ESPRI homepage at MPIA

Detecting exoplanets with PRIMA

The goal of ESPRI is to detect the presence of extra-solar planets using astrometric measurements performed at the VLTI near-infrared interferometer. As exoplanets orbit their parent star, they cause the star to perform a reflex motion (caused by the gravitational pull of the planet on the star). This causes the position of the host star to oscillate with each orbital period of the planet. Figure 1 is a schematic image showing the reflex motion (red circle) of a star produced by the circular orbit of a planet (following blue circle). Both objects orbit the centre of mass of the system (at the centre of Figure 1). A movie showing this motion can be seen by clicking here. ESPRI will make very accurate measurements of the motion of exoplanet host candidates with respect to background stars located at a small distance on the sky, thus allowing planets to be detected.

Figure 1 — reflex motion of a star as a planet orbits it. Click here to see a movie.

Astrometric measurements with an interferometer

High-precision measurements of a star's position are required in order to measure the reflex motion due to a planet. At optical wavelengths, the angular resolution of astrometric measurements is usually limited by one of two factors:

the diameter of the telescope used; or
for the case of large ground-based telescopes, the blurring effects of the Earth's atmosphere.

The first of these limits comes from optical diffraction effects at the telescope aperture. The second of these limits can only be overcome if the perturbing effects of the atmosphere are recorded at high speed, and these effects are then compensated for (using e.g. speckle imaging, adaptive optics or interferometry with fast-frame-rate detectors).

The technique ESPRI will be using to obtain high-resolution information is optical interferometry. This method involves the combination of light from a star observed through separated telescopes and combined to produce interference fringes. These fringes are bands of light caused by optical interference, like those seen in a Young's double-slit experiment (Figure 1).

In an astronomical interferometer, the light source is the star which is being observed. Instead of using a mask with two holes followed by a large lens (as in Figure 2), two telescopes are positioned on the ground some distance apart, and the light from these telescopes is redirected to a central location using mirrors (see Figure 3). A telescope array such as this can record high-resolution information about a source without requiring the large (expensive) lens used in Figure 2.

By combining light from different telescopes and using them as an optical interferometer array, information can be obtained about much higher-resolution structure than could be observed using one of the individual telescopes which make up the array. The resolution of observations can be increased by positioning the telescopes a long way from each other — the resolution is similar to that of a diffraction-limited space telescope with a diameter equal to the maximum separation of the telescopes in the array. This is the principle of performing optical observations with higher angular resolution than given by the diffraction limit of the individual telescopes.

Figure 2 — Young's double-slit experiment. Light from a small source (in this case the illuminated hole Q) is passed through two holes in a cardboard mask. A lens is then used to produce a focused image of the original light source. Optical interference effects convert the image of the point source into a fringe pattern (at point P). By taking photographs of the fringe pattern with a range of different positions for the holes in the mask and processing these images, an image of the original light source (Q, the illuminated hole) can be produced.

Interferometers combine the starlight collected at two or more different telescopes in order to gather high-resolution information about the star. One parameter that can be measured very precisely is the position of the star — this type of measurements is called astrometry. The angle of the incoming wavefronts from a star is determined geometrically from the telescope separation and the value of OPD_extern, as shown in Figure 3. Constructive interference only occurs at all optical wavelengths when OPD_extern is precisely matched by OPD_intern, which is the optical path introduced by a delay line in the optical laboratory. By monitoring the position of the delay line and measuring the amount of constructive interference, it is possible to accurately calculate the angle of the star from the baseline meridian. An animation showing how OPD_extern and OPD_intern vary with varying can be viewed by clicking here.

Figure 3 — If a star is at an angle from the baseline vector, additional optical path is introduced (OPD_extern) equal to cos() times the telescope separation. Constructive interference is found when the optical paths are equal, something which only occurs when OPD_intern=OPD_extern. This allows OPD_extern (and hence ) to be determined experimentally. Click here for an animation showing how the paths change if the angle of the star changes.

Atmospheric turbulence and temperature fluctuations corrupt the phase of the starlight as it passes through the Earth's atmosphere. This normally prevents us from measuring the position of stars with very high accuracy. However, if two stars are located close to each other on the night sky, then the light from the two stars will travel through essentially the same part of the atmosphere, as shown in Figure 3. In this case, the Earth's atmosphere has almost the same effect on the light from the two stars, allowing the relative positions (angular separation) of the two stars to be measured with very high accuracy.

The ESPRI project will use this technique to measure the motion of a target star relative to a reference star. The reference star must be located within one isoplanatic angle from the target star — stars within that angular distance are close enough on the sky that the Earth's atmosphere affects the incoming starlight in the same way.

This will allow the reflex motion of a star (caused by a planet orbiting it) to be detected. We will compare the positions of nearby stars which are likely to host extra-solar planets with other stars (reference stars) which lie within the isoplanatic angle on the night sky. Typically the reference stars are so much further from Earth that any planetary signal detected in this way must come from the nearby target star. Further details of the target and reference star selection can be found in the Science section of this website.

Figure 4 — Schematic showing off-axis observations through Earth's atmosphere when two turbulent layers are present. The reference star is at an angle from the target star, and the light from the reference star passes through the turbulent layers at a position which is offset by an amount (indicated by x₁ and x₂ in the figure) proportional to the height of the layer above the telescope and the angular separation of the stars.