song, S. T. Linden, A. S. Evans, L. Barcos-Muñoz, E. J. Murphy, E. Momjian, T. Díaz-Santos, K. L. Larson, G. C. Privon, X. Huang, L. Armus, J. M. Mazzarella, V. U, H. Inami, V. Charmandaris, C. Ricci, K. L. Emig, J. McKinney, I. Yoon, D. Kunneriath, T. S.-Y. Lai, E. E. Rodas-Quito, A. Saravia, T. Gao, W. Meynardie, D. B. Sanders
Figure caption: IRAS F16516-0948. (a): Pan-STARRS1 y-band image, displayed in arcsinh stretch with bilinear interpolation. (b): Spitzer channel 1 image, overlaid with 33 GHz VLA continuum (magenta contours) observed with the C-configuration (beam shown on the lower left in magenta). (c): the same as panel (b) but on the Spitzer channel 4 image. The lime square outlines the field of view of the 15 GHz VLA continuum. (d): 15 GHz VLA continuum observed with the A-configuration.
Paper: Saturation Level of Turbulence in Collapsing Gas Clouds
Authors: Sho Higashi, Hajime Susa, Gen Chiaki
Figure caption: The evolution of the turbulent velocity v turb as a function of the mean density ρ mean in the Jeans volume. The solid curves with different colors denote the numerical results for different γ eff. The dotted lines denote the mean sound speed in the Jeans volume.
Paper: Saturation Level of Turbulence in Collapsing Gas Clouds
Authors: Sho Higashi, Hajime Susa, Gen Chiaki
Figure caption: The same as Figure 1, but for the different ﹩{{ \mathcal M }}_{0}﹩ and rotation energies (LowA, Middle, Middle w/r, and High). The solid curves show the numerical results for each model. The magenta dotted line denotes the averaged sound speed in the Jeans volume for γ eff = 1.09. The black dashed line is obtained by an analytic estimate (Equation (14) of HSC21).
Paper: Characterizing Compact 15–33 GHz Radio Continuum Sources in Local U/LIRGs
Authors: Y. Song, S. T. Linden, A. S. Evans, L. Barcos-Muñoz, E. J. Murphy, E. Momjian, T. Díaz-Santos, K. L. Larson, G. C. Privon, X. Huang, L. Armus, J. M. Mazzarella, V. U, H. Inami, V. Charmandaris, C. Ricci, K. L. Emig, J. McKinney, I. Yoon, D. Kunneriath, T. S.-Y. Lai, E. E. Rodas-Quito, A. Saravia, T. Gao, W. Meynardie, D. B. Sanders
Figure caption: IRAS 18090+0130. HST F132N image (left), displayed in arcsinh stretch with bilinear interpolation. The yellow square outlines the field of view of the 33 GHz (middle) and 15 GHz (right) VLA continuum observed with the A-configuration, showing at least two radio components of undetermined nature.
Paper: Saturation Level of Turbulence in Collapsing Gas Clouds
Authors: Sho Higashi, Hajime Susa, Gen Chiaki
Figure caption: The same as Figure 1, but for different initial seeds of turbulence (LowA, LowB, and LowC). The differences in line style correspond to the differences between the initial seeds and the differences in color correspond to the differences in γ eff. For ease of viewing, we multiply the results by factors of x for each γ eff model.
Paper: Characterizing Compact 15–33 GHz Radio Continuum Sources in Local U/LIRGs
Authors: Y. Song, S. T. Linden, A. S. Evans, L. Barcos-Muñoz, E. J. Murphy, E. Momjian, T. Díaz-Santos, K. L. Larson, G. C. Privon, X. Huang, L. Armus, J. M. Mazzarella, V. U, H. Inami, V. Charmandaris, C. Ricci, K. L. Emig, J. McKinney, I. Yoon, D. Kunneriath, T. S.-Y. Lai, E. E. Rodas-Quito, A. Saravia, T. Gao, W. Meynardie, D. B. Sanders
Figure caption: CGCG 043-099. Left: archival HST 160W image, displayed in arcsinh stretch with bilinear interpolation. Middle: 33 GHz VLA continuum observed with the A-configuration. Right: 15 GHz VLA continuum observed with the A-configuration.
Paper: Characterizing Compact 15–33 GHz Radio Continuum Sources in Local U/LIRGs
Authors: Y. Song, S. T. Linden, A. S. Evans, L. Barcos-Muñoz, E. J. Murphy, E. Momjian, T. Díaz-Santos, K. L. Larson, G. C. Privon, X. Huang, L. Armus, J. M. Mazzarella, V. U, H. Inami, V. Charmandaris, C. Ricci, K. L. Emig, J. McKinney, I. Yoon, D. Kunneriath, T. S.-Y. Lai, E. E. Rodas-Quito, A. Saravia, T. Gao, W. Meynardie, D. B. Sanders
Figure caption: IRAS 09111-10. Left: archival HST 160W image, displayed in arcsinh stretch with bilinear interpolation. Right: 15 GHz VLA continuum observed with the A-configuration.
Paper: Internal Rotation and Inclinations of Slowly Pulsating B Stars: Evidence of Interior Angular Momentum Transport
Authors: May G. Pedersen
Figure caption: Comparison between four different age indicators t/t MS, X c/X ini, ﹩\mathrm{log}g﹩, and Π0 for different masses and exponential diffusive overshooting. Panels (a), (c), and (g) show t/t MS as a function of X c/X ini, ﹩\mathrm{log}g﹩, and Π0, respectively. Different masses correspond to different line styles: 2.5 M ⊙ (full), 5 M ⊙ (dashed), 7.5 M ⊙ (dotted–dashed), and 10 M ⊙ (dotted). Black lines correspond to models with f ov = 0.01, whereas models with f ov = 0.04 are shown in gray. Panels (b), (e), and (h) show the differences in X c/X ini, ﹩\mathrm{log}g﹩, and Π0 obtained for a given t/t MS between the highest and lowest mass model, e.g., ﹩{\rm{\Delta }}\left({X}_{{\rm{c}}}/{X}_{\mathrm{ini}}\right)={\left.{X}_{{\rm{c}}}/{X}_{\mathrm{ini}}\right|}_{10\,{M}_{\odot }}-{\left.{X}_{{\rm{c}}}/{X}_{\mathrm{ini}}\right|}_{2.5\,{M}_{\odot }}﹩. Panels (c), (f), and (i) give the same differences but between the same mass models with different overshooting parameters, e.g., ﹩{\rm{\Delta }}\left({X}_{{\rm{c}}}/{X}_{\mathrm{ini}}\right)={\left.{X}_{{\rm{c}}}/{X}_{\mathrm{ini}}\right|}_{{f}_{\mathrm{ov}}=0.01}-{\left.{X}_{{\rm{c}}}/{X}_{\mathrm{ini}}\right|}_{{f}_{\mathrm{ov}}=0.04}﹩.