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Polarization Statistics of Extra-Solar Systems

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Polarization Statistics of Extra-Solar Systems 1 Abstract. We have analysed the optical polarimetric properties of nearby intermediate-late type MS stars and examined in some detail the pecularities displayed by those known to have planets. We find that i) the polariza- tion degree is not strictly correlated with the presence of planets; ii) there is a lack of high eccentricity planets at high optical linear polarization levels; iii) no clear correla- tion is seen between metallicity and polarization amongst extra-solar systems; iv) the contribution to the polariza- tion by the interstellar medium seems to become effective only after ∼ 70 pc. Key words: Stars: planetary systems, protoplanetary disks – Polarization arXiv:astro-ph/0204352v2 5 Aug 2002 A&A manuscript no. ASTRONOMY (will be inserted by hand later) AND Your thesaurus codes are: missing; you have not inserted them ASTROPHYSICS Polarization statistics of extra-solar systems F. Tamburini1, S. Ortolani2, and A. Bianchini2 1 Institute of Cosmology and Gravitation, Univ. of Portsmouth, PO2 1EG, Portsmouth, UK email: [email protected] 2 Universit`adi Padova, Dipartimento di Astronomia, Vicolo dell’Osservatorio 2, I-35122 Padova, Italy emails: [email protected], [email protected] Received ; accepted 1. Introduction Yudin, 2000). Some polarization could also be produced by a giant planet in a close orbit around the star (Saeger The search for extra-solar planets represents an exciting et al. 2000), but the resulting effect is too weak to be new frontier for modern astronomy. The results obtained responsible for the polarizations actually observed. with Doppler surveys are still strongly limited both by the In this paper, we investigate the statistical properties sensitivity of the detectors and by the long recording of of the linear polarization of a sample of extrasolar systems observations in time needed. This selection effect seems and compare them with those of nearby stars. In section to be the main reason why most of the planets within a 2 we report the statistical properties of our data sample few parsecs of the Sun are massive and fast revolving in related to the polarization in white light. In section 3 we very close orbits around their central stars. Nevertheless, draw our conclusions. we can try to identify some general characteristics by an- alyzing the statistical properties of the available data. The statistical properties of extra-solar systems show 2. Polarization properties that stars harbouring massive planets display metal-rich The polarization data are taken from the Heiles catalogue features with respect to nearby field stars (Reid 2001, San- (Heiles 2000) by selecting stars within a distance of 70 pc, tos et al. 2001). At sufficient distances from the star, the that roughly corresponds to the largest distance amongst decreasing temperature of the circumstellar disks allows the observed extrasolar planet systems so far observed. for the presence of ∼ 1 − 2% of solid particles, interstellar The main characteristics of the extra-solar planetary sys- grains or condensates, that can be detected from polariza- tems within our sample are taken from the Planet Ency- tion measurements (Voshchinnikov & Kr¨ugel 1999) as, for clopedia (Schneider 2002). The errors in the polarization example, in β Pictoris. measurements are those reported in Heiles catalogue, and Investigation of our solar system showed that the dom- whenever a star is listed in more than one catalogue, the inant source of dust inside Jupiter’s orbit is represented polarization values are given as weighted averages. The by short-period comets. Outside Jupiter’s orbit, the con- typical error of the polarization degree at the 1σ level centration of particles is a function of the distance from ranges from 0.032% to 0.1%. Very uncertain data are ex- the Sun and the material moves along randomly eccen- cluded in our sample of planetary systems. tric orbits (Humes 1980). Landgraf et al. (2002) showed To analyse the statistical polarization properties of the that the dust between Jupiter and Saturn is still mainly observed extrasolar systems, we have compared their po- produced by comets, while, outside Saturn’s orbit, it is larization distribution to those of stars of our sample that mainly formed of micrometer-sized grains produced by are not known to host planets. Since we do not observe mutual collisions of the Edgeworth-Kuiper Belt objects extrasolar systems with p> 0.09, we have taken this value and also by the impact of interstellar dust grains. Data as an upper limit also for the sample of single stars. We from Voyager 1 and 2 spacecrafts show also the existence notice in Fig. 1 that the two distributions are different of a high concentration of particles beyond 50 au (Gurnett as confirmed by the Kolmogorov-Smirnov test at the 99% et al. 1997). confidence level. Although both the distributions show a These results boosted the hunt for planets around dis- peak at low polarization followed by a decrease towards tant stars through the detection of circumstellar dusty larger values, it appears that single stars show a max- disks. These disks can produce observable effects such imum between p = 0.01 − 0.02, while stars with planets as infrared emission excess (Beckwith and Sargent, 1996; show a well defined maximum around p ∼ 0.0 and a rather Spangler et al., 2001) and partial polarization of the star steeper decline towards higher polarization degrees. This light reflected via scattering (Mauron and Dole, 1998; seems indeed a quite surprising result. F. Tamburini et al.: Polarization of extra-solar systems 3 The general negative trend at increasing polarization Polarization vs eccentricity 0.8 might appear reasonable for both the samples, but why d<10 pc should extrasolar systems cluster around zero? 0.7 10<d<20 pc 0.6 20<d<30 pc Heiles (2000) Polarization distribution p<0.09 eEri 140 d>30 pc 0.5 HD 83443 Distance d < 70 pc 0.4 120 0.3 HD 114762 100 Eccentricity 0.2 Gliese 876 80 0.1 47 Uma HD 179949 0 60 t Boo Ups And. 0.1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 40 Polarization Fig. 2. Polarization vs orbital eccentricity. The extrasolar 20 systems are mainly distributed in the lower left region of the diagram. The diagonal line tentatively separates the 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 two regions in the diagram. The exception of HD 114762 Polarization is discussed in the text. There is indication that larger Polarization distribution for exoplanetary systems polarizations are allowed at lower eccentricities. Multiple 7 systems reported in Table 1 are shown connected by dot- ted lines. Symbol sizes correspond to different distances: 6 no distance effects can be seen. Sample of stars with detected giant planets 5 per right region is almost empty. Given this surprising re- sult, we investigated possible systematic effects. Distance 4 effects seem to be irrelevant for the observed distribution because distances are randomly distributed with respect 3 to the polarization. This is confirmed in Fig. 3 where the polarization of FGK stars is plotted against the distances. 2 We see that within the distance of about 70 pc which corresponds to the limit of our sample, no correlation is seen. Considering that the mass of the disks have been 1 suggested to be a function of their age (Spangler et al., 2001), we checked if the observed higher polarization of 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 HD 179949 and Tau Bootis could be due to a younger age. Polarization HD 179949 is 3.31 Gyr old, and Tau Bootis is 2.52 Gyr Fig. 1. (Upper panel) Histogram of the distribution of (Chen, 2001; Marsakov, 1995), while, for example Epsilon p . the polarization within 70pc and p < 0.09 of stars from Eridani, which has a rather low polarization ( =0 01), is Heiles (2000) Catalogue within 70pc and p< 0.09. instead rather younger (about 1 Gyr). Figure 2 suggests (Lower panel) Polarization distribution of the sample that highly eccentric orbits can only have low polarization of stars with detected giant planets. A well defined peak levels, while high polarizations are detected only in low ec- around p ∼ 0 is evident. centricity systems. In any case the polarization levels of According to the Kolmogorov-Smirnov test the two distri- many of the stars with planetary systems plotted in the butions are different. figure appear surprisingly higher than predicted by both current theoretical models and observational evidence. The extra-solar systems can then be compared to β Plotting in Fig. 2 the orbital eccentricities of the ex- Pic, in which the polarization is rather high, but in our trasolar planets vs the observed polarization, we find a case the dusty discs around them are very rarefied and peculiar distribution of the data points, since only the no polarization above ∼ p = 0.01 has so far been found lower left part of the diagram is populated, while the up- (Spangler et al., 2001). 4 F. Tamburini et al.: Polarization of extra-solar systems The data used (Heiles catalogue) are very uncertain: Polarization vs Metallicity the error bars in the polarization degree are often larger 0.14 than the measured polarization, but at low eccentricity 0.12 values they are significantly smaller than the data disper- HD 114762 sion. [Fe/H]=−0.79 HD 179949 At present it is not clear what the mechanism could 0.1 be for the observed polarization levels in our sample. If 0.08 the trend of the diagram in Fig.
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