Issue 
A&A
Volume 631, November 2019



Article Number  A152  
Number of page(s)  12  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/201936521  
Published online  13 November 2019 
Dusty phenomena in the vicinity of giant exoplanets
^{1}
Space Research Institute (IWF), Austrian Academy of Sciences,
Schmiedlstrasse 6, 8042 Graz, Austria
email: oleksiy.arkhypov@oeaw.ac.at
^{2}
Institute of Laser Physics, SB RAS,
Novosibirsk 630090, Russia
email: maxim.khodachenko@oeaw.ac.at
^{3}
Institute of Physics, KarlFranzens University of Graz, Universitätsplatz 5,
8010 Graz, Austria
email: arnold.hanslmeier@unigraz.at
Received:
19
August
2019
Accepted:
1
October
2019
Context. Hitherto, searches for exoplanetary dust have focused on the tails of decaying rocky or approaching icy bodies only at short circumstellar distances. At the same time, dust has been detected in the upper atmospheric layers of hot jupiters, which are subject to intensive mass loss. The erosion and/or tidal decay of hypothetic moonlets might be another possible source of dust around giant gaseous exoplanets. Moreover, volcanic activity and exozodiacal dust background may additionally contribute to exoplanetary dusty environments.
Aims. In the present study, we look for photometric manifestations of dust around different kinds of exoplanets (mainly giants).
Methods. We used linear approximation of pre and posttransit parts of the longcadence transit light curves (TLCs) of 118 Kepler objects of interest after their preliminary whitening and phasefolding. We then determined the corresponding flux gradients G_{1} and G_{2}, respectively. These gradients were defined before and after the transit border for two different time intervals: (a) from 0.03 to 0.16 days and (b) from 0.01 to 0.05 days, which correspond to the distant and adjoining regions near the transiting object, respectively. Statistical analysis of gradients G_{1} and G_{2} was used for detection of possible dust manifestation.
Results. It was found that gradients G_{1} and G_{2} in the distant region are clustered around zero, demonstrating the absence of artifacts generated during the light curve processing. However, in the adjoining region, 17 cases of hot jupiters show significantly negative gradients, G_{1}, whereas the corresponding values of G_{2} remain around zero. The analysis of individual TLCs reveals the localized pretransit decrease of flux, which systematically decreases G_{1}. This effect was reproduced with the models using a stochastic obscuring precursor ahead of the planet.
Conclusions. Since only a few TLCs show the presence of such pretransit anomalies with no analogous systematic effect in the posttransit phase, we conclude that the detected pretransit obscuration is a real planetrelated phenomenon. Such phenomena may be caused by dusty atmospheric outflows or background circumstellar dust compressed in front of the masslosing exoplanet, the study of which requires dedicated physical modeling and numeric simulations. Of certain importance may be the retarding of exozodiacal dust relative to the planet by the PoyntingRobertson effect leading to dust accumulation in electrostatic or magnetic traps in front of the planet.
Key words: planets and satellites: general / interplanetary medium / zodiacal dust
© ESO 2019
1 Introduction
Exoplanetary environments are nowadays the focus of extensive theoretical modeling and dedicated observations, traditionally in spectral lines (Lammer & Khodachenko 2015). The available broadband photometry may provide additional valuable environmental information for significantly larger number of objects, as compared to those studied by spectral methods. At the same time, only the signatures of the dust component are detectable in such studies. Until now, the manifestations of dust have been noticed on decaying rocky planets in the form of tails (e.g., Brogi et al. 2012; Budaj 2013; Garai 2018; SanchisOjeda et al. 2015). The presence of dust was also reported at altitudes of ~3000 km in gaseous giant exoplanets (Huitson et al. 2012; Wang & Dai 2019), and it is quite possible that such dust is dragged by the escaping planetary upper atmospheric material driven by stellar Xray and ultraviolet (XUV) heating and tidal forces (Shaikhislamov et al. 2016). Among the sources of the dust at giant exoplanets could be the erosion of moonlets by meteoroids and plasma flows, tidal decay and evaporation of heated and liquified satellites, satellite volcanic activity, and magnetospheric capture of interplanetary (e.g., exozodiacal) dust (Spahn et al. 2019). The dust product of any of these processes can manifest itself as dusty obscuring matter (DOM), which transits over a stellar disk ahead of or behind the planet, generating tiny anomalies in the exoplanetary transit light curves (TLCs), especially before and after planetary eclipses.
In that respect, the TLCs provided by the space telescope Kepler represent promising but still superficially studied source of information on the pre/posttransit anomalies and the related manifestations of DOM. Hitherto, the outoftransit parts of exoplanetary TLCs have only been studied for a cumulative search of exomoons and evaluation of particular candidates around Kepler1625b (Teachey et al. 2018). Here we analyze for the first time the transit vicinities of many individual Kepler objects of interest (KOIs). The maximal duration of available data records and their highest precision make Kepler data the best choice to search for tenuous photometric effects of DOM.
The analysis presented here involves a specially elaborated method, which is explained in Sect. 2. The obtained results are described in Sect. 3 and conclusions are presented in Sect. 4.
Fig. 1 Example of the light curve processing for the star KIC 5780885. Panel a: approximation of the transit background (open squares) with a sixthorder polynomial F_{b} (t_{k}) (solid line); panel b: phasefolded TLC, ΔF(Δt), with neartransit border parts BP1 and BP2 indicated (blue boxes); panel c: clipped border parts (labeled) vs. the border distance δt ready for comparison. The black horizontal bar in (c) corresponds to the radius ingress (egress) time of the planet. 

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Fig. 2 Distributions of the preingress, G_{1}, and postegress, G_{2}, gradientestimates of TLC for the distant pre and posttransit regions with τ_{min} = 0.03 days and τ_{max} = 0.16 days for 114 KOIs with errors < 0.05%∕day: panel a: G_{2} vs. G_{1} diagram; panel b: histogram of G_{1}; panel c: histogram of G_{2}. The value n is the number of estimates within a bin of histogram. 

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2 Analysis method and stellar set
A natural way to detect DOM structures comoving with the transiting object in broadband photometry is to search for flux variations a short time before the ingress of the planet on the stellar disk and after the egress. For this purpose we use the publicly available light curves from the Kepler mission (NASA Exoplanet Archive^{1}) after Presearch Data Conditioning (F_{PDC} hereinafter), where instrumental drifts, focus changes, and thermal transients are removed or suppressed (Jenkins et al. 2010). Our survey uses the longcadence data with photon accumulation (i.e., exposure) period of δt_{L} = 29.4 min. This approach provides the highest precision of the input light curves, although it cannot resolve the details of the ingress and egress parts of the TLCs. The shortcadence data with the counting period of δt_{S} = 1 min, in spite of higher time resolution, are available for a lesser number of stars and not for all quarters; and they also increase the detection threshold of DOM by a factor of .
To remove the residual instrumental drifts as well as the stellar variability at timescales longer than the transit duration, after removal of the transit parts of duration Δt_{tr} plus the margins of ± 0.01 days, we approximate the normalized light curve F_{PDC}(t_{k})∕⟨F_{PDC}(t_{k})⟩, which covers the time interval ± 10Δt_{tr} centered at the particular transit, (see Fig. 1a), with a sixthorder polynomial , where t_{k} is the flux measurement time, a, b, c, d, e, f, g are the fitted coefficients, and ⟨F_{PDC}(t_{k})⟩ is the average flux of the light curve. This approximation is an iterative process (10 iterations), with the consequent exclusion of remaining stellar flares and transit counts above the threshold [F_{PDC}(t_{k})∕⟨F_{PDC}(t_{k})⟩] − F_{b}(t_{k}) > 3 σ_{b}, where σ_{b} is a standard deviation from the approximation F_{b}(t_{k}). Since the final approximation F_{b}(t_{k}) is insensitive to the transit (Fig. 1a), we use it as reference level to determine the flux decrease during the transit: ΔF_{k} = [F_{PDC}(t_{k})∕⟨F_{PDC}(t_{k})⟩] − F_{b}(t_{k}), which is used in further analysis.
This light curve “whitening” procedure enables us to finally obtain a phasefolded TLC ΔF(Δt) (Fig. 1b), where Δt = t_{k} − t_{E} is the time counted for each transit with number E = 0, 1, 2, … relative to its midtime, t_{E} = t_{0} + P_{tr}E. The cumulative reference time t_{0} and the transit period P_{tr} are taken from the NASA Exoplanet Archive.
To detect the possible manifestation of DOM, which is supposedly concentrated around an exoplanet, the linear gradients G_{1,2} ≡ ∂(ΔF)∕∂(δt) were calculated in the time intervals − τ_{max} < δt < −τ_{min} and τ_{min} < δt < τ_{max} for the preingress and postegress parts of the TLCs, respectively. Here, δt = Δt ± 0.5Δt_{tr} is the border distance time counted from the transit border in folded TLC, calculated with the cumulative transit duration Δt_{tr} from the NASA Exoplanet Archive. The gradients G_{1} and G_{2} were found in two interval ranges: (a) in the adjoining pre/posttransit region, i.e., between τ_{min} = 0.01 days (the halfexposure of the flux record) and τ_{max} = 0.05 days; (b) in the distant region, that is, between τ_{min} = 0.03 days and τ_{max} = 0.16 days, which correspond approximately to the planetocentric distances from ~ 2 to ~ 17 planetary radii.
Altogether, a set of 118 KOIs with “confirmed” or “candidate” status in the NASA Exoplanet Archive was compiled. This set consists of selected objects from the lists in Aizawa et al. (2018), whose shortcadence light curves were used to search for exorings (i.e., specific structures of the dusty matter around planets). Since in our study we deal with the longcadence data only, the set of corresponding longcadence light curves of the objects from Aizawa et al. (2018) was extended with other highquality light curves of objects from the NASA Exoplanet Archive with the nominated signaltonoise ratio (S/N) ≳ 10^{3} (i.e., the transit depth normalized by the mean uncertainty in the flux during the transits as it was published in the KOI cumulative table of the NASA Exoplanet Archive). For the selection of KOIs from the list in Aizawa et al. (2018), the same version of the S/N definition as that used in the NASA Exoplanet Archive was considered, but with a less conservative selection threshold of ≳ 100. In cases of multiplanet systems, the objects with maximal transit depth were taken (one per system). The total set of KOIs selected for our analysis is listed in Table C.1.
To visualize the possible DOM effects, the phasefolded TLC (Fig. 1b) is clipped according to Fig. 1c. The clipping consists in the combination of the neartransit border parts (BP1 and BP2 in Fig. 1b) of the folded TLC to simplify their comparison. The nullpunkt of the abscissa scale in Fig. 1c δt = 0 corresponds to the time Δt ± 0.5Δt_{tr} of the borders of transit. In fact, the observable transit borders in longcadence light curves are shifted from those, defined as above, on half exposure period, i.e., on δt_{L}∕2, that is −0.01 and +0.01 days for the transit start and end times, respectively. Correspondingly, the clipped border parts of folded TLC show the sharp minimum in Fig. 1c.
Fig. 3 Distributions of preingress (G_{1}) and postegress (G_{2}) gradients estimated in the adjoining regions (τ_{min} = 0.01 and τ_{max} = 0.05 days). Panel a: G_{2} vs. G_{1} diagram for90 KOIs with gradient errors (marked by bars) of less than 0.2%/day; panel b: diagram analogous to (a), but for all 114 KOIs considered; panel c: histogram of G_{1} for all estimates (i.e., all objects); panel d: histogram of G_{2} for all estimates (i.e., all objects). The value n is the number of estimates within a bin of a histogram. 

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Fig. 4 Effect of imperfect approximation of the transit reference level F_{b}(t_{k}) in the case of KIC 5780885 in Fig. 1c. Panel a: approximation with a sixthorder polynomial, commonly used in our study, which gives G_{1} = −0.26 ± 0.05 and G_{2} = 0.05 ± 0.05%/day; panel b: trial approximation with firstorder polynomial covering the whole P_{tr}, which gives G_{1} = −0.32 ± 0.10 and G_{2} = 0.04 ± 0.11%/day. 

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3 Results
First, we present the results obtained for the distant region with τ_{min} = 0.03 days and τ_{max} = 0.16 days (Fig. 2). One can see that most of the G_{1,2} estimate points cluster around G_{1} = G_{2} = 0. Several deviated estimates with G_{1} > 0 and G_{2} < 0 could be a manifestation of the forwardscattering by micron dust. Atmospheric aerosols could result in the increase of flux only by δ(ΔF_{k}) = 32.5 ppm for ~1 μm particles (see Table 2 in García & Cabrera 2018) on the phaseangle scale 20^{o} (Eq. (2) in DeVore et al. 2016), which corresponds to the timescale τ_{s} ~ (20^{o}∕360^{o})P_{tr} for the transit period P_{tr}. Taking the typical P_{tr} ~ 10 days, one can estimate τ_{s} ~ 0.6 days and G_{1,2}~ δ(ΔF_{k})∕τ_{s} < 0.005%∕day. This atmospheric aerosol contribution appears negligible in comparison with the obtained gradients G_{1,2} > 0.05%∕day, which may however be not sufficiently reliable. For example, the TLC of Kepler26b orbiting around KIC 9757613 shows the transits with maximal scatteringlike gradients: G_{1} = 0.105 ± 0.040%∕day and G_{2} = −0.158 ± 0.047%∕day at 2.6 and 3.3 standarderror confidence level, respectively.
Another population of the deviating gradient estimates with G_{1} < 0 could be a manifestation of the large (≫1 μm) obscuring particles. However, the contribution of such negative gradient cases in the total G_{1} distribution in Fig. 2b is insignificant. This is confirmed by an insignificant skewness, 0.35 ± 0.23, of the G_{1} distribution (see Appendix A).
In summary, one can conclude that insignificant gradients G_{1,2} in the distant region correspond to the mainly dustless environments. This nondetection result can also be considered as a verification of the light curve processing method used, which does not generate any systematic errors or artifacts.
Closer to planets, that is, in the adjoining pre and posttransit regions with τ_{min} = 0.01 days and τ_{max} = 0.05 days, the analogous G_{2} versus G_{1} diagram has a different appearance (Fig. 3). One can see the shift of many estimate points towards the negative G_{1} (Fig. 3a,b) as well as the bimodal character of the G_{1}histogram (Fig. 3c). There is also an undisturbed normal population of gradient estimates clustered around G_{1} = 0 (Fig. 3c) and G_{2} = 0 (Fig. 3d). Another population of gradient estimates with G_{1} < 0 and G_{2} ~ 0 (see Fig. 3d) might be related with the pretransit manifestations of DOM; its existence is also confirmed by the significant skewness − 0.96 ± 0.23 of the G_{1} distribution in Fig. 3c.
Theoretically, the known phenomenon of transit timing variations (TTVs), that is, the timeshifts of a TLC as a whole, could blur the transit borders in the folded TLC and create misleading gradients, namely G_{1} < 0 and G_{2} > 0. However, such shifts are known to oscillate in time around the linearly predicted ephemeride time of the transit t_{E} (Holczer et al. 2016). Correspondingly, the TTV effect should blur both ingress and egress parts of the folded TLC. Hence, TTV cannot explain the observed just pretransit flux drops without a detectable posttransit effect.
Anotherfactor that may affect a light curve is variation of the planetary phase (e.g., Esteves et al. 2015). However, variation of this kind gives negligible gradients G_{ph} ~ 10^{−4}A_{p}∕(0.5P_{tr}), where A_{p} ≤ 150 ppm is the planetary brightness amplitude (see Table 58 in Esteves et al. 2015), and the factor 10^{−4} is the transforming coefficient from ppm flux units into percent used here. Taking a typical transit period P_{tr} ~ 3 days for hot Jupiters, one can estimate that G_{ph} ≲ 0.01%/day. Therefore, the second peak at G_{1} ≈ 0.3%/day in Fig. 3c cannot be attributed to planetary phase variability.
An imperfect polynomial approximation of the transit reference level F_{b} (t_{k}) might hypothetically produce a misleading DOMlike effect. However, since the polynomial approximation is made for the sufficiently long part of the light curve (±10 Δt_{tr} around the mid of transit) without account of the transit itself (i.e., with the removed transit), the planetary circumference would not significantly affect this approximation. We simulated the effects of imperfect definition of F_{b} (t_{k}) using its linear approximation instead of a sixthorder polynomial. The result was an increased dispersion of ΔF before and after the folded TLC without a noticeable systematic effect on G_{1} or G_{2} (see Fig. 4).
Figure 5d shows that significantly (above three standard errors) negative values of G_{1} are clearly associated with the Jupitertypeplanets with radii 10 ≲ R_{p} ≲ 25 (i.e., 1.0 ≲ log(R_{p}) ≲ 1.4) in units of the Earth radius. Since our data set includes the transits of objects sized up to ≈ 0.1 Jovian radii, the appearance of a pronounced negative G_{1} feature by the Jupitertype and larger objects is not a selection effect (compare Figs. 5a and d). According to Fig. 5e, the significantly negative gradients G_{1} were found exclusively by hot Jupiters at extremely short orbits with radii 0.026 ≲ a_{orb} ≲ 0.065 au, although the analyzed sample includes a wide range of objects with orbital distances of up to 1 au. A summary of the individual parameters of 17 KOIs, showing the most significant values of G_{1}, is given in Table 1. This may indicate that the large size and short orbital distance of a planet are prerequisites of detectable DOM signatures. Moreover, the intensive material escape and massloss typical for the closeorbit hot jupiters might affect the evolution and distribution of the obscuring DOM. We note that no significant (beyond three standard errors) deviations of G_{2} from zero were found among the considered objects (Figs. 5g–i), meaning the absence of any measurement and/or calculation artifacts in the performed analysis. Therefore, the negative deviations of G_{1} detected in the adjoining regions of a significant group of the studied objects appear to be real phenomena.
In Table 1 we also present estimations of the effective area obscured by DOM on the stellar disk as for the case of G_{1} defined in the adjoining pretransit region. Here the coefficient 0.01 adopts the gradient, G_{1}, values, expressed in units of percent/day; the minus reflects the increase of the DOM particle concentration towards the planet; τ_{max} = 0.05 days; and R_{*} is the stellar radius from the NASA Exoplanet Archive. The estimated effective DOM area expressed in percent of the planetary crosssection varies in the considered set of objects from the minimal value of 0.4% achieved for KOI 1.01, up to the maximal value of 3.3% for KOI 203.01.
The average value ⟨S_{DOM}⟩ = 4.8 × 10^{8} km^{2} corresponds to the dust cloud of N ≈ S_{DOM}∕(QA) ~ 2.8 × 10^{24} grains with the typical diameter d ~ 10 μm (like in the Solar System zodiacal cloud) and the geometrical crosssection . Here, Q = 2.19 is the extinction efficiency, that is, the ratio of the shadow crosssection of the particle and its geometrical crosssection A, which is calculated for a transparent sphere with the refractive index of 1.5 and the average wavelength of the Kepler photometry λ = 0.66 μm using the Mie scattering theory^{2}.
The integral volume of all these dust grains is . It is in fact very small, as compared to the scales of potential dust sources; for example the SolarSystemlike zodiacal cloud with an integral volume of its dust particles ~1.4 × 10^{4} km^{3}, which is equivalent to a 15 kmsized asteroid (Mennesson et al. 2019); a Jupitertype KOI (~ 1.4 × 10^{15} km^{3}) or its Iolike moon (~2.5 × 10^{10} km^{3}). Altogether, the amount of dust estimated above, needed for the detected DOM manifestations, seems to be achievable with such ordersofmagnitudelarger sources.
Figure 6 shows the examples of the DOMrelated features visible as an occasional decrease (arrowed) of radiation flux ΔF in the folded TLCs clustered in a narrow (≈0.01 day) range of preingress time δt. There is a tendency for such features to repeat with the flux counting period 0.02 days (the best pronounced is the case of KIC 9941662). Apparently, this is a result of artificial clustering of flux measurements at midexposure times.
The most manifested DOMrelated feature in the TLC of KIC 10619192 (Fig. 6a) was studied in detail as a typical case. Figure 7 shows the difference between the preingress and postegress parts of the folded TLC. One can see that the arrowed DOMrelated feature is unique over the whole transit period. This means that this effect is really associated with the transiting object and its comoving DOM structure, and is therefore unlikely to be an artifact.
We tried to simulate the DOM phenomenology assuming a hypothetic obscuring precursor (Fig. 8d) before the real planet (see also Appendix B). This precursor imitates a dust cloud ahead of the planet at a distance of five planetary radii. Since the same flux drop could be obtained with very different geometries and transparency of dust cloud, the equivalent opaque circular disk of the precursor was assumed for simplicity in the simulation.
Using the pixelbypixel integration over the stellar disk as in Fig. 8d, we achieved a certain resemblance between the modeled and real phasefolded TLCs (Figs. 8a,b) including the clustering effect (Fig. 8c). It is worth noting that the model parameters used in this simulation were neither fitted nor optimized to obtain an evident DOMtype effect. Only a rough empirical selection of parameters was done to find an appropriate scenario. An interesting feature consists in the fact that the synthetic TLC with the most similar behavior to observations was obtained in the simulations with a precursor that is stochastic in character. Specifically, the radius of the precursor was randomly taken in the range between zero and 0.5 R_{p}, whereas its appearance time was randomized in the range [0; 375 days] with an average time interval of 0.0375 days between individual DOM events. The duration of each DOM event was 0.02 days (i.e., the exposure time) with a constant area of eclipsing DOM for each individual event. The specific planetary and stellar parameters used in the simulation were taken for the object KIC 10619192 from the NASA Exoplanet Archive. Altogether, the model realistically reproduces the stochastic variability of flux decrease within the pretransit time interval − 0.02 < δt < −0.01 days, related to the investigated DOM effect (see Fig. 9).
Fig. 5 Gradients G_{1} and G_{2}, measured in the adjoining regions, versus planetary parameters: radius R_{p} of planet in (a), (d), and (g); radius a_{orb} of orbit in (b), (e), and (h); and the orbital period P_{tr} in (c),(f), and (i). The plots (a)–(c) and (g)–(i) show all the studied objects (squares with error bars) from Table C.1, while the middle row panels (d)–(f) present only significant (above three standard errors) deviations of G_{1}  from zero (listed in Table 1). 

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Fig. 6 Examples of DOM manifestations (arrowed) in the preingress parts of folded and clipped TLCs (pluses), showing significant values of gradient G_{1}. The horizontal bars correspond to the radii of considered planets, i.e., ingresstime. 

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Objects with a significant manifestation of pretransit DOM.
Fig. 7 Visualization of the pretransit DOM manifestation (arrowed) in the light curve of KIC 10619192 above the background of cleared (panel a) and noncleared (panel b) folded outoftransit parts (P_{tr} − Δt_{tr}) of the light curve, i.e., during the whole transit period except for the transit itself. 

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Fig. 8 Modeling of the pretransit DOM manifestations (arrowed) in the case of KIC 10619192. Panel a: real folded TLC; panel b: synthetic folded TLC; panel c: clipped TLC to visualize the synthetic DOM effect like in Fig. 5; panel d: model geometry with the real planet, crossing the stellar disk along the solid line together with an idealized DOM precursor (arrowed). 

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Fig. 9 Temporal variability of DOM effect as a pretransit flux drop, measured at − 0.02 < δt < −0.01 days. Panel a: extraction from the real light curve of KIC 10619192; panel b: analogous plot for synthetic light curve based on the used model. The abscissa scale is in differential barycentric Julian days ΔJD, counted from the reference day 2454833.0. 

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4 Conclusions
Below we summarize the major points, which may be concluded from the performed analysis and detections made.
 1.
The absence of systematic deviation of the outoftransit gradients G_{1} and G_{2} from zero in the distant regions (0.03 < δt < 0.16 days), and the same in the adjoining posttransit region (0.01 < δt < 0.05 days), but only for G_{2}, means that there are no detectable DOM manifestations far from exoplanets, and in the closer regions behind them. This assures also the absence of influential artifacts from photometry or light curve processing.
 2.
Since the discovered significant photometrical peculiarities (irregular drops of stellar radiation flux) take place only before the ingress (Figs. 3 and 4) in close vicinity of the transit border (Figs. 5 and 6) of only shortperiod giant exoplanets, and this effect was not pointed out in previous studies, we deal here with a hitherto unknown exoplanetary phenomenon. It appears to be a new aspect of hot Jupiter nature requiring investigation.
 3.
The entirely pretransit location of the found peculiarities excludes the possibility that these are photometric or processing artifacts (as explained in Sect. 3) or the manifestation of orbiting bodies (exomoons, moonlets, exorings, etc.) as a source of obscuring matter.
 4.
The obtained results inspire the modeling work to simulate dusty atmospheric outflows (suggested in e.g., Wang & Dai 2019), which interact with the stellar winds, being compressed in front of the materiallosing exoplanets (like in Shaikhislamov et al. 2016; Dwivedi et al. 2019). An alternative scenario could involve the retarding of exozodiacal dust relative to the planet by the PoyntingRobertson effect leading to dust accumulation in an electrostatic, magnetic, or dynamic trap before the planet. These scenarios require a dedicated modeling which will be the subject of future work.
Acknowledgements
The authors acknowledge the projects I2939N27 and S11606N16 of the Austrian Science Fund (FWF) for the support. M.L.K. is grateful also for the grant No. 181200080 of the Russian Science Foundation.
Appendix A Skewness of G_{1,2} distributions
To characterize the asymmetry of a distribution, we calculated the sample skewness (Joanes & Gill 1998) of the obtained estimates of gradients G_{1,2} (A.1)
where: is the estimate of G_{1,2} for an individual KOI with a number i; n is the total number of considered objects; ⟨G_{1,2}⟩ is the average value over all estimates . For the normal distribution the sample skewness has an expected value S_{1,2} = 0 and the variance (Kendall & Stuart 1969).
Appendix B Modeling of DOM effect in a TLC
Since various shapes and transparencies of a transiting dust cloud are possible, a universal method of pixelbypixel integration (Juvan et al. 2018) suitable for any shape of transiting object is applied to compute the corresponding TLCs. The dimming of stellar flux during transit is characterized by the part of starlight blocked by the transiting object (B.1)
where the coordinate system cocentered with the stellar disk with xaxis parallel to the planet orbit projection on the stellar disk is used; I_{s} is radiation intensity at a given position (x,y) on the visible stellar disk, and I is the same intensity but disturbed by the transiter. The abovementioned integrals can be replaced by sums over N_{p} pixels with serial number i in the identical sets: (B.2)
The stellar limb darkening is taken into account according to the best (four coefficients) approximation by Claret & Bloemen (2011), depending on particular stellar effective temperature and gravity, adopted from the NASA Exoplanet Archive. The planetary data (radius R_{p}, semimajor axis a_{orb} of the orbit, impact parameter β, midtime t_{0} of the first observed transit, transit period P_{tr}) are also taken from the NASA Exoplanet Archive.
In the used reference system, the center exoplanetary shadow has coordinates (B.3) (B.4)
where R_{s} is the stellar radius from the NASA Exoplanet Archive. The DOM is imitated by an opaque equivalent disk (see explanation in Sect. 3) at x_{DOM} = x_{p} + d and y_{DOM} = y_{p}. Here parameter d = 5R_{p} is a constant effective distance selected empirically but without a detailed fitting. The time step for ΔF calculation is adopted as τ_{s} = 0.00204 days. The next procedure consists in the smoothing of the obtained synthetic light curve with time step 10τ_{s} which reproduces the real effect of the longcadence integration time 0.0204 days. Consequently, the smoothing reproduces a certain widening of the longcadence TLC, manifested as sharp outoftransit minima (synthesized in Fig. 8c) at 0 < δt < 0.01 days as seen in Figs. 1c and 6 for real TLCs. Moreover, the association of flux counts with the medial times of longcadence exposures generates the 0.02days periodicity in TLC, as for example in the case of KIC 9941662 in Fig. 6. We note that the synthetic light curves are treated further with the same processing pipeline as the real light curves.
Appendix C Supplementary material
Analyzed target set and processing results.
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All Tables
All Figures
Fig. 1 Example of the light curve processing for the star KIC 5780885. Panel a: approximation of the transit background (open squares) with a sixthorder polynomial F_{b} (t_{k}) (solid line); panel b: phasefolded TLC, ΔF(Δt), with neartransit border parts BP1 and BP2 indicated (blue boxes); panel c: clipped border parts (labeled) vs. the border distance δt ready for comparison. The black horizontal bar in (c) corresponds to the radius ingress (egress) time of the planet. 

Open with DEXTER  
In the text 
Fig. 2 Distributions of the preingress, G_{1}, and postegress, G_{2}, gradientestimates of TLC for the distant pre and posttransit regions with τ_{min} = 0.03 days and τ_{max} = 0.16 days for 114 KOIs with errors < 0.05%∕day: panel a: G_{2} vs. G_{1} diagram; panel b: histogram of G_{1}; panel c: histogram of G_{2}. The value n is the number of estimates within a bin of histogram. 

Open with DEXTER  
In the text 
Fig. 3 Distributions of preingress (G_{1}) and postegress (G_{2}) gradients estimated in the adjoining regions (τ_{min} = 0.01 and τ_{max} = 0.05 days). Panel a: G_{2} vs. G_{1} diagram for90 KOIs with gradient errors (marked by bars) of less than 0.2%/day; panel b: diagram analogous to (a), but for all 114 KOIs considered; panel c: histogram of G_{1} for all estimates (i.e., all objects); panel d: histogram of G_{2} for all estimates (i.e., all objects). The value n is the number of estimates within a bin of a histogram. 

Open with DEXTER  
In the text 
Fig. 4 Effect of imperfect approximation of the transit reference level F_{b}(t_{k}) in the case of KIC 5780885 in Fig. 1c. Panel a: approximation with a sixthorder polynomial, commonly used in our study, which gives G_{1} = −0.26 ± 0.05 and G_{2} = 0.05 ± 0.05%/day; panel b: trial approximation with firstorder polynomial covering the whole P_{tr}, which gives G_{1} = −0.32 ± 0.10 and G_{2} = 0.04 ± 0.11%/day. 

Open with DEXTER  
In the text 
Fig. 5 Gradients G_{1} and G_{2}, measured in the adjoining regions, versus planetary parameters: radius R_{p} of planet in (a), (d), and (g); radius a_{orb} of orbit in (b), (e), and (h); and the orbital period P_{tr} in (c),(f), and (i). The plots (a)–(c) and (g)–(i) show all the studied objects (squares with error bars) from Table C.1, while the middle row panels (d)–(f) present only significant (above three standard errors) deviations of G_{1}  from zero (listed in Table 1). 

Open with DEXTER  
In the text 
Fig. 6 Examples of DOM manifestations (arrowed) in the preingress parts of folded and clipped TLCs (pluses), showing significant values of gradient G_{1}. The horizontal bars correspond to the radii of considered planets, i.e., ingresstime. 

Open with DEXTER  
In the text 
Fig. 7 Visualization of the pretransit DOM manifestation (arrowed) in the light curve of KIC 10619192 above the background of cleared (panel a) and noncleared (panel b) folded outoftransit parts (P_{tr} − Δt_{tr}) of the light curve, i.e., during the whole transit period except for the transit itself. 

Open with DEXTER  
In the text 
Fig. 8 Modeling of the pretransit DOM manifestations (arrowed) in the case of KIC 10619192. Panel a: real folded TLC; panel b: synthetic folded TLC; panel c: clipped TLC to visualize the synthetic DOM effect like in Fig. 5; panel d: model geometry with the real planet, crossing the stellar disk along the solid line together with an idealized DOM precursor (arrowed). 

Open with DEXTER  
In the text 
Fig. 9 Temporal variability of DOM effect as a pretransit flux drop, measured at − 0.02 < δt < −0.01 days. Panel a: extraction from the real light curve of KIC 10619192; panel b: analogous plot for synthetic light curve based on the used model. The abscissa scale is in differential barycentric Julian days ΔJD, counted from the reference day 2454833.0. 

Open with DEXTER  
In the text 
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