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

**Authors:** C. A. L. Bailer-Jones  
**arXiv:** [2311.00374](https://arxiv.org/abs/2311.00374)  
**Date:** 2023-11-01  
**Summary page:** https://www.summarizepaper.com/en/paper/2311.00374v1/

## Key points

- Accuracy of distance estimates based solely on parallaxes decreases with increasing distance
- Proper motion measurements can provide independent information about stellar distances
- A model is developed to incorporate direction and distance-dependent distributions of stellar velocities
- Kinegeometric distances are 1.25 times more accurate than geometric distances across the entire Gaia catalogue
- Kinegeometric distances outperform geometric ones considerably beyond several kiloparsecs
- Kinegeometric distances have an average accuracy of 19%
- Velocities can be determined with median absolute deviations of 16 km/s
- Distant stars tend to have smaller kinegeometric distances compared to geometric ones on average in Gaia DR3, but the pattern is more complex in bulge and disk regions
- Gaia DR5 is expected to provide much more accurate proper motion measurements, improving distance accuracy by a factor of approximately 1.35 on average
- Kinegeometric distances are still projected to be 1.25 times more accurate than geometric ones in Gaia DR5 due to being limited by the width of the velocity prior

## Summary

In this study, the author focuses on the accuracy of stellar distance measurements inferred from parallaxes and proper motions. It is well-known that the accuracy of distance estimates based solely on parallaxes decreases rapidly with increasing distance. However, by incorporating proper motion measurements and considering typical velocities, independent information about stellar distances can be obtained. To achieve this, the author develops a model that takes into account both direction and distance-dependent distributions of stellar velocities in the Galaxy. This model is then used in conjunction with parallax and proper motion data from Gaia Data Release 3 (DR3) to infer kinegeometric distances and transverse velocities for stars. To assess the performance of this method, noisy simulations are conducted comparing its accuracy to purely parallax-based (geometric) distances. The results reveal that on average kinegeometric distances are 1.25 times more accurate than geometric ones across the entire Gaia catalogue. However, there is a significant variation in relative performance among different stars; particularly beyond several kiloparsecs (kpc), kinegeometric distances outperform geometric ones considerably. The study finds that kinegeometric distances can be measured with an average accuracy of 19%, while velocities (sqrt[vra^2 + vdec^2]) can be determined with median absolute deviations of 16 km/s. In Gaia DR3 distant stars tend to have smaller kinegeometric distances compared to geometric ones on average; however, the pattern becomes more complex in bulge and disk regions. Looking ahead to Gaia Data Release 5 (DR5), which is expected to provide much more accurate proper motion measurements, a further improvement in distance accuracy by a factor of approximately 1.35 on average is predicted. Despite this improvement, kinegeometric distances are still projected to be 1.25 times more accurate than geometric ones due to being limited by the width of the velocity prior unlike improvements from better parallaxes which are not constrained by the distance prior. In conclusion, this study presents a method for inferring stellar distances and transverse velocities using parallaxes, proper motions and a model of stellar velocities in the Galaxy.