# Fabricius et al. — Gaia EDR3 Catalogue Validation (PSF/LSF and Chromaticity) (2021) **C. Fabricius, X. Luri, F. Arenou, C. Babusiaux et al.** *A&A* 649, A5 (2021). arXiv:2012.06242. --- ## Overview The Gaia DR3/EDR3 PSF and chromaticity validation paper. Fabricius et al. document that the Gaia image-parameter determination (IPD) has inevitable asymmetric PSFs due to coma-like wavefront errors, and that **the shape and location of every measured stellar image depend on the star's spectrum** (chromaticity). Only for $G > 13$ are chromatic effects "almost completely removed" by the IPD pipeline. For brighter stars ($G < 13$ — including all Cepheids, RR Lyrae, and bright calibrators), the chromaticity is not fully corrected and propagates into parallax bias. --- ## PDF p.1 — Title and abstract ![[Fabricius2021_PSF-001.png]] ## PDF p.2 — Chromaticity problem ![[Fabricius2021_PSF-002.png]] From the paper: > "Inevitable coma-like wavefront errors produce asymmetric PSFs in which both the shape and location depend on the spectrum." > "Only for G > 13 are chromatic effects almost completely removed during image parameter determination." > [!critical] Bright stars retain chromatic centroid bias > Gaia's optical system has unavoidable wavefront errors that produce asymmetric PSFs. The asymmetry depends on the star's colour spectrum: red stars and blue stars have differently-shaped PSFs, which means their image centroids are offset by different amounts from the true star position. For faint stars (G > 13) the IPD pipeline corrects the chromaticity to negligible levels. For bright stars (G < 13), the residual chromaticity is not fully corrected and contaminates the astrometric solution. --- ## What the chromaticity does to parallax The effective wavenumber $\nu_{\text{eff}}$ (derived from BP−RP colour) is one of the arguments in the Lindegren 2021 Z5 correction function precisely because of this chromaticity effect. The Z5 correction has a coefficient $q_{10}$ that scales as $\nu_{\text{eff}}$ and carries error bars of ~15 µas·µm. This means for a bright star with an extreme colour (BP−RP = 2.5 or −0.5), the chromatic correction is ~40 µas — comparable to the DR3 global zero-point offset itself. --- ## PDF p.8 — The 5-parameter vs 6-parameter solution split ![[Fabricius2021_PSF-008.png]] Fabricius distinguishes two astrometric solution types: - **5-parameter solution**: uses measured BP−RP colour. Applies to 585 million Gaia EDR3 sources with good photometry. - **6-parameter solution**: solves for a pseudo-colour $\hat{\nu}_{\text{eff}}$ simultaneously with the astrometry. Applies to 882 million sources without reliable photometry. The 6-parameter solution is circular: the "colour" used in the chromaticity correction is itself fitted from the same data being corrected. > [!warning] 59% of Gaia EDR3 uses a circular colour calibration > 882 million EDR3 sources (about 59% of the catalogue) use the 6-parameter solution where the pseudo-colour is fitted jointly with astrometry. The colour and position are solved from the same observations; the chromaticity "correction" applied is literally a function of the pipeline's own fit. This is not an external calibration; it is internal consistency. --- ## Hydrogen-deficient carbon stars A 2024 follow-up paper (A&A, https://www.aanda.org/articles/aa/full_html/2024/04/aa48005-23/aa48005-23.html) applied Fabricius's chromaticity framework to hydrogen-deficient carbon (HdC) and extreme helium (EHe) stars and confirmed chromatic PSF bias affects these specific classes — an example of how rare spectral types inherit extra parallax uncertainty beyond the quoted formal errors. --- ## Summary | Claim | Fabricius et al. (2021) | |---|---| | Gaia PSFs are symmetric and colour-independent | No. Coma-like wavefront errors + colour-dependent shape and location. | | Chromaticity is removed for all stars | No. Only for G > 13; bright stars retain residual bias. | | All Gaia stars use the same astrometric solution | No. 5-param (with BP−RP) and 6-param (with fitted pseudo-colour) split. | | The 6-param pseudo-colour is externally calibrated | No. It is fitted from the same data. | --- ## Citation Fabricius, C. et al., 2021. "Gaia EDR3 — Catalogue validation." *Astronomy & Astrophysics* 649, A5. arXiv:2012.06242. Local copy: . --- ## See also - [[2021_Lindegren_EDR3_Parallax_Bias]] - [[2021_Fardal_Gaia_Parallax_Scar_Map]] - [[2021_Groenewegen_Parallax_ZeroPoint_Offset]]