# Paper III

# Using hidden states to infer gaps, detection efficiencies and the scanning law from the DR2 light curves

## Douglas Boubert, Andrew Everall, Jack Fraser, Amery Gration and Berry Holl.

Published in MNRAS and available here.

## Abstract

The completeness of the Gaia catalogues heavily depends on the status of that space telescope through time. Stars are only published with each of the astrometric, photometric, and spectroscopic data products if they are detected a minimum number of times. If there is a gap in scientific operations, a drop in the detection efficiency or Gaia deviates from the commanded scanning law, then stars will miss out on potential detections and thus be less likely to make it into the Gaia catalogues. We lay the groundwork to retrospectively ascertain the status of Gaia throughout the mission from the tens of individual measurements of the billions of stars, by developing novel methodologies to infer both the orientation and angular velocity of Gaia through time and gaps and efficiency drops in the detections. We have applied these methodologies to the Gaia data release 2 variable star epoch photometry - which are the only publicly available Gaia time-series at the present time - and make the results publicly available. We accompany these results with a new Python package ScanningLaw that you can use to easily predict Gaia observation times and detection probabilities for arbitrary locations on the sky.

## Inferring the Gaia scanning law (... again ...)

In Paper I we used the epoch photometric measurements of variable stars to infer where Gaia was pointing through time, by correcting the nominal scanning law published by the Gaia DPAC. Those corrections were highly simplistic and only involved small-angle rotations of Gaia's orientation in the across-scan direction. In this Paper we implemented a full quaternion attitude model of Gaia which could infer where Gaia was looking at every point in time completely independently of the nominal scanning law. The two plots below show the across-scan and along-scan offsets between our model and the nominal scanning law. The 15 arcsecond shift in the across-scan offset between the two fields-of-view is likely due to small errors in our model of Gaia's geometry. The scatter suggests that the nominal scanning law is accurate to a few arcseconds, on average. We discoverd that the along-scan offset drifts over the course of the mission, suggesting a small discrepancy between the nominal angular velocity of Gaia and the true value.

## What is the probability that Gaia sees a star when it looks at one?

We can predict when each variable star was visited by Gaia and we know which visits resulted in measurements. We decided to model the probability that a Gaia visit results in a measurement as a function of time and magnitude.

The first step was to predict how bright each variable star was at each visit without a photometric measurement. These being variable stars, we could not simply assume the mean magnitude of the star! We opted to model each time-series as a Gaussian Process, as illustrated in the right-hand figure.

For every Gaia visit to a variable star we then knew the magnitude of that star and whether that visit resulted in a detection. We decided to model this with two components. The first component was a Hidden Markov Model describing whether Gaia was experiencing a data-taking gap or not. If Gaia was in a data-taking gap then no stars of any magnitude were being detected. The second component was an independent Gauss-Markov process in each magnitude bin that modelled the probability that a visit outside of a gap would result in a detection. The resulting model is shown in the figure below.

## What's the point?

A star makes it into the Gaia source catalogue if Gaia detected it at least five times. Being able to predict when a hypothetical star would have been visited and the probability that each of those visits would have resulted in detections is thus crucial to calculating the Gaia selection function. These two methodological breakthroughs lay the groundwork for a comprehensive Gaia selection function in future.