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J. Phys. IV France 1 (2001) Pr1-1 c EDP Sciences, Les Ulis Duplicity and masses F. Arenou 1 , J.-L. Halbwachs 2 , M. Mayor and S. Udry 3 1 2 3 Observatoire de Paris, UMR 8633 CNRS Observatoire Astronomique de Strasbourg, UMR 7550 CNRS Observatoire de Genève, 51 chemin des Maillettes, CH–1290 Sauverny, Suisse Abstract 1 INTRODUCTION Duplicity is a key question in astrophysics, and there is no doubt that the Milky Way would look entirely different if stars were single. Binaries provide direct measurements of stellar or galactic quantities and several astronomical phenomena occur only in binary systems. The binary rate, the distribution of mass ratio between components inform on stellar formation in relation with the place of formation. Stellar physics needs masses, luminosities and radii obtained through the studies of binaries. Galactic physics benefits also from this studies, e.g. the galactic potential can be tested using wide binaries, and the chemical evolution depends on binaries through the supernovae Ia process. Remembering the large number of doubles detected or suspected by Hipparcos, so large that the need of an adequate classification emerged – five different categories in the Double and Multiple Stars Annex – one could simply consider that GAIA will rescale the number of double stars to a Catalogue of one billion stars. But there is something more important, and what will be learned from GAIA may be easily summarized: GAIA will be a complete on-orbit observatory since it will provide homogeneous astrometric, photometric, and spectroscopic measurements; GAIA will at last provide large and unbiased samples of all kind of binaries, for an extremely large range of periods and mass ratios, at all evolution stages. Some of the questions which will be solved by GAIA may be mentioned. First, the parallaxes and proper motions will allow to distinguish between optical doubles and physical binaries. The binary rate will be known down to low mass companions and in particular may allow to study the low mass companion rate at large separation. The mass ratio distribution will be shown either random or as a formation product. The formation of close versus wide binaries will be better known. For large separations, the mass ratio distribution and binary rate will allow to know the evolution process of such systems. For multiple system, the hierarchy and relative inclination will be accessible. For contact binaries, the accurate knowledge of the masses will allow to address the question of mass transfer, evolution and space distribution. . . The GAIA study report [1] describes largely the science case concerning binaries. After a brief remainder from this report concerning the general GAIA capabilities, we will mention a few complementary applications. Pr1-2 2 JOURNAL DE PHYSIQUE IV GAIA CAPABILITIES GAIA will discover about 60 million binaries, that is 3/4 of the nearby binaries brighter than 20m , and about 35% of them at 1 kpc. The final mission product could be more than 107 astrometric binaries, 106 eclipsing binaries, 106 spectroscopic binaries, 107 resolved binaries within 250 pc and 10, 000 stars with masses within 1%. Due to the huge number of detected binaries, even short-lived evolution stages will be reachable. And the duplicity will be studied in the field, in clusters or star-forming regions, where a majority of young stars are in binary systems [2]. Even at large separations, the high precision of the obtained three-dimensional velocity will permit to locate easily ‘common proper motion’ pairs. Orbits of nearby visual binaries can be recovered up to 40 yr periods, and precise masses will be obtained for short enough periods, with the astrometry alone or in combination with the spectroscopic data. This will allow to put severe constraints on stellar evolution models, where a 2% precision on masses is needed [4]. The impressive number of expected astrometric binaries is due to the extreme GAIA sensitivity to non-linear proper motions. As an example, a pair of one solar-mass stars with a 1 000 yr period would have an acceleration of 10µas.yr−2 (i.e. significant for the brightest stars) at 300 pc [3]. 3 ON-BOARD DOUBLE STAR DETECTION The small angular size (37 mas) of the pixels in the GAIA astrometric focal plane, with a PSF of FWHM=2.2 pixels, will allow to easily detect close (0.1”) visual binaries. In the Astrometric Sky Mapper (ASM) where the on-board detection takes place, the sample size is 2 × 2 pixels, and the readout noise higher than in the astrometric field [5], but the detection of double stars in ASM is of interest for at least two reasons: a) the detection defines the patches which are observed in the astrometric field, and an undetected duplicity would render the astrometric and photometric data reduction much harder if the patches are too small; b) a subsample of well-behaved (single) stars will be needed for the data reduction. Fig. 1. Detection limit of double stars in the Astrometric Sky Mapper, from [6] The Figure 1 shows the minimum separation between components for which a duplicity de- WILL BE SET BY THE PUBLISHER Pr1-3 tection could be done, and it also shows where larger patches would be needed. This theoretical minimum separation will most probably not be reached by the on-board detection algorithm. Moreover spurious double star detection may occur since the PSF is larger for a red star, and this may be attributed to duplicity as nothing is known about the star’s colour when it enters the sky mapper. 4 PHOTOCENTRIC BINARIES Apart from the 16 CCD dedicated to astrometric measurements, each GAIA astrometric instrument also includes 4 broad bands photometers (BBP) primarily used for chromaticity corrections. However, these BBPs could also be useful for the duplicity detection: the photocentre of an (unresolved) double pair will not be identically positioned in each of these BBP, provided that the two companions do not have the same color. GAIA could then introduce a new category of photocentric or ‘color-induced’ binaries in the terminology of [7, 8]. Using only the BBPs of the Astro 1 instrument, where the along-scan resolution√is the same as in the astrometric fields, the expected precision in one BBP will then be about 2 × 16 less precise than the final astrometric precision. Assuming this precision for a G-type primary, and projecting randomly the separation between components for each of the 67 transits expected on the average during the mission, main-sequence secondaries of various periods and magnitude differences have been simulated in [9] for different distances. Then the separation ρ, position angle, magnitude and color of each components have been recovered by least-square. As may be seen in Figure 2, where are indicated the solutions with ρ > 3σρ , GAIA may be able to resolve the brighter binaries down to the milliarcsec level, provided that the magnitude difference is in the range 1 to 3 mag. V magnitude difference = 1 mag V magnitude difference = 6 mag 100 Separation between components (mas) Separation between components (mas) 100 10 0.1 yr 0.5 1 5 10 50 100 500 1000 yr 1 0 12 14 16 Primary V apparent magnitude 18 10 0.1 yr 0.5 1 5 10 50 100 500 1000 yr 1 0 12 14 16 Primary V apparent magnitude 18 Fig. 2. Simulation of 3σ detection of main-sequence binaries in the BBP, for a 1m magnitude difference between components (left) and 6m (right). The oblique line is a empirical fit, and gives approximately the minimum detectable separation between components as a function of the apparent magnitude of the primary. Pr1-4 5 JOURNAL DE PHYSIQUE IV MASS RATIO DISTRIBUTION WITH GAIA SPECTROSCOPIC BINARIES Thanks to its spectroscopic measurements, GAIA will obtain radial velocity curves up to about magnitude 17. In what follows, we will assume that GAIA will achieve a 2.3 km/s precision per field transit at G = 14. This is slightly lower than what is predicted by [10] for a 0.5Å/pix dispersion spectrum for late-F to early-M stars. From our experience in orbit computation, we assume that an orbit will be obtained for the single–lined spectroscopic binaries (SB1) with p K1 1 − e2 sin i > 5 × 2.3 = 11.5 km/s if this orbit is well covered by the observations (where K1 is the semi-amplitude of the radial velocity, e the eccentricity and i the orbital inclination). In practice, if the primary is G0V, the reflex orbit due to a M0V secondary of period smaller than 1.5 year will be computable; at the transition between brown and red dwarfs (M2 = 0.08), the orbit will be obtained if the period is smaller than 3 days. For double-lined binaries (SB2) with components with nearly equal brightness, the condition above is no more valid since the spectral lines are blended; in practice, the limit in K1 is six times larger than for SB1, giving the condition K1 > 69 km/s. In what follows we will study how GAIA will contribute to the knowledge of the mass-ratio distribution. Many binary studies suffer from biases, since the definition of an unbiased sample is far from obvious. The situation will radically change with GAIA. If we consider solar type stars brighter than 14, the volume from which a complete sample can be extracted is limited by the apparent magnitude, not by the astrometric precision on distance. This limiting distance is about 500 pc for G stars, while it will be 150 pc for K stars, neglecting the interstellar extinction. In order to compute how many stars are included in this volume, one may extrapolate what is known from the solar neighborhood. The Gliese Catalogue contains 10 spectroscopic binaries of period smaller than 4 years, closer than 21.7 pc with declination above −15◦ . Half of these are F7-G, the other being K stars. Thus, for each of these two categories, the density is about 1.85 10−4 SB/pc3 whether we assume a constant volumic density or 0.0054 BS/ pc2 for a constant surfacic density. This would give between 4 240 and 96 900 G-type SB of period less than 4 years within 500 pc, and between 380 and 2 620 K-type SB within 150 pc. For a given mass-ratio q, a small inclination of the orbit implies a smaller K1 . Assuming isotropic orientations of the orbit, half of the inclinations are above 60◦ , so half of our SB sample will have p 11.5 K1 1 − e2 > = 13.3 km/s sin(60◦ ) and the limiting period corresponding to a 50 % detection rate will be 3 212.9 q3 P (0.5) = M1 days 13.3 (1 + q)2 For each limiting period P (0.5), the proportion of binaries with P < P (0.5) in our sample is computed. A constant distribution of log P is assumed, from 3 days until 4 years. We consider a 0.8 M primary, at the transition between G and K, and we assume that q will be directly known for the SB2, when q > 0.7, provided that the radial velocity curves of both components can be obtained. For q < 0.7, the mass-ratio will be obtained in combination with the astrometric orbit, although it could be deduced from the mass function using the iterative method from [11]. The astrometric orbit will have a minimum reflex semi-major axis a1 (D) = P (0.5)days ×13.3×103 /(212.9×Dpc ×365.252/3 ) mas at the limiting distance D = 150 WILL BE SET BY THE PUBLISHER Pr1-5 or 500 pc. Getting an astrometric orbit will easily be obtained with GAIA if a1 > 10σ$ ≈ 0.1 mas. The results are indicated in Table 1. The largest achievable periods, for q near the SB1– SB2 transition, is larger than 1 year. For q > 0.2, there will be enough stars to get a good determination of the mass ratio distribution, provided that the selection effects are corrected (as may be seen from the variations of P (0.5) with q). For mass ratio of the same order of the flux ratio, the astrometry will prove less useful, since the motion of the photocentre will be small. Then, above q > 0.7, the determination of the mass-ratio will effectively depend on the GAIA capability of deconvolving the primary and secondary spectra. Table 1. Half-sample limiting period, proportion of stars and limiting semi-major axis as a function of mass ratio for GAIA spectroscopic binaries. q P (0.5) days prop(P ) % a1 (150pc) mas a1 (500pc) mas 0.1 2.7 0.02 0.006 0.2 18 29 0.15 0.045 0.3 52 46 0.43 0.13 0.4 107 62 0.87 0.26 0.5 182 66 1.49 0.45 0.6 277 73 2.26 0.68 0.7 389 79 3.18 0.95 1.0 3.8 Assuming this will be possible, the mass ratio distribution for q > 0.2 will be obtained using the GAIA spectroscopic capabilities, which will allow to study its variation as a function of spectral type, population, formation place, etc. Now, below q = 0.2, the mass-ratio will hardly be known through astrometry of resolved components, since a magnitude difference between components larger than 10 mag (corresponding to q < 0.1) will hardly be observed. Smaller mass ratios will be obtained with the astrometric binaries, though here an assumption on the mass of the primary will be needed. 6 ECLIPSING BINARIES AND LIGHT-TIME TRAVEL EFFECTS One unexpected result of Hipparcos has been the number of new eclipsing binaries, even bright (7m ) ones, showing that the completeness of eclipsing and contact binaries was not assured. Concerning GAIA, several million eclipsing binary light curves will probably be obtained. The multi-epoch photometry (between 60 to 300 measurements) and the individual precision will be of the order of 0.001 mag at G = 14 to 0.05 mag at G = 20. Combining the G band measurements to the 4 broad bands and the 11 medium bands and to the spectroscopic measurements will allow to obtain masses and radii to better than one per cent for thousands of binaries [10]. The colour and fundamental parameters (luminosity, temperature) will be obtained for total eclipses. Short periods eclipsing binaries are especially of interest for contact binaries, and more generally for interacting binary systems. As the GAIA sample will be unbiased down to faint magnitudes, W UMa-type or Algol-type contact binaries will be common, and their mass distribution, structure, evolution, kinematics and distribution in space will be better known, combining the radial velocity measurements with the astrometric measurements. Another kind of duplicity detection may be done using eclipsing binaries (or other variable stars with stable short-period variations) which host a long period companion. In this case, the reflex motion of this ‘clock in orbit’ can be detected through a light-time travel effect. An Pr1-6 JOURNAL DE PHYSIQUE IV 1 1000 0.1 1 Msun 0.01 10 0.1 Msun 0.001 10-5 0.01 1 10 Mjup 0.0001 Radial velocity (km/s) Light-time (day=173 A.U.) 100 0.1 0.1 1 10 100 Period (yr) Fig. 3. Maximum amplitude for light-time travel (plain, left) and radial velocity (dash, right) as a function of period, for a one solar mass primary, and a secondary of 1, 0.1 and 0.01 solar mass. example of the combination of the Hipparcos astrometric data with the Hipparcos photometric data and ground-based times of minima may be found with R CMa [12]. Compared to the radial velocity method, this method is sensitive to long periods (Figure 3) and returns the same orbital elements (a1 sin i, P, T, e, ω), which would give the full orbital elements when combined with the astrometric data, and the mass of the companion if the primary mass is assumed. The detection would be obtained if an acceleration term is present both in the astrometry and in the light curve, possibly complemented by ground-based light curves. In the GAIA Catalogue, a light-time travel effect could then be tested for a 10 Jupitermass companion of period larger than 11 yr on more than 105 stars [13]. 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Arenou, GAIA-FA-01, Gaia technical report (2001).