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Register a new userEclipse Mapping: Astrotomography of Accretion Discs
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Authors
Raymundo Baptista
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The Eclipse Mapping Method is an indirect imaging technique that transforms the shape of the eclipse light curve into a map of the surface brightness distribution of the occulted regions. Three decades of application of this technique to the investigation of the structure, the spectrum and the time evolution of accretion discs around white dwarfs in cataclysmic variables have enriched our understanding of these accretion devices with a wealth of details such as (but not limited to) moving heating/cooling waves during outbursts in dwarf novae, tidally-induced spiral shocks of emitting gas with sub-Keplerian velocities, elliptical precessing discs associated to superhumps, and measurements of the radial run of the disc viscosity through the mapping of the disc flickering sources. This chapter reviews the principles of the method, discusses its performance, limitations, useful error propagation procedures, as well as highlights a selection of applications aimed at showing the possible scientific problems that have been and may be addresses with it.
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We present the Dynamic Eclipse Mapping (DEM) method designed specifically to reconstruct the surface intensity patterns of non-radial stellar oscillations in eclipsing binaries. The method needs a geometric model of the binary, accepts the light curve and the detected pulsation frequencies on input, and on output yields estimates of the pulsation patterns, in form of images -- thus allowing a direct identification of the surface mode numbers$(ell,m)$. Since it has minimal modelling requirements and can operate on photometric observations in arbitrary wavelength bands, DEM is well suited to analyze the wide-band time series collected by space observatories. The method was extensively tested on simulated data, in which almost all photometrically detectable modes with a latitudinal complexity $ell-|m|le 4$ were properly restored. Multimode pulsations can be also reconstructed in a natural manner, as well as pulsations on components with tilted rotation axis of known direction. It can also be used in principle to isolate the contribution of hidden modes from the light curve. Sensitivity tests show that moderate errors in the geometric parameters and the assumed limb darkening can be partially tolerated by the inversion, in the sense that the lower degree modes are still recoverable. Tidally induced or mutually resonant pulsations, however, are an obstacle that neither the eclipse mapping, nor any other inversion technique can ever surpass. We conclude that, with reasonable assumptions, Dynamic Eclipse Mapping could be a powerful tool for mode identification, especially in moderately close eclipsing binary systems, where the pulsating component is not seriously affected by tidal interactions so that the pulsations are intrinsic to them, and not a consequence of the binarity.
We show that discs accreting onto the magnetosphere of a rotating star can end up in a trapped state, in which the inner edge of the disc stays near the corotation radius, even at low and varying accretion rates. The accretion in these trapped states can be steady or cyclic; we explore these states over wide range of parameter space. We find two distinct regions of instability, one related to the buildup and release of mass in the disk outside corotation, the other to mass storage within the transition region near corotation. With a set of calculations over long time scales we show how trapped states evolve from both nonaccreting and fully accreting initial conditions, and also calculate the effects of cyclic accretion on the spin evolution of the star. Observations of cycles such as found here would provide important clues on the physics of magnetospheric accretion. Recent observations of cyclic and other unusual variability in T Tauri stars (EXors) and X-ray binaries are discussed in this context.
It is quite likely that self-gravity will play an important role in the evolution of accretion discs, in particular those around young stars, and those around supermassive black holes. We summarise, here, our current understanding of the evolution of such discs, focussing more on discs in young stellar system, than on discs in active galactic nuclei. We consider the conditions under which such discs may fragment to form bound objects, and when they might, instead, be expected to settle into a quasi-steady, self-regulated state. We also discuss how this understanding may depend on the mass of the disc relative to the mass of the central object, and how it might depend on the presence of external irradiation. Additionally, we consider whether or not fragmentation might be stochastic, where we might expect it to occur in an actual protostellar disc, and if there is any evidence for fragmentation actually playing a role in the formation of planetary-mass bodies. Although there are still a number of outstanding issue, such as the convergence of simulations of self-gravitating discs, whether or not there is more than one mode of fragmentation, and quite what role self-gravitating discs may play in the planet formation process, our general understanding of these systems seems quite robust.
The growth process of proto-planets can be sped-up by accreting a large number of solid, pebble-sized objects that are still present in the protoplanetary disc. It is still an open question on how efficient this process works in realistic turbulent discs. Here, we investigate the accretion of pebbles in turbulent discs that are driven by the purely hydrodynamical vertical shear instability (VSI). For this purpose, we perform global three-dimensional simulations of locally isothermal, VSI turbulent discs with embedded protoplanetary cores from 5 to 100 $M_oplus$ that are placed at 5.2 au distance from the star. In addition, we follow the evolution of a swarm of embedded pebbles of different size under the action of drag forces between gas and particles in this turbulent flow. Simultaneously, we perform a set of comparison simulations for laminar viscous discs where the particles experience stochastic kicks. For both cases, we measure the accretion rate onto the cores as a function of core mass and Stokes number ($tau_s$) of the particles and compare it to recent MRI turbulence simulations. Overall the dynamic is very similar for the particles in the VSI turbulent disc and the laminar case with stochastic kicks. For the small mass planets (i.e. 5 and 10 $M_oplus$), well-coupled particles with $tau_s = 1$, which have a size of about one meter at this location, we find an accretion efficiency (rate of particles accreted over drifting inward) of about 1.6-3%. For smaller and larger particles this efficiency is higher. However, the fast inward drift for $tau_s = 1$ particles makes them the most effective for rapid growth, leading to mass doubling times of about 20,000 yr. For masses between 10 and 30 $M_oplus$ the core reaches the pebble isolation mass and the particles are trapped at the pressure maximum just outside of the planet, shutting off further particle accretion.
Planetary rotation rates and obliquities provide information regarding the history of planet formation, but have not yet been measured for evolved extrasolar planets. Here we investigate the theoretical and observational perspective of the Rossiter-McLauglin effect during secondary eclipse (RMse) ingress and egress for transiting exoplanets. Near secondary eclipse, when the planet passes behind the parent star, the star sequentially obscures light from the approaching and receding parts of the rotating planetary surface. The temporal block of light emerging from the approaching (blue-shifted) or receding (red-shifted) parts of the planet causes a temporal distortion in the planets spectral line profiles resulting in an anomaly in the planets radial velocity curve. We demonstrate that the shape and the ratio of the ingress-to-egress radial velocity amplitudes depends on the planetary rotational rate, axial tilt and impact factor (i.e. sky-projected planet spin-orbital alignment). In addition, line asymmetries originating from different layers in the atmosphere of the planet could provide information regarding zonal atmospheric winds and constraints on the hot spot shape for giant irradiated exoplanets. The effect is expected to be most-pronounced at near-infrared wavelengths, where the planet-to-star contrasts are large. We create synthetic near-infrared, high-dispersion spectroscopic data and demonstrate how the sky-projected spin axis orientation and equatorial velocity of the planet can be estimated. We conclude that the RMse effect could be a powerful method to measure exoplanet spins.
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