Extending the occultations sample with Gaia 

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The Gaia Mission

The Gaia mission by ESA with has primary goal of creating a precise 3D map of our galaxy. This will be achieved via unprecedented results in parameters such as position, proper motion, parallax, radial velocity and temperature of stars. This mission is studying over 1:7 109 objects, representing over 1% of all stars in the Milky Way.
Gaia was launched in 2013 and started observations in 2014 with a pre-dicted mission end in 2019, which has since been extended to 2022 and may be extended to 2024, the maximum possible limit for the spacecraft until its fuel is completely consumed. It orbits in the Sun-Earth L2 (Lagrangian) point, roughly 1.5 million km away from Earth. This is a commonly used spot for space missions, as it allows for a stable orbit of the spacecraft and thermal stability of the equipment. It also allows observations uninterrupted by Earth eclipses. Other space telescopes in this region include, for example, Herschel23, WMAP24 and Planck25, with the James Webb Space Telescope (JWST)26, Euclid27, PLATO28, SPICA29, WFIRST, now the Nancy Grace Roman Telescope30 and ATHENA31 are also planned to launch towards that region.

Goals and Structure of this Thesis

• The blue boxes represent catalogues that exist prior to the observa-tion: Gaia DR2 is the star catalogue most used nowadays, Astorb and MPC are, alongside AstDyS, the asteroid catalogues, with the orbital elements and uncertainties of each body, DAMIT37 [Durech et al., 2010] and ISAM38 [Marciniak et al., 2012] are shape model databases, with one or multiple models for about 2 400 asteroids ( 0.4% of all num-bered asteroids) and WISE is the asteroid diameter database previously mentioned as NEOWISE.
• Green boxes represent the generated predictions. By using all of the previously mentioned catalogues, a first step is made by cross-matching stars and asteroids from a geocentric perspective, to create a global set of predictions. Afterwards, each observer applies their own filters, to account both for location (latitude/longitude/altitude and local hour) and limitations (star magnitude, magnitude drop, duration, minimum star altitude, among others). This way, each of them can have a fine-tuned set of viable occultations observable.
• The yellow and red boxes represent the observation. This may either be a single observer, the most typical case, or, as in the yellow box, a « campaign », where several observers target a specific event. This is not always possible, but whenever possible, campaigns are suggested in mailing lists or prediction websites.
• The white boxes represent the results of the observation: the astrometry obtained from the position of the star and whether the occultation was positive or negative, a light curve of the event for each observer and, with several observers and depending on the target, possible special features. All of these results will then be incorporated in the existing databases, refining the relevant information accordingly.
In this work, we address several aspects of this process; we exploited the DR2 star catalogue, both from software tools (Occult, Linoccult with all DR2 stars up to magnitude 14) and by building our own from querying the Gaia archive (stars up to magnitude 15.5); used the available asteroid databases, mainly Astorb, to get predictions for the Calern site, to determine the vi-ability of a 50 cm telescope with Gaia data on stars and asteroids, aiming for smaller targets (meaning shorter events) and for a systematic observation plan (robotic telescope); made observations to recover the astrometry and lightcurve data of several occultation events, both independently and as part of campaign projects; measured the improvement to orbits by adding Gaia asteroid data and by using an updated debiasing and error weighting models.
Following the introduction to the main topics addressed in this work, here is an overview to the thesis and its structure:
In Chapter 2, the focus was on checking the improvements verified and the ones expected through the application of Gaia data to stellar occultations, analysing the improvements on both the star catalogue and the asteroid orbits. Some statistics are presented on how this impacts the use of a 50 cm telescope.
Chapter 3 features all of the work done on the creation of a routine that simulated thousands of light curves under limit conditions for that 50 cm telescope, to assess its expected performance. A description is made to the method of building these light curves to be as close to real observations as possible, the bayesian inference method applied to fit the occultations, how this compares to other tools and how real observations in the recent past behaved compared to our simulated results. Most of this work was published as an article, as can be seen in Appendix D.
A summary of every observation made throughout this work is presented in Chapter 4, with special focus to the positives, where an occultation was detected, but a general description of negatives, where we missed the occulta-tion, as well. The BIM used in Chapter 3 was applied to our own observations to check the uncertainties, and we also used it on photometry data from other observations, as a collaboration.
Chapter 5 features the work made towards the improvement of asteroid orbits by exploiting the data from Gaia present in DR2 for all 14 099 asteroids there featured. A comparison between the standard debiasing and weighting schemes and the ones developed by the team, and a comparison was made between the resulting predictions for real events by OrbFit from this work and from other sources.
Finally, Chapter 6 has the conclusions of this thesis, as well as the plans for future work.
The main body of the thesis is then followed by the appendices:
• A: Theoretical work on orbital improvement of asteroids, used for the respective chapter.
• B: Important snippets of code used throughout this work.
• C: Most commonly used abbreviations. All of them are explained within the work, but this short list helps the reader find their meaning more easily.

Limitations to account for in DR2

Some considerations have been made regarding the limitations3 present in the DR2 catalogue, most notably:
• Incompleteness at G<12 and G>20.
• Incompleteness of fast moving stars, with velocities above 600 mas/year.
• Problems processing binary sources at the limit of resolution, which can affect up to 30% of the sources.
• About 20% of the stars only have a 2-parameter astrometric solution rather than 5-parameter, limiting their usefulness for long term predic-tions due to propagation issues.
• Systematic errors on parallax of bright stars, of G smaller than 5.
Other known issues of DR2 can be found in the source listed above, but these are the main concerns for the stellar occultation predictions. Any issue on the astrometric precision can affect the overall uncertainty of an event, and photometric issues can affect both the predicted star magnitude and drop caused by the event, as well as mislead observers once the observation is attempted.

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After Gaia’s DR2 was released, some of the predictions tools, such as winOc-cult and Linoccult, started using it as a catalogue for the stars, specifically up to magnitude 14.
With the drastic improvements on both position and proper motion, most stars had such well defined coordinates that their uncertainties no longer played a significant role in the overall error margin of the predictions, which now depended almost exclusively on the ephemeris errors of the asteroids. This was tested for a large sample of events. An example is shown in Figures 2.6 and 2.7.

Star and Asteroid Uncertainties

Before going any further, we also analyzed the typical position and proper motion uncertainties of stars in this magnitude range (G 6 14) with Gaia DR2. By making a query to this database restricting stars on their magnitude, we found the uncertainty distributions displayed in Figures 2.12 and 2.13, for which we made a quadratic sum of RA and Dec uncertainties.
Afterwards, a constraint made on a specific geographical location lets us look at actual predictions with given probabilities and realistic prospects of being observed. For this, we used the Calern Observatory as our location (43º 45’ 16.92” N, 6º 55’ 14.16” E), restricted the star’s altitude to at least 5º to avoid being very affected by air mass. We also constrained to events with at least 1% of probability of being observed, to leave out the ones that were too far away to be realistically seen, but still include enough events to have relevant statistics to use. In the end, 11 864 events followed these criteria. Distance here is important to know how far away we are of the asteroid’s shadow with relation to its size, with distances at least 3x larger usually meaning a 0% chance of observing the event.
Of all the remaining events, we extracted the asteroids involved and checked their ephemeris uncertainties through a query to JPL Horizons, where we could extract the RA and Dec uncertainty on the ephemeris of asteroids. By approximating RA and Dec as the main axes of the asteroid’s orbital uncer-tainty, we can approximate the total uncertainty through a quadratic sum.
Now that we had the uncertainties on the asteroids, a cross-match was made between our table and Gaia DR2 using the star’s RA, Dec and magni-tude. All of the events with a good match were then analyzed to compare the uncertainties of star and asteroid and check which dominates. With this work, we confirm that in most cases, the star’s uncertainty is indeed no longer relevant when compared to the asteroid’s, as it will be typically an order of magnitude below (see Figures 2.14, 2.15 and 2.16). And we can also show that this was not the case prior to Gaia. The most common catalogue used for occultation predictions prior to Gaia DR2 was UCAC4 4 (UCAC – U.S. Naval Observatory CCD Astrograph Catalog). Using the same set of events, we can compare the star/asteroid uncertainty ratio using DR2 with the obtained using UCAC4. For this, we further had to restrict to stars that have position and proper motion uncertainty estimates on both catalogues. The results were as seen in Figure 2.17.

Statistics on events per size

For this section, we discarded the data on orbital improvements by a factor of 50 or 100, looking at the more realistic values of orbital improvement, and because these two regimes did not have enough events for the following analysis. The goal was to check, for different sizes, what the impact was on improving the asteroid orbits in terms of amount of viable observations, as well as efficiency of predictions. For this, the following steps were made:
1. Separate the asteroids in four size groups: 5 to 10 km, 10 to 20 km, 20 to 40 km and over 40 km;
2. Filter, for each improvement factor, the amount of events with a prob-ability of positive observation at Calern of over 20%, 50% and 75%.
3. Analyze how many positives were expected, and how many events passed each probability filter.
As can be seen from these size groups, asteroids smaller than 5 km were left out of this analysis. While going smaller on the size limit would expo-nentially increase the number of available events, their corresponding orbital improvement with Gaia would be more delicate.

Table of contents :

1 Introduction 
1.1 Asteroids History
1.1.1 How have they been observed?
1.1.2 Observation Methods and Missions
1.2 Stellar Occultations
1.2.1 General properties
1.2.2 Why are they important?
1.3 The Gaia Mission
1.4 Goals and Structure of this Thesis
2 Extending the occultations sample with Gaia 
2.1 Context
2.2 UniversCity Telescope
2.3 Limitations to account for in DR2
2.4 Set-up
2.5 Star and Asteroid Uncertainties
2.6 Orbit improvements with Gaia
2.7 Statistics on events per size
3 Simulations 
3.1 Context
3.2 Least Squares and Bayes’ Theorem
3.2.1 Least Squares Fit Method
3.2.2 Bayes’ Theorem and Bayesian Analysis
3.3 Setup
3.4 Results
3.4.1 Gaussian and Uniform priors
3.4.2 False positives
3.4.3 Comparison of BIM to LSF
3.4.5 BIM vs Real Cases
4 Observations 
4.1 Context
4.2 Positives
4.2.1 Triton
4.2.2 Aemilia
4.2.3 Phaethon
4.2.4 Millman
4.3 Negatives
4.3.1 2000 HD22
4.3.2 Gezelle
4.3.3 Sveta
4.3.4 Paijanne
4.3.5 Nolde
4.3.6 Modestia
4.3.7 1993 FE48
4.3.8 Deikoon
4.3.9 Elektra
4.3.10 Phaethon
4.3.11 Europa
4.3.12 Alfaterna
4.3.13 2002 MS4
4.4 Analysis to other observations
4.4.1 Europa event – RIO team
4.4.2 Galatea
4.4.3 Euphrosyne
5 Exploiting Occultation Astrometry 
5.1 Context
5.1.1 Debiasing
5.1.2 Error Models
5.2 Setup
5.3 Testing error models with occultations
5.3.1 Best occultations
5.3.2 Full Scale Runs on Occultations
5.4 Orbital Elements with Gaia
5.4.1 Full Scale Run on DR2 Asteroids
6 Conclusions and Future Work 
6.1 UniversCity and Robotic Telescopes
6.2 Simulation of events
6.3 Comparing astrometry: occultations and other sources
6.4 Future Work
6.4.1 Gaia DR3 and beyond
6.4.2 Exploiting Single Chord Occultations
6.4.3 NEA Events


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