All Figures

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...includegraphics[width=0.4\textwidth]{8997f1b.eps}\\ \end{array} $ \end{figure}$ Figure 1: Left: distribution of period and signature for the planets missed by Solver A's broad criterion (A1). If more than one planet is present, the one with the largest signature is plotted. Right: distribution of period and signature for the planets missed by criterion B1.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=0.4\textwidth]{8997f2.eps} \end{figure}$ Figure 2: Inclination and eccentricity of the planets simulated for the T1 experiment. Black dots are planets with $\alpha < 15$ $\mu$ as and P < 6 yr not detected by the A1 criterion.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{rr} \includegraphics[width=0.4\textwidth]{8997... ...cludegraphics[width=0.39\textwidth]{8997f3b.eps}\\ \end{array} $ \end{figure}$ Figure 3: Left: same as Fig. 2, but here the results are expressed in terms of inclination angle and number of observations. Right: same as Fig. 2, in the e- $N_{\rm obs}$ plane.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.43\textwidth]{899... ...cludegraphics[width=0.43\textwidth]{8997f4b.eps}\\ \end{array} $ \end{figure}$ Figure 4: Distribution of fitted period as a function of true period for Solver A ( left) and B ( right).
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.43\textwidth]{899... ...cludegraphics[width=0.43\textwidth]{8997f5b.eps}\\ \end{array} $ \end{figure}$ Figure 5: Distribution of estimated error in the period as a function of true period for Solver A ( left) and B ( right).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=0.4\textwidth]{8997f6.eps} \end{figure}$ Figure 6: Distribution of estimated periods and their errors for orbits with signature larger than 0.4 mas as a function of true period. The lines with error bars show the median and interquartile range for the period estimated by Solver A (solid) and B (dashed). The lines without error bars represent the median estimated errors from the fitting procedure for Solver A (solid) and B (dashed).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=17cm]{8997f7.eps} \end{figure}$ Figure 7: Error in period as a function of astrometric signature for different period ranges and for both solvers. The dots show the difference between fitted and true period (blue, left axis) and the estimated uncertainty from the solution (red, right axis). Shown on the left panels are the solutions by Solver A, and on the right those by Solver B. Heavy dots represent the median values, binned in astrometric signature; error bars represent the interquartile range.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...\includegraphics[width=0.4\textwidth]{8997f8b.eps}\\ \end{array} $ \end{figure}$ Figure 8: Fitted vs. true orbital eccentricity for Solver A ( left) and Solver B ( right). Included are the orbits with signature larger than 0.4 mas - approximately 75% of the cases studied - and period shorter than 5 years.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...ncludegraphics[width=0.4\textwidth]{8997f9b.eps}\\ \end{array} $ \end{figure}$ Figure 9: Fitted vs. true values of the Thiele-Innes parameters A and B, according to the solution by Solver B. As in Fig. 8, included are orbits with $\alpha > 0.4$ mas and P > 5 yr.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=11.4cm,clip]{8997f10.eps} \end{figure}$ Figure 10: Top left and right: distributions of well-measured values of P and e for the two Solvers in the case of $5<\alpha /\sigma _\psi <10$ . Bottom left and right: the same, but for the case of $3<\alpha /\sigma _\psi <5$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.5cm]{8997f11.eps} \end{figure}$ Figure 11: Histogram of scaled period differences for planets with period between 1 and 5 years and signature larger than 0.4 mas. The red histogram is for Solver A, blue for Solver B. The dashed lines represent a Gaussian distribution with zero mean and unit dispersion.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...cludegraphics[width=0.4\textwidth]{8997f12b.eps}\\ \end{array} $ \end{figure}$ Figure 12: Scaled period differences for Solver A ( left) and Solver B ( right), for all orbits with signature larger than 0.4 mas. The curve and error bar represent the median and quartiles in 1-year bins in true period.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...cludegraphics[width=0.4\textwidth]{8997f13b.eps}\\ \end{array} $ \end{figure}$ Figure 13: Distribution of scaled difference in the Thiele-Innes parameter B for the Solver B solution. The left panel shows all data points; the right panel only the planets with signature larger than 0.4 mas and period shorter than 5 years. The dashed curve in each plot is a reference Gaussian with zero mean and unit dispersion.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=18cm]{8997f14.eps} \end{figure}$ Figure 14: Distribution of orbital periods in the multiple-planet solutions (dashed and dashed-dotted lines), compared with the true underlying distributions (solid lines). Top two panels: results for planet 1 and 2 obtained by Solver A (all stars). Panels 3 and 4: the same for Solver B, including stars with both two and three planets found. Panels 5 and 6: the same for Solver B, but excluding stars with three planets fitted. Bottom two panels: the true distribution of the second planet compared with the same distributions for planet two and three obtained by Solver B in the sample of three-planet orbital fits.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{8997f15.eps} \end{figure}$ Figure 15: True distributions for planet 1 and 2 (solid histogram) compared with the same distributions derived by Solver A ( top two panels) and Solver B ( bottom two panels) when the fitted values of the periods lie within 10% of the simulated values.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=8cm]{8997f16a.eps} ... ...c.eps} & \includegraphics[width=8cm]{8997f16d.eps}\\ \end{array} $ \end{figure}$ Figure 16: Fraction of systems with good orbital solutions ( $P(\chi ^2)\geq 0.0027$ ) in the T3b experiment for which both orbital periods are recovered by Solver A with a fractional uncertainty $\leq$ $10\%$ , as a function of period (0.5-yr bins). For comparison, the same results are displayed for the T2 test. Top left: all stars. Top right: systems with both periods $\leq$ 5 yr. Bottom left: systems with both periods $\leq$ 5 yr, and with $\alpha /\sigma _\psi \geq 10$ . Bottom right: systems with both periods $\leq$ 5 yr, $\alpha /\sigma _\psi \geq 10$ , and with $N_{\rm oss}\geq 45$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.5cm]{8997f17.eps} \end{figure}$ Figure 17: Histogram of scaled period differences $\Delta P/\sigma _P$ for good two-planet fits ( $P(\chi ^2)\geq 0.0027$ ) with periods accurate to better than 10% for the T3a (green solid and dashed lines) and T3b (red solid and dashed lines) experiments. The dotted curves are reference Gaussians with zero mean and unit dispersion.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.44\textwidth]{899... ...ncludegraphics[width=0.44\textwidth]{8997f18b.eps}\\ \end{array} $ \end{figure}$ Figure 18: Left: fraction of systems with good orbital solutions ( $P(\chi ^2)\geq 0.0027$ ) in the T3b experiment for which both eccentricities are determined within 0.05 of the true values. For comparison, analogous results for the T2 test sample are displayed. Left: all stars. Right: systems with both periods $\leq$ 5 yr, with $\alpha /\sigma _\psi \geq 10$ , and with $N_{\rm oss}\geq 45$ .
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.44\textwidth]{899... ...ludegraphics[width=0.44\textwidth]{8997f19d.eps}\\ \end{array} $ \end{figure}$ Figure 19: Top left: fraction of systems in the T3a experiment with satisfactory goodness-of-fit ( $P(\chi ^2)\geq 0.0027$ ) for which $i_{\rm rel}$ is determined to within $10{\hbox {$^\circ $ }}$ of the true value, as a function of $i_{\rm rel}$ itself (10 deg bins). Top right: the same for the T3b test (1 deg bins in $i_{\rm rel}$ ). Solid lines: all stars; dashed line: both orbital periods $\leq 5$ years; dashed-dotted line: $\alpha /\sigma _\psi \geq 10$ ; long-dashed line: both orbital periods $\leq$ 5 years and $\alpha /\sigma _\psi \geq 10$ ; dotted line: both orbital periods $\leq$ 5 years, $\alpha /\sigma _\psi \geq 10$ , and $N_{\rm oss}\geq 45$ . Bottom left and right: same as the top two panels, this time as a function of the inclination angle of one of the two planets.
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.44\textwidth]{899... ...ncludegraphics[width=0.44\textwidth]{8997f20d.eps}\\ \end{array} $ \end{figure}$ Figure 20: Top left and right: same as the two upper panels of Fig. 19, but for the formal uncertainties on $i_{\rm rel}$ as calculated by propagating the formal errors on the Thiele-Innes elements from the covariance matrix of the solutions. Bottom left and right: same as the two lower panels of Fig. 19, but for the formal uncertainties on $i_{\rm rel}$ calculated as for the top two panels.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{8997f21.eps} \end{figure}$ Figure 21: Boundaries of secure ( $\simeq$ $3\sigma$ , for $\sigma = 8$ $\mu$ as) detection and accurate mass and orbital parameters determination with Gaia compared to the known extrasolar planets (data from http://exoplanet.eu), which are plotted for the minimum case: orbit viewed edge-on, true mass equals radial velocity minimum mass, and astrometric signature minimum. Lines of different shape represent the minimum astrometric signature for 95% probability of a 3 $\sigma$ detection (solid line), the minimum astrometric signature needed to determine at least 50% of the time the mass of a planet with better than 15% accuracy (dash-dotted line), the eccentricity with uncertainties <0.1 (short-dashed line), and the inclination angle with uncertainties < $10{\hbox {$^\circ $ }}$ (long-dashed line), respectively. The true astrometric signature, which is proportional to the true mass, will be generally higher, much higher in some cases, with the effect that more reliable detections and orbital fits will be possible.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=12cm,clip]{8997f22.eps} \end{figure}$ Figure 22: Gaia discovery space for planets of given mass and orbital radius compared to the present-day sensitivity of other indirect detection methods, namely Doppler spectroscopy and transit photometry. Red curves of different styles have the same meaning as in Fig. 21 assuming a 1- $M_\odot$ G dwarf primary at 200 pc, while the blue curves are for a 0.5- $M_\odot$ M dwarf at 25 pc. The radial velocity curve (pink line) is for detection at the $3\sigma _{\rm RV}$ level, assuming $\sigma _{\rm RV} = 3$ m s^-1, $M_\star = 1 ~M_\odot$ , and 10-yr survey duration. For transit photometry (green curve), the assumptions of Gaudi et al. (2005) are used, i.e. $\sigma _V = 5$ milli-mag, S/N = 9, $M_\star =1$ $M_\odot$ , $R_\star = 1$ $R_\odot$ , uniform and dense (>1000 datapoints) sampling. Black dots indicate the inventory of exoplanets as of September 2007. Transiting systems are shown as light-blue filled pentagons. Jupiter and Saturn are also shown as red pentagons.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{8997f23.eps} \end{figure}$ Figure 23: Stellar content to d<200 pc, as function of the spectral type, for V<13 (solid line) and V<12 (dotted line).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{8997f24.eps} \end{figure}$ Figure 24: Stellar distribution in the solar neighborhood (d<200 pc) as function metallicity, for V<13 (solid line) and V<12 (dotted line).
Open with DEXTER

In the text

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...includegraphics[width=0.4\textwidth]{8997f1b.eps}\\ \end{array} $ \end{figure}$	Figure 1: Left: distribution of period and signature for the planets missed by Solver A's broad criterion (A1). If more than one planet is present, the one with the largest signature is plotted. Right: distribution of period and signature for the planets missed by criterion B1.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=0.4\textwidth]{8997f2.eps} \end{figure}$	Figure 2: Inclination and eccentricity of the planets simulated for the T1 experiment. Black dots are planets with $\alpha < 15$ $\mu$ as and P < 6 yr not detected by the A1 criterion.
Open with DEXTER

$\begin{figure} \par$\begin{array}{rr} \includegraphics[width=0.4\textwidth]{8997... ...cludegraphics[width=0.39\textwidth]{8997f3b.eps}\\ \end{array} $ \end{figure}$	Figure 3: Left: same as Fig. 2, but here the results are expressed in terms of inclination angle and number of observations. Right: same as Fig. 2, in the e- $N_{\rm obs}$ plane.
Open with DEXTER

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.43\textwidth]{899... ...cludegraphics[width=0.43\textwidth]{8997f4b.eps}\\ \end{array} $ \end{figure}$	Figure 4: Distribution of fitted period as a function of true period for Solver A ( left) and B ( right).
Open with DEXTER

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.43\textwidth]{899... ...cludegraphics[width=0.43\textwidth]{8997f5b.eps}\\ \end{array} $ \end{figure}$	Figure 5: Distribution of estimated error in the period as a function of true period for Solver A ( left) and B ( right).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=0.4\textwidth]{8997f6.eps} \end{figure}$	Figure 6: Distribution of estimated periods and their errors for orbits with signature larger than 0.4 mas as a function of true period. The lines with error bars show the median and interquartile range for the period estimated by Solver A (solid) and B (dashed). The lines without error bars represent the median estimated errors from the fitting procedure for Solver A (solid) and B (dashed).
Open with DEXTER

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...\includegraphics[width=0.4\textwidth]{8997f8b.eps}\\ \end{array} $ \end{figure}$	Figure 8: Fitted vs. true orbital eccentricity for Solver A ( left) and Solver B ( right). Included are the orbits with signature larger than 0.4 mas - approximately 75% of the cases studied - and period shorter than 5 years.
Open with DEXTER

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...ncludegraphics[width=0.4\textwidth]{8997f9b.eps}\\ \end{array} $ \end{figure}$	Figure 9: Fitted vs. true values of the Thiele-Innes parameters A and B, according to the solution by Solver B. As in Fig. 8, included are orbits with $\alpha > 0.4$ mas and P > 5 yr.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=11.4cm,clip]{8997f10.eps} \end{figure}$	Figure 10: Top left and right: distributions of well-measured values of P and e for the two Solvers in the case of $5<\alpha /\sigma _\psi <10$ . Bottom left and right: the same, but for the case of $3<\alpha /\sigma _\psi <5$ .
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.5cm]{8997f11.eps} \end{figure}$	Figure 11: Histogram of scaled period differences for planets with period between 1 and 5 years and signature larger than 0.4 mas. The red histogram is for Solver A, blue for Solver B. The dashed lines represent a Gaussian distribution with zero mean and unit dispersion.
Open with DEXTER

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...cludegraphics[width=0.4\textwidth]{8997f12b.eps}\\ \end{array} $ \end{figure}$	Figure 12: Scaled period differences for Solver A ( left) and Solver B ( right), for all orbits with signature larger than 0.4 mas. The curve and error bar represent the median and quartiles in 1-year bins in true period.
Open with DEXTER

$\begin{figure} \par$\begin{array}{cc} \includegraphics[width=0.4\textwidth]{8997... ...cludegraphics[width=0.4\textwidth]{8997f13b.eps}\\ \end{array} $ \end{figure}$	Figure 13: Distribution of scaled difference in the Thiele-Innes parameter B for the Solver B solution. The left panel shows all data points; the right panel only the planets with signature larger than 0.4 mas and period shorter than 5 years. The dashed curve in each plot is a reference Gaussian with zero mean and unit dispersion.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=12cm,clip]{8997f15.eps} \end{figure}$	Figure 15: True distributions for planet 1 and 2 (solid histogram) compared with the same distributions derived by Solver A ( top two panels) and Solver B ( bottom two panels) when the fitted values of the periods lie within 10% of the simulated values.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.5cm]{8997f17.eps} \end{figure}$	Figure 17: Histogram of scaled period differences $\Delta P/\sigma _P$ for good two-planet fits ( $P(\chi ^2)\geq 0.0027$ ) with periods accurate to better than 10% for the T3a (green solid and dashed lines) and T3b (red solid and dashed lines) experiments. The dotted curves are reference Gaussians with zero mean and unit dispersion.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{8997f23.eps} \end{figure}$	Figure 23: Stellar content to d<200 pc, as function of the spectral type, for V<13 (solid line) and V<12 (dotted line).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=9cm,clip]{8997f24.eps} \end{figure}$	Figure 24: Stellar distribution in the solar neighborhood (d<200 pc) as function metallicity, for V<13 (solid line) and V<12 (dotted line).
Open with DEXTER