Astrometric Detectability of Habitable Exoplanets: An Open-Source Framework Using Gaia DR3

Astrometric Detectability of Habitable Exoplanets: An Open-Source Framework Using Gaia DR3 Kishor Baniya Caldwell University / C-STEM Laboratories [email protected] Abstract—In this paper, I investigate the astrometric detection limits for potentially habitable exoplanets orbiting within 100 parsecs in the solar neighborhood. Using Gaia DR3 data, I developed a model that uses parallax, photometry, and stellar parameters to estimate the minimum detectable astrometric signature per star. The model assesses data across a range of stellar types with corresponding planetary data, accounting for instrumental uncertainty and a conservative jitter floor to model astrophysical noise. The pipeline reveals that while Gaia can currently detect habitable Jupiter-analogs around hundreds of nearby stars, Earth, Super-Earth, and Sub-Neptune analogs remain out of reach due to current astrometric detection thresholds. The objective of this paper, therefore, is to provide a snapshot of Gaia’s current detection limit and to assess the landscape of habitable worlds detection in the near future with this scalable framework. Index Terms—Astrometry, Astrometric Precision, Detection Thresholds, Exoplanet Detection, Gaia DR3, Habitable Zones, Planetary Habitability, Stellar Jitter I. INTRODUCTION Since the discovery of the first exoplanet around a Sun-like star in 1995 [1], thousands of exoplanets have been detected using methods such as radial velocity and transits. However, a lesser-utilized yet powerful technique is astrometry, which measures the tiny reflex motion or “wobble” of a star caused by an orbiting planet. Astrometry provides direct access to fundamental planetary parameters such as mass, orbital inclination, and semi-major axis [2]. Although ground-based astrometry has historically faced challenges due to atmospheric distortion, the launch of the Gaia mission by the European Space Agency in 2013 marked a turning point in space-based astrometry [3]. Gaia continuously scans the sky and has provided highly precise astrometric measurements through its data releases. For instance, Data Release 2 achieved a parallax precision of 0.04–0.1 mas and proper motion precision of 0.05–0.2 mas/yr for stars with G≲17 [4]. These have been further improved in EDR3, achieving astrometric uncertainties below 10 µas for the brightest stars [5]. With such precision, astrometry has become a promising tool for detecting long-period and potentially habitable exoplanets. This work presents an open-source framework based on Gaia DR3 to estimate the minimum detectable astrometric signal (αmin) for a given astrometric observatory, such as Gaia, and to evaluate its capability to detect stars hosting planets (especially those within their habitable zones). By comparing planetary-induced stellar wobbles to the system’s astrometric noise floor, the framework also provides a predictive guide on which systems are most likely to yield detectable planets and their demography within astrometric reach. Hence, it can help guide the scientific strategies of nextgeneration missions such as Theia or NEAT [6], [7]. II. DATA SELECTION This study utilizes data from Gaia Data Release 3 (DR3), which provides astrometric and photometric measurements for over 1.8 billion stars [5]. DR3 includes high-precision parallaxes, proper motions, and broadband photometry in the G, BP, and RP bands, enabling detailed studies of stellar kinematics and the detectability of exoplanets via astrometric signals. To construct a clean and reliable sample suitable for astrometric modeling, I selected Gaia DR3 sources within 100 pc by applying several quality filters: parallax >10 mas, parallax signal-to-noise ratio >10, Renormalized Unit Weight Error (RUWE) <1.4to ensure astrometric reliability, and G-band magnitude <15 for high signal-to-noise. Additional filters included valid BP and RP photometry and surface gravity log(g)>4.0to restrict the sample to main-sequence stars. The complete ADQL query and data processing scripts used in this analysis are available on GitHub [8]. III. DATA PRE-PROCESSING A. Minimum Detectable Signal The minimum detectable astrometric wobble amplitude (αmin) for each star in the sample is a function of right ascension (RA) and declination (Dec) components, each with associated errors (σµαand σµδ). Since the true astrometric signal can manifest in both coordinates, the model combines the uncertainties by computing the quadrature sum: σtotal =qσ2 µα+σ2 µδ.(1) To adopt a conservative detection threshold, the minimum detectable signal is set at 3×σtotal, corresponding to a 3σsignificance level commonly used in astrometric planet detection [6], [9]. Furthermore, the parallax measurements are inverted to estimate distances, allowing the astrometric wobble amplitudes to be interpreted in physical units (microarcseconds). The minimum detectable wobble, therefore, depends on both measurement precision and stellar distance. To characterize Gaia’s astrometric noise floor as a function of G-band magnitude, the framework adopts an empirical noise model calibrated by Lindegren et al. (2021) [10], which captures the rise in astrometric uncertainties for fainter stars. Figure 1 below shows the resulting minimum detectable astrometric wobble amplitudes plotted against G magnitude for the sample, along with the Gaia noise model as a reference. It becomes evident from this that as the magnitude increases, the detection limit gets crowded with noise. 4 6 8 10 12 14 G magnitude 101 102 103 Minimum Detectable Astrometric Wobble ( as) Minimum Detectable Astrometric Wobble vs. G Magnitude Gaia noise model (G-dependent) Fig. 1. Minimum detectable astrometric wobble amplitude αmin as a function of G-band magnitude for the stellar sample. The red dashed curve represents the empirical Gaia noise floor model [10]. B. Stellar Classification To further refine the sample of nearby main-sequence stars, each star was classified into spectral types using two independent metrics: the Gaia DR3 color index BP−RP [11], and the effective temperature (Teff) from the teff_gspphot [12] The BP-RP index provides the empirical threshold, on which the standard temperature bins are cross-checked to classify the stars. This dual confirmation step refined the dataset from 35,827 to 19,726 stars, improving the reliability of the spectral type assignments and data accuracy in overall. (Table III-B). The distribution of effective temperatures as a function of the effective temperature is shown in Figure 2. Spectral Type Number of Stars G 8238 K 8080 M 1702 F 1530 A 176 104 3 × 1034 × 1036 × 103 Effective Temperature (K) 0 500 1000 1500 2000 2500 3000 Number of stars Distribution of Teff in your dataset A type F type G type K type M type Fig. 2. Distribution of stellar effective temperatures in the refined dataset. Vertical dashed lines indicate approximate spectral type boundaries. IV. DETECTING EXOPLANETS To assess the detectability of different planetary types across various stellar hosts, the model uses a simplified mass-based classification scheme grounded in both Solar System analogs and prevailing exoplanet taxonomy [13]. Each planet class is assigned a characteristic mass (M⊕) in Earth masses, which is used to estimate the minimum detectable semi-major axis (amin) for each star in our dataset, given its astrometric sensitivity. The following summarizes the adopted planet types and their corresponding masses: •Mercury-like (0.055 M⊕) •Earth-like (1.0 M⊕): Anchor point. •Super-Earth (5.0 M⊕) •Sub-Neptune (10.0 M⊕) •Neptune-like (17.0 M⊕) •Sub-Saturn (30.0 M⊕) •Saturn-like (95.0 M⊕) •Jupiter-like (317.8 M⊕) •Super-Jupiter (1000.0 M⊕) A. Minimum Required Semi-major Axis The minimum semi-major axis (amin) required for a planet to induce a detectable astrometric signal in its stellar host can be computed using the formula: amin =αmin ·d·M∗ Mp .(2) where: •αmin is the minimum detectable astrometric signature (converted to arcseconds), •dis the distance to the star (in parsecs), •M∗is the stellar mass (converted to Earth masses), and •Mpis the planetary mass (in Earth masses). With this measure, amin is calculated in Astronomical Unit, which the models uses as a parameter to derive if a certain planet can be flagged as detectable or not, given the astrometric limit during observation. B. Stellar Luminosity To determine the Habitable Zone (HZ) for each star, stellar luminosity plays a key role, as it governs a planet’s ability to sustain liquid water at a given semi-major axis. Considering the diversity of stellar parameters, the model estimates the HZ using two distinct approaches. The primary method, based on Gaia DR3 photometry, involves computing the absolute G-band magnitude. Combined with a bolometric correction derived from the BP–RP color index, this yields an estimate of stellar luminosity using the empirical relation proposed by Torres et al. [14]. L∝M3.5(3) . For stars lacking complete photometry, the model uses the classical mass–luminosity relation, valid for main-sequence stars with masses between 0.1and 2.0M⊙[15] C. Range of Habitability and Detection With luminosities established, the model computes Habitable Zone (HZ) boundaries using the formalism of Kopparapu et al. [16]. This method determines the effective stellar flux required at the inner and outer HZ edges (Runaway and Maximum Greenhouse limits) via a temperature-dependent polynomial fit. For cool stars (Teff <3700 K), corrections are applied following updated coefficients from Kopparapu et al. [17] to account for spectral energy distribution differences. The corresponding HZ distances in astronomical units (AU) are then derived using: a=rL Seff (4) The Habitable Zone boundaries across different stellar types are illustrated in Figure 3. 300040005000600070008000900010000 Effective Temperature (K) 0 2 4 6 8 10 Habitable Zone Boundary (AU) Habitable Zone Boundaries vs Stellar Effective Temperature Inner HZ Outer HZ A-type F-type G-type K-type M-type Fig. 3. Distribution of inner and outer habitable zone limits as a function of stellar effective temperature. V. CONCLUSION This study presents a scalable astrometric framework to assess the detectability of potentially habitable exoplanets using Gaia DR3 data. By integrating stellar astrometry, photometry, spectral classification, and empirical noise models, the analysis establishes a robust threshold for the minimum detectable astrometric signal for the purpose. Key findings: •Detection limits remain a major constraint for finding smaller planets via astrometry. Even with Gaia’s sub100 µas precision for bright stars, habitable Earth-like and Super-Earth analogs remain undetectable around the vast majority of nearby stars due to their weak gravitational influence on host stars. •Spectral-type variation in detectability: G-type stars dominate habitable-zone detectability for gas giants in Gaia, with 90 detectable Jupiter-like planets. Although such potential gas giants mightn’t harbor life as we know it, their moon(s), however, can be an interesting topic to study. In contrast, the more abundant M-type stars pose a significant challenge due to their low luminosities and small stellar masses, despite tighter and better-defined habitable zones. TABLE I NUMBER OF DETECTABLE JUPITER-LIKE AND SUPER-JUPITER-LIKE PLANETS PER SPECTRAL TYPE Spectral Type Jupiter-like Super-Jupiter-like A0 57 F5 1077 G90 5988 K28 2585 M1 56 This paper highlights both the potential and the limitations of astrometry in the search for habitable worlds. While Gaia’s precision marks a significant improvement over ground-based measurements, its sensitivity remains insufficient for detecting low-mass planets and conclusively assessing their habitability. Nevertheless, the presented framework offers a solid foundation for evaluating future missions such as THEIA and NEAT. As astrometric sensitivity pushes into the microarcsecond regime, this model can be used to benchmark mission performance, guide observational strategy, and prioritize stellar targets for detecting potentially habitable exoplanets. REFERENCES [1] M. Mayor and D. Queloz, “A Jupiter-mass companion to a solar-type star,” Nature, vol. 378, no. 6555, pp. 355–359, 1995. [2] A. Sozzetti, “Astrometric methods and instrumentation to detect and characterize extrasolar planets: A review,” Publ. Astron. Soc. Pac., vol. 117, no. 834, pp. 1021–1048, 2005. [3] Gaia Collaboration, T. Prusti et al., “The Gaia mission,” Astron. Astrophys., vol. 595, A1, 2016. [4] L. Lindegren et al., “Gaia Data Release 2: The astrometric solution,” Astron. Astrophys., vol. 616, A2, 2018. [5] Gaia Collaboration, A. G. A. Brown et al., “Gaia Early Data Release 3: Summary of the contents and survey properties,” Astron. Astrophys., vol. 649, A1, 2021. [6] M. A. C. Perryman, The Exoplanet Handbook, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2014. [7] J. Holler et al., “Astrometric detection of exoplanets: A comparative overview and prospects for future missions,” Exp. Astron., vol. 53, pp. 217–245, 2022. [8] K. Baniya, “Astrometric Precision Framework: GitHub Repository,” 2025. [Online]. Available: https://github.com/kishorrbaniyaa/astrometricprecision [Accessed: Aug. 2025]. [9] A. Sozzetti, “Astrometric methods and instrumentation to detect and characterize extrasolar planets,” EAS Publ. Ser., vol. 65–66, pp. 371– 411, 2014. [10] L. Lindegren et al., “Gaia Early Data Release 3: The astrometric solution,” Astron. Astrophys., vol. 649, A2, 2021. [11] M. J. Pecaut and E. E. Mamajek, “Intrinsic colors, temperatures, and bolometric corrections of pre-main-sequence stars,” Astrophys. J. Suppl. Ser., vol. 208, no. 9, 2013. [12] R. O. Gray and C. J. Corbally, Stellar Spectral Classification. Princeton, NJ, USA: Princeton Univ. Press, 2005. [13] J. Chen and D. Kipping, “Probabilistic forecasting of the masses and radii of other worlds,” Astrophys. J., vol. 834, no. 1, p. 17, 2017. [14] G. Torres, J. Andersen, and A. Gim´ enez, “Accurate masses and radii of normal stars: Modern results and applications,” Astron. Astrophys. Rev., vol. 18, no. 1–2, pp. 67–126, 2010. [15] O. Demircan and G. Kahraman, “Mass–luminosity relation for stars,” Astrophys. Space Sci., vol. 181, no. 2, pp. 313–322, 1991. [16] R. K. Kopparapu et al., “Habitable zones around main-sequence stars: Dependence on planetary mass,” Astrophys. J. Lett., vol. 787, no. 2, L29, 2014. [17] R. K. Kopparapu et al., “The inner edge of the habitable zone for synchronously rotating planets around low-mass stars using general circulation models,” Astrophys. J., vol. 819, no. 1, 2016.