The NEAT/Theia mission concepts and the science case for μas astrometry

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Exoplanet detection and characterization techniques

This section quickly presents each one of the exoplanet detection techniques that are in use today. We will see how indirect detection methods use observations of a physical quantity over time to detect changes related to either the orbital dynamics of a couple star/planet (radial velocities, pulsars, astrometry or transits) or galactic dynamics (gravitational lenses). In order words, we can find the planets because they move! On the contrary, with direct imaging, as the same suggest, the photons from the planet itself are detected. For simplicity, the formulas are given for cir-cular orbits: eccentricity e=0. In this simple case the equations presented for the radial velocities and astrometry methods are directly derived from the fundamental principles of dynamics and the law of gravitation.

Radial velocities of the host star

Using radial velocities means monitoring the velocity of the host star projected in the direction of the observer. The orbiting motion of a couple of bodies (star and planet) causes the star to have a periodic radial velocity that is characteristic of the planet orbit and mass: the planet and star periods are identical and their radial velocities are proportional. This is illustrated by Fig. I.3. The relative radial speed between the observer and the star causes a shifts of the star spectrum, first predicted by [Doppler, 1842].
By looking at Eq. (I.1), one can see that radial velocities are best adapted to small mass stars and small period planets (small orbits) seen on an edge-on configuration (i = 90◦). For face-on configurations (i = 0◦), no signal is detected. For statistics on a large number of detections, unknown inclinations are not a problem: face-on configurations are less frequent and the statistical bias due to the sin i term is low. However for a given individual case, it is often not possible to be certain of the planet mass when information on the inclination is not available: only the product MPlanet sin(i) is known.

Pulsar timing

Pulsars are highly magnetized residual cores of dead stars which are spinning very quickly. They emit regular radio signals as they spin, they are very accurate natural clocks [Matsakis et al., 1997]. The same Doppler effect that occurs in radial velocities is affecting the pulsar signal in the exact same way: the time between the pulses changes with the speed relative to the observer.

Astrometry of the host star

Astrometry measures the motion of the star on the plane of the celestial sphere. Just like for the radial velocities, the presence of a planet causes the star to have an orbit which is characteristic of the planet, called reflex motion or wobble. The star lateral position is measured instead of its radial velocity. This is also illustrated by the Fig. I.3. An observer perpendicular to the orbital plane would sees the star wobbling, but this angular motion at real scale is very small. The angular amplitude of the astrometric signal is given by Eq. I.2:
Where D is the distance between the Sun and the observed star, MPlanet is the exoplanet mass, a is the exoplanet semi major axis and MStar is the mass of the observed host star. The constant 3 µas (3 × 10−6 arcseconds) corresponds to the signal of an exo-Earth observed from a distance of 1 pc.
Astrometry of the host star is best adapted to intermediate period planets (near HZ)… and longer, as long as the period does not exceed the time span of the observations. The astrometric signal is stronger for small stars (all other parameters being equal) but for detection of planets in HZ,… the method is more sensitive for massive stars, as the habitable zone is in this case further away from the star, as we will see in the chapter II. At last, astrometry works best with a face-on geometric configurations, but edge-on systems are also detected. Note that it is also possible to do astrometry directly on the planets if they are detected by direct imaging. In this manuscript when we simply refer to astrometry, we implicitly mean astrometry of the host star. Section 3 will give a much more detailed presentation of astrometry.
The transit method looks at the decrease in apparent brightness of an host star as an exoplanet transits between the star and the observer. This is illustrated by Fig. I.5.
The depth of a transit (the relative decrease in luminosity of the host star) depends on the relative radius of the star and the planet:
If we refer to Table I.1, we have a straightforward estimation of the depth of the transit of an exo-Earth (around a Sun-like star): 10−4. Furthermore, to see a planet which has a random orientation transiting, the geometric configuration must be such that the planet passes by chance between the observer and the star, the probability (for a circular orbit of semi major axis a) is given by Eq. I.4 [Winn, 2010]:
Where Rstar is the diameter of the star and a the orbital distance. In most cases the planet is much smaller than the star and the approximation in equation I.4 is valid. The geometric probability of transit decrease with the orbital distance. The number of transits seen in a given time span also decrease with the orbital period. In order to confirm a transit detection one has to see at least 3 transit events: the longest period that can be detected is only 13 of the time span of the observations [Koch et al., 2010]. This makes transits best suitable for short periods (or small orbits). However, exo-Earth detection is possible (transit probability of 0.5%) provided an adequate time span of more than 3 years of observations is available for large number of stars.
It is sometimes possible to obtain the mass of planets or to discover other non transiting planets with transits alone, when planets are in resonance or have very close orbital periods. In this cases they perturb each other and produce Transit timing variations (TTV). The amplitude of the perturbations depends on the masses and periods of the planets. If both planets transits and show visible TTV, both masses can be known, otherwise we mainly have additional information about the non transiting planet[Holman and Murray, 2005].
There is a secondary event, which is frequently found in association with transits: the eclipse, which happens when the planet disappears when passing behind the star. Some systems can have only a transit or an eclipse, if the orbit is not circular. The effect of the eclipse is similar (a relative decrease in luminosity) but it is harder to detect because the planet has a much lower irradiance (W.m−2) than the star.

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Gravitational microlensing

Figure I.6: Schematic of a gravitational microlensing event. The magnitude of the secondary peak is greatly exaggerated to be visible.
This method takes advantage of galactic dynamics. When looking towards the center of the Galaxy, there is a non negligible probability to have a temporary near perfect alignment of two stars with the Earth as each object moves within the Galaxy.
When the chance alignment occurs, the star at the back (in the galactic center) is magnified by the one that is closer to the observer, producing a light curve roughly shaped like a bell. If a planet is present around the closer star, it will produce a secondary intensity peak that can be detected (Fig. I.6). Inverting this curve gives information about the planet mass and orbital distance. This method has an optimal sensitivity from 1 to 10 AU…. from the host star [Gaudi, 2012]. Until now this method has been relatively marginal and has the obvious disadvantage of not being reproducible: chance alignments only occur once. Furthermore, detections are hard to follow-up with other techniques because they occur at great distances (typically thousands of parsecs).
As the name suggests, this method goal is to obtain images of exoplanets around their host star(s). The problem is that current telescopes barely resolve the closest planet systems. The light from the star, which is typically billions of times greater than the one of the planet, is spread over by diffraction into a PSF…… The dim signal from the planet is drown into the much brighter PSF….. and indistinguishable from noise. In order to see the planet, astronomers have thought of several ways to cancel the star light: for example using a coronagraph (Fig. I.7) or interferometric nulling [Oppenheimer and Hinkley, 2009], [Guyon et al., 2006].
The greater the apparent angle between a star and a planet, the easier it is to separate them: direct imaging is best adapted to large periods and close stars. There is a trade-off though, at large periods, the planets are less luminous. However there is a notable exception: very young planets are hot because they have not had the time to cool down after their formation. In this case they emit a lot of infrared radiation and the contrast with the star in the infrared is more favorable [Oppenheimer and Hinkley, 2009].

Table of contents :

I Introduction 
1 Context
1.1 The beginning of a new field: exoplanetology
1.2 Exoplanet detection and characterization techniques
1.3 Understanding planetary formation and searching for life outside of the Solar System
2 Space borne missions and ground based instruments for exoplanet science
2.1 Transits
2.2 Radial velocities
2.3 Imaging, coronagraphy and nulling interferometry
2.4 The case for μas astrometry
3 Astrometry, exoplanets and NEAT
3.1 Historical presentation of Astrometry
3.2 The recent developments
3.3 Exoplanet detection using astrometry
4 My contribution in the context of NEAT
4.1 NEAT mission: science case and optimization
4.2 NEAT lab demo
II NEAT mission 
1 Presentation of NEAT
1.1 Principle of the pointed differential astrometric measure
1.2 Single epoch astrometric accuracy of NEAT
1.3 How NEAT reaches μas accuracy?
1.4 Error budget
2 Optimization of the number of visits per target
2.1 Description of the model
2.2 Numerical results
2.3 Discussion
3 Construction of the catalog of NEAT targets and references
3.1 The NEAT catalogs
3.2 Creation of the NEAT columns
4 Statistical analysis of the NEAT catalogs
4.1 Availability of reference stars
4.2 Astrometric signal in HZ versus stellar mass
4.3 Crossmatch with already known exoplanets
5 Allocation strategies and science yields
6 Conclusion
III NEAT lab demo: concept, specifications, design and test results 58
1 Foreword
2 High level specifications and concept
3 Specifications
3.1 Mechanical supports and environment
3.2 Detector/pixel specifications
3.3 Pseudo stars specifications
3.4 Metrology specifications
4 Critical design constraints
4.1 Nyquist sampling of pseudo stars and pupil size
4.2 Photometric relations
5 Design
5.1 Overview
5.2 Sub-systems
5.3 Baffles
5.4 Parameters and components summary
6 Compliance and tests
6.1 Photometric budgets
6.2 Diffraction limited PSF
6.3 Safe operation of the CCD: temperature and critical pressure
6.4 Mechanical and thermal stability
6.5 Individual components tests
6.6 CCD calibration results
6.7 Compliance table
IV NEAT lab demo: data analysis methods and simulations 
1 Introduction
2 Data analysis: methods
2.1 Overview
2.2 Dark and flat fields
2.3 Metrology
2.4 Pseudo stars
3 Results on simulated data
3.1 Metrology
3.2 Pseudo stars
V NEAT lab demo: results and conclusions
1 Result on actual data
1.1 Dark and flat fields
1.2 Metrology
1.3 Pseudo stars
2 Conclusions on the data analysis
2.1 Metrology
2.2 Flat fields
2.3 Stray light
2.4 Centroids (plus corrections from flat and metrology)
VI Conclusions and perspectives 
1 The NEAT/Theia mission concepts and the science case for μas astrometry
1.1 Results for the science case
1.2 The new mission concept: Theia
1.3 Future use of the catalog of targets and references
1.4 Improvements on the catalogs of targets and references and yield simulator
1.5 Near and mid-term perspectives in exoplanetology
2 The NEAT lab demo
2.1 General feedback on the project and teamwork aspects
2.2 Possible improvements for the NEAT lab demo
2.3 Lessons learned for the NEAT lab demo
2.4 Future applications of the NEAT demo experiment
3 After my PhD

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