A Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 19 October 2018 (MN L TEX style file v2.2) Feasibility of transit photometry of nearby debris discs S.T. Zeegers1,3⋆, M.A. Kenworthy1, P. Kalas2 1 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, the Netherlands 2 Astronomy Department, University of California, Berkeley, CA 94720 3 SRON-Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA, Utrecht, The Netherlands Accepted for publication 20 December 2013 ABSTRACT Dust in debris discs is constantly replenished by collisions between larger objects. In this paper, we investigate a method to detect these collisions. We generate models based on recent results on the Fomalhaut debris disc, where we simu- late a background star transiting behind the disc, due to the proper motion of Fomalhaut. By simulating the expanding dust clouds caused by the collisions in the debris disc, we investigate whether it is possible to observe changes in the brightness of the background star. We conclude that in the case of the Fomal- haut debris disc, changes in the optical depth can be observed, with values of the optical depth ranging from 10−0.5 for the densest dust clouds to 10−8 for the most diffuse clouds with respect to the background optical depth of ∼ 1.2×10−3. Key words: techniques: photometric – occultations – circumstellar matter – stars: individual: Fomalhaut. 1 INTRODUCTION diameters > 2000 km) stir up the disc and start a cascade of collisions (Kenyon and Bromley 2005). However, it is Debris discs are circumstellar belts of dust and debris not clear from these models how the dust is replenished around stars. These discs are analogous to the Kuiper over a time-scale of more than 100 Myr (Wyatt 2008). belt and the asteroid belt in our own Solar system. They provide a stepping stone in the study of planet formation, The first debris discs were discovered with the In- because the evolution of a star’s debris disc is indicative frared Astronomical Satellite (IRAS; (Neugebauer et al. of the evolution of its planetesimal belts (Wyatt 2008). 1984)), which measured the excess emission in the in- Debris discs can be found around both young and frared caused by dust in the debris disc. The dust is more evolved stars. For the youngest stars, the dust in heated by the central star and therefore re-emits ther- the disc can be considered a remnant of the protoplan- mal radiation, which causes the observed spectrum of etary disc. In these young debris discs, gas might still the system to deviate from that of a stellar black body be present, which is not the case for debris discs around radiation curve. The debris disc around Vega was the more evolved (main sequence) stars. For older stars, it first debris disc discovered in this way (Aumann et al. is more likely that debris discs indicate the place where 1984) and after that more than 100 discs have been subsequently discovered. Observations from recent sur- arXiv:1402.7227v1 [astro-ph.SR] 28 Feb 2014 a planet has failed to form. This can either be because the formation time-scale was too long, like in the So- veys indicate that at least 15 per cent of FGK stars lar system’s Kuiper Belt, or because the debris disc was and 32 per cent of A stars have a detectable amount of stirred up by gravitational interactions of other planets circumstellar debris (Bonsor et al. (2014), Bryden et al. before a planet could form, which probably happened in (2006), Moro-Martín et al. (2007), Hillenbrand et al. the Solar system’s Asteroid belt (Wyatt 2008). The dust (2008),Greaves et al. (2009) and Su et al. (2006)). in debris discs is thought to be constantly replenished Until improved coronagraph techniques became by collisions between the planetesimals. These planetesi- available, the only ground-based resolved example of mals start to grow in the disc during the protoplanetary a debris disc observed in scattered light at an optical disc phase. Models indicate that when the planetesimals wavelength of 0.89 µm was the debris disc of Beta Pic- begin to reach the size of ∼ 2000 km in diameter, the toris (Smith and Terrile 1984). However, during the past process of growth reverses and the disc begins to erode. decade many resolved debris discs have been observed The dynamical perturbations of these large objects (with at optical and near-infrared wavelengths. Debris discs have been observed in scattered light using the Advanced Camera for Surveys (ACS; (Clampin et al. 2004)) as well ⋆ E-mail: [email protected] as the Space Telescope Imaging Spectrograph (STIS) c 0000 RAS 2 Zeegers, Kenworthy and Kalas and in the near-infrared (1.1 µm) using the Near-Infrared Quillen et al. (2007)) and therefore the dust clouds will Camera and Multi-Object Spectrometer (NICMOS) com- be difficult to detect either in reflected optical light or at bined with the usage of coronagraphs on the Hubble Space longer wavelengths. Telescope (HST). Examples of debris disc observed with Current observations of debris discs show us the dis- − these instruments are: the debris disc of HD 202628 ob- tribution of small dust particles, with radii from 10 5 served with STIS (see Figure 14 and Krist et al. (2012)), m to 0.2 m (Wyatt and Dent 2002). We are not able the debris disc of AU Microscopii (Krist et al. 2005) with to directly observe planetesimals or large boulders. This the ACS and the NICMOS image of the debris disc HR means that we do not have an observational confirma- 4769A (Schneider et al. 1999). Debris discs are also ob- tion of the distribution of these larger parent particles. served at infrared and (sub)millimetre wavelengths where Observing the debris resulting from collisions would make the dust emits the reprocessed stellar light as thermal it possible to put constraints on the particle-size distribu- radiation, for example the debris disc of Epsilon Eri tion in debris discs. In this paper, we explore a technique observed at 850 µm with the Submillimetre Common- that would make it possible to indirectly observe colli- User Bolometer Array (SCUBA) at the James Clerk sions between large planetesimals. When a background Maxwell Telescope (Greaves et al. 1998) and Beta Pic- object, like a star, passes behind a debris disc, dust gen- toris observed with Herschel Photodetector Array Cam- erating collisions will cause the star to dim slightly. The era & Spectrometer (PACS) and Spectral and Photo- change in brightness depends on the optical depth of the metric Imaging Receiver (SPIRE; (Vandenbussche et al. dust clouds, which in turn depends on the amount of de- 2010)). These direct observations of debris discs show a bris created in the collision between two planetesimals. wide variety of disc morphology. Some of these discs have The outline of the paper is as follows. Section 2 ex- narrow dust rings, while other discs are more widespread. plains the method we use to observe collisions in debris Systems can have multiple and even warped discs. Models discs in more detail and gives a general introduction to show that the shape of debris discs can be caused by shep- the Fomalhaut debris disc. In Section 3, we explain the herding planets around these rings (Deller and Maddison theoretical background of the collision model used. Sec- (2005); Quillen et al. (2007)). The first hints that this tion 4 explains the difference between three models of col- might be the case are given by observations of β Pic- lisions in the debris disc of Fomalhaut. Section 5 shows toris (Lagrange et al. (2010); Quanz et al. (2010)) and differences in the observations for systems with different HD 100456 (Quanz et al. 2013). inclinations. In Section 6 we show other debris discs with One such a star with a debris disc is the nearby background objects passing behind the disc, and we con- [7.668 ± 0.03 pc (Perryman et al. 1997)] A star Foma- clude in Section 7 with a summary and a discussion of lhaut. The most prominent feature of the disc is the our results. main dust ring at a radius of 140 au from the star (Kalas et al. 2005), which is ∼ 25 au wide. This debris disc has been imaged by the HST in 2005 (Kalas et al. 2 DETECTING COLLISIONS IN DEBRIS 2005) and more recently by the Herschel Space Telescope DISC BY OBSERVING A BACKGROUND (Acke et al. 2012) and the Atacama Large Milimeter Ar- STAR ray (ALMA) (Boley et al. 2012). The dust around the Fo- malhaut debris disc has been observed in both reflected In this project, we investigate whether it is possible to optical light and at 10 − 100µm wavelength, where the observe collisions between planetesimals in debris discs thermal radiation of the dust in the disc is observed ra- by observing changes in the brightness while a distant diation (Holland et al. 1998). star transits behind the disc. By observing changes in − The ring has a mass-loss rate of 2 × 1021 g yr 1 optical depth, we can deduce the size distribution of the (Acke et al. 2012), which can be compared to the loss colliding objects. In Fig. 1 we can see that such a tran- of the total mass of the rings of Saturn per year. This siting event has already started in the case of the debris huge amount of mass suggests a high collision rate. disc surrounding Fomalhaut. The blue dot indicates the Wyatt and Dent (2002) investigated the possibility of location of a background star at 2012 September 15.