stars, the prior information is taken from @book:newhip and set up exactly as for the HTPM solution (see Sect. 2.6 in the HTPM paper). In addition to this nominal scenario, we show in Sect. \[sec:noparallaxprior\] that a solution can be made without the [Hipparcos]{} parallaxes.

For a [*Tycho*]{}-only star the prior information in the [*Tycho*]{} Catalogue consists of the position $\alpha$, $\delta$ at the epoch J1991.25 together with its uncertainties $\sigma_{\alpha*}$, $\sigma_{\delta}$ and correlation coefficient $\rho$. Remaining parameters should be treated as essentially unknown, which means that they can be set to some arbitrary values with very large uncertainties. For the simulated solutions in Sect. \[sec:sim\] they are set to zero with uncertainties $\sigma_{\varpi} = 1000$ mas, $\sigma_{\mu\alpha*} = \sigma_{\mu\delta} = 1000$ mas yr$^{-1}$, and $\sigma_{\mu r} = \sigma_{v r} \sigma_{\varpi}/A$, where $\sigma_{v r} = 100$ km s$^{-1}$ is the prior radial velocity uncertainty and $A$ the astronomical unit (HTPM paper, Eq. 17). The prior astrometric parameters at J1991.25 are thus taken to be $(\alpha, \delta, 0, 0, 0, 0)$ with covariance $$\begin{aligned}
{\boldsymbol}{C}_\text{pri} = \begin{bmatrix}
        \sigma_{\alpha *}^2 & \rho\sigma_{\alpha*}\sigma_{\delta} & 0 & 0 & 0 & 0\\
        \rho\sigma_{\alpha*}\sigma_{\delta} & \sigma_{\delta}^2   & 0 & 0 & 0 & 0\\
        0 