Roman+Gaia Astrometry Tool

Summary

This tool (available at this GitHub site) simulates the effect of combining Gaia catalogues with future Roman images to estimate the resulting astrometric precision for stars (or any source moving with a relatively constant PM over decades, such as free-floating exoplanets). This tool is especially useful for planning observations with the goal of reaching a particular astrometric/proper motion precision, as well as for predicting the types of dynamical measurements that will be possible in the Roman era (e.g., bulk motions of nearby galaxies, full 2D velocity profiles and dispersions of nearby globular clusters and galaxies, kinematics of stellar streams).

Users are able to specify which data release of Gaia to compare with, Roman observing plans (e.g., image exposure time, epoch of observation, number of dithers), and stellar information (e.g. magnitudes in Gaia and Roman filters) and get back uncertainties in position, parallax, and proper motion. An example notebook on the GitHub repo (gaia+roman_astrometry.ipynb) shows how to use the code for arbitrary observation configurations. Additional notebooks use the specific survey strategies outlined in the ROTAC report for the HLWAS and HLTDS.

This tool does not fully simulate putting realistic sources in an image, measuring positions of those sources at different epochs, aligning images onto a global reference frame, and then determining astrometric measurements (though this may be explored in the future). It assumes that the change in position of a star on the sky is described by the proper motion and parallax; it does not account for changes in position on the sky/distance due to radial velocity. The proper motion for each star is assumed to be constant, meaning the precision calculations do not strictly apply to stars experiencing signficant changes in PM over human timescales (e.g., near the center of the galaxy, perturbations from a binary companion). However, this tool may still be useful for these non-constant-PM cases, in terms of determining when the constant-PM null hypothesis can be rejected (e.g., for binary systems or massive exoplanets).

Process

Step 0: Estimate Roman Position Uncertainties:

• This step was run on a laptop (with results saved into the various csv files in the data directory on the GitHub site) and does not need to be re-run again.
• The stpsf package was used to input simulated stars of different fluxes at the center position of the center detector. The positional uncertainties as a function of Roman filter, magnitude, and exposure time were then estimated from how well one is able to centroid those simulated stars.
• See Figure 1 for an example of the positional uncertainty versus magnitude in different Roman filters when the exposure time is about 200 seconds.

Step 1: Define Observation Plan

• Following the cells of the gaia+roman_astrometry.ipynb notebook, the user first defines some choices, such as the Gaia data release (gaia_era), as well as a lower limit on Roman positional uncertainties (i.e., ~1% of a pixel width is the standard choice; roman_pos_err_floor).
• The user then definies stellar properties by choosing the filters that will be used (roman_filters), the stellar magnitudes in those filters (roman_mags), and the corresponding magnitudes of those stars in Gaia G (gaia_mags). In the example notebook, these values were set by assuming constant color offsets between filters, but this could be adjusted to include information from stellar isochrones for more realistic conditions.
• The user next sets the Roman observation plan using the epoch of observation (must be defined in MJD; epoch_MJDs), the Roman filters used at each of those epochs (epoch_filters), the number of dithers at each epoch (n_images_per_epoch), and the exposure time (epoch_MAs; Roman MultiAccum names defined here).
• Finally, the user can specify a target RA, Dec coordinate if one wishes to include parallax information in the astrometric precision calculation.

Step 2: Explore Astrometric Precision Outputs

• The outputs are saved into a python class (in the gaia+roman_astrometry.ipynb notebook, new_precision contains the results), which contains information about the Gaia astrometric precision (e.g., gaia_pos_errs, gaia_pm_errs, gaia_parallax_errs) as well as the final Gaia+Roman astrometric precision (e.g., final_pos_errs, final_pm_errs, final_parallax_errs).
• The astrometry precision can be compared in summary figures, such as the example in Figure 2.

Caveats about Results

• These calculations assume that there are enough stars in common between a Roman image and Gaia such that the uncertainty on the alignment contributes negligibly to Roman position uncertainty on the Gaia refrence frame. If a user would like to explore the impact of this uncertainty, they can increase the roman_pos_err_floor parameter to be larger than the nominal 1% of a pixel.
• The parallax calculation places Roman at Earth, instead of at L2 (the code was originally implemented for an Earth frame), though the impact of this choice should be fairly minor on the astrometry precision calculations. This will need to be changed when working with real Roman data (or other telescopes at L2).
• For numerical stability, there is an extremely diffuse global prior applied to the PM and parallax measurements (i.e., uncertainties are ~10 times larger than the largest possible stellar proper motion or parallax seen from Earth). This may lead to the output plots having Gaia+Roman PM uncertainties around 10⁵ mas/yr and parallax uncertainties of 10⁴ mas.
• At the bright end, the position uncertainty of sources in Roman is likely optimistic because many of the brightest sources will likely be saturated. Determination of how well a saturated star will behave has not been attempted.
• The Roman position uncertainty estimates as a function of magnitude are likely a little optimistic, since they were only simulated measuring positions at the center pixels of the center detector. Future work may explore how the centroiding changes across the focal plane.

Acknowledgments

• The statistics underpinning this code is scientifically inspired by the Bayesian Positions, Parallaxes, Proper Motions (BP3M) tool presented in McKinnon et al. 2024.
• This work uses the predicted Gaia astrometric precision for positions, parallaxes, and proper motions for DR3 to DR5 as presented by the Gaia Collaboration.
• This code uses the pandeia and stpsf packages to simulate Roman PSFs and observations.
• Thanks to Eddie Schlafly (STScI) for sharing example code for calculating Roman positional uncertainties and helpful conversations that improved this tool.
• If users have questions about or feedback on the code, they can email Kevin McKinnon, University of Toronto, Cananda.