An Observational Hertzsprung–Russell Diagram and Fundamental Parameters of Galactic BA Supergiants

Abstract

Galactic B- and A-type supergiants serve as critical observational anchors for testing massive-star evolution models and calibrating extragalactic distance indicators. Building upon a uniform $T_{\mathrm{eff}}$ scale established in our previous work, we construct a self-consistent observational Hertzsprung–Russell diagram (HRD) for a homogeneous sample of 84 Galactic BA supergiants to evaluate their fundamental parameters, evolutionary masses, ages, and evolutionary status. Absolute bolometric luminosities are derived by combining Gaia DR3 astrometry with 3D spatial dust reddening maps and theoretical bolometric corrections. Comparison with Geneva evolutionary tracks for solar metallicity ($Z=0.014$), incorporating stellar wind mass loss and rotational mixing, demonstrates that the vast majority of the program stars represent massive post-main-sequence objects with initial masses of approximately 7–$25M_{\odot }$ and ages of $\sim 8$–57 Myr. Our homogeneous analysis also reveals a distinct subgroup of eight low-luminosity objects ($log(L/L_{\odot })<3.5$), including stars whose cataloged luminosity classes are inconsistent with supergiant status as well as objects retaining supergiant spectral classifications despite their unexpectedly low derived luminosities. These findings highlight the importance of combining uniform spectroscopic calibrations with Gaia astrometry to refine Galactic supergiant censuses and improve the empirical basis of the flux-weighted gravity–luminosity relation.

1. Introduction

Galactic supergiants of spectral types B and A occupy a transitional evolutionary stage between the main sequence and the subsequent, more advanced phases of massive-star evolution. They are characterized by low surface gravities and large radii, with luminosities (L) typically ranging from $log(L/L_{\odot })\approx 3.5$ to 5.8 while maintaining effective temperatures ($T_{\mathrm{eff}}$) in the range $T_{\mathrm{eff}}\sim 8000$–20,000 K [1,2]. With initial masses typically in the range of ∼7–25 $M_{\odot }$, these stars are among the optically brightest stellar populations, reaching absolute visual magnitudes as bright as $M_V\approx -9$ [3], which makes them detectable and spectroscopically accessible out to several megaparsecs.

Massive stars play a pivotal role in the chemical and dynamical evolution of galaxies. During their post-main-sequence evolution, these objects traverse the upper Hertzsprung–Russell diagram (HRD), appearing observationally as luminous BA-type supergiants. This transitional phase is characterized by complex internal physics, including significant mass loss, rotational mixing, and structural readjustments [4,5]. Despite their brightness and significance, the evolutionary status of Galactic BA supergiants remains a subject of active debate, particularly regarding whether they are evolving redward for the first time or undergoing blue loops after a red supergiant phase [6]. Their upper luminosity boundary in the HRD, empirically known as the Humphreys–Davidson limit [7], provides an important observational constraint on the mass-loss histories and evolutionary pathways of the most massive stars. The location and distribution of BA supergiants therefore provide valuable empirical constraints on post-main-sequence evolution, including possible transitions toward and excursions from the red supergiant phase.

The HRD serves as the fundamental diagnostic tool for testing stellar evolution theories. However, the accurate placement of stars on the HRD requires highly precise determinations of both $T_{\mathrm{eff}}$ and L. Historically, luminosity estimates for Galactic hot supergiants suffered from large uncertainties in distance measurements, often relying on kinematic distances or membership in OB associations [8]. Modern distance determinations based on Gaia DR3 astrometry [9], together with quality-control procedures accounting for astrometric systematics and RUWE-based reliability criteria [10], provide substantially improved constraints on the distances and hence luminosities of Galactic hot supergiants.

Interpreting the observed positions of BA supergiants on the HRD requires comparison with modern stellar evolutionary models. The evolutionary grids computed by the Geneva group [4], spanning 0.8–120 $M_{\odot }$ at solar metallicity, provide a comprehensive set of models for massive stars, explicitly incorporating the effects of initial rotation and mass-loss rates. Rotation, in particular, enhances interior mixing, significantly altering the main-sequence lifetime, the surface chemical abundances, and the subsequent evolutionary tracks across the HRD. Comparison of a statistically significant, homogeneously analyzed sample of supergiants with these evolutionary models provides a valuable observational test of their predictions. Beyond their diagnostic value for evolutionary theory, precisely calibrated BA supergiants also underpin the flux-weighted gravity–luminosity relation (FGLR) [11,12], an extragalactic distance indicator that depends critically on accurate luminosity and gravity determinations of BA supergiants.

In our previous study [13], we established a uniform empirical $T_{\mathrm{eff}}$ scale for a sample of 84 Galactic BA supergiants based on a homogeneous set of optical spectral lines. This work forms part of our broader effort to develop consistent, model-driven approaches to spectroscopic analysis, including the MERLIS framework for measuring spectral-line parameters in heterogeneous stellar spectra [14]. In contrast to many previous studies based on heterogeneous datasets, the present analysis relies on a homogeneous temperature scale and uniformly determined stellar parameters for the entire sample, enabling a self-consistent comparison with modern stellar evolutionary models.

Building upon this foundation, the present work derives absolute luminosities for the sample and uses them to investigate the masses, ages, and positions of the program stars relative to the evolutionary tracks. By combining our robust, internally consistent $T_{\mathrm{eff}}$ estimates with modern Gaia astrometry, interstellar extinction, and appropriate bolometric corrections, we construct an observational HRD for the entire sample.

The primary objective of this paper is to compare our homogeneous sample of Galactic BA supergiants with the Geneva evolutionary tracks [4] in order to determine their masses and ages, and to identify the corresponding locations along the theoretical tracks, while identifying low-luminosity objects inconsistent with a supergiant classification. This homogeneous HRD forms the basis for the evolutionary analysis presented in this work.

2. Materials and Methods

To assess the evolutionary status of the program stars, we constructed an observational HRD and compared their positions with theoretical evolutionary tracks computed by the Geneva group [4]. These models were adopted because they consistently incorporate the effects of stellar rotation and mass loss, which are essential for describing the evolution of BA supergiants. Constructing a reliable HRD requires a rigorous, fully reproducible derivation of stellar absolute bolometric luminosities, combining optical photometry, high-precision astrometry, 3D interstellar dust mapping, and model atmosphere calibrations.

2.1. Distances and Astrometry

The individual distances d to the program stars are adopted from recent re-evaluations based on high-precision astrometry from the Gaia DR3 mission [9]. These astrometric distances carefully account for systematic zero-point offsets, RUWE-based quality filters, and Lutz–Kelker bias treatments, as detailed in [10].

2.2. Interstellar Extinction and 3D Reddening Mapping

Interstellar extinction along individual lines of sight is a critical parameter when evaluating the intrinsic luminosities of distant Galactic supergiants. To avoid the systematic overestimation inherent to integrated 2D Galactic maps, we queried the 3D spatial dust reddening model of Bayestar (bayestar2019 ) using the dustmaps Python package [15,16]. For each object, the median line-of-sight color excess $E{(B-V)}_{\mathrm{med}}$ was extracted at the stellar sky coordinates and Gaia-derived distance d using the median query mode.

To account for the impact of distance uncertainties (${\sigma }_d$) on the derived reddening, $E(B-V)$ was additionally sampled at the lower ($d-{\sigma }_d$) and upper ($d+{\sigma }_d$) distance bounds. The corresponding uncertainty in the color excess was estimated as

$${\sigma }_{E(B-V)}={\displaystyle \frac{\left|E{(B-V)}_{d+{\sigma }_d}-E{(B-V)}_{d-{\sigma }_d}\right|}{2}}.$$

(1)

The total visual extinction $A_V$ and its uncertainty ${\sigma }_{A_V}$ were then computed assuming the standard total-to-selective extinction ratio $R_V=3.1$:

$$A_V\pm {\sigma }_{A_V}=3.1\times \left(E{(B-V)}_{\mathrm{med}}\pm {\sigma }_{E(B-V)}\right).$$

(2)

2.3. Bolometric Corrections and Luminosity Derivation

The absolute visual magnitude $M_V$ for each star was determined from catalog apparent visual magnitudes $m_V$, distance d, and extinction $A_V$ via

$$M_V=m_V-5.0{log}_{10}\left({\displaystyle \frac{d}{10\mathrm{pc}}}\right)-A_V.$$

(3)

The absolute bolometric magnitude $M_{\mathrm{bol}}$ was subsequently obtained by applying the bolometric correction $B{C}_V$:

$$M_{\mathrm{bol}}=M_V+B{C}_V.$$

(4)

The bolometric corrections $B{C}_V$ represent catalog-adopted values interpolated from the theoretical model atmosphere calibration tables of [17] using our previously derived uniform $T_{\mathrm{eff}}$ scale [13].

Finally, the absolute bolometric luminosity relative to the Sun, $log(L/L_{\odot })$, was calculated using the standard relation

$${log}_{10}\left({\displaystyle \frac{L}{L_{\odot }}}\right)=-0.4\left(M_{\mathrm{bol}}-M_{\mathrm{bol},\odot }\right),$$

(5)

adopting the standard solar absolute bolometric magnitude $M_{\mathrm{bol},\odot }=4.74$ mag. All parameters used are presented in Appendix A.

2.4. Error Propagation for Luminosities

The formal uncertainty on the logarithmic bolometric luminosity, ${\sigma }_{logL}$, is evaluated by propagating the primary observational variance sources in quadrature:

$${\sigma }_{logL}=\sqrt{{\left({\displaystyle \frac{2}{ln10}}{\displaystyle \frac{{\sigma }_d}{d}}\right)}^2+{\left(0.4{\sigma }_{A_V}\right)}^2},$$

(6)

where ${\sigma }_d$ is the Gaia DR3 astrometric distance error and ${\sigma }_{A_V}=3.1\times {\sigma }_{E(B-V)}$ represents the $1\sigma$ uncertainty derived from the 3D bayestar2019 dust maps along each individual line of sight.

In this formulation, catalog apparent magnitudes ($m_V$) and derived bolometric corrections ($B{C}_V$) are treated as nominal baseline quantities. Omitting explicit formal error terms (${\sigma }_{m_V},{\sigma }_{B{C}_V}$) from Equation (6) is physically and mathematically justified by demonstrating that their combined variance contribution is negligible relative to the dominant distance and extinction uncertainties:

• Temperature-Propagated $B{C}_V$ Uncertainty: The bolometric correction $B{C}_V$ is tied to the spectroscopic effective temperature ($T_{\mathrm{eff}}$). Evaluating the local derivative $|\mathrm{d}B{C}_V/\mathrm{d}{T}_{\mathrm{eff}}|$ along the [17] calibration grid for BA supergiants (8000–15,000 K) yields typical slopes of $\left(0.5–1.5\right)\times {10}^{-4}$ mag K⁻¹. For our spectroscopic temperature precision of ${\sigma }_{T_{\mathrm{eff}}}\approx \pm 150$ K [13], the propagated uncertainty in bolometric correction is ${\sigma }_{B{C}_V}\approx 0.01–0.02$ mag, which corresponds to a marginal luminosity variance contribution of only $0.4{\sigma }_{B{C}_V}\approx 0.004–0.008$ dex.
• Photometric Catalog Precision and Variability: The program stars are bright optical sources with high photometric precision (${\sigma }_{m_V,\mathrm{stat}}\le 0.01–0.02$ mag). Even when accounting for potential low-amplitude intrinsic photometric variability ($\sim 0.03–0.05$ mag) characteristic of massive supergiant atmospheres and cross-catalog heterogeneity, the resulting variance contribution to ${\sigma }_{logL}$ is $\le 0.012–0.020$ dex.

By comparison, astrometric distance uncertainties (${\sigma }_d/d\sim 5–15\%$) and line-of-sight extinction errors (${\sigma }_{A_V}\sim 0.1–0.3$ mag) generate individual variances of $0.04–0.13$ dex and $0.04–0.12$ dex, respectively. Combining the omitted terms in quadrature with the primary error budget (${0.08}^2+{0.015}^2\approx {0.0814}^2$) alters the net calculated uncertainty ${\sigma }_{logL}$ by less than $1.5\%$. Consequently, omitting explicit ${\sigma }_{m_V}$ and ${\sigma }_{B{C}_V}$ terms introduces no systematic bias and avoids artificial noise inflation.

2.5. Evolutionary Mass and Age Estimation

To determine initial masses (M) and evolutionary ages (t), observed stellar positions in the HRD were evaluated against the theoretical Geneva evolutionary grids for solar metallicity ($Z=0.014$) with standard rotation ($v/v_{\mathrm{crit}}=0.4$) [4]. Objects with $log(L/L_{\odot })<3.5$ ($N=8$) were omitted prior to matching, leaving a primary target sample of 76 supergiants.

Rather than assigning parameters directly from discrete, nearest-neighbor grid points, parameter determination is formulated as a continuous two-dimensional interpolation across local track segments in the $log{T}_{\mathrm{eff}}$–$log(L/L_{\odot })$ plane.

2.5.1. Error-Weighted Distance Metric

Proximity between observed positions and theoretical model tracks is evaluated using an observational error-normalized ${\chi }^2$-like distance metric,

$$d^2={\left({\displaystyle \frac{log{T}_{\mathrm{eff},i}-log{T}_{\mathrm{eff},\mathrm{mod}}}{{\sigma }_{logT,i}}}\right)}^2+{\left({\displaystyle \frac{log{L}_i-log{L}_{\mathrm{mod}}}{{\sigma }_{logL,i}}}\right)}^2,$$

(7)

where ${\sigma }_{logT,i}={\sigma }_{T_{\mathrm{eff},i}}/(T_{\mathrm{eff},i}ln10)$ and ${\sigma }_{logL,i}$ are the individual observational uncertainties derived in Section 2.4. Normalizing by observational errors guarantees scale invariance between the temperature and luminosity axes, ensuring that parameters constrained with higher relative observational precision carry appropriate statistical weight.

Rather than assigning parameters directly from discrete, nearest-neighbor grid points, parameter determination is formulated as a continuous two-dimensional interpolation across local track segments in the $log{T}_{\mathrm{eff}}$–$log(L/L_{\odot })$ plane. Probabilistic approaches, such as Markov Chain Monte Carlo (MCMC) sampling, provide an alternative framework for exploring parameter uncertainties and degeneracies in stellar systems [18]; however, such sampling is beyond the scope of the present grid-based analysis.

2.5.2. Continuous Track Interpolation Scheme

Theoretical Geneva tracks were interpolated into continuous piecewise linear paths along chronological evolutionary age sequences (t). For a target star i, parameter estimation proceeds as follows:

1.

Bounding Track Selection: The algorithm identifies the pair of adjacent evolutionary tracks with initial masses $M_1<M<M_2$ that bracket the star’s observational domain in temperature and luminosity.

2.

Local Segment Optimization: On each bounding track, the point minimizing $d^2$ (Equation (7)) is located, yielding closest model coordinates $(log{T}_1,log{L}_1)$ at age $t_1$ on track $M_1$, and $(log{T}_2,log{L}_2)$ at age $t_2$ on track $M_2$.

3.

Interpolated Parameter Assignment: Initial stellar mass $M_0$ and age $t_0$ are calculated by linear interpolation along the segment connecting the two minimal track points, inversely weighted by their normalized distances $d_1$ and $d_2$:

$$M_0={\displaystyle \frac{d_2{M}_1+d_1{M}_2}{d_1+d_2}},t_0={\displaystyle \frac{d_2{t}_1+d_1{t}_2}{d_1+d_2}}.$$

(8)

2.5.3. Resolution of Multiple Track Crossings (Blue Loops)

Evolutionary tracks of massive stars may cross or overlap in the same region of the HRD, particularly during the post-MS Hertzsprung gap transit and subsequent core-He-burning blue loop excursions. This can result in multiple locations along theoretical tracks being consistent with the observed $(T_{\mathrm{eff}},L)$ position. To account for this positional degeneracy:

• Theoretical tracks are divided chronologically into distinct evolutionary phases: (i) post-MS Hertzsprung gap transit, and (ii) blue loop excursion.
• For stars located within degenerate HRD regions, $d^2$ is evaluated independently for each candidate phase.
• The global minimum $d^2$ defines the primary solution. In cases of statistically degenerate minima ($\Delta d^2<1$), phase assignment is weighted by the characteristic timescale of the phase ($\Delta t_{\mathrm{phase}}$), favoring the evolutionary stage with the longer duration due to its higher intrinsic likelihood of observation given standard IMF and lifetime considerations.

While our current framework relies on a global minimum metric and phase prioritization to resolve grid crossings, we acknowledge that a fully probabilistic treatment assigning relative likelihoods or fractional weights to competing evolutionary paths is conceptually superior for population-wide statistics. Implementing such a framework, alongside rigorous evaluation of the initial mass function (IMF), requires sophisticated Bayesian or MCMC-based population synthesis methods, which are deferred to future specialized studies.

2.5.4. Formal Nature of Derived Uncertainties

Uncertainties on initial mass (${\sigma }_M$) and age (${\sigma }_t$) are computed by projecting the $1\sigma$ observational confidence ellipse $(log{T}_{\mathrm{eff}}\pm {\sigma }_{logT},logL\pm {\sigma }_{logL})$ through the continuous interpolation scheme onto the local track geometry.

We emphasize that ${\sigma }_M$ and ${\sigma }_t$ represent formal local uncertainties conditional on the adopted single-star evolutionary grid ($Z=0.014,v/v_{\mathrm{crit}}=0.4$). They quantify how observational precision maps onto the local topology of the model grid. They do not encapsulate total systematic uncertainties in stellar evolutionary theory, such as variations in convective overshooting, initial rotation distributions, mass-loss history, or binary interactions.

3. Results

The resulting observational HRD for the main evolutionary sample is shown in Figure 1. Of the 84 program stars, 76 objects have $log(L/L_{\odot })\ge 3.5$ and constitute the main evolutionary sample. The remaining eight objects have luminosities below this threshold and are excluded from the HRD and from the evolutionary mass and age analysis. The derived luminosities, initial evolutionary masses, and ages of the 76 stars in the main sample are listed in Table 1, while the eight low-luminosity objects are presented separately in Table 2.

Figure 1. Observational Hertzsprung–Russell diagram of the 76 stars in the main evolutionary sample compared with Geneva evolutionary tracks for solar metallicity ($Z=0.014$) and an initial rotational velocity of $v/v_{\mathrm{crit}}=0.4$ [4]. The eight objects with $log(L/L_{\odot })<3.5$ are not included in the diagram and are considered separately in Table 2.

Table 1. Spectral types, bolometric luminosities, derived evolutionary masses, and ages of the 76 stars in the main sample with $log(L/L_{\odot })\ge 3.5$.

No.	Star	Sp. Type	$log(\mathit{L}/{\mathit{L}}_{\odot })$	M (${\mathit{M}}_{\odot }$)	Age (Myr)	No.	Star	Sp. Type	$log(\mathit{L}/{\mathit{L}}_{\odot })$	M (${\mathit{M}}_{\odot }$)	Age (Myr)
1	BD+60 51	A2Iab	$4.29\pm 0.09$	$8.8\pm 0.4$	$34.1\pm 0.2$	39	HD 35600	B9Ib	$4.01\pm 0.04$	$9.0\pm 0.4$	$31.6\pm 1.0$
2	BD+61 153	A0Ib	$4.10\pm 0.07$	$9.0\pm 0.2$	$31.6\pm 2.1$	40	HD 40297	A0Ib	$4.13\pm 0.05$	$9.0\pm 0.2$	$31.6\pm 2.1$
3	BD+60 331	B8Iab	$4.56\pm 0.13$	$11.9\pm 2.8$	$18.6\pm 5.0$	41	HD 40589	A0Iab	$4.41\pm 0.07$	$11.9\pm 0.4$	$18.6\pm 1.0$
4	BD+60 333	B5Ib	$4.76\pm 0.08$	$14.7\pm 0.4$	$13.6\pm 1.0$	42	HD 42400	B5II	$4.40\pm 0.23$	$11.9\pm 2.9$	$18.6\pm 13.0$
5	BD+56 591	A2Ia	$4.33\pm 0.07$	$11.9\pm 0.2$	$18.6\pm 0.5$	43	HD 43384	B3Iab	$4.84\pm 0.07$	$14.7\pm 0.4$	$13.6\pm 1.0$
6	BD+43 1168	B9Iab	$4.44\pm 0.10$	$11.9\pm 0.4$	$18.6\pm 1.0$	44	HD 43910	B9	$4.28\pm 0.05$	$8.8\pm 0.4$	$34.1\pm 0.2$
7	BD+62 2210	B9Ia	$4.87\pm 0.06$	$14.7\pm 0.4$	$13.6\pm 1.0$	45	HD 46769	B7Ib	$3.88\pm 0.06$	$6.9\pm 2.1$	$57.0\pm 5.4$
8	BD+62 2313	B7Ib	$4.37\pm 0.06$	$11.9\pm 0.4$	$18.6\pm 1.0$	46	HD 46783	B9Ib	$3.95\pm 0.05$	$9.0\pm 2.1$	$31.6\pm 1.0$
9	BD+60 2542	A1Iab	$4.20\pm 0.07$	$8.8\pm 0.4$	$33.9\pm 0.3$	47	HD 48452	A5	$4.32\pm 0.12$	$8.8\pm 0.4$	$34.1\pm 0.2$
10	HD 1070	A4II	$4.35\pm 0.09$	$11.9\pm 0.2$	$18.6\pm 0.5$	48	HD 50064	B5Ia+	$5.23\pm 0.14$	$19.5\pm 0.4$	$9.6\pm 1.0$
11	HD 2928	A2Iab	$4.49\pm 0.14$	$11.9\pm 0.4$	$18.6\pm 1.0$	49	HD 55036	A2Ib	$4.48\pm 0.09$	$11.9\pm 0.2$	$18.6\pm 0.5$
12	HD 3940	A1Ia	$4.99\pm 0.08$	$8.8\pm 0.4$	$10.2\pm 1.0$	50	HD 55493	A0	$4.90\pm 0.10$	$14.7\pm 0.4$	$13.6\pm 1.0$
13	HD 4717	A2Iab	$4.27\pm 0.06$	$8.8\pm 0.4$	$34.1\pm 0.2$	51	HD 58131	B9Iab	$4.74\pm 0.10$	$14.7\pm 2.8$	$13.6\pm 5.0$
14	HD 4841	B5Ia	$5.39\pm 0.07$	$23.5\pm 0.4$	$8.0\pm 1.0$	52	HD 58439	A2Ib	$4.75\pm 0.11$	$14.7\pm 2.8$	$13.7\pm 4.9$
15	HD 5776	A2Iab	$4.38\pm 0.10$	$11.9\pm 0.2$	$18.6\pm 0.5$	53	HD 58764	B9Ia	$3.93\pm 0.10$	$9.0\pm 2.1$	$31.6\pm 1.0$
16	HD 7720	B5II	$4.61\pm 0.07$	$11.9\pm 2.8$	$18.6\pm 5.0$	54	HD 59612	A7Iab	$4.29\pm 0.09$	$8.8\pm 0.4$	$34.2\pm 0.2$
17	HD 9233	A4Iab	$4.42\pm 0.07$	$11.9\pm 0.2$	$18.6\pm 0.5$	55	HD 62888	B9.5Iab	$4.34\pm 0.17$	$11.9\pm 2.9$	$18.6\pm 13.0$
18	HD 9311	B5Ib	$4.65\pm 0.06$	$11.9\pm 2.8$	$18.6\pm 5.0$	56	HD 161695	A0Ib	$4.16\pm 0.05$	$8.8\pm 0.2$	$33.7\pm 2.1$
19	HD 9811	A6Ia	$5.02\pm 0.06$	$8.8\pm 0.4$	$10.2\pm 1.0$	57	HD 167356	A0Ib	$4.47\pm 0.08$	$11.9\pm 0.4$	$18.6\pm 1.0$
20	HD 10756	B8Iab	$4.77\pm 0.08$	$14.7\pm 0.4$	$13.6\pm 1.0$	58	HD 167838	B3Ia	$4.88\pm 0.10$	$14.7\pm 0.4$	$13.6\pm 1.0$
21	HD 11831	A2Ia	$4.54\pm 0.09$	$11.9\pm 0.2$	$18.6\pm 0.5$	59	HD 175687	A0Ib	$3.83\pm 0.06$	$6.9\pm 0.4$	$57.0\pm 0.1$
22	HD 13267	B5Ia	$4.57\pm 0.05$	$11.9\pm 0.4$	$18.6\pm 1.0$	60	HD 197345	A2Ia	$5.07\pm 0.03$	$8.8\pm 0.4$	$10.2\pm 1.0$
23	HD 14010	B9Ia	$4.68\pm 0.05$	$14.7\pm 2.8$	$13.6\pm 5.0$	61	HD 209900	A0Ib	$4.18\pm 0.09$	$8.8\pm 0.2$	$33.9\pm 2.3$
24	HD 14322	B8Iab	$4.58\pm 0.05$	$11.9\pm 0.4$	$18.6\pm 1.0$	62	HD 211971	A2Ib	$4.38\pm 0.02$	$11.9\pm 0.2$	$18.6\pm 0.5$
25	HD 14542	B8Iab	$4.71\pm 0.05$	$14.7\pm 0.4$	$13.6\pm 1.0$	63	HD 216927	B9Ia	$4.64\pm 0.15$	$11.9\pm 2.8$	$18.6\pm 5.0$
26	HD 14899	A0Ib	$4.25\pm 0.05$	$8.8\pm 0.4$	$33.9\pm 0.2$	64	HD 222275	A5	$4.25\pm 0.04$	$8.8\pm 0.4$	$34.1\pm 0.2$
27	HD 15316	A2Iab	$4.63\pm 0.06$	$11.9\pm 2.8$	$18.6\pm 5.0$	65	HD 223767	A5Ib	$4.91\pm 0.08$	$14.7\pm 0.2$	$13.7\pm 1.0$
28	HD 15497	B6Ia	$5.04\pm 0.06$	$19.5\pm 0.4$	$9.6\pm 1.0$	66	HD 228347	A0Ib	$4.32\pm 0.14$	$8.8\pm 0.4$	$34.1\pm 0.5$
29	HD 15620	B8Iab	$4.64\pm 0.06$	$11.9\pm 2.8$	$18.6\pm 5.0$	67	HD 236995	A0Ib	$4.23\pm 0.06$	$9.0\pm 2.9$	$31.6\pm 13.0$
30	HD 16778	A1Ia	$4.88\pm 0.06$	$14.7\pm 0.2$	$13.7\pm 0.7$	68	HD 237153	B8Ib	$4.43\pm 0.05$	$11.9\pm 0.4$	$18.6\pm 1.0$
31	HD 17086	A5+II	$3.67\pm 0.02$	$7.0\pm 0.2$	$51.7\pm 1.4$	69	HD 239886	B8Ia	$4.74\pm 0.11$	$14.7\pm 2.8$	$13.6\pm 5.0$
32	HD 17088	B9Ia	$5.00\pm 0.24$	$8.8\pm 1.6$	$10.2\pm 0.3$	70	HD 239895	B8Ia	$5.32\pm 0.09$	$11.3\pm 2.6$	$8.2\pm 2.0$
33	HD 17145	B6Iab	$4.63\pm 0.06$	$11.9\pm 2.8$	$18.6\pm 5.0$	71	HD 239950	B8	$4.08\pm 0.12$	$9.0\pm 0.2$	$31.6\pm 2.3$
34	HD 17378	A5Ia	$5.12\pm 0.06$	$8.8\pm 0.4$	$10.2\pm 1.0$	72	HD 248587	A0Iab	$3.89\pm 0.07$	$6.9\pm 2.1$	$57.1\pm 0.1$
35	HD 17857	B8Ib	$4.71\pm 0.05$	$14.7\pm 0.4$	$13.6\pm 1.0$	73	HD 253250	A0Iab	$3.94\pm 0.13$	$9.0\pm 2.1$	$31.6\pm 1.0$
36	HD 21389	A0Ia	$5.37\pm 0.33$	$23.5\pm 0.4$	$8.0\pm 1.0$	74	HD 332757	A2Iab	$5.24\pm 0.13$	$7.2\pm 1.6$	$10.5\pm 0.3$
37	HD 27381	A4Ib	$4.37\pm 0.03$	$11.9\pm 0.2$	$18.6\pm 0.5$	75	HD 332996	A0Ib	$4.00\pm 0.04$	$9.0\pm 0.4$	$31.6\pm 1.0$
38	HD 34578	A5II+	$4.26\pm 0.10$	$8.8\pm 0.4$	$34.1\pm 0.5$	76	HD 333030	A0Ia	$4.39\pm 0.03$	$11.9\pm 0.2$	$18.6\pm 0.5$

Table 2. Spectral types and bolometric luminosities of the eight low-luminosity objects excluded from the evolutionary mass and age analysis ($log(L/L_{\odot })<3.5$).

No.	Star	Sp. Type	$log(\mathit{L}/{\mathit{L}}_{\odot })$
1	HD 11577	B9.5IV	$2.87\pm 0.02$
2	HD 13717	B9III	$3.30\pm 0.03$
3	HD 28747	B9	$3.33\pm 0.02$
4	HD 43820	A2Ib	$1.11\pm 0.01$
5	HD 47314	B8Ib	$2.74\pm 0.03$
6	HD 67456	A3Ib	$3.19\pm 0.03$
7	HD 71833	B8II	$2.60\pm 0.02$
8	HD 147084	A5II	$2.60\pm 0.04$

The main sample is concentrated in the upper, luminous region of the HRD and is broadly consistent with the Geneva evolutionary tracks for solar metallicity ($Z=0.014$) and an initial rotational velocity of $v/v_{\mathrm{crit}}=0.4$ [4]. Grid-based matching of the observed positions to the evolutionary models yields initial masses of approximately 7–$25M_{\odot }$ and evolutionary ages ranging from about 8 to 57 Myr. Most objects are located in regions of the Geneva tracks associated with the termination of core-hydrogen burning and subsequent post-main-sequence evolution. However, the positions of individual stars in the HRD may remain consistent with more than one evolutionary phase.

The uncertainties in $log(L/L_{\odot })$ vary across the sample and are particularly large for several objects, including HD 21389, HD 17088, and HD 42400. In these cases, the luminosity uncertainty is dominated by the uncertainty in the adopted interstellar extinction ${\sigma }_{A_V}$. Such uncertainties may arise from steep extinction gradients, unresolved small-scale structure, and limited tracer-star sampling along individual lines of sight in the 3D dust map.

The eight low-luminosity objects have derived values of $log(L/L_{\odot })<3.5$ and are therefore excluded from Figure 1 and from the evolutionary mass and age analysis. Their properties are listed separately in Table 2. Comparison of their derived luminosities with their current spectral classifications reveals two distinct groups: five objects have cataloged luminosity classes III–IV or II, or lack a clear luminosity class, and are therefore inconsistent with classical supergiant status, whereas three objects retain supergiant classifications despite their unexpectedly low derived luminosities. These objects are discussed separately in Section 4.

4. Discussion

As shown in Figure 1, the 76 stars in the main evolutionary sample occupy the upper part of the observational HRD and are broadly consistent with the Geneva evolutionary tracks for rotating solar-metallicity models ($Z=0.014,v/v_{\mathrm{crit}}=0.4$) [4]. The derived luminosities and corresponding evolutionary parameters indicate a population dominated by luminous, evolved massive stars with initial masses of $M\approx 7–25M_{\odot }$ and ages ranging from $t\sim 8$ to 57 Myr. Most objects are located in HRD regions associated with the termination of core-hydrogen burning and subsequent post-main-sequence evolution.

4.1. Physical Homogeneity and Catalog Sanity Checking

A major strength of the uniform framework established in this work—combining a single empirical $T_{\mathrm{eff}}$ calibration scale, Gaia DR3 astrometry, and 3D Bayestar extinction mapping—is its capacity to rigorously test the physical homogeneity of classical supergiant samples. Spectral classifications in heterogeneous literature catalogs often rely on subjective visual criteria. By pairing uniform spectroscopic temperatures with absolute bolometric luminosities derived from 3D extinction mapping, our methodology acts as a stringent diagnostic filter to identify objects whose assigned luminosity classes are physically inconsistent with their placement on the HRD.

Out of the initial sample of 84 cataloged BA supergiants and bright stars, our unified analysis reveals that eight objects ($\sim 10\%$ ) fall below the luminosity threshold adopted for the evolutionary analysis, $log(L/L_{\odot })=3.5$; Table 2). These low-luminosity outliers naturally divide into two distinct categories:

1.

Misclassified Subgiants and Giants: Five objects—HD 11577 (B9.5IV), HD 13717 (B9III), HD 28747 (B9), HD 71833 (B8II), and HD 147084 (A5II)—possess cataloged luminosity classes of III–IV, II, or lack a clear class. Their low derived luminosities ($log(L/L_{\odot })\sim 2.6–3.3$) confirm that they are intrinsically less evolved intermediate-mass stars rather than classical supergiants.

2.

Low-Luminosity Spectral Anomalies: Three objects—HD 43820 (A2Ib), HD 47314 (B8Ib), and HD 67456 (A3Ib)—retain supergiant or bright-supergiant classifications despite remarkably low derived luminosities ($log(L/L_{\odot })=1.11$, $2.74$, and $3.19$, respectively). In particular, HD 43820 has $log(L/L_{\odot })\approx 1.11$, which is incompatible with the luminosity expected for a classical massive supergiant. These objects therefore require independent spectroscopic and evolutionary classification. Their low luminosities may indicate that they are lower-luminosity evolved stars rather than classical massive supergiants; possible alternatives include evolved low-mass objects, although their specific evolutionary nature cannot be established from the present HRD analysis alone. Dedicated follow-up observations, including detailed non-LTE atmospheric modeling and chemical-abundance analysis, are required to constrain their $T_{\mathrm{eff}}$, $logg$, and evolutionary nature.

Eliminating these non-supergiant contamination sources prevents significant systematic bias when constructing empirical calibration baselines.

4.2. Morphological Substructure of the HRD

Inspection of the observational HRD (Figure 1) reveals an interesting morphological feature: the distribution shows a distinct separation between a tighter, nearly vertical sequence at cooler temperatures and a more scattered population of hotter, highly luminous objects transitioning away from the main sequence. While individual evolutionary tracks suffer from the phase degeneracies discussed below, this apparent visual separation—echoed in independent censuses of evolved high-mass stars—may reflect differences in evolutionary residence times between post-main-sequence transits and advanced core-helium-burning states. Further statistical mapping and abundance analyses are planned to test whether this empirical substructure maps cleanly to distinct evolutionary pathways.

4.3. Systematics, HRD Degeneracies, and Binary Interactions

An inherent complexity in interpreting the evolutionary status of individual massive stars is the spatial degeneracy in the upper HRD caused by multiple track crossings [19]. A star of a given $T_{\mathrm{eff}}$ and L may be traversing the Hertzsprung gap redward for the first time or undergoing a subsequent blueward excursion during core-helium burning after a red supergiant phase. Our grid-matching algorithm resolves this by identifying the global minimum in the error-weighted distance metric ($d^2$), prioritizing longer evolutionary phases in rare ambiguous cases.

Furthermore, the derived masses and ages are conditional model-dependent estimates tied to single-star Geneva tracks incorporating rotational mixing and mass loss [4]. Unresolved binary interaction represents another key systematic factor: mass transfer, mergers, or stripping can drastically alter a star’s surface abundances, temperature, and apparent age [20]. Identifying specific binary survivors or fast rotators within the sample will require follow-up high-resolution spectroscopy to constrain detailed atmospheric chemical abundances.

The importance of binarity and circumstellar environments in interpreting the evolutionary status of peculiar B-type stars has been demonstrated for several B[e] and emission-line objects, including HD 85567 and MWC 645 [21,22]. More generally, the growing evidence for a high binary fraction among Be and B[e] stars highlights the need to consider binary interaction and mass-transfer histories when interpreting objects with anomalous spectroscopic properties [23].

A related caveat concerns the treatment of multiple track crossings (e.g., blue loops versus post-MS transitions). As noted in Section 2.5, our current analysis adopts a deterministic phase-assignment scheme based on timescale likelihoods. While this prevents artificial noise inflation in individual mass and age estimates, it inherently suppresses faster evolutionary phases in individual cases. A comprehensive statistical assessment—including a rigorous derivation of the stellar mass function and tracking fractional probabilities across overlapping Geneva grid segments—remains an important goal for subsequent work utilizing dedicated population synthesis modeling.

5. Conclusions

By integrating a uniform empirical $T_{\mathrm{eff}}$ scale with Gaia DR3 astrometry and 3D spatial dust maps, we have constructed a self-consistent observational HRD for a sample of 84 Galactic BA stars. The primary conclusions of this study are:

1.

Diagnostic Power for Catalog Purity: Combining homogeneous spectroscopic temperatures with precision Gaia astrometry and 3D Bayestar extinction maps provides a robust methodology for auditing literature supergiant catalogs. This approach successfully identified eight low-luminosity stars ($log(L/L_{\odot })<3.5$) that contaminate the supergiant domain, purifying the sample for evolutionary analysis.

2.

Fundamental Parameters of the Main Sample: The primary evolutionary sample of 76 Galactic BA supergiants forms a coherent population of evolved massive stars. Comparison with Geneva evolutionary models ($Z=0.014,v/v_{\mathrm{crit}}=0.4$) yields initial masses of $M\approx 7–25M_{\odot }$ and ages of $t\sim 8–57$ Myr, representing post-main-sequence objects near or after the termination of core-hydrogen burning.

3.

Impact on Extragalactic Distance Anchors: Purifying Galactic supergiant samples by filtering out misclassified subgiants and low-luminosity contaminants provides a cleaner empirical foundation for calibrating the FGLR and testing mass-loss and mixing physics in massive stars.