Evaluating Gaia Astrometric Quality and Distances for Galactic Hot Supergiants

Abstract

Distances to Galactic BA supergiants are essential for determining their luminosities, radii, and positions on the Hertzsprung–Russell diagram, yet Gaia parallaxes for these bright, extended sources are often affected by systematics. We compiled a homogeneous sample of 132 B0–A5 supergiants and re-evaluated their distances using a consistent, quality-controlled approach. Parallaxes from Gaia DR3 and EDR3 were corrected for a magnitude–colour zero-point bias and adjusted for excess noise through RUWE-dependent uncertainty inflation. A Bayesian inference with an exponentially decreasing space–density prior was then applied, adopting the catalogue with the smallest penalised total uncertainty. Distances were accepted only when the corrected parallax signal-to-noise ratio exceeded 2.5, the relative uncertainty was below 40%, and key Gaia quality indicators were nominal. The resulting catalogue delivers robust, quality-vetted distances with realistic uncertainties for each star, providing a reliable foundation for deriving fundamental parameters and for future studies of the flux-weighted gravity–luminosity relation and the evolution of Galactic BA supergiants.

1. Introduction

Galactic hot supergiants of spectral types B and A occupy a transitional region between the main sequence and the subsequent phases of massive-star evolution. While many of them are believed to have evolved beyond core-hydrogen burning, others may still reside near or just beyond the terminal-age main sequence due to enhanced internal mixing and rotationally induced extension of main-sequence lifetimes [1].

They develop large radii, exhibit low surface gravities, and reach luminosities up to $log(L/L_{\odot })\sim 4.5–5.8$ while maintaining effective temperatures in the range $T_{\mathrm{eff}}\sim 8000–\mathrm{20,000}$ K [2,3]. Their strong radiation fields and reduced gravities give rise to line-driven winds and extended outflowing atmospheres, similar to those observed in B[e] supergiants and luminous blue variables.

Spectroscopically, BA supergiants exhibit wind-sensitive Balmer line profiles (notably H $\alpha$), while diagnostics such as He i and Mg ii are frequently used across the transition from B to A types. In the ultraviolet, classical morphological studies have demonstrated that B0.5 Ia and B0.7 Ia supergiants are qualitatively distinct in their UV spectra: the presence or absence of P-Cygni signatures in C ii and Al iii, and a marked change in the morphology of the Si iv$\lambda \lambda 1393,1402$ absorptions. In particular, between subtypes B0.5 and B0.7, the blue-shifted Si iv lines become noticeably narrower and deeper, reversing the smoother trend seen toward earlier B types [4,5,6].

Supergiants from mid-B to mid-A types are relatively massive ($7–15M_{\odot }$) and among the optically brightest stellar populations, detectable out to tens of Mpc. Late B- and early A-type supergiants are among the most luminous stars, reaching visual absolute magnitudes around $M_V\approx -9$ [7]. This makes them promising extragalactic standard candles, provided that their fundamental parameters—effective temperature and luminosity—are reliably determined. Several spectroscopic surveys have targeted this group [8,9,10,11,12], including recent efforts on BA-type binaries and emission-line supergiants [13]. Yet, hundreds of such objects within a few kiloparsecs from the Sun remain accessible to small- and medium-class telescopes. A medium-resolution spectroscopic study, when combined with spectral energy distribution (SED) analysis, offers an efficient pathway to independently verify parameters derived from high-resolution modelling and to establish purely observational criteria for classification and parameter estimation [14,15,16].

Historically, BA supergiants have been central to two long-standing themes. First, their locus on the Hertzsprung–Russell diagram (HRD) is intertwined with the empirical Humphreys–Davidson limit, which marks the paucity of very luminous cool supergiants and points to enhanced mass loss and instabilities at high luminosity [17]. Second, the flux-weighted gravity–luminosity relation (FGLR) provides a spectroscopic distance indicator comparatively insensitive to reddening and metallicity and validated out to several Mpc [3]. Robust classification frameworks and quantitative $T_{\mathrm{eff}}$–$logg$ calibrations—from digital OB atlases to modern NLTE analyses—underpin current parameter scales for BA supergiants and related luminous binaries [18,19].

Despite their importance, BA supergiants pose observational challenges. They are rare and typically distant, limiting sample sizes and data quality. Their extended, dynamic atmospheres mean that a star need not behave as a point source: spatial inhomogeneities and temporal variability in surface brightness can shift the photocentre, degrading single-star astrometric solutions [20]. In practice, Gaia measurements of many luminous supergiants show anomalous residuals. The Renormalised Unit Weight Error (RUWE) quantifies the goodness-of-fit of the Gaia five-parameter model; values near 1 indicate acceptable fits, whereas elevated values flag departures from the single-star, point-source assumption. A pragmatic threshold of $\mathrm{RUWE}>1.4$ is commonly used to identify suspect astrometry [21,22]. Elevated RUWE is frequent among BA supergiants and luminous blue variables (LBVs); for example, the bright B-type supergiant $\rho$ Leo has $\mathrm{RUWE}\simeq 2.46$, implying an unreliable parallax [23], and several Galactic LBVs in Gaia DR2 showed highly uncertain distances due to excess noise [24].

Distance is the pivotal external parameter for inferring intrinsic properties. With a reliable distance, one can convert the observed flux or apparent magnitude into absolute quantities and determine the bolometric luminosity; in combination with $T_{\mathrm{eff}}$, this also constrains the stellar radius. Conversely, biases in distance propagate directly into systematic errors in luminosity, radius, and even mass, complicating placement on the HR diagram and comparisons to evolutionary tracks.

Recent analyses of early-B supergiants based on Gaia DR3 astrometry (e.g., [25,26]) relied primarily on catalogue parallaxes and Bailer-Jones distance estimates to investigate the evolutionary status and luminosity distribution of these massive stars.

While such studies provided valuable astrophysical context, they did not explicitly address the underlying astrometric quality or the impact of excess noise on the derived distances. In the present work, we focus on this methodological aspect by performing a homogeneous re-evaluation of Gaia parallaxes for a broader sample of Galactic BA supergiants. Our approach incorporates magnitude–colour zero-point corrections, RUWE-dependent uncertainty inflation, a penalised DR3/EDR3 catalogue choice, and Bayesian distance inference with exponentially decreasing space–density prior techniques designed to produce quality-vetted, statistically consistent distances for subsequent astrophysical analysis. This framework complements evolutionary studies by providing a robust astrometric baseline for luminosity calibration and comparison with stellar models, building upon methodologies successfully applied to other luminous systems [4,18].

2. Materials and Methods

The adopted sample of 132 BA-type supergiants (B0–A5, luminosity classes I–Ia⁺) was assembled in the course of our ongoing observational program on bright Galactic supergiants. The targets were selected primarily for their brightness ($V\lesssim 9$ mag) and observability from northern sites, ensuring suitability for medium- and high-resolution follow-up spectroscopy. Although these objects are not drawn from a uniform spectroscopic survey, they represent well-classified BA supergiants distributed across a broad range of effective temperatures, surface gravities, and wind strengths. The present work focuses on establishing reliable Gaia-based distances and astrometric quality metrics for this sample; a detailed spectroscopic analysis and modelling of their physical parameters will be presented in subsequent papers of this series. While not volume-complete, the sample provides a consistent and observationally well-defined subset of bright Galactic supergiants, suitable for validating the RUWE-aware distance recalibration and for future confrontation with evolutionary predictions.

2.1. Distance Determination Pipeline

To obtain robust distances for our sample, we developed a comprehensive pipeline in Python (3.11.5). The procedure involves four main stages: (1) target identification and data retrieval from astronomical catalogs; (2) parallax processing and error recalibration; (3) Bayesian inference of distances; and (4) a quality control assessment leading to the final adopted distance for each star.

2.1.1. Object Identification and Data Retrieval

For each target, we first established precise equatorial coordinates (ICRS). If right ascension and declination were available in the input table, we used them directly. Otherwise, we resolved the object name with SIMBAD [27], automatically generating common variants of Bayer and Flamsteed designations.

Once coordinates were fixed, we queried VizieR [28] for three Gaia-related catalogues using their official CDS identifiers: (1) the Bailer-Jones Gaia EDR3 distance catalogue I/352 [29], (2) the main Gaia DR3 catalogue I/355 [30], and (3) the main Gaia EDR3 catalogue I/350 [31,32]. All queries were executed via astroquery [33] in Python, with astrometric/coordinate handling by Astropy [34]. Network requests used up to three retries with exponential backoff.

Cone Searches and Source Association

For I/352 [29], we performed a cone search of $8^{″}$ around the target position and selected the nearest match; the resulting angular separation is recorded in the output table. For I/355 [31], we first attempted a direct lookup by the Bailer-Jones Source identifier (when available); otherwise, we used a $5^{″}$ cone search around either the BJ position or the SIMBAD position and again adopted the nearest neighbour. We tracked the DR3 match separation and treated $\le 2^{″}$ as good in our QC flags. All angles are in arcseconds and all coordinates are in degrees (ICRS).

2.1.2. Parallax Processing and Error Recalibration

Raw Gaia parallaxes of BA supergiants are often impacted by systematics and model misfits (e.g., binarity, saturation/gating, and crowding), which is frequently reflected in an elevated RUWE. We therefore recalibrate parallaxes and their uncertainties before distance inference using three steps: (i) a magnitude–colour dependent zero-point (ZP) correction, (ii) RUWE-based inflation of the formal parallax uncertainty with floors and micro-systematics, and (iii) a catalogue choice (DR3 vs. EDR3) that minimises the total post-recalibration uncertainty subject to quality penalties.

Zero-Point Correction

We correct measured parallaxes, $\varpi$, to ${\varpi }^{\prime }$ by subtracting an empirical ZP term that depends on G and $BP-RP$:

$$\Delta \varpi (G,BP-RP)=\left\{\begin{array}{cc}-0.010+0.002\left[\right(BP-RP)-1.0],\hfill & G<13,\hfill \\ -0.017+0.001\left[\right(BP-RP)-1.0],\hfill & 13\le G<17,\hfill \\ -0.025+0.002\left[\right(BP-RP)-1.0],\hfill & G\ge 17,\hfill \end{array}\right.$$

so that ${\varpi }^{\prime }=\varpi -\Delta \varpi$ (mas). When G or colours are unavailable, we adopt a constant $\mathrm{ZP}=-0.017$ mas. This pragmatic prescription is inspired by the documented magnitude/colour dependence of the Gaia EDR3 parallax bias [35] and yields corrections of the right order for bright BA supergiants (see also [36]). The total uncertainty propagated to the Bayesian stage is ${\sigma }_{\mathrm{tot}}=\sqrt{{\sigma }_{\varpi ,\mathrm{infl}}^2+{\sigma }_{\mathrm{sys}}^2}$, and we always use $({\varpi }^{\prime },{\sigma }_{\mathrm{tot}})$ thereafter.

RUWE-Based Uncertainty Inflation

Let ${\sigma }_{\varpi }$ be the catalogue parallax uncertainty (mas). For sources with $\mathrm{RUWE}>1.0$ we inflate the random part via

$${\sigma }_{\varpi ,\mathrm{infl}}=max\left[f\left(\mathrm{RUWE}\right){\sigma }_{\varpi },{\sigma }_{\mathrm{floor}}\right],f\left(\mathrm{RUWE}\right)=1+(f_{max}-1)\left(1-e^{-\alpha (\mathrm{RUWE}-1)}\right),$$

where

$$f_{max}=f_0{\left({\displaystyle \frac{max({\varpi }^{\prime },0.01)}{10}}\right)}^{\beta }{\left({\displaystyle \frac{{\sigma }_{\eta }\left(G\right)}{0.1}}\right)}^{\gamma }.$$

We use the constants $\alpha =2.77$, $f_0=3.73$, $\beta =0.065$, $\gamma =-0.056$, a random floor ${\sigma }_{\mathrm{floor}}=0.02$ mas, and add a micro-systematic in quadrature ${\sigma }_{\mathrm{sys}}=0.015$ mas to form the total post-recalibration uncertainty

$${\sigma }_{\mathrm{tot}}=\sqrt{{\sigma }_{\varpi ,\mathrm{infl}}^2+{\sigma }_{\mathrm{sys}}^2}.$$

The along-scan reference term ${\sigma }_{\eta }\left(G\right)$ (mas) is obtained by linear interpolation through anchor points:

$$\left\{(G,{\sigma }_{\eta })\right\}=\begin{array}{cc}& \left\{\right(6,0.02),(10,0.03),(12,0.04),(13,0.05),\hfill \\ & (14,0.06),(16,0.10),(18,0.20),(19,0.30),(20,0.50)\}.\hfill \end{array}$$

This scheme operationalises community guidance that high-RUWE solutions understate true uncertainties (e.g., [22,37,38]); in our QC we also flag $\mathrm{RUWE}>1.4$ as “high” following common usage.

Catalogue Choice (DR3 vs. EDR3)

For each star, we compute ${\varpi }^{\prime }$ and ${\sigma }_{\mathrm{tot}}$ for both DR3 and EDR3 (when available) and adopt the one with the smallest penalised total uncertainty. Problematic astrometric solutions are down-weighted by multiplicative penalties:

$$\mathrm{score}={\sigma }_{\mathrm{tot}}\times p,p=p_{\mathrm{dup}}{p}_{N_{\mathrm{per}}}{p}_{\mathrm{solved}},$$

(1)

where $p_{\mathrm{dup}}=1.5$ for duplicated sources, $p_{N_{\mathrm{per}}}=1.3$ if the number of visibility periods is below 8, and $p_{\mathrm{solved}}=1.3$ if the astrometric solution type is lower than 31. If the parallax uncertainty is missing, we adopt $e_{\varpi }=0.5$ mas as a conservative fallback. Negative or near-zero parallaxes are allowed, since the Bayesian inference stage naturally accommodates them.

Implementation Notes

All quantities are in mas (parallaxes) and pc (distances). We propagate the ZP-corrected parallax ${\varpi }^{\prime }$ and ${\sigma }_{\mathrm{tot}}$ to the Bayesian step (Section 2.1.3) and record the chosen catalogue in posterior_catalog.

2.1.3. Bayesian Distance Inference

Calculating distance via simple inversion ($d=1/\varpi$) is statistically biased. We therefore used a Bayesian framework with an exponentially decreasing space density (EDSD) prior. For each star, we adopt a scale length L anchored to the Bailer-Jones median distance, $L=\mathrm{clip}\left(0.8r_{\mathrm{BJ},50},300\mathrm{pc},2500\mathrm{pc}\right)$. (We record the ecliptic latitude for context, but it is not used in the baseline L.)

The posterior for distance r is

$$P(r\mid {\varpi }^{\prime },{\sigma }_{\mathrm{tot}})\propto exp\left[-\frac{1}{2}{\left({\displaystyle \frac{{\varpi }^{\prime }-1000/r}{{\sigma }_{\mathrm{tot}}}}\right)}^2\right]\times r^{2}exp(-r/L),$$

where ${\varpi }^{\prime }$ is the ZP-corrected parallax (mas) and ${\sigma }_{\mathrm{tot}}$ is the RUWE-inflated uncertainty with a micro-systematic term added in quadrature (see Section 2.1.2). Negative and low-S/N parallaxes are naturally handled by the prior. We compute the posterior numerically on an adaptive grid and report the median $r_{50}$ as our distance estimate, with $r_{16}$ and $r_{84}$ defining the 68% credible interval.

2.1.4. Quality Control and Final Distance Adoption

In the final stage, the pipeline decides which distance to adopt for each star based on a set of quality criteria. The logic is as follows:

• The new Bayesian distance is preferred if it meets strict quality standards:
  • The parallax signal-to-noise ratio ($\varpi /{\sigma }_{\mathrm{total}}$) is $\ge 2.5$.
  • The relative distance error is $\le 40\%$.
  • Key Gaia quality metrics are nominal (e.g., $\mathrm{RUWE}\le 1.4$ and the source is not flagged as duplicated).
• Otherwise, the old Bailer-Jones et al. [29] distance is used as a fallback, provided its relative error does not exceed 60%.
• If neither estimate is reliable, the value with the smaller relative error is adopted, but it is flagged as having low quality.

Code Availability

This study made use of the open-source Gaia Distance Pipeline https://github.com/nva1dman/gaia_distance_pipeline (accessed on 24 October 2025), a Python-based workflow implementing all recalibration and Bayesian inference steps described above. The repository is publicly available under the MIT licence and ensures reproducibility of all results.

3. Results

3.1. Overview of the Sample

We compiled a working list of Galactic hot (BA–type) supergiants for which Gaia EDR3/DR3 astrometry and Bailer-Jones distances are available. For each target, we applied the pipeline described in Section 2: ZP correction, RUWE-based error inflation, catalog choice (EDR3/DR3) by penalised uncertainty, and Bayesian distance inference with an EDSD prior. The full per-object output is provided in

Table A1. Distances and Gaia parameters for Galactic BA supergiants. The table lists the principal astrometric quantities used for the adopted distances: Name, RUWE, G magnitude, Bailer-Jones distance $d_{\mathrm{BJ}}$, our recalculated Bayesian distance $d_{\mathrm{new}}$ with its uncertainty, the total parallax signal-to-noise ratio ${\mathrm{SNR}}_{\mathrm{tot}}$, and the adopted prior scale length L. These values represent the quality-controlled subset for astrophysical analysis; the extended dataset with all intermediate fields and flags is provided in Table A2.

N	Name	${\mathit{d}}_{\mathbf{BJ}}$ [pc] [29]	${\mathit{\sigma }}_{\mathit{d},\mathbf{BJ}}$ [pc]	RUWE	G [mag]	${\mathit{d}}_{\mathbf{new}}$ [pc]	${\mathit{\sigma }}_{\mathit{d}}$ [pc]	${\mathbf{SNR}}_{\mathbf{tot}}$	L [pc]
1	HD 1070	2516.03	97.81	0.92	7.83	2641.01	174.85	15.32	2012.80
2	BD+60 51	3638.11	126.18	0.83	9.01	3909.82	385.57	10.46	2500.00
3	HD 2928	3470.70	203.04	0.90	8.42	3707.81	346.55	11.02	2500.00
4	HD 3283	905.65	23.96	1.04	5.70	924.96	34.35	26.96	724.52
5	V755 Cas	3003.46	119.14	0.82	7.03	3246.23	265.09	12.53	2402.77
6	BD+61 153	2678.26	91.62	0.98	8.97	2836.91	201.97	14.28	2142.61
7	HD 4717	2649.40	115.80	0.94	7.87	2790.89	195.42	14.51	2119.52
8	HD 4841	2865.90	126.44	0.98	6.69	3044.85	232.95	13.33	2292.72
9	HD 5776	2762.44	144.38	0.97	7.89	2928.01	215.26	13.85	2209.95
10	HD 7902	2486.87	93.87	0.92	6.84	2671.20	178.88	15.15	1989.50
11	HD 7720	2689.60	102.29	0.92	8.65	2848.03	203.57	14.23	2151.68
12	HD 8065	1422.80	77.63	0.85	5.94	1454.44	96.62	15.27	1138.24
13	BD+62 246	2755.14	117.73	0.93	8.40	2902.38	211.49	13.97	2204.11
14	HD 9233	3055.95	175.56	0.88	7.78	3281.61	270.98	12.40	2444.76
15	HD 9311	2682.46	126.20	0.93	7.17	2853.45	204.34	14.20	2145.97
16	HD 9811	2489.39	101.69	0.93	6.16	2630.70	173.47	15.37	1991.51
17	HD 15316	2392.85	118.71	1.03	6.94	2533.83	179.86	14.32	1914.28
18	HD 62888	3573.01	268.11	1.18	7.72	3931.83	737.39	5.97	2500.00
19	BD+60 331	2672.52	97.41	0.98	8.63	2800.26	196.76	14.47	2138.02
20	BD+60 333	2764.91	134.23	1.07	8.66	2898.32	232.99	12.73	2211.93
21	BD+60 339	2636.87	103.49	0.86	8.29	2744.04	188.88	14.76	2109.49
22	V819 Cas	2712.90	129.14	0.82	6.65	2886.33	209.12	14.05	2170.32
23	BD+56 386	658.79	11.91	0.96	7.68	668.68	15.06	44.27	527.03
24	HD 11831	2857.63	132.35	0.92	7.74	3061.94	235.58	13.26	2286.11
25	53 Cas	904.55	36.27	1.00	5.48	923.89	41.38	22.42	723.64
26	V472 Per	2495.27	331.56	1.10	5.48	2838.95	655.00	5.17	1996.22
27	HD 13476	2333.18	109.95	1.04	6.25	2493.47	187.99	13.52	1866.55
28	HD 13744	2309.02	99.28	0.93	7.35	2436.47	148.65	16.57	1847.22
29	HD 14010	2358.87	86.65	0.96	6.94	2457.91	151.30	16.43	1887.09
30	HD 14322	2316.43	93.66	0.93	6.69	2443.34	149.50	16.53	1853.14
31	HD 14433	2094.68	82.48	0.95	6.23	2184.89	119.40	18.45	1675.74
32	V474 Per	1297.55	144.55	0.93	5.06	1294.72	139.53	9.709	1038.04
33	V553 Per	2439.60	106.20	1.07	7.22	2586.58	211.78	12.504	1951.68
34	HD 14542	2143.04	99.86	0.93	6.80	2244.92	126.08	17.961	1714.43
35	HD 14899	2166.67	86.64	0.97	7.26	2278.07	132.39	17.374	1733.33
36	V425 Per	2502.90	131.77	0.99	6.78	2659.64	177.33	15.210	2002.32
37	HD 15620	2256.84	107.41	1.02	8.01	2344.08	153.33	15.496	1805.47
38	HD 16778	2416.62	117.91	0.97	7.35	2540.80	161.74	15.906	1933.30
39	HD 236995	2248.83	94.23	0.97	8.34	2390.97	143.11	16.881	1799.06
40	HD 17088	2708.47	248.03	1.37	7.27	3315.13	879.98	4.636	2166.78
41	HD 17145	2224.57	91.21	0.95	7.81	2376.82	146.03	16.46	1779.66
42	V480 Per	2173.80	136.90	1.01	5.89	2292.00	168.91	13.82	1739.04
43	HD 20041	924.89	45.72	1.00	5.53	939.27	53.42	17.75	739.91
44	CS Cam	972.28	113.12	0.93	4.07	983.37	130.80	8.06	777.83
45	CE Cam	1067.36	125.38	0.99	4.34	1113.95	152.70	7.84	853.89
46	HD 237153	2269.98	57.80	1.00	8.80	2414.17	145.92	16.72	1815.98
47	BD+55 838	4143.10	183.91	0.87	9.01	4659.88	548.23	8.83	2500.00
48	AZ CMi	148.30	1.09	1.03	6.43	148.66	1.58	93.47	300.00
49	HD 19978	78.93	0.98	3.03	5.40	79.65	3.76	21.37	300.00
50	BD+43 1168	3816.67	183.15	1.01	9.02	4340.53	475.59	9.46	2500.00
51	19 Aur	1164.20	144.37	0.98	4.93	1189.11	138.46	9.05	931.36
52	HD 35600	880.38	29.83	0.75	5.63	901.34	36.32	24.87	704.31
53	HD 248587	2405.98	131.82	0.93	7.69	2608.82	193.46	13.73	1924.78
54	HD 39970	1748.44	89.53	0.93	5.88	1866.62	124.42	15.21	1398.76
55	HD 40297	1845.22	79.19	0.87	7.17	1945.99	100.82	19.43	1476.18
56	HD 40589	1632.58	92.97	1.07	5.95	1734.28	148.78	11.97	1306.06
57	HD 42400	1513.45	62.08	1.09	6.78	1589.54	114.39	14.14	1210.76
58	HD 253250	2613.94	143.99	1.17	9.10	2815.77	314.09	9.39	2091.15
59	9 Gem	1713.19	98.60	1.05	6.11	1823.50	144.99	12.86	1370.55
60	HD 43910	2023.94	102.62	0.95	7.21	2133.92	126.73	17.01	1619.15
61	13 Mon	816.45	82.32	0.86	4.44	833.54	78.71	10.95	653.16
62	HR 2409	773.37	51.53	1.00	5.76	770.03	51.40	15.20	618.70
63	HD 46783	1842.53	69.05	0.98	7.95	1963.23	102.94	19.20	1474.03
64	HD 48452	4192.87	360.64	0.97	8.41	4652.44	613.30	7.96	2500.00
65	MWC 536	4711.58	538.24	0.93	7.90	5375.84	852.42	6.66	2500.00
66	HD 55036	3346.96	250.72	1.04	6.91	3604.67	383.99	9.77	2500.00
67	HD 58439	3045.25	296.61	0.96	6.17	3127.35	304.66	10.64	2436.20
68	HD 59612	1283.74	117.67	0.93	4.77	1343.25	137.62	10.15	1026.99
69	HR 3183	493.17	14.64	0.96	5.30	496.66	16.58	29.95	394.54
70	HR 3345	393.84	5.62	1.03	6.67	397.42	7.05	56.19	315.07
71	HD 164865	1498.81	47.44	0.82	7.22	1546.98	60.48	25.62	1199.05
72	HD 165784	1496.85	94.48	0.89	6.10	1586.69	101.20	15.88	1197.48
73	V4387 Sgr	1967.68	165.63	0.84	5.96	2052.42	188.85	11.22	1574.14
74	HD 167838	1675.29	66.41	0.97	6.57	1751.84	100.29	17.63	1340.23
75	BD-12 4970	1994.59	90.17	0.96	8.30	2114.58	112.15	18.99	1595.67
76	AS 314	1620.24	30.77	0.84	9.50	1688.66	71.18	23.79	1296.19
77	HD 175687	655.83	62.98	0.91	4.98	682.96	44.14	15.68	524.67
78	HD 332757	5402.02	523.13	0.91	8.20	5863.48	864.09	7.05	2500.00
79	HT Sge	2168.42	120.57	0.93	6.25	2307.81	152.49	15.34	1734.74
80	HR 7699	1204.73	32.14	0.88	6.09	1233.24	43.72	28.23	963.78
81	42 Cyg	1128.54	24.61	0.95	5.74	1155.33	37.00	31.21	902.83
82	55 Cyg	1827.14	265.45	1.04	4.67	1988.52	416.10	5.58	1461.72
83	HD 199478	2423.10	222.36	0.90	5.53	2566.64	286.47	9.39	1938.48
84	9 Cep	996.03	84.07	0.98	4.65	993.88	105.73	9.82	796.82
85	Nu Cep	994.02	14.86	0.89	11.54	1022.91	26.07	39.15	795.22
86	HD 207673	1524.55	35.04	0.95	6.34	1579.30	62.23	25.42	1219.64
87	13 Cep	1076.95	43.92	0.96	5.50	1088.93	46.18	23.65	861.56
88	HD 209900	3659.71	176.50	0.86	8.57	3873.49	378.40	10.56	2500.00
89	V399 Lac	2289.32	173.34	0.85	6.04	2330.67	199.96	11.97	1831.46
90	HD 239886	3463.39	178.85	0.90	8.48	3688.59	342.95	11.07	2500.00
91	HD 239895	3712.42	302.20	0.89	8.15	3993.59	402.36	10.25	2500.00
92	HD 211971	1104.51	17.89	0.95	6.48	1117.52	31.12	35.85	883.61
93	4 Lac	785.87	50.84	0.96	4.51	793.63	57.16	14.14	628.70
94	HD 239950	3956.84	187.56	0.99	9.39	4214.75	448.35	9.73	2500.00
95	HD 213470	3819.55	215.93	0.87	6.49	4135.61	431.61	9.91	2500.00
96	BD+62 2210	2643.54	99.68	0.98	7.91	2774.32	193.10	14.60	2114.83
97	BD+60 2542	3073.78	141.42	0.95	8.59	3268.04	268.75	12.45	2459.02
98	BD+61 2472	2574.31	72.51	0.92	9.06	2694.84	182.11	15.02	2059.45
99	HD 22227	979.64	19.75	0.87	6.40	991.69	24.50	40.38	783.71
100	6 Cas	2319.84	330.23	1.00	5.29	2460.86	427.28	6.45	1855.87
101	BD+62 2313	2750.29	83.12	0.84	8.70	2841.36	202.64	14.26	2200.24
102	HD 223767	2858.64	126.34	0.91	7.02	3042.45	232.58	13.34	2286.91
103	HD 186745	1968.87	64.68	0.89	6.67	2057.47	105.81	19.57	1575.10
104	HD 184943	4090.44	235.91	0.92	7.93	4478.59	506.39	9.17	2500.00
105	HD 161695	1800.44	82.27	0.91	6.22	1872.66	103.81	18.19	1440.35
106	HD 43820	190.69	0.95	0.98	8.35	191.53	1.13	168.50	300.00
107	HD 17086	780.54	10.08	0.90	6.33	792.66	15.65	50.49	624.43
108	HD 17857	2331.07	81.29	0.95	7.45	2435.92	148.59	16.58	1864.86
109	HD 216912	235.09	1.67	0.98	7.05	235.59	2.06	113.64	300.00
110	HD 13717	1044.92	27.13	1.00	7.81	1070.89	34.73	30.83	835.93
111	HD 28747	843.69	19.28	1.00	7.57	861.97	20.64	41.66	674.95
112	BD+60 2582	2972.21	124.72	0.92	8.35	3115.06	243.96	13.04	2377.77
113	HD 58131	3200.86	241.41	0.94	7.23	3431.40	381.71	9.41	2500.00
114	HD 47314	902.82	26.91	0.89	8.42	931.36	34.07	27.36	722.25
115	HD 58585	1437.45	40.42	0.97	5.97	1460.79	56.71	25.80	1149.96
116	HD 58764	2119.39	88.52	0.89	7.12	2173.08	119.64	18.31	1695.52
117	44 Cas	277.18	2.87	1.09	5.76	279.25	6.02	46.27	300.00
118	GQ Cam	5431.24	614.88	0.93	7.84	6232.23	972.80	6.64	2500.00
119	$ϵ$ CMa	131.01	0.35	0.96	8.38	131.05	0.46	283.79	300.00

(Appendix A).

3.2. Astrometric Quality of the Sample

Figure 1 shows RUWE as a function of the Gaia G magnitude. Most stars cluster around RUWE $\approx$ 1, indicating well-behaved single-star solutions, while a minority of bright or complex sources exceed the nominal threshold RUWE = $1.4$ (red dashed line). These high-RUWE objects are retained in the catalogue for completeness, but their parallaxes are treated with caution and typically fail our adoption criteria once ZP corrections and RUWE-based uncertainty inflation are applied (see Section 2). We stress that RUWE alone does not determine adoption: the decisive quantity for distance inference is the effective parallax signal-to-noise, ${\mathrm{SNR}}_{\mathrm{tot}}={\varpi }^{\prime }/{\sigma }_{\mathrm{tot}}$, computed after ZP and uncertainty inflation.

3.3. Recomputed Distances Versus Bailer-Jones

Figure 2 compares the recalculated Bayesian distances, $d_{\mathrm{new}}$, with the Bailer-Jones catalogue values, $d_{\mathrm{BJ}}$ (one-to-one line shown in red). For high-information parallaxes (large ${\mathrm{SNR}}_{\mathrm{tot}}$), $d_{\mathrm{new}}$ closely tracks $d_{\mathrm{BJ}}$, with changes dominated by modest ZP shifts and slightly broader posteriors. At intermediate information content (${\mathrm{SNR}}_{\mathrm{tot}}\sim 2.5$–5), we observe systematic, yet moderate, deviations at large distances, consistent with the combined effect of the catalogue choice (EDR3 vs. DR3) and the EDSD prior. For low-information cases (${\mathrm{SNR}}_{\mathrm{tot}}\lesssim 2.5$), posteriors become visibly prior-dominated and median distances drift toward a few L; such values are reported for reference but not adopted.

3.4. Comparison with Previous Works

A recent study by Vink and Oudmaijer [25] investigated Gaia DR3 distances for a smaller, physically homogeneous sample of early-B supergiants from Crowther et al. [26], focusing on their evolutionary status and the width of the main sequence. Their analysis adopted BJ distances directly from Gaia DR3 to derive luminosities and to discuss enhanced convective overshooting as a possible explanation for the “blue supergiant problem.” In contrast, the present work concentrates on the astrometric quality of a broader BA supergiant sample, applying magnitude–colour zero-point corrections, RUWE-dependent uncertainty inflation, and Bayesian distance inference that combines DR3 and EDR3 parallaxes. For several overlapping objects, our recalculated distances agree with those of Vink and Oudmaijer [25] within the quoted uncertainties, indicating that the additional RUWE-aware corrections do not introduce systematic shifts but rather yield more realistic error estimates. This methodological consistency supports the reliability of both approaches while underlining that the two studies address complementary aspects—the astrometric calibration presented here and the evolutionary interpretation developed by Vink and Oudmaijer [25].

3.5. Adoption Outcomes

We adopt $d_{\mathrm{new}}$ when three objective conditions are simultaneously met as follows: (i) ${\mathrm{SNR}}_{\mathrm{tot}}\ge 2.5$, (ii) relative uncertainty ${\sigma }_d/d_{\mathrm{new}}\le 40\%$, and (iii) satisfactory Gaia quality control (no duplication, sufficient visibility periods, and RUWE within nominal bounds). Objects failing any of these criteria revert to the Bailer-Jones value and are labelled BJ_old; those passing are labelled EDSD_new. Per-object decisions and diagnostic notes (quality_note: low_SNR, high_RUWE, duplicated, etc.) are summarised in Table A1.

3.6. Outliers and Informative Counterexamples

A handful of sources with elevated RUWE or complex astrometric solutions appear above the one-to-one line in Figure 2. For these objects, the single-star parallax carries limited information, and the Bayesian posterior becomes prior-dominated, with median distances near ∼2–3$L$. We retain such values in the catalogue for completeness, but they are not recommended for quantitative use (e.g., luminosity or radius estimates). Accordingly, for these stars, we adopt BJ_old distances instead.

3.7. Tables and Recommended Usage

The compact summary table in the main text (Table A1) lists the essential parameters: Name, RUWE, G [mag], $d_{\mathrm{BJ}}$ [pc], ${\sigma }_{d,\mathrm{BJ}}$, $d_{\mathrm{new}}$ [pc], ${\sigma }_d$ [pc], ${\mathrm{SNR}}_{\mathrm{tot}}$, and L [pc]. This concise set is sufficient to illustrate when and why $d_{\mathrm{new}}$ deviates from $d_{\mathrm{BJ}}$, based on the astrometric signal-to-noise ratio and the prior scale length. The complete machine-readable dataset, including all intermediate parameters and quality flags, is provided as Appendix A (

Table A2. Full machine-readable output of the Gaia distance pipeline for the BA supergiant sample. For each star, we list $d_{\mathrm{BJ}}$ and its uncertainty, RUWE, G magnitude, the recalculated Bayesian distance $d_{\mathrm{new}}$, its uncertainty, ${\mathrm{SNR}}_{\mathrm{tot}}$, and the adopted prior scale length L. Low-S/N and high-RUWE entries are included for completeness but are not recommended for quantitative use; this table is provided primarily for transparency and reproducibility.

N	Name	${\mathit{d}}_{\mathbf{BJ}}$ [pc] [29]	${\mathit{\sigma }}_{\mathit{d},\mathbf{BJ}}$ [pc]	RUWE	G [mag]	${\mathit{d}}_{\mathbf{new}}$ [pc]	${\mathit{\sigma }}_{\mathit{d}}$ [pc]	${\mathbf{SNR}}_{\mathbf{tot}}$	L [pc]
1	$\phi$ Cas	4171.53	1012.79	0.92	4.74	5723.41	2433.01	2.63	2500.00
2	$\sigma$ Cyg	876.46	111.66	1.69	4.18	1328.49	697.28	2.49	701.17
3	HD 10756	3238.28	247.73	1.38	7.43	3855.04	1062.31	4.51	2500.00
4	$\theta$ Aql	70.39	2.69	2.75	3.25	75.60	11.64	7.44	300.00
5	5 Per	1816.45	108.88	1.79	6.28	2227.79	690.05	4.18	1453.16
6	HD 55493	6002.90	692.51	1.06	7.93	6784.44	1463.86	4.81	2500.00
7	V455 Cep	3270.64	325.32	1.77	8.00	4332.08	1694.60	3.42	2500.00
8	67 Oph	797.18	162.31	2.51	3.93	1510.49	879.10	1.33	637.74
9	$\eta$ Leo	558.27	86.20	3.74	3.49	1011.80	562.32	1.62	446.61
10	HD 187982	1772.63	365.72	1.67	5.31	3047.79	1693.48	1.63	1418.10
11	${\theta }^2$ Tau	45.84	0.89	4.61	3.38	46.80	3.55	13.61	300.00
12	o Sco	175.54	7.11	6.42	4.12	195.87	39.63	6.02	300.00
13	$\chi$ Aur	1213.98	299.79	1.16	4.59	1755.71	940.05	2.53	971.18

). While Table A2 lists the full distances and Gaia astrometric parameters for transparency, we caution that it contains low-SNR and high-RUWE entries and should therefore not be used directly for downstream astrophysical analysis.

4. Conclusions

We presented a quality-controlled Bayesian recalculation of Gaia parallaxes for Galactic hot supergiants. Our pipeline applies ZP corrections, RUWE-aware uncertainty inflation, a penalised DR3/EDR3 catalogue choice, and an EDSD prior, and then adopts distances using objective criteria.

• Operational quantity. RUWE is a diagnostic, but adoption is governed by the effective information content ${\mathrm{SNR}}_{\mathrm{tot}}={\varpi }^{\prime }/{\sigma }_{\mathrm{tot}}$ computed after all corrections.
• Agreement at high S/N. For informative parallaxes (large ${\mathrm{SNR}}_{\mathrm{tot}}$), the recalculated distances $d_{\mathrm{new}}$ closely match Bailer-Jones values $d_{\mathrm{BJ}}$; differences are dominated by ZP shifts and slightly broader posteriors.
• Intermediate regime. At $2.5\lesssim {\mathrm{SNR}}_{\mathrm{tot}}\lesssim 5$, we find modest, interpretable offsets (typically ∼10–30% at large distances) arising from the combination of ZP, catalogue choice, and the EDSD prior.
• Low-information cases. For ${\mathrm{SNR}}_{\mathrm{tot}}\lesssim 2.5$ or problematic Gaia QC, the posterior becomes prior-dominated and we do not adopt $d_{\mathrm{new}}$, reverting to $d_{\mathrm{BJ}}$.
• Adoption logic. We adopt $d_{\mathrm{new}}$ only when (i) ${\mathrm{SNR}}_{\mathrm{tot}}\ge 2.5$, (ii) ${\sigma }_d/d_{\mathrm{new}}\le 0.40$, and (iii) Gaia QC is satisfactory; otherwise, we label the entry BJ_old and record the cause in quality_note.
• Practical outcome. The catalogue provides one adopted distance per star with transparent flags and uncertainties, enabling safe propagation to absolute magnitudes, luminosities, and radii while avoiding overconfident inferences for high-RUWE/low-S/N objects.

The refined, quality-vetted distances derived here provide a reliable basis for reassessing the evolutionary placement of Galactic BA supergiants on the Hertzsprung–Russell diagram. Because luminosity scales as $L\propto d^2$, systematic effects in parallax (and thus in d) translate directly into amplified shifts in $logL$, especially for high-RUWE or low-S/N cases. By mitigating these systematics, our distances reduce spurious luminosity offsets, aiding (i) a cleaner separation between objects just leaving the main sequence and those consistent with an extended hydrogen-burning phase, and (ii) a more robust calibration of the flux-weighted gravity–luminosity relation (FGLR). In this way, the catalogue supports evolutionary tests of massive-star models without introducing overconfident inferences for problematic astrometric solutions.