Gaia’s potential for the discovery of circumbinary planets

Gaia’s potential for the discovery of circumbinary planets

Abstract

The abundance and properties of planets orbiting binary stars – circumbinary planets – are largely unknown because they are difficult to detect with currently available techniques. Results from the Kepler satellite and other studies indicate a minimum occurrence rate of circumbinary giant planets of 10 %, yet only a handful are presently known. Here, we study the potential of ESA’s Gaia mission to discover and characterise extrasolar planets orbiting nearby binary stars by detecting the binary’s periodic astrometric motion caused by the orbiting planet. We expect that Gaia will discover hundreds of giant planets around binaries with FGK dwarf primaries within 200 pc of the Sun, if we assume that the giant planet mass distribution and abundance are similar around binaries and single stars. If on the other hand all circumbinary gas giants have masses lower than two Jupiter masses, we expect only four detections. Gaia is critically sensitive to the properties of giant circumbinary planets and will therefore make the detailed study of their population possible. Gaia’s precision is such that the distribution in mutual inclination between the binary and planetary orbital planes will be obtained. It also possesses the capacity to establish the frequency of planets across the H-R diagram, both as a function of mass and of stellar evolutionary state from pre-main sequence to stellar remnants. Gaia’s discoveries can reveal whether a second epoch of planetary formation occurs after the red-giant phase.

keywords:
Binaries: close – Planetary systems – Astrometry – Stars: low-mass.
12

1 Introduction

A number of systems composed of planets orbiting both components of a binary - circumbinary planets - have been detected in recent years. This includes systems detected from radial velocity data such as HD 202206 (Correia et al., 2005), such as NN Serpentis using eclipse timing variations (e.g. Beuermann et al. 2010; Marsh et al. 2013), like Kepler-16 detected from transits by the Kepler spacecraft (e.g. Doyle et al. 2011), like Ross 458, a planetary-mass object directly imaged around an M-dwarf binary (Burgasser et al., 2010), and like PSR B162026, a pulsarwhite-dwarf binary that hosts a Jupiter-mass planet (Thorsett et al., 1999; Sigurdsson et al., 2008).

While the reality of circumbinary planets was for a time questioned, the small harvest of systems identified by Kepler indicated these systems are fairly common. The occurrence rate of gas giants in the circumbinary configuration has been estimated to be of order 10% (Armstrong et al., 2014; Martin & Triaud, 2014), similar to the abundance of gas giants orbiting single stars (Cumming et al., 2008; Mayor et al., 2011). This came a bit as a surprise since planet formation mechanisms were thought to be stifled by mixing caused by the binary into the protoplanetary disc (e.g. Meschiari 2012), or by the very formation mechanism of close binaries (Mazeh & Shaham, 1979; Fabrycky & Tremaine, 2007).

Gaia (Perryman et al., 2001) was launched in December 2013 and began its survey in July 2014. Over the next five years, it will survey the entire sky and measure the positions and motions of approximately one billion stars. Individual measurements will be collected with a precision of 30 micro-arcseconds (as) for sources with apparent optical magnitudes brighter than 12. This is sufficient to allow for the detection of thousands of planets in nearby systems. Casertano et al. (2008) and Sozzetti et al. (2014) investigated the potential for Gaia to detect gas giants using the astrometric method, and Neveu et al. (2012) studied the interest of combining astrometric and radial-velocity data, very much like what was achieved for brown dwarfs using Hipparcos (Sahlmann et al., 2011b). However, this body of work only considered planets orbiting single stars.

It is reasonable to think that a large fraction of the systems where Gaia has the sensitivity to detect gas giants will be binary star systems, a number of which will have fairly short separations. In this paper, we look into whether gas giants in circumbinary orbits can be discovered using Gaia’s measurements. First we describe the importance of Gaia’s contribution to the study of circumbinary planets. Then, in Sect. 3, we present the type, precision, and number of measurements we can hope to obtain by the end of Gaia’s nominal mission, as well as the orbital elements required to be calculated to make a detection. We study some benchmark examples, before expanding our study to the nearby population of binaries in Sect. 4. Finally, we discuss our results.

2 Science case

Astrometric planet detection has limitations that are very different from the other four observing techniques currently employed in the discovery of circumbinary planets: transit photometry, eclipse-timing or transit-timing variations, radial velocimetry, and direct imaging. The most important distinction is the wide range of binary star properties that is accessible for planet detection. Transit photometry, eclipse-timing variations, and radial velocimetry are mostly confined to the shortest period binaries, whereas direct imaging can mostly access common proper motion companions on extremely wide orbits.

Direct imaging observations are most sensitive to self-luminous planets that can be resolved next to the binary host and so far revealed planetary-mass objects at orbital separations of 80-1000 AU around two young and low-mass M-dwarf binaries (Goldman et al., 2010; Scholz, 2010; Burgasser et al., 2010; Delorme et al., 2013).

Transit and eclipse probabilities have strongly decreasing functions with orbital period. Consequently, transiting planet discoveries have been limited to sub-AU separations around binaries with periods of a few tens of days at most. In addition, the region immediately outside a binary’s orbit is unstable, which further restrains the available parameter space. Stable orbits start appearing for circumbinary periods greater than 4.5 times the binary period (Dvorak, 1986; Dvorak, Froeschle & Froeschle, 1989; Holman & Wiegert, 1999; Pilat-Lohinger, Funk & Dvorak, 2003). Radial-velocity surveys are also best suited to short-period systems and are impacted by the instability region (e.g. Konacki et al. 2009). The method of eclipse-timing variations (ETV) is sensitive to long-period planets ( days) since the ETV amplitude increases with the planet period (Borkovits et al., 2011). Whilst the ETV amplitude is independent of the binary period, short-period binaries ( days) are favoured since they allow us to reach the temporal precision required to detect the light travel time effect induced by a planet.

Astrometry, therefore, is a complementary technique: its sensitivity improves with lengthening periods making it less affected by the instability region. This implies that a wide range of binary periods can be included in the search. Furthermore, unlike the other techniques, an astrometric survey can reach any binary (eclipsing or not), and allows the calculation of all binary and planetary orbital elements. Particularly, it is not impaired by a particular orbital plane orientation on the sky: true planetary masses can be measured and no transits are required for detection. Its limitations principally come from the distance to the system, the precision on individual measurements, and the timespan of the survey itself.

Results from Gaia will help us understand better the systems discovered by the Kepler satellite, which has provided the largest and best-understood sample of circumbinary planets. A degeneracy exists between the abundance of circumbinary gas giants and the distribution in mutual inclination between the planetary and binary orbital planes. Only a minimum frequency of could be inferred from the Kepler systems (Armstrong et al., 2014; Martin & Triaud, 2014), corresponding to a coplanar distribution of planets. If circumbinary planets instead exist on a range of mutual inclinations, this abundance increases, e.g. a Gaussian distribution with standard deviation of corresponds to an abundance of . The latest observations suggest such a scenario: Kepler-413 has a mutual inclination of and two candidates found by the ETV method have mutual inclinations of and (Welsh et al. presented at Litomsy̌l, Czech Republic, 2014).

The astrometric method can measure the distribution of mutual inclinations and hence produce a true occurrence rate. Observational evidence points out that circumbinary discs can be partially inclined (Winn et al., 2006; Plavchan et al., 2008, 2013), and that gas giants in circumstellar orbits are regularly found on inclined orbits (Schlaufman, 2010; Winn et al., 2010; Triaud et al., 2010; Albrecht et al., 2012). The prevalence of inclined systems would be an important marker of the formation and dynamical evolution of circumbinary planets.

Several massive and long period planets have been claimed from eclipse-timing variations orbiting post-common envelope binaries (see Beuermann et al. 2012 for a list). It is unclear whether these planets existed during the main-sequence or whether they formed as a second generation using matter ejected from their hosts (Schleicher & Dreizler, 2014). Mustill et al. (2013) notably show that it is hard to recover NN Ser’s architecture from a dynamical evolution of the system influenced by heavy mass loss. Gaia will survey binaries like NN Ser and systems that are similar to the progenitors of these binaries. Gaia will test results from eclipse-timing variations and permit to study the architecture and mass evolution of planetary systems pre and post red-giant phase. Thanks to its sensitivity, it may even be able to independently verify the existence of some of the currently claimed systems (see Sect. 5).

3 Gaia astrometric measurements

The Gaia satellite is performing an all-sky survey in astrometry, photometry, and spectroscopy of all star-like objects with Gaia magnitudes (Perryman et al., 2001; de Bruijne, 2012), where the passband covers the 400–1000 nm wavelength range with maximum transmission at 715 nm and a FWHM of 408 nm (Jordi et al., 2006). The nominal bright limit of was recently overcome and it is now expected that Gaia astrometry will be complete at the bright end (Martín-Fleitas et al., 2014). The spinning satellite’s scanning law results in an average number of 70 measurements per source over the five-year nominal mission lifetime, where we identify a measurement as the result of one pass in the instrument’s focal plane. The exact number of measurements varies as a function of sky position and is highest for objects located at 45° ecliptic longitude.

The responsibility for processing the Gaia telemetry lies with ESA and the Data Processing and Analysis Consortium (DPAC), where the latter consists of 400 European scientists and is responsible for producing the science data. The processing chain is complex (DPAC, 2007) and we highlight here only the concepts relevant for our study. After a global astrometric solution has been obtained from a reference star sample, the astrometric motions of other stars are modelled with the standard astrometric model consisting of positions, parallax, and proper motions. If excess noise in the residuals are detected and sufficient data are present, a sequence of increasingly complex models that include acceleration terms and/or orbital motion are probed until a satisfactory solution is found.

Many nearby binary stars will be solved as astrometric and/or radial velocity binaries by the Gaia pipeline. Others will be detected in radial velocity only, because the photocentre motion of the binary is diluted. The purpose of our study is to demonstrate that for some Gaia binaries, an additional astrometric signature will be detectable that is caused by a circumbinary planet.

3.1 Orbit detection

In most cases, the dominant orbital motion will originate from the binary whose period we designate . We assume that this motion can me modelled to the level of the Gaia single-measurement precision . The signature of the circumbinary planet will then become apparent as an additional periodic term in the residuals of the binary model that has the planet’s orbital period .

The two most important parameters for the detection of orbital motion are the number of measurements and the measurement precision . We either assumed the average number of 70 measurements over five years or we obtained a refined estimate using DPAC’s Gaia Observation Schedule Tool3, which yields predicted observation times as a function of user-provided object identifiers or target coordinates. Gaia’s astrometric precision is a complex function of source magnitude and we used the prescription of de Bruijne (2014), which yields the along-scan uncertainty as a function of apparent Gaia magnitude and colour4. For sources brighter than 12th magnitude, the precision is approximately 30 as, see Fig. 1. This picture neglects the CCD gating scheme that modulates the precision for sources, yet it is sufficient for our purposes.

Figure 1: Simplified estimate of the Gaia single-measurement precision as a function of magnitude, following de Bruijne (2014).

The scaling between a binary’s photocentre and barycentre orbit size is determined by the magnitude difference between the components and their mass ratio (Heintz, 1978; Gontcharov & Kiyaeva, 2002). The fractional mass,

(1)

and the fractional luminosity in a certain passband,

(2)

where is the magnitude difference, help to define the relationship between the semimajor axis of the photocentre orbit and the semimajor axis of the relative orbit, where both are measured in mas:

(3)

The relative semimajor axis is related to the component masses and the orbital period through Kepler’s law:

(4)

were G is the gravitational constant, is measured in metres and is in seconds. The relation between and is given by the parallax. These equations define the astrometric signal for the central binary, where and are the binary masses and is the binary period , and of the binary motion caused by the planet, where the central mass is and the period is the planet period .

We use the astrometric signal-to-noise ratio defined as

(5)

to define the threshold for detecting an orbit with a semimajor axis of the photocentre’s orbit. The relationships between orbital parameters, distance, component masses, and signal amplitude can be found, e.g., in Hilditch (2001) and Sahlmann (2012). It was shown that allows for the robust detection of an astrometric orbit, which includes the determination of all orbital parameters with reasonable uncertainties (Catanzarite et al., 2006; Neveu et al., 2012). More detail on the choice of this threshold is given in Appendix A. Finally, Gaia’s detection capability will be slightly influenced by the actual sampling of the orbital motion and by the orientation distribution scan angles along which the essentially one-dimensional measurement will be made. Due to the way Gaia scans the sky, typically two – four observations will be grouped within 6 – 12 hours equivalent to one – two revolutions of the spinning satellite. We neglected the influence of sampling and scan orientation for the sake of simplicity and computation speed.

An additional complication concerning detectability of circumbinary planets stems from the presence of three signatures: (a) the parallax and proper motion of the binary, (b) the orbital motion of the binary with amplitude , and (c) the orbital motion of the binary caused by the planet with amplitude , where is the barycentric orbit size, because in the vast majority of cases the light contribution by the planet is negligible. These three signals have a total of 19 free parameters and will have to be disentangled.

As we will show, this should not be problematic in the majority of cases, because there are 70 data points on average and the parallax and the binary orbital motion are detected at much higher than the planet signature.

In addition, circumbinary planets are not expected to exist at periods shorter than the stability limit (see Holman & Wiegert (1999) for a more thorough criterion), which results in a natural period separation of binary and planet signals. A simulated example of the orbital photocentre motion of a planet-hosting binary is shown in Fig. 9.

3.2 Example 1: Kepler-16

To showcase the principles of circumbinary planet detection with astrometry, we discuss the Kepler-16 system (Doyle et al., 2011). It consists of a 41.1-day binary with component masses of and , orbited by a planet with mass in a 228.8-day orbit. The Kepler magnitude of the system is 11.7 and its distance was estimated at 61 pc.

Astrometric signature of the binary

The astrometric semimajor axis of the primary is as and the relative semimajor axis is mas. Thus the components are not resolved by Gaia. Using the binary flux ratio of 0.0155 measured by Kepler, we find that the photocentric semimajor axis is as. Over five years, Gaia will observe Kepler-16 about 89 times, where we included a 10 % margin to account for dead time that the observation time predictor does not incorporate, with an uncertainty of 30 as. The binary’s astrometric motion in Kepler-16 will therefore be detected by Gaia astrometry with .

Astrometric signature of the planet

The planet’s gravitational pull will displace the system’s barycentre with a semimajor axis of as. As shown in Fig. 2, this is too small to be detected by Gaia at a distance of 61 pc. Yet, Fig. 2 illustrates the discovery potential of Gaia for circumbinary planets. If a Kepler-16 - like binary were located at 10 pc, Gaia would detect all orbiting planets more massive than 1 in orbits longer than days.

At the actual distance, Gaia will be able to place a constraint on the existence of a second planet in the Kepler-16 system with a mass larger than two to five times the mass of Jupiter depending on its period.

Figure 2: Estimated detection limits for planets around Kepler-16 using Gaia astrometry. The system is set to distances of 61, 25, 10, and 4 pc and planets above the respective curves would be detected. The vertical dashed line is located at the stability limit , i.e. planets are thought to be restricted to the right of this line. The circle marks the location of the planet Kepler-16b, whose orbital signature would be detectable only if Kepler-16 were located at a distance of 4 pc.

3.3 Example 2: Nearby spectroscopic binaries

We examined the sample of 89 spectroscopic binaries studied by Halbwachs et al. (2003). An analysis of the Kepler results shows a tendency for circumbinary planets to exist in orbits near the inner stability limit, with an over-density at (Orosz et al., 2012a; Martin & Triaud, 2014). We selected a subsample only including the 38 binaries that have periods in the range 10 days 304 days ( years), to ensure that a putative planet would complete a revolution around its binary host within the nominal five-year Gaia mission.

Distances to these systems were retrieved from the Hipparcos catalogue (ESA, 1997) or from van Altena, Lee & Hoffleit (1995) (GJ 92.1, GJ 423 A, GJ 433.2B, GJ 615.2A) and Crissman (1957) (GJ 1064 B). The distances to objects in the Pleiades and Praesepe were assumed constant at 120 pc (e.g. Palmer et al. 2014) and 182 pc (e.g. Boudreault et al. 2012), respectively. Orbital parameters, primary masses, and mass ratios were taken from Halbwachs et al. (2003). When only the minimum mass ratio was known, we used an estimate of , which corresponds to the median correction in a sample of randomly oriented orbits (see, e.g., Sahlmann 2012). When only the maximum mass ratio was known, we assumed .

Figure 3 shows the planet detection limits for these systems. For about half of the field binaries, Gaia could detect Jupiter-mass planets (and lighter) with orbital periods close to the nominal mission lifetime. For five binaries, Gaia could detect sub-Jupiter-mass planets with , which corresponds to the currently observed pile-up of Kepler circumbinary planets.

We performed these calculations with the average number of measurements (grey curve in Fig. 3c) and with a more accurate estimate obtained from the observation time predictor (black curve in Fig. 3c), again accounting for a 10 % margin. Both cases lead essentially to the same conclusion.

The 23 field binaries are located closer than 52 pc, meaning that their parallaxes will be detected with . 18 of those have relative separations smaller than 30 mas, i.e. will hardly be resolved by Gaia5 and their binary photocentric motions will be detected with . Importantly, if a planet is detected orbiting any of these binaries, the 3-d mutual inclination between the binary and planetary orbital planes can be calculated with an accuracy of , similar to what is achieved for the spin-orbit obliquity6 by observing the Rossiter-McLaughlin effect of single stars (e.g. Lendl et al. 2014).

For the binaries in clusters, which are at larger distances, Gaia will be able to detect the most massive circumbinary planets in the range of and with orbital periods shorter than the mission lifetime.

This shows that Gaia will set constraints on the presence of planets around many nearby known binaries. Since Gaia is an all-sky survey, many nearby binaries are expected to be newly discovered. This will result in a large sample of binaries and renders the detection of circumbinary planets with Gaia astrometry very likely.

Figure 3: Panel a: Estimated detection limits for planets around 38 spectroscopic binaries having 10 days days. The display is similar to Fig. 2. Red and blue curves correspond to binaries in Praesepe (9 objects) and the Pleiades (6 objects), respectively. The black curves correspond to the 23 field binaries, which are at distances 52 pc. All curves terminate at the binary period, and appear as dotted lines for . Dots mark the location of hypothetical planets with . Panels b and c show cumulative histograms of these planets.

4 Estimation of Gaia’s circumbinary planet discovery yield within 200 pc

To estimate the number of circumbinary planets Gaia may detect, we simulated the population of binary stars with FGK-dwarf primaries in the solar neighbourhood. We set the horizon at 200 pc distance to be able to extrapolate the ‘locally‘ measured properties with high confidence. The principal uncertainty originates in the true occurrence and distribution of circumbinary planets, which are unknown. We extrapolated the planet properties from their better known population around single FGK-dwarfs. This approach is analogous to the work of Martin & Triaud (2014), yet adapted to the specificities of astrometric planet detection.

4.1 Binary sample

Our synthetic binary sample is constructed from a combination of the results from Kepler and from radial velocity surveys, using a methodology similar to Martin & Triaud (2014) that we remind briefly here. We first select stars in the Kepler target catalog with Data Availability Flag = 2, meaning that the star has been logged and observed, and with measured effective temperatures, surface gravities and metallicities. We then use a relation from Torres, Andersen & Giménez (2010) to estimate masses for each star. The list is cut to only include stars with masses between 0.6 and 1.3, so that it coincides with the Halbwachs survey.

These stars are made the primary stars in binaries constructed using the results from radial velocity surveys. The secondary masses come from the mass ratio distribution in Halbwachs et al. (2003). The binary periods are drawn from the log-normal distribution calculated in Duquennoy & Mayor (1991), and restricted to be within 1 day and 10 years, to correspond to the Halbwachs survey. The inclination of the binary on the sky was randomised according to a uniform distribution in .

We compute absolute magnitude from stellar masses with the relationships of Henry & McCarthy (1993) and obtain colours on the main-sequence from Cox (2000). The absolute magnitude is obtained as in Jordi et al. (2010) and de Bruijne (2014). Given a distance, we can obtain all relevant parameters of a binary system, in particular the systems apparent magnitude, the relative orbit size, and the semimajor axis of the photocentric binary orbit.

4.2 Simulated binaries in the solar neighbourhood

We assumed a constant space density of FGK dwarfs within a 200 pc sphere around the Sun on the basis of the RECONS number count (ESA, 1997; Henry et al., 2006). There are 70 FGK dwarfs within 10 pc of the Sun7, which corresponds to a density of 0.0167 pc. The fraction of main-sequence stars in multiple systems with periods 10 years was determined to % (Halbwachs et al., 2003), which is the rate we used.

Because the astrometric planet detection capability depends critically on the target’s distance from the Sun, we generated star populations in spherical shells with equal distance spacing, i.e. spanning ranges of 0–5 pc, 5–10 pc, 10–15 pc and so forth. Every shell was populated with stars on the basis of its volume (Table 2) and the number of binaries was calculated. The properties of these binaries were determined by parameter distributions of randomly selected binary systems from the synthetic binary sample.

4.3 Simulated giant circumbinary planets

We assumed a constant rate of giant planet occurrence around binary stars of 10 % and we supposed that every planet is located at the stability limit pile-up of with one planet per binary star8. To draw planet masses, we synthesised a mass-dependent relative abundance of giant planets in the range of 0.31 – 30 from the results of radial velocity surveys (Ségransan et al., 2010; Mayor et al., 2011; Sahlmann et al., 2011a), see Fig. 4. Our simulations are thus strictly limited to giant planets more massive than Saturn. For every simulated binary hosting a planet, the planet mass is determined via the probability density function (PDF) defined by the normalised version of this distribution. We discuss the effects of altering these assumptions in Sect 4.5.

Figure 4: The mass distribution of giant planets used in the simulation.

4.4 The population of detectable planets

We set up our simulation to process a sequence of spherical shells. For every shell we obtain a set of synthesised binary systems and we discard binaries with periods longer than 304 days, because we impose that planets can only be detected if one complete orbital period is observed. The remaining binaries are conservatively set to the distance of the outer shell limit and are assigned planets according to the 10 % occurrence rate.

For every binary with a planet we compute the astrometric detection mass-limit for a planet orbiting at the pile-up period . The mass detection-limit takes into account the total mass of the binary, its combined magnitude and the corresponding single-measurement precision, and the requirement of , where we used . The probability of detecting this planet corresponds to the integral of over masses larger than the detection limit . By averaging this probability for all binaries, we obtain the mean probability of a planet detection in every shell. The number of detected circumbinary planets is obtained from , where the meaning of and other variables is summarised in Table 1.

Symbol Description Value
Number of stars in shell Table 2
Binary fraction 13.9 %
Fraction of binaries with one planet 10 %

Number of accessible binaries ( days)

Table 2

Number of planets around

accessible binaries

Table 2

Average probability that

a giant planet is detectable

Table 2
Number of planets detected in shell Table 2
Rate of potentially resolved binaries Table 2
Rate of binaries with Table 2
Table 1: Relevant parameters
Shell
(pc)
9 1 0.1 0.857 0.0 0.21 1.0
61 4 0.4 0.743 0.3 0.13 0.9
166 11 1.1 0.651 0.7 0.09 0.9
324 22 2.2 0.587 1.3 0.06 0.9
534 36 3.6 0.527 1.9 0.04 0.8
796 53 5.3 0.475 2.5 0.02 0.8
1111 75 7.5 0.438 3.3 0.01 0.8
1479 101 10.1 0.402 4.0 0.00 0.8
1899 130 13.0 0.379 4.9 0.00 0.7
2371 160 16.0 0.353 5.7 0.00 0.7
2896 195 19.5 0.329 6.4 0.00 0.7
3474 236 23.6 0.301 7.1 0.00 0.7
4104 277 27.7 0.285 7.9 0.00 0.7
4786 324 32.4 0.275 8.9 0.00 0.7
5521 375 37.5 0.257 9.7 0.00 0.6
6309 421 42.1 0.245 10.3 0.00 0.6
7149 483 48.3 0.232 11.2 0.00 0.6
8041 550 55.0 0.222 12.2 0.00 0.6
8986 602 60.2 0.207 12.4 0.00 0.6
9984 675 67.5 0.200 13.5 0.00 0.6
11034 751 75.1 0.187 14.0 0.00 0.6
12136 812 81.2 0.186 15.1 0.00 0.6
13291 888 88.8 0.177 15.8 0.00 0.5
14499 953 95.3 0.167 15.9 0.00 0.5
15759 1071 107.1 0.160 17.2 0.00 0.5
17071 1148 114.8 0.155 17.8 0.00 0.5
18436 1264 126.4 0.147 18.5 0.00 0.5
19854 1330 133.0 0.138 18.4 0.00 0.5
21324 1444 144.4 0.134 19.3 0.00 0.5
22846 1538 153.8 0.133 20.5 0.00 0.5
24421 1665 166.5 0.121 20.1 0.00 0.4
26049 1767 176.7 0.121 21.3 0.00 0.5
27729 1874 187.4 0.111 20.8 0.00 0.4
29461 1967 196.7 0.109 21.4 0.00 0.4
31246 2121 212.1 0.105 22.2 0.00 0.4
33084 2202 220.2 0.100 22.0 0.00 0.4
34974 2314 231.4 0.096 22.1 0.00 0.4
36916 2501 250.1 0.090 22.6 0.00 0.4
38911 2627 262.7 0.090 23.5 0.00 0.4
40959 2725 272.5 0.084 22.9 0.00 0.4
Total 37691 3769 516
Table 2: Results of the simulation
Figure 5: Mass histogram of detectable circumbinary planets. The four curves correspond to planets detected within spheres of pc (25 planets), pc (124 planets), pc (297 planets), and pc (516 planets).
Figure 6: Period histogram of detectable circumbinary planets. By construction, the distribution of binary periods follows the same distribution function, shifted to one sixth of the period. The greyscale coding is like in Fig. 5.

The simulation results are summarised in Table 2. Figures 5 and 6 show the histograms of masses and periods of detected planets and Figs. 10 and 11 show their cumulative versions.

In this simulation we find that Gaia will discover 516 planets orbiting binary stars within 200 pc. Within spheres of pc, pc, and pc around the Sun, we predict 25, 124, and 297 planet detections, respectively. Before discussing these absolute numbers, we can observe the characteristics of the planet population. The probability of detecting a planet decreases with the distance of the shell. This is because the sky-projected astrometric orbit size becomes smaller, hence the minimum detectable planet mass increases. Yet, the number of detected planets increases with distance, because the number of binaries increases as distance to the third power. Most planets are found at long periods, because the astrometric signal increases with orbital period. Finally, we see that the large majority of detected planets have masses . Although those are less frequent around binaries (Fig. 4), they can be detected out to large distances and thus around many more binary stars.

Table 2 also lists two parameters related to the binaries themselves. Complications in the photocentre measurement process can arise when binaries are visually resolved in the Gaia focal plane. We assume that this can be the case if the projected separation of the binary components is larger than 30 mas and their magnitude difference is smaller than two magnitudes. The rate of such binaries is indicated by the parameter and is smaller than 10 % and 1 % for binaries beyond 20 pc and 40 pc, respectively. Therefore, resolved binaries will have to be considered only for very few, very nearby circumbinary discoveries.

The other binary parameter represents the rate of binaries whose photocentric motions are detected with . This rate reaches unity for the most nearby systems and decreases slowly to 0.5 at 200 pc. This means that most of the binary motions will be detected with . In addition, the measurement timespan covers at least 6 orbital periods, thus the accurate determination of the binary parameters is almost guaranteed. The parallax of most FGK-dwarf binaries within 200 pc will be measured with . This validates what we claimed in Sect. 3.1: Since the two dominant signals, the parallax and the binary orbit, will be detected with very high , it will be generally possible to disentangle the planetary orbit at , even with uneven time sampling and 19 free parameters constrained by 70 independent measurements.

4.5 Revisiting our assumptions

We quantify the effect of altering our initial assumptions by repeating the simulation and changing the main parameters one by one.

  • The density of FGK dwarfs, the binary rate, and the circumbinary planet rate are proportional factors in the sense that changing them will influence the number of detected planets directly. If the planet rate is only 5 %, the number of detected planets is reduced to 258, i.e. half of the initial count.

  • Period of the planet: It is unlikely that all planets orbit with periods of and we therefore repeated simulations with values of and , yielding 479 (93 %) and 454 (88 %) detections, respectively. The decrease is attributable to the smaller number of accessible binaries when restricting their period range due to the requirement of covering one planet period with Gaia data.

  • Single-measurement precision and number of measurements: Both parameters influence the detection criterion in . We found that degrading the precision by 20 % yields 422 (82 %) planets and assuming a smaller number of 60 measurements over 5 years results in 474 (92 %) planet detections.

  • threshold: As shown in Fig. 7, some orbital signals can be detected with . Lowering our detection threshold to this value results in 689 planets (134 %), whereas increasing it to yields 317 planets (62 %). This parameter will determine the false positive rate of the planet discovery.

  • The planet mass distribution is the most sensitive parameter in our simulation. We have initially assumed that the mass distribution is the same for giant planets around single stars and around binaries. If circumbinary giant planets do not exceed masses of 2 9, we predict that Gaia will discover only four of them (0.807 %). Such planets can be discovered only around the most nearby binaries, which are few in number.

    This sensitivity to planet mass means that Gaia will disclose the mass distribution of giant planets around binaries, thus making new insights into planet formation processes possible.

  • Gaia mission duration: Our simulations assumed the nominal mission duration of five years. In the hypothetical case that the mission could be extended to a lifetime of 10 years, the number of circumbinary planets increases by a factor of 2.5 to 1249. The higher than proportional gain is caused by three factors: (1) the higher number of measurements leads to improved detection limits; (2) a longer mission allows to detect planets of longer orbital period, i.e. the number of accessible binary stars is also larger; (3) a longer mission allows to detect planets of lower mass, because the astrometric signal increases with orbital period.

  • Incomplete orbit coverage: Our detection criterion required full coverage of the planet period during the mission. The number of detections is thus conservative, because Gaia will also detect some planets with incomplete orbit coverage ( %) from curvature in the binary fit residuals.

  • Multi-planet systems: We assumed one single planet per binary, which neglected multi-planet systems like Kepler-47 (Orosz et al., 2012b). The presence of additional bodies in a system may complicate the data analysis if their signatures are comparable to the measurement precision. Like around single stars, we expect that circumbinary giant planets are rarely found in tightly packed systems. Because the period of a second planet will then be much longer than the simulated inner planet period , we expect that such systems may reveal themselves through an additional long-term drift.

In summary, we find that the Gaia circumbinary planet yield in terms of the order of magnitude of discoveries is relatively insensitive to the assumed parameters, except for the high-mass tail of the planet mass distribution. Assuming that very massive giant planets () exist around binaries as they do around single stars, the number of Gaia discoveries will be in the range of 200–600. This is one order of magnitude higher than the number of currently known circumbinary planets.

5 Discussion

It is clear that the sheer number of predicted planets around FGK-dwarf binaries discovered by the Gaia survey is the main result of this study. Yet, there are some considerations that further emphasize the importance of this work.

5.1 Mutual inclinations

Since most of the binaries studied here will have their orbital inclination measured to better than 1–5°, the uncertainty on the mutual inclination will be dominated by the planetary orbit determination (cf. the discussion in Appendix A and Fig. 8). On average, we expect the latter to be uncertain at the 10° level.

We will then have a sample of potentially hundreds of circumbinary planets with measured mutual orbit inclinations, leading to insights into their formation history and dynamical evolution.

5.2 Combination with auxiliary data

At distances larger than 100 pc, the determination of binary orbital parameters can be enhanced by complementing the Gaia astrometry with radial velocity data, either from the on-board radial velocity spectrometer or from independent observations. Radial velocity measurements with km/s precision that are quasi-independent of distance within 200 pc help detecting the astrometric binary orbit and leave more degrees of freedom for the detection of the circumbinary planet orbit.

For specific systems, ground-based high-resolution spectrographs, built for the detection of exoplanets, will complement unclosed orbits and may reveal the precession of planetary orbits inclined with respect to the binary plane through follow-up observations10. Those will refine measurements on the mutual inclination.

5.3 Direct detection of circumbinary planets

Our detection criterion imposed that the planet’s orbital period is fully covered by the Gaia measurement timespan. Consequently the projected relative separation between a binary and its planet is very small, typically 25 mas. In our simulation, there is only one planet with a relative separation 100 mas (assuming a 10-year mission, we predict six planets with separation 100 mas). Therefore, most circumbinary planets whose orbits are characterised by Gaia will lie beyond the capabilities of present and upcoming instruments.

However, Gaia will also detect nearby binary stars that exhibit nonlinear deviations from proper motion, which can be indicative of an orbiting planet. These are excellent targets for follow-up studies in particular those aiming at direct detection. Because the planets discovered by non-linear motion are at larger separation from their host star, they can be directly detected with coronagraphic or interferometric instruments on the ground, e.g. GPI (Macintosh et al., 2014) and SPHERE (Beuzit et al., 2006), or in space, e.g. JWST/NIRISS (Artigau et al., 2014).

5.4 Planets around non-FGK binaries

We considered FGK binaries in our study because the planet population around FGK dwarfs is the best studied so far. Yet, we expect that Gaia will discover planets around other types of binaries on and off the main sequence. Although the binary fraction drops as primary mass decreases (Raghavan et al., 2010), since M dwarfs are 3.5 times more abundant than FGK dwarfs in the solar neighbourhood, there will be plenty of M dwarf binaries amendable for planet search with Gaia. On the hotter side, A star binaries could be searched for planets too, with the particular interest of detecting them at younger ages, which is important for an eventual detection using direct imaging.

A large sample of circumbinary planets will open a meaningful study of the effect of stellar mass on the presence of planets. Gaia is not as sensitive to adverse effects associated to a star’s spectral type, e.g. photometric and spectroscopic variability or the availability of spectral lines, as the other detection methods. This means it will explore a wider mass range than the radial-velocity and transit techniques. In addition, the binary nature of the host can become a big help as well: Protoplanetary disc masses scale with the central mass, be it a single or binary star (Andrews et al., 2013), and heavier discs are expected to produce more gas giants (Mordasini et al., 2012). A G dwarf + G dwarf binary, for instance, had a disc mass equivalent to a single A star.

Furthermore, Gaia will contribute to the study of planets affected by the natural evolution of binaries across the H-R diagram, from pre-main sequence to stellar remnants. There are several claims of circumbinary planet detection around eclipsing binaries and post-common envelope binaries using measurements of eclipse-timing variations. We list the systems with available distance estimation in Table 3 and computed approximate astrometric parameters for the proposed planetary solutions and the Gaia observations. All planet periods are longer than the five-year nominal Gaia mission with fractional orbit coverages of . The probability of detecting the planet signal depends on and . The best candidate for validation with Gaia is QS Vir (Qian et al., 2010b) that has a large predicted signal amplitude of 443 as () and an orbital period that is almost covered by Gaia measurements ().

Finally, there is no expected limitation of Gaia’s planet detection capability caused by stellar activity (Eriksson & Lindegren, 2007). For a similar total mass, Gaia’s main constraint is the distance and apparent magnitude of a system. Thanks to this, it will be possible to detect planets from the pre-main sequence to stellar remnants and through the red-giant phase, thereby quantifying the influence of stellar evolution on the abundance, architecture, and mass distribution of planetary systems. This way, Gaia will confront theories about the consequences of mass loss and about the existence and efficiency of an eventual second epoch of planet formation11.

5.5 Circumbinary brown dwarfs

Gaia’s sensitivity to circumbinary companions increases rapidly with the companion mass. Brown dwarfs in orbits with periods not much longer than the mission lifetime around nearby binaries will therefore be efficiently discovered and characterised by Gaia. Again, this will provide a critical test for the comparison with brown dwarf companions within 10 AU of single stars (Sahlmann et al., 2011b), in particular the distribution of masses and orbital parameters.

6 Conclusion

Starting from empirical assumptions about the population of binary stars and of gas giants, we built a model of the circumbinary planet population in a volume of 200 pc. The precision of individual astrometric measurements by Gaia and the length of the survey inform that of the order of 500 circumbinary gas giants could be detected. The vast majority, however, will have masses in excess of fives times that of Jupiter. If the lack of planets more massive than Jupiter in the Kepler results reflects an intrinsic property of the circumbinary planet population, Gaia will produce a stringent null result that can enter planet formation models. In reverse, if those planets do exist as very recent results suggest, by the sheer number that will be produced, we will obtain the opportunity to study circumbinary planet properties and abundances in detail, not least to study how those are influenced by the evolution of their hosts.

The aptitude to deliver mutual inclinations between the binary and planetary orbital planes, will further our understanding of dynamical processes happening post planet-formation, completing the information collected on hot Jupiters thanks to the Rossiter-McLaughlin effect, to long period planets and a wide range of stellar properties.

According to the mission schedule, the first circumbinary planet discoveries of Gaia can be expected in the fourth data release, i.e. not before 2018.

As a final remark, we note that the 10 % rate of circumbinary planets that we used is a conservative number. About 20–30 % of the Kepler binaries are in fact fairly tight triple systems (Rappaport et al., 2013), which is compatible with what is found in the 100 pc solar neighbourhood (Tokovinin et al., 2006), and Gaia will easily identify these triple-star systems. It is likely that tertiary stars, if close enough, will disrupt any circumbinary protoplanetary discs, and hence inhibit planet formation (Mazeh & Shaham, 1979). This effectively increases the planet rate to 13 %. Furthermore, new circumbinary planets keep being found with Kepler, of which some have misaligned orbits. All these factors augment the expected Gaia discovery rate.

Acknowledgments

J.S. is supported by an ESA research fellowship. A. H. M. J. Triaud is a Swiss National Science Foundation fellow under grant number P300P2-147773. D. V. Martin is funded by the Swiss National Science Foundation. This research made use of the databases at the Centre de Données astronomiques de Strasbourg (http: //cds.u-strasbg.fr/); of NASA’s Astrophysics Data System Service (http://adsabs.harvard.edu/abstract_service.html; of the paper repositories at arXiv; and of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al., 2013). JS and AT attended the Cambridge symposium on Characterizing planetary systems across the HR diagram, which inspired some elements of our discussion. We acknowledge the role of office 443 B at Observatoire de Genève for stimulating this research. We thank the anonymous referee whose comments helped to improve the presentation of our results. JS thanks the members of the Gaia Science Operations Centre at ESAC for creating an excellent collaborative environment.

Appendix A On the choice of detection threshold

The three principal parameters that define the probability of astrometric orbit detection are the photocentric orbit size , the single-measurement uncertainty , and the number of measurements . Several studies define a detection criterion on the basis of a test in a simulation that includes the generation of synthetic observation (Sozzetti et al., 2014; Casertano et al., 2008), which in practice translates into for detected systems.

We instead apply a detection criterion on the basis of for orbits with periods shorter than the measurement timespan. In all these considerations we neglect the potential effects of extreme eccentricities, which can reduce the astrometric signature by a factor in the worst case, and we assume a sufficient amount of degrees of freedom to solve the problem, i.e. about twice as many data points as free model parameters.

Setting a detection threshold always involves a trade-off between detectability, false-alarm probability, and resulting parameter uncertainties. We tried to quantify the implications of our detection criterion by inspecting the binary detections with Hipparcos data, which are analogous to exoplanet and binary detections with Gaia. We used three catalogues, the original Hipparcos double and multiple catalog (ESA, 1997) and the two binary catalogues of Goldin & Makarov (2006) and Goldin & Makarov (2007). For every binary with period 1500 day, we computed the and the result is shown in Fig. 7.

Figure 7: Cumulative histogram of for Hipparcos binary solutions published by ESA (1997) (ESA97), Goldin & Makarov (2006) (GM06), and Goldin & Makarov (2007) (GM07). The number of binaries is given in the legend.

Only 11 % of the ESA (1997) binaries were found with . Using more sophisticated methods, Goldin & Makarov (2006) and Goldin & Makarov (2007) could increase this fraction to 18 % and 44 % for their respective samples of Hipparcos stars with ‘stochastic‘ astrometric solutions.

A figure of merit of particular interest for circumbinary planets is the uncertainty with which the orbital inclination can be determined. Figure 8 shows the inclination uncertainty for the binary solutions in the literature. We see that for , the inclination is typically determined to better than 10°. For larger than 100, the inclination uncertainty drops to a few degrees.

We conclude that a threshold of leaves a safe margin in terms of false-alarm probability and provides us with an inclination uncertainty of . It also has the advantage of being easy to implement and fast to compute.

Figure 8: Uncertainty in the orbit’s inclination as a function of .

Appendix B Additional figures and tables

Figure 9: Example of the photocentre motion for a circumbinary planet detected with taken from our simulation. For simplicity, we show a face-on and coplanar configuration, where parallax and proper motion have been removed. The binary with an orbital period of 40 days at 50 pc distance has a photocentric amplitude of as (dashed line). The planet with a mass of 7.9 induces orbital motion with as amplitude and 240 days period (dotted line). The combined photocentre motion about the centre of mass (‘x‘) is shown as a solid curve. The bar in the lower-left corner indicates the single-measurement uncertainty of as.
Figure 10: Cumulative mass histogram of detectable circumbinary planets. The greyscale coding is like in Fig. 5.
Figure 11: Cumulative period histogram of detectable circumbinary planets. The greyscale coding is like in Fig. 5.
Name Ref.
() (mag) (pc) (days) () (as) (as)
CM Dra 0.44 12.9 16 6757 1.5 43 1085 212.0 0.27 1
NN Ser 0.65 16.6 500 2776 1.7 231 17 0.6 0.66 2
NN Ser 0.65 16.6 500 5661 7.0 231 110 4.0 0.32 2
DP Leo 0.69 17.5 400 8693 6.3 356 158 3.7 0.21 3
HW Vir 0.63 10.9 180 4639 14.3 30 554 153.3 0.39 4
HW Vir 0.63 10.9 180 20089 65.0 30 6372 1763.6 0.09 4
QS Vir 1.21 14.4 48 2885 6.4 84 443 44.3 0.63 5
NY Vir 0.6 13.3 710 2885 2.3 51 17 2.8 0.63 7
Table 3: Circumbinary planet candidates discovered by eclipse timing that have a distance measurement or estimate. The reference codes are (1) Deeg et al. (2008); (2) Beuermann et al. (2010); (3) Qian et al. (2010a); (4) Beuermann et al. (2012); (5) Qian et al. (2010b); (7) Qian et al. (2012).

Footnotes

  1. pagerange: Gaia’s potential for the discovery of circumbinary planetsB
  2. pubyear: 2014
  3. http://gaia.esac.esa.int/tomcat_gost/gost/index.jsp?extra.
  4. See also http://www.cosmos.esa.int/web/gaia/science-performance.
  5. The short side of one of Gaia’s rectangular pixels measures 59 mas on the sky and corresponds to approximately 1 FWHM of the short-wavelength PSF.
  6. Here, obliquity denotes the projected spin-orbit angle.
  7. http://www.recons.org/census.posted.htm in August 2014.
  8. Placing all planets at the pile-up period results in a lower limit on the detectability, because further out induce a larger astrometric signal, thus are easier to detected as long as their period is covered by the measurement timespan.
  9. At a recent conference in Litomsy̌l, Czech Republic, Welsh et al. presented three circumbinary candidates discovered using the ETV method, one of which has a mass of 2.6 .
  10. A precessing planet is not following a Keplerian orbit, and hence fitting Keplerians to a radial velocity curve will fail if data with sufficient precision and timespan are available.
  11. These arguments are applicable to single stars as well, although they have not been explored in the literature.

References

  1. Albrecht S. et al., 2012, ApJ, 757, 18
  2. Andrews S. M., Rosenfeld K. A., Kraus A. L., Wilner D. J., 2013, ApJ, 771, 129
  3. Armstrong D. J., Osborn H. P., Brown D. J. A., Faedi F., Gómez Maqueo Chew Y., Martin D. V., Pollacco D., Udry S., 2014, MNRAS, 444, 1873
  4. Artigau É. et al., 2014, Proc. SPIE, 9143
  5. Astropy Collaboration, Robitaille T. P., Tollerud E. J., Greenfield P., Droettboom M., et al., 2013, A&A, 558, A33
  6. Beuermann K., Dreizler S., Hessman F. V., Deller J., 2012, A&A, 543, A138
  7. Beuermann K. et al., 2010, A&A, 521, L60
  8. Beuzit J.-L., Feldt M., Dohlen K., Mouillet D., Puget P., Antichi J., Baruffolo A., et al., 2006, The Messenger, 125, 29
  9. Borkovits T., Csizmadia S., Forgács-Dajka E., Hegedüs T., 2011, A&A, 528, A53
  10. Boudreault S., Lodieu N., Deacon N. R., Hambly N. C., 2012, MNRAS, 426, 3419
  11. Burgasser A. J. et al., 2010, ApJ, 725, 1405
  12. Casertano S. et al., 2008, A&A, 482, 699
  13. Catanzarite J., Shao M., Tanner A., Unwin S., Yu J., 2006, PASP, 118, 1319
  14. Correia A. C. M., Udry S., Mayor M., Laskar J., Naef D., Pepe F., Queloz D., Santos N. C., 2005, A&A, 440, 751
  15. Cox A. N., 2000, Allen’s astrophysical quantities
  16. Crissman B. G., 1957, AJ, 62, 280
  17. Cumming A., Butler R. P., Marcy G. W., Vogt S. S., Wright J. T., Fischer D. A., 2008, PASP, 120, 531
  18. de Bruijne J. H. J., 2012, Ap&SS, 341, 31
  19. —, 2014, ArXiv e-prints
  20. Deeg H. J., Ocaña B., Kozhevnikov V. P., Charbonneau D., O’Donovan F. T., Doyle L. R., 2008, A&A, 480, 563
  21. Delorme P. et al., 2013, A&A, 553, L5
  22. Doyle L. R., Carter J. A., Fabrycky D. C., Slawson R. W., Howell S. B., et al., 2011, Science, 333, 1602
  23. DPAC, 2007, DPAC: Proposal for the Gaia Data Processing, http://www.rssd.esa.int/doc_fetch.php?id=2720336
  24. Duquennoy A., Mayor M., 1991, A&A, 248, 485
  25. Dvorak R., 1986, A&A, 167, 379
  26. Dvorak R., Froeschle C., Froeschle C., 1989, A&A, 226, 335
  27. Eriksson U., Lindegren L., 2007, A&A, 476, 1389
  28. ESA, 1997, VizieR Online Data Catalog, 1239, 0
  29. Fabrycky D., Tremaine S., 2007, ApJ, 669, 1298
  30. Goldin A., Makarov V. V., 2006, ApJS, 166, 341
  31. —, 2007, ApJS, 173, 137
  32. Goldman B., Marsat S., Henning T., Clemens C., Greiner J., 2010, MNRAS, 405, 1140
  33. Gontcharov G. A., Kiyaeva O. V., 2002, A&A, 391, 647
  34. Halbwachs J. L., Mayor M., Udry S., Arenou F., 2003, A&A, 397, 159
  35. Heintz W. D., 1978, Geophysics and Astrophysics Monographs, 15
  36. Henry T. J., Jao W.-C., Subasavage J. P., Beaulieu T. D., Ianna P. A., Costa E., Méndez R. A., 2006, AJ, 132, 2360
  37. Henry T. J., McCarthy, Jr. D. W., 1993, AJ, 106, 773
  38. Hilditch R. W., 2001, An Introduction to Close Binary Stars, Hilditch, R. W., ed.
  39. Holman M. J., Wiegert P. A., 1999, AJ, 117, 621
  40. Jordi C. et al., 2010, A&A, 523, A48
  41. Jordi C., Høg E., Brown A. G. A., Lindegren L., Bailer-Jones C. A. L., Carrasco J. M., Knude J., 2006, MNRAS, 367, 290
  42. Konacki M., Muterspaugh M. W., Kulkarni S. R., Hełminiak K. G., 2009, ApJ, 704, 513
  43. Lendl M. et al., 2014, A&A, 568, A81
  44. Macintosh B. et al., 2014, Proceedings of the National Academy of Science, 111, 12661
  45. Marsh T. R. et al., 2013, MNRAS
  46. Martin D. V., Triaud A. H. M. J., 2014, ArXiv e-prints
  47. Martín-Fleitas J., Mora A., Sahlmann J., Kohley R., Massart B., L’Hermitte J., Le Roy M., Paulet P., 2014, Proc. SPIE, 9143
  48. Mayor M. et al., 2011, eprint arXiv:1109.2497
  49. Mazeh T., Shaham J., 1979, A&A, 77, 145
  50. Meschiari S., 2012, ApJ, 761, L7
  51. Mordasini C., Alibert Y., Benz W., Klahr H., Henning T., 2012, A&A, 541, A97
  52. Mustill A. J., Marshall J. P., Villaver E., Veras D., Davis P. J., Horner J., Wittenmyer R. A., 2013, MNRAS, 436, 2515
  53. Neveu M., Sahlmann J., Queloz D., Ségransan D., 2012, Proceedings of the workshop ”Orbital Couples: Pas de Deux in the Solar System and the Milky Way”, 81
  54. Orosz J. A. et al., 2012a, ApJ, 758, 87
  55. —, 2012b, Science, 337, 1511
  56. Palmer M., Arenou F., Luri X., Masana E., 2014, A&A, 564, A49
  57. Perryman M. A. C. et al., 2001, A&A, 369, 339
  58. Pilat-Lohinger E., Funk B., Dvorak R., 2003, A&A, 400, 1085
  59. Plavchan P., Gee A. H., Stapelfeldt K., Becker A., 2008, ApJ, 684, L37
  60. Plavchan P., Güth T., Laohakunakorn N., Parks J. R., 2013, A&A, 554, A110
  61. Qian S.-B., Liao W.-P., Zhu L.-Y., Dai Z.-B., 2010a, ApJ, 708, L66
  62. Qian S.-B., Liao W.-P., Zhu L.-Y., Dai Z.-B., Liu L., He J.-J., Zhao E.-G., Li L.-J., 2010b, MNRAS, 401, L34
  63. Qian S.-B., Zhu L.-Y., Dai Z.-B., Fernández-Lajús E., Xiang F.-Y., He J.-J., 2012, ApJ, 745, L23
  64. Raghavan D. et al., 2010, ApJS, 190, 1
  65. Rappaport S., Deck K., Levine A., Borkovits T., Carter J., El Mellah I., Sanchis-Ojeda R., Kalomeni B., 2013, ApJ, 768, 33
  66. Sahlmann J., 2012, PhD thesis, Observatoire de Genève, Université de Genève
  67. Sahlmann J., Lovis C., Queloz D., Ségransan D., 2011a, A&A, 528, L8
  68. Sahlmann J. et al., 2011b, A&A, 525, A95
  69. Schlaufman K. C., 2010, ApJ, 719, 602
  70. Schleicher D. R. G., Dreizler S., 2014, A&A, 563, A61
  71. Scholz R.-D., 2010, A&A, 515, A92
  72. Ségransan D. et al., 2010, A&A, 511, A45+
  73. Sigurdsson S., Stairs I. H., Moody K., Arzoumanian K. M. Z., Thorsett S. E., 2008, in Astronomical Society of the Pacific Conference Series, Vol. 398, Extreme Solar Systems, Fischer D., Rasio F. A., Thorsett S. E., Wolszczan A., eds., p. 119
  74. Sozzetti A., Giacobbe P., Lattanzi M. G., Micela G., Morbidelli R., Tinetti G., 2014, MNRAS, 437, 497
  75. Thorsett S. E., Arzoumanian Z., Camilo F., Lyne A. G., 1999, ApJ, 523, 763
  76. Tokovinin A., Thomas S., Sterzik M., Udry S., 2006, A&A, 450, 681
  77. Torres G., Andersen J., Giménez A., 2010, A&A Rev., 18, 67
  78. Triaud A. H. M. J. et al., 2010, A&A, 524, A25
  79. van Altena W. F., Lee J. T., Hoffleit E. D., 1995, The general catalogue of trigonometric [stellar] parallaxes
  80. Winn J. N., Fabrycky D., Albrecht S., Johnson J. A., 2010, ApJ, 718, L145
  81. Winn J. N., Hamilton C. M., Herbst W. J., Hoffman J. L., Holman M. J., Johnson J. A., Kuchner M. J., 2006, ApJ, 644, 510
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
122453
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description