Probing exoplanetary materials using sublimating dust

Planetary systems consist of more than just planets orbiting a central star. They also include a wide range of smaller bodies, such as asteroids, comets, and interplanetary dust grains. All these materials can be investigated to increase our understanding of planetary systems. In the study of extrasolar systems, the dust component can be particularly useful, because it constitutes a relatively large cross-section, making it observationally accessible to modern telescopes. To correctly make the step from dust observations to inferring properties of an exoplanetary system, one must understand in detail how dust grains are produced, how they behave after being released, and how they are destroyed or removed. Understanding the physics of circumstellar dust is the subject of my thesis work. The thesis focusses specifically on dust grains orbiting extremely close to their host star, at only a few stellar radii, where temperatures can be reached that are sufficient to sublimate rocks. I studied two astrophysical problems in which dust sublimation is relevant. (1) Hot exozodiacal dust. This is dust located in the close vicinity of a star that can be detected through near-infrared interferometry. Some 10% to 30% of all stars seem to have such a population of dust, but its origin is still unclear. I tested possible mechanisms that could explain the phenomenon, and made an in-depth study of the inner parts of the Fomalhaut system. (2) Dusty tails of evaporating exoplanets. I demonstrated how the composition of dust released by an evaporating rocky exoplanet, which trails the planet in a comet-like tail, can be inferred from detailed shape of the transit light curve produced by these objects

Near-infrared emission from sublimating dust in collisionally active debris disks

Hot exozodiacal dust is thought to be responsible for excess near-infrared (NIR) emission emanating from the innermost parts of some debris disks. The origin of this dust, however, is still a matter of debate. We test whether hot exozodiacal dust can be supplied from an exterior parent belt by Poynting-Robertson (P-R) drag, paying special attention to the pile-up of dust that occurs due to the interplay of P-R drag and dust sublimation. Specifically, we investigate whether pile-ups still occur when collisions are taken into account, and if they can explain the observed NIR excess. We compute the steady-state distribution of dust in the inner disk by solving the continuity equation. First, we derive an analytical solution under a number of simplifying assumptions. Second, we develop a numerical debris disk model that for the first time treats the complex interaction of collisions, P-R drag, and sublimation in a self-consistent way. From the resulting dust distributions we generate thermal emission spectra and compare these to observed excess NIR fluxes. We confirm that P-R drag always supplies a small amount of dust to the sublimation zone, but find that a fully consistent treatment yields a maximum amount of dust that is about 7 times lower than that given by analytical estimates. The NIR excess due this material is much smaller (<10^-3 for A-type stars with parent belts at >1 AU) than the values derived from interferometric observations (~10^-2). Pile-up of dust still occurs when collisions are considered, but its effect on the NIR flux is insignificant. Finally, the cross-section in the innermost regions is clearly dominated by barely bound grains.Comment: 18 pages, 10 figures, A&A accepte

Chromatic transit light curves of disintegrating rocky planets

Context. Kepler observations have revealed a class of short period exoplanets, of which Kepler-1520 b is the prototype, which have comet-like dust tails thought to be the result of small, rocky planets losing mass. The shape and chromaticity of the transits constrain the properties of the dust particles originating from the planet's surface, offering a unique opportunity to probe the composition and geophysics of rocky exoplanets. Aims. We aim to approximate the average Kepler long-cadence light curve of Kepler-1520 b and investigate how the optical thickness and transit cross-section of a general dust tail can affect the observed wavelength dependence and depth of transit light curves. Methods. We developed a new 3D model that ejects sublimating particles from the planet surface to build up a dust tail, assuming it to be optically thin, and used 3D radiative transfer computations that fully treat scattering using the distribution of hollow spheres (DHS) method, to generate transit light curves between 0.45 and 2.5 $\mu$m. Results. We show that the transit depth is wavelength independent for optically thick tails, potentially explaining why only some observations indicate a wavelength dependence. From the 3D nature of our simulated tails, we show that their transit cross-sections are related to the component of particle ejection velocity perpendicular to the planet's orbital plane and use this to derive a minimum ejection velocity of 1.2 kms$^{-1}$. To fit the average transit depth of Kepler-1520 b of 0.87%, we require a high dust mas-loss rate of 7 $-$ 80 M$_\oplus$ Gyr$^{-1}$ which implies planet lifetimes that may be inconsistent with the observed sample. Therefore, these mass-loss rates should be considered to be upper limits.Comment: 22 pages, 22 figures, accepted for publication in A&

Dusty tails of evaporating exoplanets. I. Constraints on the dust composition

Recently, two exoplanet candidates have been discovered, KIC 12557548b and KOI-2700b, whose transit profiles show evidence for a comet-like tail of dust trailing the planet, thought to be fed by the evaporation of the planet's surface. We aim to put constraints on the composition of the dust ejected by these objects from the shape of their transit light curves. We derive a semi-analytical expression for the attenuation of dust cross-section in the tail, incorporating the sublimation of dust grains as well as their drift away from the planet. This expression shows that the length of the tail is highly sensitive to the sublimation properties of the dust material. We compute tail lengths for several possible dust compositions, and compare these to observational estimates of the tail lengths of KIC 12557548b and KOI-2700b, inferred from their light curves. The observed tail lengths are consistent with dust grains composed of corundum (Al2O3) or iron-rich silicate minerals (e.g., fayalite, Fe2SiO4). Pure iron and carbonaceous compositions are disfavoured. In addition, we estimate dust mass loss rates of 1.7 +/- 0.5 M_earth/Gyr for KIC 12557548b, and > 0.007 M_earth/Gyr (1-sigma lower limit) for KOI-2700b.Comment: 10 pages, 7 figures, A&A accepte

An Inner Gaseous Disk around the Herbig Be Star MWC 147

We present high-spectral-resolution, optical spectra of the Herbig Be star MWC 147, in which we spectrally resolve several emission lines, including the [O I] lines at 6300 and 6363\deg. Their highly symmetric, double-peaked line profiles indicate that the emission originates in a rotating circumstellar disk. We deconvolve the Doppler-broadened [O I] emission lines to obtain a measure of emission as a function of distance from the central star. The resulting radial surface brightness profiles are in agreement with a disk structure consisting of a flat, inner, gaseous disk and a flared, outer, dust disk. The transition between these components at 2 to 3 AU corresponds to the estimated dust sublimation radius. The width of the double-peaked Mg II line at 4481\deg suggests that the inner disk extends to at least 0.10 AU, close to the corotation radius.Comment: accepted for ApJ Letters (Oct. 2010

Modelling the KIC8462852 light curves : compatibility of the dips and secular dimming with an exocomet interpretation

This paper shows how the dips and secular dimming in the KIC8462852 light curve can originate in circumstellar material distributed around a single elliptical orbit (e.g. exocomets). The expected thermal emission and wavelength dependent dimming is derived for different orbital parameters and geometries, including dust that is optically thick to stellar radiation, and for a size distribution of dust with realistic optical properties. We first consider dust distributed evenly around the orbit, then show how to derive its uneven distribution from the optical light curve and to predict light curves at different wavelengths. The fractional luminosity of an even distribution is approximately the level of dimming times stellar radius divided by distance from the star at transit. Non-detection of dust thermal emission for KIC8462852 thus provides a lower limit on the transit distance to complement the 0.6 au upper limit imposed by 0.4 d dips. Unless the dust distribution is optically thick, the putative 16 per cent century-long secular dimming must have disappeared before the WISE 12 mum measurement in 2010, and subsequent 4.5 mum observations require transits at >0.05 au. However, self-absorption of thermal emission removes these constraints for opaque dust distributions. The passage of dust clumps through pericentre is predicted to cause infrared brightening lasting tens of days and dimming during transit, such that total flux received decreases at wavelengths <5 mum, but increases to potentially detectable levels at longer wavelengths. We suggest that lower dimming levels than seen for KIC8462852 are more common in the Galactic population and may be detected in future transit surveys

Modelling the KIC8462852 light curves : compatibility of the dips and secular dimming with an exocomet interpretation

This paper shows how the dips and secular dimming in the KIC8462852 light curve can originate in circumstellar material distributed around a single elliptical orbit (e.g. exocomets). The expected thermal emission and wavelength dependent dimming is derived for different orbital parameters and geometries, including dust that is optically thick to stellar radiation, and for a size distribution of dust with realistic optical properties. We first consider dust distributed evenly around the orbit, then show how to derive its uneven distribution from the optical light curve and to predict light curves at different wavelengths. The fractional luminosity of an even distribution is approximately the level of dimming times stellar radius divided by distance from the star at transit. Non-detection of dust thermal emission for KIC8462852 thus provides a lower limit on the transit distance to complement the 0.6 au upper limit imposed by 0.4 d dips. Unless the dust distribution is optically thick, the putative 16 per cent century-long secular dimming must have disappeared before the WISE 12 mum measurement in 2010, and subsequent 4.5 mum observations require transits at >0.05 au. However, self-absorption of thermal emission removes these constraints for opaque dust distributions. The passage of dust clumps through pericentre is predicted to cause infrared brightening lasting tens of days and dimming during transit, such that total flux received decreases at wavelengths <5 mum, but increases to potentially detectable levels at longer wavelengths. We suggest that lower dimming levels than seen for KIC8462852 are more common in the Galactic population and may be detected in future transit surveys

Luminosity- and morphology-dependent clustering of galaxies

How does the clustering of galaxies depend on their inner properties like morphological type and luminosity? We address this question in the mathematical framework of marked point processes and clarify the notion of luminosity and morphological segregation. A number of test quantities such as conditional mark-weighted two-point correlation functions are introduced. These descriptors allow for a scale-dependent analysis of luminosity and morphology segregation. Moreover, they break the degeneracy between an inhomogeneous fractal point set and actual present luminosity segregation. Using the Southern Sky Redshift Survey~2 (da Costa et al. 1998, SSRS2) we find both luminosity and morphological segregation at a high level of significance, confirming claims by previous works using these data (Benoist et al. 1996, Willmer et al. 1998). Specifically, the average luminosity and the fluctuations in the luminosity of pairs of galaxies are enhanced out to separations of 15Mpc/h. On scales smaller than 3Mpc/h the luminosities on galaxy pairs show a tight correlation. A comparison with the random-field model indicates that galaxy luminosities depend on the spatial distribution and galaxy-galaxy interactions. Early-type galaxies are also more strongly correlated, indicating morphological segregation. The galaxies in the PSCz catalog (Saunders et al. 2000) do not show significant luminosity segregation. This again illustrates that mainly early-type galaxies contribute to luminosity segregation. However, based on several independent investigations we show that the observed luminosity segregation can not be explained by the morphology-density relation alone.Comment: aastex, emulateapj5, 20 pages, 13 figures, several clarifying comments added, ApJ accepte

Dusty tails of evaporating exoplanets. II. Physical modelling of the KIC 12557548b light curve

Evaporating rocky exoplanets, such as KIC 12557548b, eject large amounts of dust grains, which can trail the planet in a comet-like tail. When such objects occult their host star, the resulting transit signal contains information about the dust in the tail. We aim to use the detailed shape of the Kepler light curve of KIC 12557548b to constrain the size and composition of the dust grains that make up the tail, as well as the mass loss rate of the planet. Using a self-consistent numerical model of the dust dynamics and sublimation, we calculate the shape of the tail by following dust grains from their ejection from the planet to their destruction due to sublimation. From this dust cloud shape, we generate synthetic light curves (incorporating the effects of extinction and angle-dependent scattering), which are then compared with the phase-folded Kepler light curve. We explore the free-parameter space thoroughly using a Markov chain Monte Carlo method. Our physics-based model is capable of reproducing the observed light curve in detail. Good fits are found for initial grain sizes between 0.2 and 5.6 micron and dust mass loss rates of 0.6 to 15.6 M_earth/Gyr (2-sigma ranges). We find that only certain combinations of material parameters yield the correct tail length. These constraints are consistent with dust made of corundum (Al2O3), but do not agree with a range of carbonaceous, silicate, or iron compositions. Using a detailed, physically motivated model, it is possible to constrain the composition of the dust in the tails of evaporating rocky exoplanets. This provides a unique opportunity to probe to interior composition of the smallest known exoplanets.Comment: 18 pages, 11 figures, A&A accepte