adsabs/AstroCLIMB huggingface dataset:
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: MGE fit (solid red line) to the observed surface brightness profile of M54 from (Noyola & Gebhardt 2006, thick black line). The individual Gaussian components are plotted with solid blue lines.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: M54 best-fit radial ϒ V  profile, according to the three-population-dynamical model described in Section 3.3, resulting from dividing the best-fit mass and luminosity MGE models of the system. The median ϒ V  profile is indicated with a thick curve, while the thin curves represent random draws from the posterior distribution. The red dashed curve shows the median ϒ V  profile according to the two-population-dynamical model described in Section 3.2. The three black vertical dashed lines correspond to M54's core, half-light, and tidal radii (GC catalog of Harris 1996, 2010 edition), while the red vertical dashed line indicates the radial limit of our kinematic data. The horizontal dashed line corresponds to the average M/L ratio for the entire system, e.g., the total mass divided by total luminosity out to the tidal radius.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Dynamical results according to the model described in Section 3.2. Top: M54 radial ϒ V  profile, resulting from dividing the best-fit mass and luminosity MGE models of the system. The median ϒ V  profile is indicated with a thick curve, while the thin curves represent random draws from the posterior distribution. The horizontal dashed line corresponds to the best-fit constant ϒ V . Bottom: Cumulative masses of the two populations (blue—MP; red—MR) and the entire system (black). The three black vertical dashed lines on both panels correspond to M54's core, half-light, and tidal radii (GC catalog of Harris (1996, 2010 edition), while the red dashed line indicates the end of the MUSE mosaic field of view.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Left panel: radial distribution functions of the two-population-dynamical components of M54 as drawn from the Section 3.2 model posterior (MR—red lines and MP—blue lines). The solid black line shows the combined surface brightness profile. Right panel: radial cumulative distribution function of the two-population-dynamical components of M54.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Top left panel: radial distribution functions of the three-population-dynamical components of M54 (Section 3.3) as drawn from the model posterior (red lines for the YMR, green lines for the IMR, and blue lines for the OMP populations). The solid black line shows the combined surface brightness profile. Top left panel: radial cumulative distribution function of the three-population-dynamical components of M54. Bottom left panel: relative fractions of the three populations as a function of radius. Bottom right panel: cumulative masses of the three populations and the entire system (black lines). The black dashed lines indicate the core, half-light, and tidal radii of the system and the red dashed line indicates the limit of the MUSE field of view.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Predictions for the rotation (left panel) and the velocity dispersion (right panel) for the two populations drawn from the model posterior (MR—red lines, MP—blue lines) according to the dynamical model described in Section 3.2, compared to the observed binned profiles (red squares and blue dots with error bars, respectively), using stars with >50% probability of belonging to either of the two populations. The horizontal error bars indicate the size of each bin. The vertical dashed line in the right panel shows the border between the NFM and WFM MUSE observations.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Predictions for the rotation (left panel) and the velocity dispersion (right panel) for the three-population-dynamical model (Section 3.3) drawn from the model posterior (YMR—red lines, IMR—green lines, OMP—blue lines), compared to the observed binned profiles (red, green, and blue dots with error bars, respectively), using stars with >50% probability of belonging to either of the three populations. The horizontal error bars indicate the size of each bin. The vertical dashed line in the right panel shows the border between the NFM and WFM MUSE observations.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Top: radial velocity vs. metallicity plot of all  M54 member stars in the sample (left panel) and a CMD (right panel), color coded by the probability of the stars belonging to the YMR (red), the IMR (green), and the OMP (blue) populations according to the three-population-dynamical model (Section 3.3). Bottom: separate CMDs of the observed stars, color coded according to the probability to belong to each of the three populations: YMR (shades of red), IMR (shades of green), and OMP (shades of blue). A darker color indicates higher probability. The best-fit Dartmouth isochrones are also plotted together with the HB model.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Metallicity vs. radial velocity plot of all stars in the sample (left panel) and a CMD (right panel), color coded by the probability of the star belonging to the MR population (shades of red) or the MP population (shades of blue), according to the dynamical model described in Section 3.2. The photometry is from Sarajedini et al. (2007).
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: MCMC corner plot showing the posterior distributions of the three-population-dynamical model parameters (Section 3.3). Covariances between parameters pertaining to the Jeans equations and isochrone fits are plotted separately.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Top: corner plot of the individual fractions of the MGE components contributing to the MP population according to the best-fit two-population-dynamical model presented in Section 3.1. Bottom: corner plot of the Legendre polynomial coefficients used to compute the YMR (left) and IMR (right) fractions of the surface brightness MGE in the three-population-dynamical model presented in Section 3.3.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: Comparison between the best-fit values for the flattening (top panel), luminosity weighted rotation in arbitrary units (middle panel), and anisotropy (bottom panel) of M54's modeled populations—YMR (red), IMR (orange), and OMP (blue), according to the three dynamical models described in Section 3.1 (two populations with constant independent ϒ k ), Section 3.2 (two populations with radially varying ϒ(r)), and Section 3.3 (three populations with radially varying ϒ(r)), respectively.
Paper: A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations
Authors: Nikolay Kacharov, Mayte Alfaro-Cuello, Nadine Neumayer, Nora Lützgendorf, Laura L. Watkins, Alessandra Mastrobuono-Battisti, Sebastian Kamann, Glenn van de Ven, Anil C. Seth, Karina T. Voggel, Iskren Y. Georgiev, Ryan Leaman, Paolo Bianchini, Torsten Böker, Steffen Mieske
Figure caption: King profiles of MP stars (blue line Trager et al. 1995) and MR stars (red line Monaco et al. 2005). The combined profile is plotted with a dashed black line and is compared to the surface brightness profile of Noyola & Gebhardt (2006, dashed green line).
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: The eight square panels show the set of diagnostics to estimate the gas density n  e  in the different ionization zones (see also Tables 2 and 3). The minor top left and right panels show the ionization potential and the range of traced densities of the diagnostics taken into account, calculated with PyNeb, using the same color coding. Specifically, in order of ionization potential, we have: [S II] λ6717/λ6731 (purple), [O II] λ3729/λ3727 (blue), [Fe III] λ4701/λ4659 (turquoise), [Si III] λ1883/Si III] λ1892 (dark green), [Cl III] λ5518/λ5538 (green), [C III] λ1907/C III] λ1909 (gold), [Ar IV] λ4714/λ4741 (orange), and N IV] λ1483/λ1487 (red). The different symbols show the CLASSY calculated values with PyNeb using the available temperature diagnostics described in Figure 4. The solid, dashed and dotted black curves represent the PyNeb predictions at T  e  = 5 × 103 K, 1 × 104 K, and 2.5 × 104 K, as reported in the legend, while the shaded red regions (very narrow due to the low dependence of the density on the temperature) show the predictions from our Cloudy models of Berg et al. (2019b, 2021).
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: Top panels: comparison of n  e  estimated from low- (n  e ([S II]) or n  e ([O II]) for J0934+5514; squares), intermediate- (n  e ([Cl III]), n  e ([Fe III]), n  e (Si III]), n  e (C III]); triangles), and high-ionization regions (n  e ([Ar IV], n  e (N IV]); pentagons, hexagons), as a function of 12+log(O/H). For clarity reasons the optical and UV diagnostics are shown on the left and right, respectively, while the optical n  e ([S II]) or n  e ([O II]) are shown in both panels. The dots are color coded consistently with Figure 3, as indicated in the legend. The uncertainties on the displayed quantities are shown in both axes. Bottom panels: difference in dex between the low-ionization density (purple squares) and the other n  e  measurements, keeping the same symbols as in the top panel. The colored dashed and dotted lines indicate the median values. The shaded regions (partially overlapped) in the bottom panel represent the 68% intrinsic scatter of each distribution, color coded accordingly. Excluding n  e ([Fe III]) for which we have mainly upper limits, clearly the highest discrepancies with respect to n  e ([S II]) are found for UV tracers, which predict average densities ∼1 − 2 dex higher.
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: Set of diagnostics to estimate the gas temperature in the CLASSY galaxies in the different ionization zones: [N II] λ5755/[N II] λ6584, [S II] λλ4069/[S II] λλ6717,31, and [O II] λλ3727,29/[O II] λλ7320,30 for the low-ionization zone, [S III] λ6312/[S III] λ9069, [O III] λ4363/[O III] λ5007, and O III] λ1666/[O III] λ5007. The different filled symbols show the CLASSY calculated values with PyNeb, as reported in the legend. The black curves represent PyNeb predictions at densities n  e  = 100 cm−3, 5000 cm−3, 104 cm−3, and 105 cm−3, while the shaded red regions show the predictions from our Cloudy models.
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: Upper panels: comparison of the T  e  estimates of the low-ionization (on the left) and intermediate-ionization (on the right) with the temperature diagnostics [N II] λ5755/λ6584, [S II] λλ4069/λ λ 6717,31, [O II] λλ3727,29/λ λ 7320,30, and [S III] λ6312/λ9071, as a function of the high-ionization temperature T([O III]([S II],[O III])), taking the available density tracers into account. The uncertainties on the displayed quantities are shown in both axes. The dotted–dashed lines in the left and right panels indicate Equation (1) and Equation (2), respectively. On the right panels there are no estimates of T([S III]([Cl III],[S III])), because we could not find finite values with PyNeb, and only one measurement for T([S III](Si III],[S III])). Lower panels: difference in dex between the prediction of Equation (1) and Equation (2), and the calculated values. The shaded regions (overlapped) in the bottom panel represent the 68% intrinsic scatter of each distribution, color coded accordingly. Overall, the median values of the computed differences are ∼ −0.1 dex and ∼ −0.05 dex (dotted lines in the minor panels) for the low-ionization and intermediate-ionization T  e , respectively.
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: Fit of the C IV λλ1548,51 and C III] λλ1907,9 emission-line doublet with S/N > 3, visible in 9 and 28 galaxies, respectively. The observed flux and the best-fit model are shown in black and red, respectively, while their uncertainties are given by the gray and red shades. The black dashed vertical lines indicate the line positions, taking z lit. into account. The margins are colored according to the binning applied to the spectrum before the fitting (HR rebinned of 15 in blue, MR rebinned of 6 in dark green, MR rebinned of 12 in light green).
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: Top panels: comparison of the E(B − V) estimated assuming T  e  = 1 × 104 K and n  e  = 102 cm−3 (E(B − V)0; empty black pentagon) with the value obtained from low- (purple squares), intermediate-, (green diamonds) and high-ionization regions (red circles), as a function of 12+log(O/H) and M⋆. The uncertainties on the displayed quantities are shown in both axes. Bottom panels: difference between the E(B − V)0 and E(B − V) measurements of each ionization zone, keeping the same symbols and colors as in the top panel. The colored dashed and dotted lines indicate the median values of the shown distributions. The shaded regions (partially overlapped) in the bottom panel represent the 68% intrinsic scatter of each distribution, color coded accordingly. At 12+log(O/H) ≲ 7.75 or stellar mass log(M ⋆/M ⊙) ≲ 6.5, E(B − V) is down to ∼ −0.04 mag lower than E(B − V)0.
Paper: CLASSY IV. Exploring UV Diagnostics of the Interstellar Medium in Local High-z Analogs at the Dawn of the JWST Era 
Authors: Matilde Mingozzi, Bethan L. James, Karla Z. Arellano-Córdova, Danielle A. Berg, Peter Senchyna, John Chisholm, Jarle Brinchmann, Alessandra Aloisi, Ricardo O. Amorín, Stéphane Charlot, Anna Feltre, Matthew Hayes, Timothy Heckman, Alaina Henry, Svea Hernandez, Nimisha Kumari, Claus Leitherer, Mario Llerena, Crystal L. Martin, Themiya Nanayakkara, Swara Ravindranath, Evan D. Skillman, Yuma Sugahara, Aida Wofford, Xinfeng Xu
Figure caption: UV emission lines fitted by our fitting routine for galaxy J0337-0502 (i.e., SBS0335-052 E): the spectrum and the fit are reported in black and red, while the spectrum and fit uncertainties are shown in shaded gray and red, respectively. The id and S/N of each zoomed line is indicated on top of each panel, whose margins are colored according to the binning applied to the spectrum before the fitting (HR rebinned of 15 in blue, MR rebinned of 6 in dark green, MR rebinned of 12 in light green). The dashed black vertical lines indicate the observed wavelength of each line according to the redshift of the galaxy z lit, reported in Table 1.
Paper: A Maximum Likelihood Calibration of the Tip of the Red Giant Branch Luminosity from High Latitude Field Giants Using Gaia Early Data Release 3 Parallaxes
Authors: Siyang Li, Stefano Casertano, Adam G. Riess
Figure caption: Final sample after the parallax cuts in the I band. Parallax values include the Lindegren et al. (2021) correction as well as the additional correction described in Section 2. Stars within the selection boundaries are shown by heavier points. The apparent magnitude selection (8.6 < I < 11.7) is driven at the bright end by the saturation limit for APASS magnitudes, and at the faint end by the incompleteness of the sample approaching I ∼ 12. The parallax selection is based on the apparent magnitude in I, and corresponds to the values derived from a nominal absolute magnitude of M  I  = −5 mag (red line) and −3 mag (blue line). The error bars on the purple diamonds show typical (median) EDR3 parallax errors at those magnitudes; note that parallax errors change very little over this magnitude range. The dashed purple line at M  I  = 4.0 mag marks a representative location of the TRGB. At bright magnitudes, corresponding to more nearby stars, the drop in density around −4.0 is apparent; at fainter magnitudes, covering the majority of the sample, the parallax uncertainties blur this transition. These identical selections are used in the normalization integral of Equation (11).