Estimating Distances from Parallaxes

By Coryn A. L. Bailer-Jones. 2015

360 citations recorded by the source corpus.

Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalog. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available—and is willing to use—concerning, e.g., the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates nonpositive parallaxes, and does not require a bias correction.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/faa48ffc8fb4c04e3d6d3ea75a763d92e1c70e6b

How researchers see this paper

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In Astronomy and Astrophysics

1. D. Huber
2. D. Stello
3. E. Gaidos
4. Keivan G. Stassun
5. J. V. van Saders
6. W. Chaplin
7. I. Minchev
8. M. J. Reid

In Instrumentation

1. D. Huber
2. Keivan G. Stassun
3. E. Gaidos
4. J. V. van Saders
5. D. Stello
6. I. Minchev
7. W. Chaplin
8. G. Torres

In Statistical and Nonlinear Physics

1. Keivan G. Stassun
2. D. Huber
3. E. Gaidos
4. G. Torres
5. J. V. van Saders
6. J. Tayar
7. R. Andrae
8. Morgan Fouesneau

Citations in the corpus

• On the Spectral Evolution of Hot White Dwarf Stars. I. A Detailed Model Atmosphere Analysis of Hot White Dwarfs from SDSS DR12 (2020, methodology): “We obtained distance estimates by simply inverting the parallaxes as this procedure agrees well with more sophisticated probabilistic methods for small parallax uncertainties (Bailer-Jones 2015; Bailer-Jones et al. 2018).”
• The vertical metallicity gradients of mono-age stellar populations in the Milky Way with the RAVE and Gaia data (2017, background): “The distance errors are not simply Gaussian with dispersion of πe/π2 (e.g. Bailer-Jones 2015).”
• The Lives of Stars: Insights from the TGAS–RAVE–LAMOST Data Set (2018, background): “In the future however, as Bailer-Jones (2015) note, roughly 80% of the Gaia catalog will be beyond this 20% error threshold, so it is worth considering, now, the types of priors which will be acceptable to use to correct for this.”
• LISA verification binaries with updated distances from Gaia Data Release 2 (2018, methodology): “To determine the mode of P(d |$, σ$ ) given our choice of the prior, we set the derivative of the posterior to be equal to zero and solve the equation (Bailer-Jones 2015): d3 L − 2d2 + $d σ2$ − 1 σ2$ = 0.”
• Asteroseismology and Gaia: Testing Scaling Relations Using 2200 Kepler Stars with TGAS Parallaxes (2017, methodology): “To convert parallaxes into distances,we used an exponentially decreasing volume density prior with a length scale of 1.35 kpc (Bailer-Jones 2015; Astraatmadja & Bailer-Jones 2016).”
• Trigonometric Parallaxes of High-mass Star-forming Regions: Our View of the Milky Way (2019, methodology): “In order to minimize the effects of distance biases, owing to asymmetric distance PDFs when converting parallaxes to distances (e.g.,Bailer-Jones 2015), we used only the 80 sources with fractional parallax uncertainties less than 20%.”
• Gaia Data Release 2 (2018, methodology): “However, as pointed out in Bailer-Jones (2015) a uniform distribution in r implies a space density of stars that falls of as 1/r2 from the position of the Sun, which is of course physically implausible.”
• Revised Radii of Kepler Stars and Planets Using Gaia Data Release 2 (2018, methodology): “For each star, we first converted parallaxes into distances using an exponentially decreasing volume density prior with a length scale of 1.35 kpc (Bailer-Jones 2015; Astraatmadja & Bailer-Jones 2016) and included a systematic parallax offset of 0.03 mas (Lindegren et al. 2018).”
• ECLIPSING BINARY STARS AS BENCHMARKS FOR TRIGONOMETRIC PARALLAXES IN THE GAIA ERA (2016, background): “We note that, as explained by Bailer-Jones (2015) and others, estimating a distance from a parallax, or in our case a parallax from a distance, is not trivial when the relative errors are larger than about 20%, and becomes sensitive to prior assumptions.”
• A Guide to Realistic Uncertainties on the Fundamental Properties of Solar-type Exoplanet Host Stars (2020, methodology): “The combination of fbol with the distance d estimated from the parallax (e.g. Bailer-Jones 2015) then allows a measurement of the luminosity: L = 4πd2fbol .”
• Evidence for a Systematic Offset of −80 μas in the Gaia DR2 Parallaxes (2018, background): “Finally, all 89 EBs have Gaia parallax errors better than 15%, and thus the choice of prior on the parallax should not be important for inferring distances (e.g., Bailer-Jones 2015).”
• Accurate Empirical Radii and Masses of Planets and Their Host Stars with Gaia Parallaxes (2016, background): “We note that the calculation of d from π can become non-trivial when s pp 20% (see, e.g., Bailer-Jones 2015).”
• Gaia Data Release 2 (2018, methodology): “…of λ = 547.7 nm (which is a parameter of the extinction law and does not depend on the intrinsic source SED). gives a biased estimate of the distance (Bailer-Jones 2015; Luri et al. 2018), the impact of this is mitigated by the fact that we only report luminosities when the fractional parallax…”
• Estimating Distance from Parallaxes. IV. Distances to 1.33 Billion Stars in Gaia Data Release 2 (2018, methodology): “We adopt the exponentially decreasing space density (EDSD) prior in distance r P (r | L) = 1 2L3 r2e−r/L if r > 0 0 otherwise (1) where L > 0 is a length scale, as described in Bailer-Jones (2015) and Astraatmadja & Bailer-Jones (2016a), and adopted by Astraatmadja & Bailer-Jones (2016b) for GDR1.”
• Parallax Systematics and Photocenter Motions of Benchmark Eclipsing Binaries in Gaia EDR3 (2021, background): “In addition, all of the EBs have distance uncertainties better than 15%, and thus the choice of prior on the EB distance should not be important for inferring their parallaxes (e.g., Bailer-Jones 2015).”
• Photo-astrometric distances, extinctions, and astrophysical parameters for Gaia DR2 stars brighter than G = 18 (2019, methodology): “1 and Bailer-Jones 2015; Astraatmadja & Bailer-Jones 2016a; Luri et al. 2018).”