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Photometric Stellar Variation Due to Extra-Solar Comets

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Photometric Stellar Variation Due to Extra-Solar Comets A&A manuscript no. ASTRONOMY (will be inserted by hand later) AND Your thesaurus codes are: 07(03.13.4; 05.15.1; 07.03.1; 08.16.2) ASTROPHYSICS Photometric stellar variation due to extra-solar comets. A. Lecavelier des Etangs1, A. Vidal-Madjar1, and R. Ferlet1 Institut d’Astrophysique de Paris, CNRS, 98bis Boulevard Arago, F-75014 Paris, France Received / Accepted Abstract. We performed numerical simulations of stel- produce the dust continuously. Second, because the cloud lar occultations by extra-solar cometary tails. We find shape is constrained by the observed light curve; the cloud that extra-solar comets can be detected by the appar- cannot be spherical, it should have a sharp edge in the part ent photometric variations of the central stars. In most pointing toward the star and a huge cloud of dust in the cases, the light curve shows a very peculiar “rounded tri- opposite direction: exactly like a cometary tail (Lecavelier angular” shape. However, in some other cases, the curve des Etangs, 1996). can mimic a planetary occultation. Photometric variations In the case of the solar system, the observations of stel- due to comet occultations are mainly achromatic. Never- lar occultation by comets have been discussed by Combes theless, if comets with small periastrons have smaller par- et al. (1983). Observations of extinction and polarization ticles, these occultations could be chromatic with a larger of star light by dust of cometary tails in the solar system extinction in the blue by few percents. have been published (Dossin 1962, Ninkov 1994, Rosen- We also estimate the number of detections expected in bush et al. 1994). a large photometric survey at high accuracy. By the ob- But the solar system is only one particular planetary servation of several tens of thousand of stars, it should be system at a given age. It is known that cometary activity possible to detect several hundreds of occultation per year. was formerly much more important, and the well-known We thus conclude that a spatial photometric survey would case of β Pictoris shows that during the first 108 years, a detect a large number of extra-solar comets. This would planetary system is expected to show large cometary ac- allow to explore the time evolution of cometary activity, tivity (Ferlet & Vidal-Madjar 1995, Vidal-Madjar et al. and consequently would probe structure and evolution of 1998). Moreover, presence of comets around stars can be extra-solar planetary systems. considered as an indirect signature for the presence of gravitational perturbations, and possibly caused by plan- Key words: Occultations – Comets – Planetary systems ets. arXiv:astro-ph/9812381v1 21 Dec 1998 In this paper, we deal with the important possibility of detecting cometary activity from a photometric sur- vey. We take the COROT space mission as an example 1. Introduction of what will be achievable in the very near future (Baglin et al. 1997). COROT, which primary aim is stellar seis- The search for extra-solar planets through photometric mology, will be launched in early 2002. It will allow a variation is a well-known problem analyzed in many as- survey of about 30 000 stars with a photometric accuracy pects for several years (Schneider et al. 1990; Schnei- of few 10−4 during several months. Here, we predict the der 1996). However, planets are not the only objects probabilities of detecting comets using such a photometric detectable by their effect on stars’ brightness, comets survey. can also induce photometric variations. In our study of In Sect 2, we describe the model of the cometary occul- β Pictoris photometric variations (Lecavelier des Etangs tation, and then give the expected light curve in Sect 3. et al. 1995), we concluded that the variations observed on Estimates of the number of comets which could be de- November 1981 could be due to the passage in front of tected are given in Sect 4. The conclusion is in Sect 5. the star of either a planet or a dusty cloud (Lecavelier des Etangs et al. 1997, Lamers et al. 1997). If the latter is the correct explanation, this cloud of dust must be a cometary 2. A model of cometary occultation tail for two reasons. First, because the lifetime of the dust in such a system is very short and one must find a way to As pointed out by Lamers et al.(1997), a geometric dis- tribution of the dust must be assumed in order to eval- Send offprint requests to: A. Lecavelier des Etangs uate the photometric stellar variation due to extra-solar 2 A. Lecavelier des Etangs et al.: Photometric stellar variation due to extra-solar comets. comets. Then, by taking into account the optical proper- for s = 0.1µm. The ejection velocity is smaller for larger ties of the cometary grains, the photometric variation can grains which have smaller cross section area to mass ratio −1 be estimated. (veject(10µm) 124km s ). We checked that any other realistic values≈ for A and B give similar light curves within 2.1. Distribution of dust in a cometary tail few percents. The evaluation of the distribution of the dust in a 2.2. Stellar parameter cometary tail can be made through particle simulation. The input parameters are the comet orbit, the dust pro- The simulations have been performed with the mass, lu- duction rate, the ejection velocity and the size distribu- minosity and radius of the central star set to solar values tion. We assume a size distribution dn(s) of the form (M∗, L∗ and R∗). Simulation with other parameters could be possible. A larger mass for the central star would induce (1 s /s)m 0 a shorter time scale; a larger luminosity would increase the dn(s)= − n (1) s effect of the radiation pressure on grains; a larger radius as observed in the solar system, where s is the dust size. would decrease the relative extinction (Eq. 6). However, We take s = 0.1µm, n = 4.2, m = n(s s )/s , and the conclusions do not strongly depend on these stellar 0 p − 0 0 sp = 0.5µm (Hanner 1983, Newburn & Spinrad 1985). properties. For instance, adopting the properties of an This distribution starts at s0 = 0.1µm with dn(s0) = 0, A5V star does not change the shape of the light curves. −n peaks at sp = 0.5µm, and has a tail similar to a s By scaling the production rate to the star luminosity, we distribution for large sizes. found a quantitative change by less than a factor of two. Dust sensitivity to radiation pressure is given by the β ratio of the radiation force to the gravitational force. We 2.3. Grain properties take −1 2.3.1. Extinction L∗/M∗ s β =0.2 (2) L /M 1µm The extinction cross-section of a dust grain is 2 ⊙ ⊙ Qext(s, λ)πs , where the extinction efficiency, Qext is where L∗/M∗ is the luminosity-mass ratio of the star. So slightly dependent on the particle size (s) and radiation the orbits of the small grains are more affected by radi- wavelength (λ). If Qsca is the scattering efficiency (see ation pressure than those of large grains. This is a very Sect. 2.3.2) and Qabs is absorption efficiency, Qext(s, λ)= good approximation for particles larger than 0.1µm of any Qsca + Qabs. We take Qabs = 1 if s λ, and Qabs = s/λ realistic composition and for the solar spectrum (Burns et if s < λ, which is a good approximation≥ for optical wave- al. 1979). lengths and grains larger than 0.1µm (Draine & Lee 1984). The dust production rate P is assumed to vary with The total extinction is hence calculated by adding the r, the distance to the star, and is taken to be extinction due to all particles in the line of sight to the − star. The optical depth τ due to the dust is r 2 P = P0 (3) 2 r0 Ngrain/part.Qext(s, λ)πs τ = part. (4) P (see, for example, A’Hearn et al., 1995; Weaver et al., 1997, S Schleicher 1998). The dust production is taken to be zero where S is the projected area of the line of sight. In the beyond 3 AU for a solar luminosity. simulation, one particle represents an optically thin cloud As soon as a grain is produced from a comet nucleus, of several dust grains. The number of physical grains per we assume that it is ejected from the parent body with particle in the simulation, Ngrain/part., is a velocity veject in an arbitrary direction. The grain then follows a trajectory defined by gravitation and radiation 3Mdust dn(s) Ngrain/part. = 3 (5) forces. The ejection velocity depends upon the particle 4πρNpart. Rs dn(s) size. We take veject = √β/(A + B√β) (Sekanina & Lar- R son 1984), which approximates the results of Probstein’s where Mdust is the total dust mass, ρ is the dust density, (1969) two-phase dusty-gas dynamics for the acceleration and Npart. is the number of particles in the simulation. 4 by the expanding gas within tens of kilometers from the Npart. is set to a few 10 in order to keep reasonable com- nucleus. The coefficient A and B depend upon many pa- puting time. rameters such as the thermal velocity of the expanding Because the cometary cloud is optically thick but its gas. We used A = B = 1 s km−1 which is a good ap- size is smaller than the size of the star, we mapped the proximation of different values measured for the comets stellar surface through a set of cells in polar coordinates.
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