[Paper Review] The Tycho-Gaia astrometric solution. How to get 2.5 million parallaxes with less than one year of Gaia data

Daniel Michalik, L. Lindegren+1 more|arXiv (Cornell University)|Dec 30, 2014

Stellar, planetary, and galactic studiesPhysics and Astronomy6 references170 citations

TL;DR

This paper proposes the Tycho-Gaia Astrometric Solution (TGAS), a method to derive precise parallaxes and proper motions for 2.5 million Tycho-2 stars using only 6–12 months of Gaia data by combining it with Tycho-2 positions from 1991. The approach enables a full five-parameter astrometric solution earlier than planned, achieving sub-milliarcsecond accuracy and validating Gaia’s calibration and instrument performance at the sub-mas level.

ABSTRACT

Context. The first release of astrometric data from Gaia will contain the mean stellar positions and magnitudes from the first year of observations, and proper motions from the combination of Gaia data with Hipparcos prior information (HTPM). Aims. We study the potential of using the positions from the Tycho-2 Catalogue as additional information for a joint solution with early Gaia data. We call this the Tycho-Gaia astrometric solution (TGAS). Methods. We adapt Gaia's Astrometric Global Iterative Solution (AGIS) to incorporate Tycho information, and use simulated Gaia observations to demonstrate the feasibility of TGAS and to estimate its performance. Results. Using six to twelve months of Gaia data, TGAS could deliver positions, parallaxes and annual proper motions for the 2.5 million Tycho-2 stars, with sub-milliarcsecond accuracy. TGAS overcomes some of the limitations of the HTPM project and allows its execution half a year earlier. Furthermore, if the parallaxes from Hipparcos are not incorporated in the solution, they can be used as a consistency check of the TGAS/HTPM solution.

Motivation & Objective

• To develop a method for deriving precise astrometric parameters (positions, parallaxes, proper motions) for Tycho-2 stars using only a fraction of Gaia's full mission data.
• To overcome limitations of the HTPM project, which relies on auxiliary stars that may bias the solution due to incomplete parameter resolution.
• To enable a full-sky, high-accuracy astrometric solution earlier than the planned Gaia data releases, validating instrument and calibration performance at the sub-milliarcsecond level.
• To provide an independent, high-accuracy catalogue of parallaxes and proper motions for stars down to V ≈ 11.5, extending beyond the Hipparcos magnitude limit.
• To allow consistency checks of the HTPM solution by using Hipparcos parallaxes as a benchmark when not incorporated into TGAS.

Proposed method

• Adapt Gaia’s Astrometric Global Iterative Solution (AGIS) to incorporate prior Tycho-2 positions from 1991 as constraints in a joint astrometric solution with early Gaia observations.
• Use the 24-year baseline between Tycho-2 and Gaia observations to disentangle parallax and proper motion effects from the limited number of Gaia scans.
• Leverage the across-scan information in Gaia observations to estimate satellite attitude and calibration parameters, reducing dependency on auxiliary stars.
• Simulate Gaia observations with realistic dead times, calibration errors, and observation counts to assess solution feasibility and performance.
• Apply a five-parameter solution (α, δ, π, μα*, μδ) to Tycho-2 stars, using Tycho-2 positions to anchor the proper motion solution and Gaia data to solve for parallax and motion.
• Ensure the reference frame of TGAS is aligned with the Hipparcos frame by incorporating Hipparcos positions and proper motions, enabling cross-validation with Hipparcos results.

Experimental results

Research questions

• RQ1 Can a five-parameter astrometric solution be reliably derived for 2.5 million Tycho-2 stars using only 6–12 months of Gaia data?
• RQ2 Can Tycho-2 positions from 1991 effectively resolve the degeneracy between parallax and proper motion in early Gaia data?
• RQ3 Does replacing auxiliary stars in HTPM with Tycho-2 stars eliminate bias in the astrometric solution?
• RQ4 Can TGAS deliver sub-milliarcsecond accuracy for parallaxes and proper motions with minimal data, enabling early validation of Gaia’s instrument and calibration?
• RQ5 What is the impact of not using Hipparcos parallaxes in the TGAS solution on the consistency and accuracy of the resulting astrometry?

Key findings

• TGAS can deliver positions, parallaxes, and proper motions for 2.5 million Tycho-2 stars with sub-milliarcsecond accuracy using only 6–12 months of Gaia data.
• The method enables a full five-parameter astrometric solution half a year earlier than the planned first Gaia data release and one year earlier than the second release with five-parameter solutions.
• The use of Tycho-2 positions instead of auxiliary stars eliminates the risk of bias in the HTPM solution, as all parameters are now resolved for the Tycho-2 stars.
• The resulting astrometry for Tycho-2 stars is expected to be similar in accuracy to the Hipparcos Catalogue, and potentially better depending on observation conditions and calibration.
• The solution remains robust even when Hipparcos parallaxes are not used in TGAS, providing a stringent consistency check against Hipparcos results.
• TGAS enables early, full-sky validation of Gaia’s instrument, calibration, and data processing at the sub-milliarcsecond level, significantly accelerating scientific validation.