Astrometric Signal Research Articles

Diffractive microlensing - III. Astrometric signatures

Gravitational lensing is generally treated in the geometric optics limit; however, when the wavelength of the radiation approaches or exceeds the Schwarzschild radius of the lens, diffraction becomes important. Although the magnification generated by diffractive gravitational lensing is well understood, the astrometric signatures of diffractive microlensing are first derived in this paper along with a simple closed-form bound for the astrometric shift. This simple bound yields the maximal shifts for substellar lenses in solar neighbourhood observed at 20 GHz, accessible to high sensitivity, high angular resolution radio telescopes such as the proposed Square Kilometre Array (SKA).

Detectability of Earth mass planets with RV techniques around Sun-like stars. The example of the Sun

AbstractWe present the results of detailed simulations of the RV and astrometric signals expected from the Sun, when taking into account its activity (spots, plages, convection). To do so, we considered all structures (2,000,000) identified on the Sun surface over a full cycle. We show that the Sun activity would prevent the detection of the Earth in the Habitable Zone with RV technics with today or future forthcoming instruments, mainly because of inhomogeneous convection. We also show that the activity-induced signal would be comparatively easier for the astrometric detection of the Earth of similar planets.

Finite-source and finite-lens effects in astrometric microlensing

The aim of this paper is to study the astrometric trajectory of microlensing events with an extended lens and/or source. We consider not only a dark lens but also a luminous lens as well. We find that the discontinuous finite-lens trajectories given by Takahashi (2003) will become continuous in the finite-source regime. The point lens (source) approximation alone gives an under (over)estimation of the astrometric signal when the size of the lens and source are not negligible. While the finiteness of the source is revealed when the lens transits the surface of the source, the finite-lens signal is most prominent when the lens is very close to the source. Astrometric microlensing towards the Galactic bulge, Small Magellanic Cloud and M31 are discussed, which indicate that the finite-lens effect is beyond the detection limit of current instruments. Nevertheless, it is possible to distinguish between self-lensing and halo lensing through a (non-)detection of the astrometric ellipse. We also consider the case where the lens is luminous itself, as has been observed where a lensing event was followed up with the Hubble Space Telescope. We show that the astrometric signal will be reduced in a luminous-lens scenario. The physical properties of the event, such as the lens-source flux ratio, the size of the lens and source nevertheless can be derived by fitting the astrometric trajectory.

Astrometric signal profile fitting for Gaia

A tool for representation of the one-dimensional astrometric signal of Gaia is described and investigated in terms of fit discrepancy and astrometric performance with respect to number of parameters required. The proposed basis function is based on the aberration free response of the ideal telescope and its derivatives, weighted by the source spectral distribution. The influence of relative position of the detector pixel array with respect to the optical image is analysed, as well as the variation induced by the source spectral emission. The number of parameters required for micro-arcsec level consistency of the reconstructed function with the detected signal is found to be 11. Some considerations are devoted to the issue of calibration of the instrument response representation, taking into account the relevant aspects of source spectrum and focal plane sampling. Additional investigations and other applications are also suggested.

Ground based astrometric search for extrasolar planets in stellar multiple systems

Using relative astrometry and ground based imaging, we study nearby stellar multiple systems in order to detect the astrometric signal of exoplanets around one of the stellar components. We suppress differential chromatic refraction effects by observing in the near infrared with a narrow-band filter and by choosing an iterative calibration strategy (using a stellar cluster) we obtain a precision down to 100 μ as in our relative astrometric measurements. This allows us to study the occurence and properties of exoplanets in nearby (less than 100 pc) stellar multiple systems. While trying to detect the astrometric signal of the exoplanet orbiting HD19994 A (Mayor et al. 2004), we detected the astrometric signal of a further object around the B component. This astrometric detection is confirmed by speckle interferometry and follow-up radial velocity (RV) observations. Thus, HD19994 is an exoplanet host-triple system.

Hipparcos preliminary astrometric masses for the two close-in companions to HD 131664 and HD 43848

[abridged] We attempt to improve on the characterization of the properties (orbital elements, masses) of two Doppler-detected sub-stellar companions to the nearby G dwarfs HD 131664 and HD 43848. We carry out orbital fits to the Hipparcos IAD for the two stars, taking advantage of the knowledge of the spectroscopic orbits, and solving for the two orbital elements that can be determined in principle solely by astrometry, the inclination angle $i$ and the longitude of the ascending node $\Omega$. A number of checks are carried out in order to assess the reliability of the orbital solutions thus obtained. The best-fit solution for HD 131664 yields $i=55\pm33$ deg and $\Omega=22\pm28$ deg. The resulting inferred true companion mass is then $M_c = 23_{-5}^{+26}$ $M_J$. For \object{HD 43848}, we find $i=12\pm7$ deg and $\Omega=288\pm22$ deg, and $M_c = 120_{-43}^{+167}$ $M_J$. Based on the statistical evidence from an $F$-test, the study of the joint confidence intervals of variation of $i$ and $\Omega$, and the comparison of the derived orbital semi-major axes with a distribution of false astrometric orbits obtained for single stars observed by Hipparcos, the astrometric signal of the two companions to HD 131664 and HD 43848 is then considered detected in the Hipparcos IAD, with a level of statistical confidence not exceeding 95%. We constrain the true mass of HD 131664b to that of a brown dwarf to within a somewhat statistically significant degree of confidence ($\sim2-\sigma$). For HD 43848b, a true mass in the brown dwarf regime is ruled out at the $1-\sigma$ confidence level. [abridged]

The Carnegie Astrometric Planet Search Program

ABSTRACTWe are undertaking an astrometric search for gas giant planets and brown dwarfs orbiting nearby low-mass dwarf stars with the 2.5 m du Pont Telescope at the Las Campanas Observatory in Chile. We have built two specialized astrometric cameras, the Carnegie Astrometric Planet Search Cameras (CAPSCam-S and CAPSCam-N), using two Teledyne HAWAII-2RG HyViSI arrays, with the cameras’ design having been optimized for high-accuracy astrometry of M dwarf stars. We describe two independent CAPSCam data reduction approaches and present a detailed analysis of the observations to date of one of our target stars, NLTT 48256. Observations of NLTT 48256 taken since 2007 July with CAPSCam-S imply that astrometric accuracies of around 0.3 mas hr-1 are achievable, sufficient to detect a Jupiter-mass companion orbiting 1 AU from a late M dwarf 10 pc away with a signal-to-noise ratio (S/N) of about 4. We plan to follow about 100 nearby (primarily within about 10 pc) low-mass stars, principally late M, L, and T dwarfs, for 10 yr or more, in order to detect very low-mass companions with orbital periods long enough to permit the existence of habitable, Earth-like planets on shorter-period orbits. These stars are generally too faint and red to be included in ground-based Doppler planet surveys, which are often optimized for FGK dwarfs. The smaller masses of late M dwarfs also yield correspondingly larger astrometric signals for a given mass planet. Our search will help to determine whether gas giant planets form primarily by core accretion or by disk instability around late M dwarf stars.

Gamma Astrometric Measurement Experiment (GAME) – Implementation and performance

The GAME mission concept is aimed at testing the General Relativity, through precise measurement of the gravitational deflection of light by the Sun, by means of an optimised telescope operating in the visible and launched in orbit on a small class satellite. We describe the proposed mission profile, the preliminary payload design and the expected performance. The targeted precision on the γ parameter of the PPN formulation of General Relativity is in the range 10 −6 to 10 −7. The measurement principle relies on the differential astrometric signature on the stellar positions. The instrument concept is based on a dual field, multiple aperture Fizeau interferometer, observing simultaneously two sky regions close to the solar limb. A beam combiner folds the telescope line of sight on two different directions on the sky, separated by a base angle of 4°. The diluted optics approach achieves an efficient rejection of the scattered solar radiation, while retaining an acceptable angular resolution on the science targets.

Perspective acceleration and gravitational redshift. Measuring masses of individual white dwarfs using Gaia + SIM astrometry

AbstractAccording to current plans, the SIM/NASA mission will be launched just after the end of operations for the Gaia/ESA mission. This is a new situation which enables long term astrometric projects that could not be achieved by either mission alone. Using the well-known perspective acceleration effect on astrometric measurements, the true heliocentric radial velocity of a nearby star can be measured with great precision if the time baseline of the astrometric measurements is long enough. Since white dwarfs are compact objects, the gravitational redshift can be quite large (40–80 km/s), and is the predominant source of any shift in wavelength. The mismatch of the true radial velocity with the spectroscopic shift thus leads to a direct measure of the Mass–Radius relation for such objects. Using available catalog information about the known nearby white dwarfs, we estimate how many masses/gravitational redshift measurements can be obtained with an accuracy better than 2%. Nearby white dwarfs are relatively faint objects (10 < V < 15), which can be easily observed by both missions. We also briefly discuss how the presence of a long period planet can mask the astrometric signal of perspective acceleration.

PRECISION ASTROMETRY WITH ADAPTIVE OPTICS

We investigate the limits of ground-based astrometry with adaptive optics using the core of the Galactic globular cluster M5. Adaptive optics systems provide near diffraction-limit imaging with the world's largest telescopes. The substantial improvement in both resolution and signal-to-noise ratio enables high-precision astrometry from the ground. We describe the dominant systematic errors that typically limit ground-based differential astrometry, and enumerate observational considerations for mitigating their effects. After implementing these measures, we find that the dominant limitation on astrometric performance in this experiment is caused by tilt anisoplanatism. We then present an optimal estimation technique for measuring the position of one star relative to a grid of reference stars in the face of this correlated random noise source. Our methodology has the advantage of reducing the astrometric errors to and faster than the square root of the number of reference stars, effectively eliminating noise caused by atmospheric tilt to the point that astrometric performance is limited by centering accuracy. Using 50 reference stars, we demonstrate a single-epoch astrometric precision of ≈1 mas in 1 s, decreasing to 100 μas in 2 minutes of integration time at the Hale 200 inch telescope. We also show that our astrometry is accurate to 100 μas for observations separated by 2 months. Finally, we discuss the limits and potential of differential astrometry with current and next-generation large-aperture telescopes. At this level of accuracy, numerous astrometric applications become accessible, including planet detection, astrometric microlensing signatures, and kinematics of distant Galactic stellar populations.

Sub-milliarcsecond precision spectro-astrometry of Be stars

The origin of the disks around Be stars is still not known. Further progress requires a proper parametrization of their structure, both spatially and kinematically. This is challenging as the disks are very small. Here we assess whether a novel method is capable of providing these data. We obtained spectro astrometry around the Pa beta line of two bright Be stars, alpha Col and zeta Tau, to search for disk signatures. The data, with a pixel to pixel precision of the centroid position of 0.3..0.4 milliarcsecond is the most accurate such data to date. Artefacts at the 0.85 mas level are present in the data, but these are readily identified as they were non-repeatable in our redundant datasets. This does illustrate the need of taking multiple data to avoid spurious detections. The data are compared with simple model simulations of the spectro astrometric signatures due to rotating disks around Be stars. The upper limits we find for the disk radii correspond to disk sizes of a few dozen stellar radii if they rotate Keplerian. This is very close to observationally measured and theoretically expected disk sizes, and this paper therefore demonstrates that spectro-astrometry, of which we present the first such attempt, has the potential to resolve the disks around Be stars.

Double-blind test program for astrometric planet detection with Gaia

We use detailed simulations of the Gaia observations of synthetic planetary systems and develop and utilize independent software codes in double-blind mode to analyze the data, including statistical tools for planet detection and different algorithms for single and multiple Keplerian orbit fitting that use no a priori knowledge of the true orbital parameters of the systems. 1) Planets with astrometric signatures $\alpha\simeq 3$ times the single-measurement error $\sigma_\psi$ and period $P\leq 5$ yr can be detected reliably, with a very small number of false positives. 2) At twice the detection limit, uncertainties in orbital parameters and masses are typically $15%-20%$. 3) Over 70% of two-planet systems with well-separated periods in the range $0.2\leq P\leq 9$ yr, $2\leq\alpha/\sigma_\psi\leq 50$, and eccentricity $e\leq 0.6$ are correctly identified. 4) Favorable orbital configurations have orbital elements measured to better than 10% accuracy $> 90%$ of the time, and the value of the mutual inclination angle determined with uncertainties $\leq 10^{\degr}$. 5) Finally, uncertainties obtained from the fitting procedures are a good estimate of the actual errors. Extrapolating from the present-day statistical properties of the exoplanet sample, the results imply that a Gaia with $\sigma_\psi$ = 8 $\mu$as, in its unbiased and complete magnitude-limited census of planetary systems, will measure several thousand giant planets out to 3-4 AUs from stars within 200 pc, and will characterize hundreds of multiple-planet systems, including meaningful coplanarity tests. Finally, we put Gaia into context, identifying several areas of planetary-system science in which Gaia can be expected to have a relevant impact, when combined with data coming from other ongoing and future planet search programs.

Micro-arcsecond relative astrometry by ground-based and single-aperture observations

AbstractWe present an observation method to obtain a relative astrometric precision of about 100 . . . 150 μas with ground-based and single-aperture observations. By measuring the separation of double or triple stars we want to determine the astrometric signal of an unseen substellar companion as a periodic change in the separation between the stellar components. Using an adaptive optics system we correct for atmospheric turbulences and furthermore by using a narrow band filter in the near infrared we can suppress differential chromatic refraction effects. To reach a high precision we use a statistical approach. Using the new observation mode “cube-mode” (where the frames were directly saved in cubes with nearly no loss of time during the readout), we obtain several thousand frames within half an hour. After the verification of the Gaussian distributed behaviour of our measurements (done with a Kolmogorov-Smirnov-Test) the measurement precision can be calculated as the standard deviation of our measurements divided by the square root of the number of frames.To monitor the stability of the pixel scale between our observations, we use the old globular cluster 47 Tuc as a calibration system.

Search for extrasolar planets with high-precision relative astrometry by ground-based and single-aperture observations

AbstractWe present our search program for substellar companions using high-precision relative astronomy. Due to its orbital motion around the star, an unseen substellar companion would produce a periodic “wobble” of the host star, which is the astrometric signal of the unseen companion. By measuring the separation between the components of stellar double and triple systems, we want to measure this astrometric signal of a possible unseen companion indirectly as a relative and periodic change of these separations. Using a new observation mode (the “cube-mode”) where the frames were directly saved in cubes with nearly no loss of time during the readout, an adaptive optics system to correct for atmospheric noise and an infrared narrow band filter in the near infrared to suppress differential chromatic refraction (DCR) effects we achieve for our first target (the double star HD 19994) a relative precision for the separation measurements of about 100. . . 150μas per epoch. To reach a precision in the μas-regime, we use a statistical approach. We take several thousand frames per target and epoche and after a verification of a Gaussian distribution the measurement precision can be calculated as the standard deviation of our measurements divided by the square root of the number of Gaussian distributed measurements. Our first observed target is the stellar binary HD 19994 A & B, where the A component has a known radial velocity planet candidate.

White-light interferometry using a channeled spectrum I General models and fringe estimation algorithms

Astrometric measurements using stellar interferometry rely on the precise measurement of the central white-light fringe to accurately obtain the optical path-length difference of incoming starlight to the two arms of the interferometer. Because of dispersion in the optical system the optical path-length difference is a function of the wavelength of the light and extracting the proper astrometric signatures requires accommodating these effects. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the path-length delay. Because of throughput considerations these channels are made sufficiently broad so that monochromatic models are inadequate for retrieving the phase/delay information. The presence of dispersion makes the polychromatic modeling problem for phase estimation even more difficult because of its effect on the complex visibility function. We introduce a class of models that rely on just a few spectral and dispersion parameters. A phase-shifting interferometry algorithm is derived that exploits the model structure. Numerical examples are given to illustrate the robustness and precision of the approach.

Detectability of Planets in Wide Binaries by Ground-Based Relative Astrometry with AO

AbstractMany planet candidates have been detected by radial-velocity variations of the primary star; they are planet candidates, because of the unknown orbit inclination. Detection of the wobble in the two other dimensions, to be measured by astrometry, would yield the inclination and, hence, true mass of the companions. We aim to show that planets can be confirmed or discovered in a close visual stellar binary system by measuring the astrometric wobble of the exoplanet host star as a periodic variation of the separation, even from the ground. We test the feasibility with HD 19994, a visual binary with one radial velocity planet candidate. We use the adaptive optics camera NACO at the VLT with its smallest pixel scale (∼ 13 mas) for high-precision astrometric measurements. The separations measured in 120 single images taken within one night are shown to follow white noise, so that the standard deviation can be divided by the square root of the number of images to obtain the precision. In this paper we present the first results and investigate the achievable precision in relative astrometry with adaptive optics. With careful data reduction it is possible to achieve a relative astrometric precision as low as 50 μ as for a 0″.6 binary with VLT/NACO observations in one hour, the best relative astrometric precision ever achieved with a single telescope from the ground. The relative astrometric precision demonstrated here with AO at an 8-m mirror is sufficient to detect the astrometric signal of the planet HD 19994 Ab as periodic variation of the separation between HD 19994 A and B.

Astrometric light-travel time signature of sources in nonlinear motion

Context. Very precise planned space astrometric missions and recent improvements in imaging capabilities require a detailed review of the assumptions of classical astrometric modeling. Aims. We show that Light-Travel Time must be taken into account in modeling the kinematics of astronomical objects in nonlinear motion, even at stellar distances. Methods. A closed expression to include Light-Travel Time in the current astrometric models with nonlinear motion is provided. Using a perturbative approach the expression of the Light-Travel Time signature is derived. We propose a practical form of the astrometric modelling to be applied in astrometric data reduction of sources at stellar distances(d > 1 pc). Results. We show that the Light-Travel Time signature is relevant at pas accuracy (or even at mas) depending on the time span of the astrometric measurements. We explain how information on the radial motion of a source can be obtained. Some estimates are provided for known nearby binary systems Conclusions. Given the obtained results, it is clear that this effect must be taken into account in interpreting precise astrometric measurements. The effect is particularly relevant in measurements performed by the planned astrometric space missions (GAIA, SIM, JASMINE, TPF/DARWIN). An objective criterion is provided to quickly evaluate whether the Light-Travel Time modeling is required for a given source or system.

Hipparcos astrometric orbits for two brown dwarf companions: HD 38529 and HD 168443

Context.HD 38529 and HD 168443 have previously been identified as systems with two substellar companion candidates using precise radial velocity measurements.Aims.We want to further constrain their orbits and the nature of the outer companions.Methods.We fit astrometric orbits of the outer substellar companions in the two systems to the Hipparcos Intermediate Astrometric Data.Results.The fit constrains all possible solutions to a small region in the parameter space of the two missing orbital parameters (inclination i and ascending node Ω). This can be interpreted as a possible real detection of the astrometric signatures of the companions in the Hipparcos data, although there is still a 14–18% chance that the signal is not detectable in the data, according to an F-test. However, even in the case of a non-detection of the companion signal in the astrometric data, the knowledge of the spectroscopic orbital parameters enables us to place tight constraints on these two missing parameters, so that the astrometric orbit is fully determined (with confidence levels of around 80% for HD 38529, 95% for HD 168443). Inclinations derived from these astrometric fits enable us to calculate masses for the substellar companions rather than lower or upper limits. The best fit solution for HD 38529, (i, Ω) = (160°, 52°), yields a mass of 37 MJup for the outer companion. For HD 168443, we derive best fit parameters of (i, Ω) = (150°, 19°), which imply a companion mass of MJup.Conclusions.The outer companions in both systems are thus brown dwarfs.

The Astrometric-Spectroscopic Binary System HIP 50796: An Overmassive Companion

We report spectroscopic observations of the star HIP 50796, previously considered (but later rejected) as a candidate member of the TW Hya association. Our measurements reveal it to be a single-lined binary with an orbital period of 570 days and an eccentricity of e = 0.61. The astrometric signature of this orbit was previously detected by Hipparcos in the form of curvature in the proper-motion components, although the period was unknown at the time. By combining our radial velocity measurements with the Hipparcos intermediate data (abscissa residuals) we are able to derive the full three-dimensional orbit and determine the dynamical mass of the unseen companion, as well as a revised trigonometric parallax that accounts for the orbital motion. Given our primary mass estimate of 0.73 M⊙ (mid-K dwarf), the companion mass is determined to be 0.89 M⊙, or ~20% larger than the primary. The likely explanation for the larger mass without any apparent contribution to the light is that the companion is itself a closer binary composed of M dwarfs. The near-infrared excess and X-ray emission displayed by HIP 50796 support this. Our photometric modeling of the excess leads to a lower limit to the mass ratio of the close binary of q ~ 0.8 and individual masses of 0.44-0.48 and 0.41-0.44 M⊙. The new parallax (π = 20.6 ± 1.9 mas) is significantly smaller than the original Hipparcos value and more precise.

Narrow‐Angle Astrometry with the Space Interferometry Mission: The Search for Extrasolar Planets. II. Detection and Characterization of Planetary Systems

ABSTRACTWe utilize (1) detailed end‐to‐end numerical simulations of sample narrow‐angle astrometric observing campaigns with the Space Interferometry Mission (SIM) and the subsequent data analysis process and (2) the set of extrasolar planetary systems discovered so far by radial velocity surveys as templates to provide meaningful estimates of the limiting capabilities of SIM for the detection and measurement of multiple‐planet systems around solar‐type stars in the solar neighborhood.We employ standard χ2 statistics, periodograms, and Fourier analysis to evaluate SIM’s ability to detect multiple planetary signatures; the probability of detecting additional companions is essentially unchanged from the single‐planet configurations, but after fitting and subtraction of orbits with astrometric signal‐to‐noise ratio α/σd→1, the false detection rates can be enhanced by up to a factor of 2. The periodogram approach results in robust multiple‐planet detection for systems with periods shorter than the SIM mission length, even at low values of α/σd, while the least‐squares technique combined with Fourier series expansions is arguably preferable in the long‐period regime. We explore the three‐dimensional parameter space defined by astrometric signature, orbital period, and eccentricity to derive general conclusions on the capability of SIM to accurately measure the full set of orbital parameters and masses for a variety of configurations of planetary systems; the accuracy of multiple‐planet orbit reconstruction and mass determination suffers a typical degradation of 30%–40% from single‐planet solutions; mass and orbital inclination can be measured to better than 10% for periods as short as 0.1 yr and for α/σd as low as ∼ 5, while α/σd ≃100 is required in order to measure with similar accuracy systems harboring objects with periods as long as 3 times the mission duration. We gauge the potential of SIM for meaningful coplanarity measurements via determination of the true geometry of multiple‐planet orbits. For systems with all components producing α/σd ≃10 or greater, quasi‐coplanarity can be reliably established with uncertainties of a few degrees, for periods in the range 0.1 yr≤T≤15 yr; in systems where at least one component has α/σd→1, coplanarity measurements are compromised, with typical uncertainties on the mutual inclinations on the order of 30°–40°. We quantify the improvement derived in full‐orbit reconstruction and planet mass determination by constraining the multiple‐planet orbital fits to SIM observations with the nominal orbital elements obtained from the radial velocity measurements; the uncertainties on orbital elements and masses can be reduced by up to an order of magnitude, especially for long‐period orbits in face‐on configurations and for low‐amplitude orbits seen edge‐on.Our findings are illustrative of the importance of the contribution SIM will make, complementing other on‐going and planned spectroscopic, astrometric, and photometric surveys, in order to fulfill the expectations for ground‐breaking science in the fields of formation and evolution of planetary systems during the next decade.