The PRIMA Astrometric Planet Search Project

Transcription

1 The PRIMA Astrometric Planet Search Project A. Quirrenbach a, T. Henning b,d.queloz c,s.albrecht a,e.bakker a,h.baumeister b, P. Bizenberger b,h.bleuler f,r.dändliker d,j.dejong a,m.fleury c,s.frink a, D. Gillet e, W. Jaffe a,s.h.hanenburg g,s.hekker a, R. Launhardt b,r.lepoole a,c.maire c,r.mathar a, P. Mullhaupt e,k.murakawa g,f.pepe c,j.pragt g,l.sache f,o.scherler d,d.ségransan c, J. Setiawan b,d.sosnowska c, R. Tubbs a, L. Venema g,k.wagner b, L. Weber c,r.wüthrich f a Leiden University, Sterrewacht Leiden, P.O. Box 9513, NL-2300 RA Leiden, The Netherlands b Max-Planck Institut für Astronomie, Königstuhl 17, D Heidelberg, Germany c ObservatoiredeGenève, 51 Ch. des Maillettes, CH-1290 Sauverny, Switzerland d Institut de Microtechnique, Université deneuchâtel, Rue A.-L. Breguet 2, CH-2000 Neuchâtel, Switzerland e Laboratoire d Automatique, Ecole Politechnique Féderale de Lausanne, Ch. des Machines MEB3, CH-1015 Lausanne, Switzerland f Laboratoire de Systèmes Robotiques, Ecole Politechnique Féderale de Lausanne, Ch. des Machines MEB3, CH-1015 Lausanne, Switzerland g ASTRON, P.O. Box 2, NL-7990AA Dwingeloo, The Netherlands ABSTRACT The PRIMA facility will implement dual-star astrometry at the VLTI. We have formed a consortium that will build the PRIMA differential delay lines, develop an astrometric operation and calibration plan, and deliver astrometric data reduction software. This will enable astrometric planet surveys with a target precision of 10 µas. Our scientific goals include determining orbital inclinations and masses for planets already known from radial-velocity surveys, searches for planets around stars that are not amenable to high-precision radial-velocity observations, and a search for large rocky planets around nearby low-mass stars. Keywords: Optical Interferometry, Astrometry, Delay Lines, Extrasolar Planets, Planet Detection 1. PRIMA: PHASE-REFERENCED IMAGING AND ASTROMETRY AT THE VLTI The PRIMA (Phase-Referenced Imaging and Microarcsecond Astrometry) facility will implement dual-beam interferometry at the European Southern Observatory s Very Large Telescope Interferometer (Quirrenbach et al. 1998, Delplancke et al. 2000). The purpose of PRIMA is threefold: 1. Provide on-axis and off-axis (within the isoplanatic angle) fringe tracking for all VLTI instruments. 2. Conduct precise differential astrometry between stars separated by a few tens of arcseconds. 3. Perform phase-referenced imaging of faint sources with off-axis fringe tracking. The science case for PRIMA has been summarized by Paresce et al. (2003); in this paper we will concentrate on the astrometric detection of extrasolar planets (Quirrenbach 2000). The present infrastructure of the VLTI consists of the four 8.2 m Unit Telescopes of the VLT, six long-stroke delay lines (each one with two ports for dual-star operation), beam relay optics, and two focal plane instruments (MIDI and AMBER). Four moveable 1.8 m Auxiliary Telescopes (ATs) will be added soon; the first AT has already seen first light on Cerro Paranal. The PRIMA hardware consists of four additional major sub-systems: Send correspondence to quirrenb@strw.leidenuniv.nl 424 New Frontiers in Stellar Interferometry, edited by Wesley A. Traub, Proceedings of SPIE Vol (SPIE, Bellingham, WA, 2004) X/04/$15 doi: /

2 Actuator Range Accuracy Frequ. Resp. Main ±35 mm 100 nm 15 Hz Fine ±2 µm 1nm 200 Hz Table 1. Characteristics of the two actuators in the VLTI Differential Delay Lines. 1. Star separator systems (sometimes also called Dual star modules ) that accept the light from two stars within a 2 field and transfer it to the two input ports of the long-stroke delay lines. 2. Differential delay lines (DDLs) that compensate the delay difference of up to a few cm between the two stars. 3. Dedicated fringe detection units for the two stars. 4. An end-to-end metrology system that will monitor the internal differential delay with high precision. The first, third, and fourth items from this list are being produced by various suppliers under contracts with ESO. We have formed a consortium that will produce the differential delay lines, work together with ESO on the analysis of the astrometric error budget and on the development of the observing strategy, and will deliver software tools required to reduce astrometric data. 2. PRIMA DIFFERENTIAL DELAY LINES The Consortium will deliver two pairs of differential delay lines, as required for the operation of a single-baseline dual-star interferometer. We are currently in the detailed design phase. The overall design of the mechanical part of the DDL is shown in Fig. 1. A monolithic cat s eye structure is mounted on top of translation stages that can move the cat s eye mirrors in the longitudinal direction over a distance of 70 mm. Parallel beam sliders with blade spring hinges ensure that a very high accuracy in the lateral directions is maintained. A two-actuator system is chosen; one to provide a long stroke, requiring a very accurate translation mechanism, and one actuator for the high frequency response over small displacements (see Tab. 1). The figure does not show the fine translation stage below the monolithic reflector. The whole system is mounted in a vacuum system to have the differential OPD independent of environmental changes in refraction properties of the air. Each pair of delay lines will have a separate vacuum vessel (l w h = 1000 mm 480 mm 500 mm). A metrology system, based on a He-Ne laser (632 nm), measures the position of the translation stage via the same cat s eye, but along different paths to avoid interfering signals. The resolution of the metrology system is 1 nm. A local control electronics system is responsible for the control of the DDL; it also provides the interface between the DDL and the PRIMA control system. 3. FUNDAMENTAL INSTRUMENTAL REQUIREMENTS The photon noise limit for the precision σ of an astrometric measurement is given by the expression σ = 1 SNR λ 2πB. (1) Since high signal-to-noise ratios can be obtained for bright stars, σ can be orders of magnitude smaller than the resolution λ/b of the interferometer. With an SNR 50, it is thus possible to attain an astrometric error of 10 µas on the longest baselines of the VLTI, comparable to the atmospheric contribution expected for an angular separation of and half-hour integrations (Shao & Colavita 1992, von der Lühe et al. 1995). In principle, only one active differential delay line would be required. For better symmetry and ease of operations, it was decided to build four identical DDLs, however. Proc. of SPIE Vol

3 Figure 1. Overall view of the VLTI Differential Delay Line concept. The fundamental instrumental requirements can be derived directly from the basic expression of the geometric delay (e.g., Quirrenbach 2001), which can be written as D D t D r = B (ŝ t ŝ r ) B s. (2) Here D t and D r denote the delay of the target and reference, respectively, B is the baseline vector, and ŝ t and ŝ r are unit vectors in the directions towards the two stars. The propagation of systematic errors in measurements of the differential delay δ D and of the baseline vector δb to errors in the derived position difference δ s can be estimated from the total differential δ s δ D B + D δ D δb = B2 B + sδb B. (3) This formula allows one to draw two important conclusions. First, the systematic astrometric error is inversely proportional to the baseline length. Together with the B 2/3 scaling of the atmospheric differential delay r.m.s. (Shao & Colavita 1992) this clearly favors longer baselines, up to the limit where the target star gets resolved by the interferometer. The second important conclusion from Eqn. 3 is that the relative error of the baseline measurement gets multiplied with s; this means that the requirement on the knowledge of the baseline vector is sufficiently relaxed to make calibration schemes possible that rely primarily on the stability of the telescope mount. For a 10 µas (50 prad)contribution to the error budget for a measurement over a 20 angle, with an interferometer with a 100 m baseline, the metrology system must measure δ D with a 5 nm precision; the baseline vector has to be known to δb 50 µm (Quirrenbach et al. 1998). For PRIMA it is foreseen that the baseline vector will be determined from repeated observations of stars in the same way that is also customary in radio interferometry (see also Hummel et al. 1994). 4. PRIMA OBSERVING AND DATA REDUCTION STRATEGY Astrometric observations with interferometers are equivalent to measurements of delays, i.e., to measurements of the difference in optical pathlength of light from a star at infinity to the two telescopes forming the interfer- 426 Proc. of SPIE Vol. 5491

4 ometer. For a 200 m baseline, an accuracy goal of 10 µas = 50 prad obviously corresponds to a total allowable error of 10 nm. This stunning accuracy can only be achieved through a triple-differential technique: 1. Two stars with small angular separation are observed simultaneously to reduce the effects of atmospheric turbulence. 2. The optical pathlength within the interferometer is monitored with a laser interferometer. The terms entering the error budgets (e.g., due to small movements of mirrors, or variations of the air pressure in the delay line tunnels) are thus the differential effects of changes within the interferometer on the starlight and metrology beams. 3. The orbits of extrasolar planets are determined from variations of the positions of their parent stars with time, measured with respect to one or several reference stars. It is important to realize that the raw delays have eleven (!) significant digits; astrometric planet detection implies taking differences of large and nearly equal numbers. The implementation of this triple-differential technique therefore requires unusual attention to detail in the understanding and calibration of varied astrophysical, atmospheric, and instrumental effects, in the construction of error budgets, in planning the operations, and in specifying and coding the data reduction software. In particular, the desired accuracy can only be achieved if all systematic sources that can possibly affect the data are understood properly, and removed in a systematic way. While the magnitude of some astrometric errors can be predicted quite reliably (e.g., those related to atmospheric turbulence), others defy simple analysis and may have to be described with parameterized models (e.g., dynamic temperature gradients in the VLTI light ducts). Experience with other forefront astrometric facilities (e.g., the HIPPARCOS spacecraft, the Mark III Interferometer, the automated Carlsberg Meridian Circle) also shows that completely unanticipated systematic effects almost inevitably show up in the actual data. The ability to detect, diagnose, and remove such unanticipated effects is of paramount importance for the success of astrometric programs. It is therefore necessary to perform a careful a priori analysis of the errors relevant for the astrometric mode of PRIMA, and to design and implement systems for a posteriori analysis of remaining trends in the data. As a first step towards a formal astrometric error budget analysis, we have classified the contributions to the error budget and constructed a top-level error tree (Fig. 2). We further need an operations and calibration strategy that will take full advantage of, and optimize use of, the triple-differential technique described above. We will finally need software to perform the initial steps of the data reduction, including carrying out said differences with appropriate corrections, and conversion of delays to angles on the sky. This data reduction software will have to allow inspection of the residuals and enable searches for remaining systematic trends over several years. The latter capability is required because the integrity of the data can only be checked after the triple-differencing process, and because the residuals are dominated by stellar parallax (which has a period of one year) and proper motion (see Fig. 4). 5. ASTROPHYSICAL GOALS OF ASTROMETRIC PLANET SURVEYS The discovery of a planet orbiting the star 51 Pegasi (Mayor & Queloz 1995) has opened a completely new field of astronomy: the study of extrasolar planetary systems. More than 100 planets outside our own Solar System are known to date, and new discoveries are announced almost every month. These developments have revolutionized our view of our own place in the Universe. We know now that other planetary systems can have a structure that is completely different from that of the Solar System. Moreover, the existential question whether other habitable worlds exist can for the first time in human history be addressed in a scientific way. Nearly all known extrasolar planets have been found with an indirect technique, the radial-velocity method. What is actually detected is not the planet itself, but the motion of its parent star around the common center of gravity. The Doppler shift due to the line-of-sight component of this motion can be detected with spectroscopic methods. While radial-velocity surveys have had tremendous successes, it must not be forgotten that they have There are additional complications if the delay lines are not evacuated, see Daigne & Lestrade (1999). Proc. of SPIE Vol

5 Total Astrometric 10 nm (200m Baseline) Astrophysical Atmospheric Instrumental Starspots etc. Persistent Sea- Land Gradient Dispersion Beam Walk Polarization Wobble of Reference Star Anisoplanatism Temperature Gradients Delay Line Alignment Differential Ageing of Coatings Star Color Uncertainty Water Vapor Articulated Gradients Mirrors Seeing Misalignment Solar System Ephemeris Zenith Angle Temperature Variable Curvature Mirror Aberration General- Relativistic Deflection Angular Separation Target - Reference Pressure Humidity Internal Turbulence Non-Common Paths before Metrology Endpoint Metrology Cyclic Metrology Phase Accuracy Laser Absolute Wavelength Laser Stability Corner Cube Quality Fringe Sensing Noise Background Noise Detector Noise FSU Systematic s Photon Noise Stellar Brightness Instrumental Efficiency Visibility Loss due to Anisoplanatism Strehl Loss Baseline VLTI Finite Element Model Baseline Calibration Delay Conditioning of Calibration Matrix Transfer of Wide- Angle to Narrow- Angle Baseline Figure 2. Top-level error tree for the astrometric mode of PRIMA. 428 Proc. of SPIE Vol. 5491

6 Figure 3. Astrometric signature (semi-amplitude) for five sample planets orbiting a Solar-mass star, as a function of distance. Anticipated detection limits for ground-based (PRIMA) and space-based (Space Interferometry Mission) instruments are also shown. technical and astrophysical limitations, which necessarily lead to a biased view of exo-planetary astrophysics. It is therefore important to develop complementary techniques, which can give additional information on the systems already detected, and find planets in situations where the radial-velocity technique cannot be used. The principle of planet detection with astrometry is similar to that behind the Doppler technique: one infers the presence of a planet from the motion of its parent star around the common center of gravity. In the case of astrometry one observes the two components of this motion in the plane of the sky; this gives sufficient information to solve for the orbital elements without sin i ambiguity. Astrometry also has advantages for a number of specific questions, because this method is applicable to all types of stars, and more sensitive to planets with larger orbital semi-major axes. From simple geometry and Kepler s Laws it follows immediately that the astrometric signal θ of a planet with mass m p orbiting a star with mass m at a distance d in a circular orbit of radius a is given by θ = m ( ) 1/3 p a G m d = m p 4π 2 =3µas mp M ( m M m 2/3 P 2/3 d ) 2/3 ( P yr ) 2/3 ( ) 1 d. pc (4) This signature is shown in Fig. 3 for five sample planets (analogues to Earth, Jupiter, Saturn, Uranus, and a Hot Jupiter with m p =1M jup and P = 4 days) orbiting a 1 M star. From this figure, the main strengths and difficulties of astrometric planet detection are readily apparent: The astrometric signature θ is small compared to the precision of traditional astrometric techniques (< 1 mas). The difficulty of detecting different types of planets varies greatly, with θ ranging from < 1 µas to 1 mas. Proc. of SPIE Vol

7 Figure 4. Illustration of parallax and orbital parameters retrieved from a global fit on the astrometric measurements for Gl 876, HD , and HD For this simulation we assumed i =84,Ω=25, and 30 measurements spread over 3 years and evenly distributed over the orbital phase. 430 Proc. of SPIE Vol. 5491

8 The sensitivity of astrometry for a given type of planet drops linearly with d (unlike the radial-velocity technique). The detection bias of astrometry with orbital radius is opposite to that of the radial-velocity method, favoring planets at larger separations from their parent stars. It should be pointed out that for circular orbits the observed astrometric signal is an ellipse with semi-major axis θ independent of the orbital inclination; the mass of the planet can therefore be derived directly from Eqn. 4 if the mass of the parent star is known. The situation is a bit more complicated for non-circular orbits, but even in that case the orbital inclination can be determined from the astrometric data with techniques analogous to those used for fitting orbits of visual binaries (e.g., Binnendijk 1960). The specific strengths of the astrometric method enable it to answer a number of questions that cannot be addressed by any other planet detection method. Among the most prominent goals of astrometric planet surveys are the following projects: Mass determination for planets detected in radial velocity surveys (without the sin i factor). The RV method gives only a lower limit to the mass, because the inclination of the orbit with respect to the line-of-sight remains unknown. Astrometry can resolve this ambiguity, because it measures two components of the orbital motion, from which the inclination can be derived. Confirmation of hints for long-period planets in RV surveys. Many of the stars with detected short-period planets also show long-term trends in the velocity residuals (Fischer et al. 2001). These are indicative of additional long-period planets, whose presence can be confirmed astrometrically. Inventory of planets around stars of all masses. The RV technique works well only for stars with a sufficient number of narrow spectral lines, i.e., fairly old stars with m < 1.2 M. Astrometry can detect planets around more massive stars and complete a census of gas and ice giants around stars of all masses. Detection of gas giants around pre-main-sequence stars, signatures of planet formation. Astrometry can detect giant planets around young stars, and thus probe the time of planet formation and migration. Observations of pre-main-sequence stars of different ages can provide a critical test of the formation mechanism of gas giants. Whereas gas accretion on 10 M cores requires 10 Myr, formation by disk instabilities would proceed rapidly and thus produce an astrometric signature even at very young stellar ages (Boss 1998). Detection of multiple systems with masses decreasing from the inside out. Whereas the astrometric signal increases linearly with the semi-major axis a of the planetary orbit, the RV signal scales with 1/ a. This leads to opposite detection biases for the two methods. Systems in which the masses increase with a (e.g., υ And, Butler et al. 1999) are easily detected by the RV technique because the planets signatures are of similar amplitudes. Conversely, systems with masses decreasing with a are more easily detected astrometrically. Determine whether multiple systems are coplanar or not. Many of the known extrasolar planets have highly eccentric orbits. A plausible origin of these eccentricities is strong gravitational interaction between two or several massive planets (Lin & Ida 1997, Papaloizou & Terquem 2001). This could also lead to orbits that are not aligned with the equatorial plane of the star, and to non-coplanar orbits in multiple systems. Search for massive terrestrial planets orbiting low-mass stars in the Solar neighborhood. With a 10 µas precision goal, PRIMA at the VLTI will be able to look for rocky planets down to a limit of a few Earth masses around nearby M stars. In summary, astrometry is a unique tool for dynamical studies of extrasolar planetary systems; its capabilities to determine masses and orbits are not matched by any other technique. Astrometric surveys of young and old planetary systems will therefore give unparalleled insight into the mechanisms of planet formation, orbital migration and evolution, orbital resonances, and interaction between planets. We intend to carry out the first such program with PRIMA at the VLTI, and thus pave the way towards future more precise astrometric surveys from space. Proc. of SPIE Vol

9 REFERENCES 1. Binnendijk L. (1960). Properties of double stars. Philadelphia: University of Pennsylvania Press. 2. Boss, A.P. (1998). Astrometric signatures of giant-planet formation. Nature 393, Butler, R.P., Marcy, G.W., Fischer, D.A., Brown, T.M., Contos, A.R., et al. (1999). Evidence for multiple companions to υ Andromedae. Astrophys. J. 526, Daigne, G., & Lestrade, J.F. (1999). Astrometric optical interferometry with non-evacuated delay lines. Astron. Astrophys. Suppl. Ser. 138, Delplancke, F., Leveque, S.A., Kervella, P., Glindemann, A., & D Arcio, L. (2000). Phase-referenced imaging and micro-arcsecond astrometry with the VLTI. In Interferometry in Optical Astronomy. Ed. Quirrenbach, A., & Léna, P., SPIE Vol. 4006, pp Fischer, D.A., Marcy, G.W., Butler, R.P., Vogt, S.S., Frink, S., & Apps, K. (2001). Planetary companions to HD 12661, HD 92788, and HD and variations in Keplerian residuals of extrasolar planets. Astrophys. J. 551, Hummel, C.A., Mozurkewich, D., Elias, N.M., Quirrenbach, A., Buscher, D.F., Armstrong, J.T., Johnston, K.J., Simon, R.S., & Hutter, D.J. (1994). Four years of astrometric measurements with the Mark III optical interferometer. Astron. J. 108, Lin, D.N.C., & Ida, S. (1997). On the origin of massive eccentric planets. Astrophys. J. 477, Mayor, M., & Queloz, D. (1995). A Jupiter-mass companion to a Solar-type star. Nature 378, Papaloizou, J.C.B., & Terquem, C. (2001). Dynamical relaxation and massive extrasolar planets. Mon. Not. Royal Astron. Soc. 325, Paresce, F., Delplancke, F., Derie, F., Glindemann, A., Richichi, A., & Tarenghi, M. (2003). Scientific objectives of ESO s PRIMA facility. In Interferometry for optical astronomy II. Ed. Traub, W.A., SPIE, Vol. 4838, pp Quirrenbach, A. (2000). Astrometry with the VLT Interferometer. In From extrasolar planets to cosmology: the VLT opening symposium. Ed. Bergeron, J., & Renzini, A., pp Quirrenbach, A. (2001). Optical Interferometry. Ann. Rev. Astron. Astrophys. 39, Quirrenbach, A., Coudé du Foresto, V., Daigne, G., Hofmann, K.-H., Hofmann, R., et al. (1998). PRIMA study for a dual-beam instrument for the VLT Interferometer. In Astronomical interferometry. Ed. Reasenberg, R.D., SPIE Vol. 3350, pp Shao, M., & Colavita, M.M. (1992). Potential of long-baseline interferometry for narrow-angle astrometry. Astron. Astrophys. 262, von der Lühe, O., Quirrenbach, A., & Koehler, B. (1995). Narrow-angle astrometry with the VLT Interferometer. In Science with the VLT. Ed. Walsh, J.R., & Danziger, I.J., pp Proc. of SPIE Vol. 5491