# Estimating distances from parallaxes. V.

Geometric and photogeometric distances to 1.47 billion stars in Gaia Early Data Release 3

### C.A.L. Bailer-Jones, J. Rybizki, M. Fouesneau, M. Demleitner, R. Andrae

Stellar distances constitute a foundational pillar of astrophysics. The publication of 1.47 billion stellar parallaxes from Gaia is a major contribution to this. Yet despite Gaia's precision, the majority of these stars are so distant or faint that their fractional parallax uncertainties are large, thereby precluding a simple inversion of parallax to provide a distance. Here we take a probabilistic approach to estimating stellar distances that uses a prior constructed from a three-dimensional model of our Galaxy. This model includes interstellar extinction and Gaia's variable magnitude limit. We infer two types of distance. The first, geometric, uses the parallax together with a direction-dependent prior on distance. The second, photogeometric, additionally uses the colour and apparent magnitude of a star, by exploiting the fact that stars of a given colour have a restricted range of probable absolute magnitudes (plus extinction). Tests on simulated data and external validations show that the photogeometric estimates generally have higher accuracy and precision for stars with poor parallaxes. We provide a catalogue of 1.47 billion geometric and 1.35 billion photogeometric distances together with asymmetric uncertainty measures. Our estimates are quantiles of a posterior probability distribution, so they transform invariably and can therefore also be used directly in the distance modulus (5log10(r)-5). The catalogue may be downloaded or queried using ADQL at various sites where it can also be cross-matched with the Gaia catalogue.

- Article: Astronomical Journal, 161, 147 (2021)

[PDF] [arXiv] [ADS] [journal] [summary presentation] [poster] - Every source in EDR3 that has a parallax has a geometric distance in our catalogue: 1467744818 sources. 1346621631 of these also have photogeometric distances. This latter number is 672090 fewer than the number of sources with the required data (parallax, G, BP-RP) because we didn't always have a QG model for the prior at all colours in all HEALpixels.
- Frequently(-ish) Asked Questions
- Factoid: As of 18 July 2023 this paper has 773 citations, making it the 4th most highly cited refereed astronomy paper of 2021 (beaten by the GDR3 release paper, results of gravitational wave detections, and a review of the Hubble tension). Source: ADS.
- Catalogue access:

- The catalogue is available from GAVO and from ESA (under "Other" then "External catalogues" then "external.gaiaedr3_distance") where it can be queried using ADQL. See the paper (section 5.4) for a query example of how to join it to the gaia_source table.
- GAVO also hosts a table called "gedr3dist.litewithdist" that has already been crossmatched to a light version of the main GeDR3 table.
- The example query in the paper
needs to be modified for the ESAC server as that uses
different table names. In principle you would just change:

gedr3dist.main -> external.gaiaedr3_distance

gaia.edr3lite -> gaiaedr3.gaia_source

However, as the ESAC archive is organized differently, the following query will run much faster (thanks to Alcione Mora for this):SELECT source_id, ra, dec, r_med_geo, r_lo_geo, r_hi_geo, r_med_photogeo, r_lo_photogeo, r_hi_photogeo, phot_bp_mean_mag-phot_rp_mean_mag AS bp_rp, phot_g_mean_mag - 5 * LOG10(r_med_geo) + 5 AS qg_geo, phot_g_mean_mag - 5 * LOG10(r_med_photogeo) + 5 AS gq_photogeo FROM ( SELECT * FROM gaiaedr3.gaia_source WHERE 1 = CONTAINS( POINT('ICRS', 56.75, 24.12), CIRCLE('ICRS', ra, dec, 1) ) OFFSET 0 ) AS edr3 JOIN external.gaiaedr3_distance using(source_id) WHERE ruwe<1.4

- The entire catalogue can also be downloaded from GAVO as a single (gzipped) file (38 GB; uncompresses to a 125 GB CSV file - smaller than the individual files below due to rounding distances to 5 decimal places in pc).
- On request I can make the catalogue available organized into the 12288 HEALpixels at level 5 (3.36 sq. deg) named dist_p.csv, where p=0:12287 (170 GB uncompressed). The number of sources per file is given in the distance_summaries.csv file available with the auxiliary information.
- The catalogue is available in Vizier as catalogue I/352.
- Various TAP servers host the catalogue. These can be accessed using, for example, TOPCAT.

- Auxiliary information:

- Prior. Plots per HEALpixel of the distance
prior, CQD, and QG models, similar to those in the paper. There is
also a CSV file with summary information the prior for each
HEALpixel.
**NEW: Functions to compute the photo(geo)metric prior and posterior.** - Distance inference. Plots per HEALpixel of the distance results and the inferred CQDs, similar to those in the paper. There is also a CSV file with summary information for each HEALpixel.
- HEALpixel look-up table giving the RA and Dec, and Galactic longitude and latitude, of the 12288 HEALpixels at level 5.
- The level-N HEALpixel number of a Gaia source can be extracted
(for 1<=N<=12) from its source_id using
floor( source_id / (2^(35)*4^(12-N)) )

which for N=5 isfloor( source_id / 562949953421312 )

Make sure you use long integers (64 bit) when calculating this. HEALpixel numbering uses the nested (rather than ring) scheme in equatorial coordinates. - R function to compute the GeDR3 parallax zeropoint. Other languages are available on the Gaia website.
- interactive notebook for estimating distances allowing adjustments in the data and prior, written by Bachelor student Elisa Haas.
- interactive notebook for displaying the prior on the sky, written by Bachelor student Elisa Haas.

- Prior. Plots per HEALpixel of the distance
prior, CQD, and QG models, similar to those in the paper. There is
also a CSV file with summary information the prior for each
HEALpixel.

## The other papers in this series

**Estimating distances from parallaxes: a tutorial.** 2015.

C.A.L. Bailer-Jones

Publications of the Astronomical Society of the Pacific, 127, 994

[abstract]
[PDF] [ADS] [arXiv] [journal link]

**Estimating distances from parallaxes II. Performance of Bayesian distance estimators on a Gaia-like catalogue.** 2016.

T. Astraatmadja, C.A.L. Bailer-Jones

Astrophysical Journal 832, 137

[ADS]
[journal]
[arXiv]

**Estimating distances from parallaxes III. Distances of two million stars in the Gaia DR1 catalogue.** 2016.

T. Astraatmadja, C.A.L. Bailer-Jones

Astrophysical Journal, 833, 119

[abstract, paper, and catalogue]
[ADS]
[arXiv]
[journal link]

**Estimating distances from parallaxes. IV. Distances to 1.33 billion stars in Gaia data release 2.** 2018.

C.A.L. Bailer-Jones, J. Rybizki, M. Fouesneau, G. Mantelet, R. Andrae

Astronomical Journal, 156, 58 (2018)

[abstract, paper, and catalogue]
[PDF]
[ADS]
[arXiv]
[journal]

**Estimating distances from
parallaxes. VI. A method for inferring distances and transverse
velocities from parallaxes and proper motions demonstrated on Gaia Data Release 3.** 2023.

C.A.L. Bailer-Jones

Astronomical Journal, 166, 269

[abstract, paper, and catalogue access]
[arXiv]
[journal link]

## Related resources

- Technical note CBJ-081: Joint inference from parallax and proper motions
- Technical note: Inference of cluster distance and geometry from astrometry
- A tutorial on estimating distances from parallaxes, also for clusters and what to do with correlated uncertainties, is available on github. This uses the prior from paper IV
- Technical note CBJ-089: Improving distance estimates for GeDR3