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S. Rappaport, A. Vanderburg, T. Jacobs, D. LaCourse, J. Jenkins, A. Kraus, A. Rizzuto, D. W. Latham, A. Bieryla, M. Lazarevic, A. Schmitt, Likely transiting exocomets detected by Kepler, Monthly Notices of the Royal Astronomical Society, Volume 474, Issue 2, February 2018, Pages 1453–1468, https://doi.org/10.1093/mnras/stx2735
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Abstract
We present the first good evidence for exocomet transits of a host star in continuum light in data from the Kepler mission. The Kepler star in question, KIC 3542116, is of spectral type F2V and is quite bright at Kp = 10. The transits have a distinct asymmetric shape with a steeper ingress and slower egress that can be ascribed to objects with a trailing dust tail passing over the stellar disc. There are three deeper transits with depths of ≃ 0.1 per cent that last for about a day, and three that are several times more shallow and of shorter duration. The transits were found via an exhaustive visual search of the entire Kepler photometric data set, which we describe in some detail. We review the methods we use to validate the Kepler data showing the comet transits, and rule out instrumental artefacts as sources of the signals. We fit the transits with a simple dust-tail model, and find that a transverse comet speed of ∼35–50 km s−1 and a minimum amount of dust present in the tail of ∼1016 g are required to explain the larger transits. For a dust replenishment time of ∼10 d, and a comet lifetime of only ∼300 d, this implies a total cometary mass of ≳3 × 1017 g, or about the mass of Halley's comet. We also discuss the number of comets and orbital geometry that would be necessary to explain the six transits detected over the 4 yr of Kepler prime-field observations. Finally, we also report the discovery of a single comet-shaped transit in KIC 11084727 with very similar transit and host-star properties.
1 INTRODUCTION
Advances in both space-based missions and ground-based observational techniques over the past dozen years have led to a huge expansion in the number of confirmed exoplanet detections. Currently, there are over 3500 exoplanets confirmed to orbit a variety of host star spectral types. Growing catalogues of short-period transiting exoplanets derived from data returned by the CoRoT (Baglin et al. 2006) and Kepler (Borucki et al. 2010) spacecraft are complementing a census of longer period objects being compiled from radial velocity and microlensing campaigns (Mayor & Queloz 1995; Marcy et al. 1997; Bond et al. 2004). Despite these successes, relatively little is known about the populations of extrasolar minor bodies within these systems (e.g. planetesimals, asteroids and comets). While planet-formation theories generally predict that such minor bodies are a ubiquitous by-product of protoplanetary disc evolution and should be found on scales loosely analogous to those observed in the Solar system, their low masses and small radii present extreme challenges to detection via solid-body transits and radial velocity techniques. Even in the most favourable cases, the detection of extrasolar minor bodies in either radial velocity variations or solid-body transits would require sensitivity orders of magnitude higher than the current state of the art.
Presently, the smallest solid body that has been detected in transit is Kepler-37b, a 0.27 R⊕ object on a 13-d period around a solar-like main sequence star (Barclay et al. 2013). The smallest object detected via its host star's reflex motion is the lunar-mass PSR B1257+12 d, detected via exquisitely sensitive pulsar-timing observations (Wolszczan 1994). In some cases, it is possible to detect even smaller sized objects in white-light transit observations because these objects are surrounded by optically thick material (e.g. dust) that increases the transit depths. Examples of such smaller objects include the so-called ‘disintegrating planets’ (KIC 12557548b, aka ‘KIC 1255b’ or KOI 3794, Rappaport et al. 2012; KOI 2700b, Rappaport et al. 2014a; K2-22b, Sanchis-Ojeda et al. 2015), which have been detected in transit. It is believed that these are rocky bodies of lunar size or smaller (Perez-Becker & Chiang 2013) in short-period orbits (9–22 h) that produce transits only by virtue of the dusty effluents that they emit (van Lieshout & Rappaport 2017). A perhaps similar scenario has been detected for the white dwarf WD 1145+017 (Vanderburg et al. 2015). This is an isolated white dwarf that is being orbited by debris with periods of ∼4.5–5 h, which apparently emit dusty effluents that can block up to 60 per cent of the star's light (Gänsicke et al. 2016; Rappaport et al. 2016; Gary et al. 2017). It is currently unknown how small the involved bodies are, but estimates range from the mass of Ceres on down.
There are other avenues to studying extrasolar minor planets that lie outside of the traditional exoplanet detection methods. Radio observations, in particular detections of circumstellar CO emission around stars such as HD 181327 (Marino et al. 2016), Eta Corvi (Marino et al. 2017) and Fomalhaut (Matrà et al. 2017), have been attributed to the presence of substantial populations of minor bodies at large orbital separations. Another sensitive method for detecting and understanding populations of extrasolar minor planets is through time series spectroscopy, rather than time series photometry (e.g. as performed by Kepler). Growing evidence for the existence of large populations of extrasolar minor bodies orbiting other stars has come from the detection of anomalous absorption features in the spectra of at least 16 A-type stars where Falling Evaporating Bodies (‘FEBs’) are proposed to randomly cross the observing line of sight (e.g. Ferlet, Hobbs & Vidal-Madjar 1987; Beust et al. 1990; Welsh & Montgomery 2015). FEBs can be classified as planetesimals or exocomets that have been perturbed into eccentric orbits resulting in a star-grazing periapsis and significant sublimation of volatiles within ≲0.5 au of the stellar photosphere. This phenomenon results in variable, often red-shifted, absorption-line features typically superposed on the Ca ii H & K photospheric lines. Such features have been demonstrated to manifest themselves on short time-scales (hours to days) for a number of known FEB systems associated with young A-B type stars including Beta Pictoris (Smith & Terrile 1984), 49 Ceti (Zuckerman & Song 2012), HD 42111 (Welsh & Montgomery 2015), HD 172555 (Kiefer et al. 2014a) and Phi Leonis (Eiroa et al. 2016). Beta Pictoris itself represents an important benchmark system as it is young (∼23 Myr), hosts a massive directly imaged exoplanet and has also been the target of an extensive 8-yr-long spectroscopic survey. The latter has revealed that the transient absorption features are bimodal in depth and may arise from two distinct populations of exocomets (Kiefer et al. 2014b).
In this work, we describe the first good evidence for exocomet transits of a host star in continuum light. The object in question is KIC 3542116, a young, magnitude 10, spectral type F2V star observed from 2009 to 2013 by the Kepler mission. The paper is organized as follows. In Section 2, we define the search methods and the analysis tools used in the identification of exocomet host-star candidates. In Section 3, we present what appear to be comet transits of KIC 3542116 with their distinctly asymmetric profiles. Section 4 discusses our data validation methods and quality assessment of the archival photometry. Section 5 describes the supplemental information we have gathered regarding the host star KIC 3542116 including its photometric properties, UKIRT image, spectrum, Keck high-resolution imaging and a study of the 100-yr photometric history based on the Harvard Plate Stack collection. Section 6 describes the model fits for the six significant transit events. In Section 7, we interpret the model results under a variety of a priori assumptions and list several possible scenarios to explain the observations. In Section 8, we present evidence for a single similar comet-shaped transit in KIC 11084727, a near twin to KIC 3542116. A number of discussion items are presented in Section 9. Section 10 offers a summary of our work and draws some overall conclusions.
2 VISUAL SEARCH OF THE KEPLER DATA SET
Much of the Kepler data base has been thoroughly and exhaustively searched for periodically occurring exoplanet transits (e.g. Borucki et al. 2010; Batalha et al. 2013) and binary eclipses (Prša et al. 2011; Slawson et al. 2011; Matijevič et al. 2012) yielding some 3000 viable planet candidates and a comparable number of eclipsing binaries. The types of algorithms employed include the Kepler team's transiting planet search (TPS, Jenkins 2002), Box Least Squares technique (BLS, Kovács, Zucker & Mazeh 2002) and Fast Fourier Transforms (‘FFTs’; see e.g. Sanchis-Ojeda et al. 2014). There have also been a number of searches carried out for single (i.e. ‘orphaned’) exoplanet transits (Wang et al. 2015; Foreman-Mackey et al. 2016; Uehara et al. 2016 ; Schmitt, Jenkins & Fischer 2017). Additionally, searches for astrophysical transit signals that are only quasi-periodic have been carried out in an automated way (see e.g. Carter & Agol 2013).
In an effort to further explore the larger Kepler data set for isolated transits or aperiodic phenomena, one of us (TJ) undertook a detailed visual search of the complete Q1-Q17 Kepler light curve archive spanning 201250 target stars for Data Release 25 (Thompson et al. 2016a) produced by the final Kepler Science Operations Center 9.3 pipeline (Jenkins 2017). The survey was conducted using the lctools1 software system (Kipping et al. 2015), a publicly available Windows-based set of applications designed for processing light curves in a fast and efficient manner. Two primary components from the system were utilized; lcgenerator for building light-curve files in bulk and lcviewer for visually inspecting plots of the light-curve files for signals of interest.
In this survey, light-curve files were built by lcgenerator in batches of 10 000 files. To build a light-curve file for a given star, lcgenerator (1) downloaded all available long-cadence time series files from MAST2 for Quarters 1–17,3 (2) extracted the time stamps and PDCSAP flux values from the files excluding data points having a non-zero SAP−QUALITY value, (3) normalized the flux values to a mean value of 1.0, and (4) wrote the combined results to a text file.
To expedite the survey, lcviewer was run concurrently with lcgenerator. As one batch was building, another batch was being inspected. To inspect a batch in lcviewer, a ‘Work Group’ set of text files was first produced. Once a Work Group was established, each file from that set could be opened and displayed sequentially at the click of a button – the process was nearly instantaneous. If the host star had associated Kepler Objects of Interest (KOIs), as obtained from the NASA Exoplanet Archive4 (Akeson et al. 2013), the KOI signals were automatically displayed in colour (highlighted) on the viewing screen with annotations when hovering the cursor over a transit signal for easy identification. Signals were highlighted for confirmed planets, planet candidates, and false positives. Any remaining signals were then examined in more detail as possible signals of interest. lcviewer allowed for rapid scrolling through each light-curve presentation of the entire 17 Kepler quarters with excellent temporal and flux resolution.
The visual survey of the 201250 unique Kepler target light curves was conducted over the course of 5 months, beginning in January 2017. Approximately 2000 light curves were studied during each active day of the survey, requiring some 5 h of visual study, allotting about 10 s to each target star that showed nothing interesting or unusual. Much more time was spent on the small percentage of stars that revealed one or more potentially interesting features. If an interesting photometric feature was noticed, the object was flagged for further study, vetting and discussion.
During the course of this comprehensive review, KIC 3542116 was identified as a target of interest due to three anomalous, asymmetric transit-like features occurring in Quarters 10, 12 and 13. These transits were not difficult to spot, with ≳0.1 per cent depths and ∼1-d durations. The Kepler light curve of KIC 3542116 and the transits are described in detail in Section 3. We also detected a similar-looking single asymmetric transit in the light curve of another target: KIC 11084727. We discuss this object in more detail in Section 8.
In addition to these two stars showing asymmetric transits in their light curve, we also identified other objects of interest such as single exoplanet transits and mutual lensing events in binaries. These objects will be discussed in detail in a future paper.
3 DISCOVERY OF EXOCOMET TRANSITS IN KIC 3542116
After KIC 3542116 was initially identified as an object of interest, we performed a more thorough inspection of the 4-yr Kepler light curve. KIC 3542116 was observed during the entire prime Kepler mission with high photometric precision of about 35 ppm per 30 min exposure thanks to its bright Kepler-band magnitude of Kp = 10. The full Kepler light curve is shown in Fig. 1.
Initially our interest was drawn to the three transit events described in Section 2. These events are high in signal-to-noise ratio, with depths about 20 times greater than the typical scatter of the Kepler data points. Upon closer inspection, we identified three additional shallower transits with depths about half that of the three deep transits we initially identified. These shallower transits have similar asymmetric profiles to the deep ones, but shorter durations. We label these six dips in the full light-curve plot shown in Fig. 1. We label the dips by the date on which they took place (in the Kepler Julian Date reference system BJD – 2454833). The deep dips are labelled D992, D1176 and D1268 and the shallow dips are labelled D140, D742 and D793.
In order to assess the harmonic content in the flux times series of KIC 3542116, we take the Fourier transform of the PDCSAP time series (similar to that shown in Fig. 1). The FFT in Fig. 2 shows two close periods at 1.092 and 1.160 d, which are likely due to the same underlying rotation period of KIC 3542116; the two periods are most probably due to differential rotation of spots at different stellar latitudes (see e.g. Reinhold, Reiners & Basri 2013). The ≃1 d signals have a semi-amplitude of about 175 ppm. The array of periodicities near 23 d is due to photometric leakage of a spot rotation period in KIC 3542117 (see also McQuillan, Mazeh & Aigrain 2014), a neighbouring star some 10 arcsec to the north. The 22–23 d signal has a similar semi-amplitude of about 150 ppm.
In order to obtain a clearer view of the six transit events, we attempted to separate the transits from the two rotational signals present in the light curve. We were easily able to filter the 22 d period signal by fitting a basis spline to the light curve while iteratively excluding outliers and dividing away the best-fitting spline. For a more detailed description and illustration of this process, see fig. 3 from Vanderburg & Johnson (2014). It proved more difficult to filter the second rotational signal from the light curve because it has a period of about a day, which is similar to the duration of the larger transits we detect around KIC 3542116. This coincidence of time-scales makes it particularly tricky to filter or remove the stellar variability while preserving the transits and not modifying their shapes. We attempted to separate the stellar variability from the transits using both Fourier filtering methods and fitting and removing splines to the data and filtering, but found the results unsatisfactory. We achieved better results filtering the data using Gaussian Process (GP) regression (Rasmussen & Williams 2006). In brief, Gaussian process regression involves modelling the covariance properties of a data set. The learned covariance properties can then be used to predict (either interpolating or extrapolating) how a data set might behave in the absence of data.
We took a snippet of the light curve around each transit with a duration of about 15–20 d and removed both 3 − σ outliers from the light curve and data points taken during and around transit. We trained a Gaussian process with a quasi-periodic kernel function (see equation 4 from Haywood et al. 2014) on the light curve, optimizing the parameters describing the kernel function to best match the light curve's covariance properties. We then used our optimized kernel function to predict the behaviour of the stellar activity during the transits, and divided the Kepler light curve by the GP prediction to obtain a filtered light curve.5
We show the flattened Kepler light curve of KIC 3542116 around the three deep transits in Fig. 3. All three transit profiles have remarkably similar widths, shapes and depths. In particular, all the transits have steeper ingresses with positive curvature, followed by longer egresses with negative curvature. The transits are typically 0.12–0.15 per cent deep and last for about a day.
The three shallower transits we have identified are shown in Fig. 4. Although these dips have lower signal-to-noise ratio, they all appear to have shapes consistent with the asymmetry that is more clearly evident in the deeper, higher signal-to-noise events. We have ignored all dip-like features whose depth was less than ∼450 ppm because of the possibility of having substantial distortions from the spot modulations.
We tentatively interpret the transits shown in Figs 3 and 4 as being due to the passage of comet tails across the disc of the host star, KIC 3542116, as viewed from the direction of the Earth. In this work, we henceforth refer to these as ‘comet transits’ and endeavour to demonstrate that they are indeed consistent with the hypothesis of transiting comet dust tails.
4 ASSESSMENT AND CHECKS ON THE TRANSIT DATA
We performed a set of validation checks on these transit-like events to establish their astrophysical nature and their likely source. These tests included assessing the difference images, analysing potential video crosstalk (van Cleve & Caldwell 2016) and inspecting the data quality flags associated with these events.
To determine the location of the source of the transit signatures, we inspected the pixels downlinked with KIC 3542116 for the quarters containing the three deep events, namely quarters 10, 12 and 13. Since this star is saturated and ‘bleeding’ due to its bright Kepler band magnitude Kp = 9.98,6 the standard difference image centroiding approach as per Bryson et al. (2013) is problematic: small changes in flux can affect the nature of the bleed of the saturated charge and induce light centroid shifts, especially along columns. Indeed, a shift in the flux weighted centroids in the column direction does occur during the Q12 transit, but the direction of the shift is away from KIC 3542116 and towards KIC 3542117, the dim Kp ≃ 15 M-dwarf discussed in Section 3 located ∼9.8 arcsec away from KIC 3542116. This shift is incompatible with the source being KIC 3542117 as the direction is consistent with KIC 3542116 being the source. Fig. 5 shows the direct images of KIC 3542116 and the mean difference image between out-of-transit data and in-transit data, along with the locations of KIC 3542116 and KIC 3542117. Inspection of the pixel time series over the data segments containing the transits reveals that the transit signatures are occurring in the pixels in the core of KIC 3542116 and at the ends of the columns where saturation and ‘bleed’ are happening. While the location of the source of the dips cannot be determined with great accuracy due to the saturation and bleeding, the fact that the transit signatures are not apparent in the saturated pixels but are visible in the pixels just above and below the saturated pixels is strong evidence that the source of the transits is in fact co-located on the sky with KIC 3542116.
As a further check on the astrophysical nature of these events, we also checked against video crosstalk. The Kepler CCD readout electronics do ‘talk’ to one another so that dim images (and sometimes negative images) of stars read out on the adjacent three CCD readout channels are electronically superimposed on the image data being read out by the fourth CCD channel (van Cleve & Caldwell 2016).
We looked for stars located on the Kepler detectors that might be the source of any video crosstalk signals by inspecting the full frame images for the quarters during which the three most prominent transits occurred. There is a fairly bright, possibly saturated star near the edge of the optimal aperture on output 3 on the CCD on which 3542116 is imaged (it's on output 1 in all cases), but the crosstalk coefficient is even smaller than for the other two outputs, −0.00001, so that a 50 per cent deep eclipse on this other star would be attenuated to a value of 5 ppm when its video ghost image is added to the direct image of KIC 3542116, assuming they are the same brightness. Furthermore, since the coefficient is negative, there would need to be a brightening event on the star on output 3 to cause a transit-like dip on output 1.
Fortunately, the largest crosstalk coefficient to the CCD output that 3542116 finds itself on is +0.00029, so given that the signal we are looking at is ∼0.1 per cent, a contaminating star would need to be at least 10× brighter than 3542116 to cause a problem. If there were, it would be highly saturated and bleeding, which would make it difficult to square with the pixel-level analysis indicating that the source is associated with the pixels under 3542116, as the extent of the bleeding would be significantly larger than for KIC 3542116.
We also inspected the quality flags associated with the flux and pixel time series for KIC 3542116 and find that the situation is nominal with flags for occasional events such as cosmic rays and reaction wheel desaturations, but no flags for rolling band noise during the transit events.7
Finally, we considered ‘Sudden Pixel Sensitivity Dropouts’ (SPSDs) in the data, which are due to radiation damage from cosmic ray hits on the CCD, as a possible explanation for the dips in flux that we observe. However, the shape and behaviour of such dips do not resemble what we see (Thompson et al. 2016b). In particular, the SPSD events have drops that are essentially instantaneous, and therefore are much shorter than the ∼20 and 8 long-cadence points on the ingresses that we see in the deeper and more shallow dips, respectively. Moreover, the location of the SPSDs on the CCD chip would not plausibly align with the source location and its bleed tracks for each and every one of the dips. Thus, we also discarded this idea as well.
We take all these evaluations as strong evidence that the dips we see are of astrophysical origin and that KIC 3542116 is indeed the source of them. However, we cannot categorically rule out the possibility that the dips are caused by some unknown peculiar type of stellar variability in KIC 3542116 itself. In spite of this caveat, we proceed under the assumption that the dips in flux are indeed due to the passage of objects in Keplerian orbit that are trailing tails of dusty effluents.
5 GROUND-BASED STUDIES OF KIC 3542116
The photometric properties of KIC 3542116 are summarized in Table 1. Fortunately, this is a relatively bright star that is amenable to follow-up ground-based study.
Parameter . | KIC 3542116 . | KIC 11084727 . |
---|---|---|
RA (J2000) | 19:22:52.94 | 19:28:41.19 |
Dec. (J2000) | 38:41:41.5 | 48:41:15.1 |
Kpa | 9.98 | 9.99 |
Bb | 10.49 | 10.45 |
ga | 10.38 | 10.13 |
Vb | 10.03 | 10.04 |
ra | 9.99 | 9.94 |
ia | 9.53 | 9.95 |
za | … | 10.00 |
Jc | 9.25 | 9.23 |
Hc | 9.10 | 9.07 |
Kc | 9.07 | 9.06 |
W1d | 9.06 | 8.98 |
W2d | 9.06 | 9.00 |
W3d | 8.97 | 9.03 |
W4d | 8.30 | 8.49 |
|$T_{\rm eff}^e$| (K) | 6918 ± 122 | 6790 ± 120 |
loggb (cgs) | 4.22 ± 0.12 | 4.18 ± 0.19 |
Mf (M⊙) | 1.47 ± 0.10 | 1.45 ± 0.12 |
Rf (R⊙) | 1.56 ± 0.15 | 1.55 ± 0.15 |
[m/H]e | 0.04 ± 0.11 | −0.06 ± 0.11 |
RVe (km s−1) | −21.1 ± 0.7 | +1.5 ± 0.5 |
Distanceg (pc) | |$260^{+30}_{-15}$| | |$250^{+30}_{-15}$| |
Distanceh (pc) | 235 − 335 | 225 − 255 |
v sin ie (km s−1) | 57.3 ± 0.3 | 32 ± 0.9 |
|$\mu _\alpha ^{h,b}$| (mas yr−1) | +7.6 ± 1.1 | +2.5 |
|$\mu _\delta ^{h,b}$| (mas yr−1) | −3.1 ± 1.1 | −22.9 |
Parameter . | KIC 3542116 . | KIC 11084727 . |
---|---|---|
RA (J2000) | 19:22:52.94 | 19:28:41.19 |
Dec. (J2000) | 38:41:41.5 | 48:41:15.1 |
Kpa | 9.98 | 9.99 |
Bb | 10.49 | 10.45 |
ga | 10.38 | 10.13 |
Vb | 10.03 | 10.04 |
ra | 9.99 | 9.94 |
ia | 9.53 | 9.95 |
za | … | 10.00 |
Jc | 9.25 | 9.23 |
Hc | 9.10 | 9.07 |
Kc | 9.07 | 9.06 |
W1d | 9.06 | 8.98 |
W2d | 9.06 | 9.00 |
W3d | 8.97 | 9.03 |
W4d | 8.30 | 8.49 |
|$T_{\rm eff}^e$| (K) | 6918 ± 122 | 6790 ± 120 |
loggb (cgs) | 4.22 ± 0.12 | 4.18 ± 0.19 |
Mf (M⊙) | 1.47 ± 0.10 | 1.45 ± 0.12 |
Rf (R⊙) | 1.56 ± 0.15 | 1.55 ± 0.15 |
[m/H]e | 0.04 ± 0.11 | −0.06 ± 0.11 |
RVe (km s−1) | −21.1 ± 0.7 | +1.5 ± 0.5 |
Distanceg (pc) | |$260^{+30}_{-15}$| | |$250^{+30}_{-15}$| |
Distanceh (pc) | 235 − 335 | 225 − 255 |
v sin ie (km s−1) | 57.3 ± 0.3 | 32 ± 0.9 |
|$\mu _\alpha ^{h,b}$| (mas yr−1) | +7.6 ± 1.1 | +2.5 |
|$\mu _\delta ^{h,b}$| (mas yr−1) | −3.1 ± 1.1 | −22.9 |
aMAST; http://archive.stsci.edu/k2/data_search/search.php; bVizieR (Ochsenbein, Bauer & Marcout 2000); http://vizier.u-strasbg.fr/; UCAC4 (Zacharias et al. 2013); c2MASS catalogue (Skrutskie et al. 2006); dWISE catalogue (Wright et al. 2010; Cutri et al. 2013); eTRES spectrum; see Section 5.2; fYonsei–Yale tracks (Yi et al. 2001); gBased on photometric parallax only; hThe Gaia Mission; Prusti et al. (2015).
Parameter . | KIC 3542116 . | KIC 11084727 . |
---|---|---|
RA (J2000) | 19:22:52.94 | 19:28:41.19 |
Dec. (J2000) | 38:41:41.5 | 48:41:15.1 |
Kpa | 9.98 | 9.99 |
Bb | 10.49 | 10.45 |
ga | 10.38 | 10.13 |
Vb | 10.03 | 10.04 |
ra | 9.99 | 9.94 |
ia | 9.53 | 9.95 |
za | … | 10.00 |
Jc | 9.25 | 9.23 |
Hc | 9.10 | 9.07 |
Kc | 9.07 | 9.06 |
W1d | 9.06 | 8.98 |
W2d | 9.06 | 9.00 |
W3d | 8.97 | 9.03 |
W4d | 8.30 | 8.49 |
|$T_{\rm eff}^e$| (K) | 6918 ± 122 | 6790 ± 120 |
loggb (cgs) | 4.22 ± 0.12 | 4.18 ± 0.19 |
Mf (M⊙) | 1.47 ± 0.10 | 1.45 ± 0.12 |
Rf (R⊙) | 1.56 ± 0.15 | 1.55 ± 0.15 |
[m/H]e | 0.04 ± 0.11 | −0.06 ± 0.11 |
RVe (km s−1) | −21.1 ± 0.7 | +1.5 ± 0.5 |
Distanceg (pc) | |$260^{+30}_{-15}$| | |$250^{+30}_{-15}$| |
Distanceh (pc) | 235 − 335 | 225 − 255 |
v sin ie (km s−1) | 57.3 ± 0.3 | 32 ± 0.9 |
|$\mu _\alpha ^{h,b}$| (mas yr−1) | +7.6 ± 1.1 | +2.5 |
|$\mu _\delta ^{h,b}$| (mas yr−1) | −3.1 ± 1.1 | −22.9 |
Parameter . | KIC 3542116 . | KIC 11084727 . |
---|---|---|
RA (J2000) | 19:22:52.94 | 19:28:41.19 |
Dec. (J2000) | 38:41:41.5 | 48:41:15.1 |
Kpa | 9.98 | 9.99 |
Bb | 10.49 | 10.45 |
ga | 10.38 | 10.13 |
Vb | 10.03 | 10.04 |
ra | 9.99 | 9.94 |
ia | 9.53 | 9.95 |
za | … | 10.00 |
Jc | 9.25 | 9.23 |
Hc | 9.10 | 9.07 |
Kc | 9.07 | 9.06 |
W1d | 9.06 | 8.98 |
W2d | 9.06 | 9.00 |
W3d | 8.97 | 9.03 |
W4d | 8.30 | 8.49 |
|$T_{\rm eff}^e$| (K) | 6918 ± 122 | 6790 ± 120 |
loggb (cgs) | 4.22 ± 0.12 | 4.18 ± 0.19 |
Mf (M⊙) | 1.47 ± 0.10 | 1.45 ± 0.12 |
Rf (R⊙) | 1.56 ± 0.15 | 1.55 ± 0.15 |
[m/H]e | 0.04 ± 0.11 | −0.06 ± 0.11 |
RVe (km s−1) | −21.1 ± 0.7 | +1.5 ± 0.5 |
Distanceg (pc) | |$260^{+30}_{-15}$| | |$250^{+30}_{-15}$| |
Distanceh (pc) | 235 − 335 | 225 − 255 |
v sin ie (km s−1) | 57.3 ± 0.3 | 32 ± 0.9 |
|$\mu _\alpha ^{h,b}$| (mas yr−1) | +7.6 ± 1.1 | +2.5 |
|$\mu _\delta ^{h,b}$| (mas yr−1) | −3.1 ± 1.1 | −22.9 |
aMAST; http://archive.stsci.edu/k2/data_search/search.php; bVizieR (Ochsenbein, Bauer & Marcout 2000); http://vizier.u-strasbg.fr/; UCAC4 (Zacharias et al. 2013); c2MASS catalogue (Skrutskie et al. 2006); dWISE catalogue (Wright et al. 2010; Cutri et al. 2013); eTRES spectrum; see Section 5.2; fYonsei–Yale tracks (Yi et al. 2001); gBased on photometric parallax only; hThe Gaia Mission; Prusti et al. (2015).
5.1 UKIRT image
The UKIRT image of KIC 3542116 is shown in Fig. 6. In addition to the bright target star KIC 3542116 at Kp = 9.98, the image shows a neighbouring star, KIC 3542117, with Kp = 14.9 some 10 arcsec to the north. This star is the source of the 23-d modulations (see McQuillan et al. 2014) that leak into the flux data train of KIC 3542116, and may be a low-mass bound companion to this star (see Section 5.3).
5.2 TRES classification spectrum
We observed KIC 3542116 with the Tillinghast Reflector Echelle Spectrograph (TRES) on the 1.5-m telescope at Fred L. Whipple Observatory (FLWO) on Mt. Hopkins, AZ. We obtained two high-resolution (λ/Δλ = 44 000) optical spectra of KIC 3542116 – the first on 2017 June 9 and the second on 2017 June 14. Exposure times of 300 s and 200 s yielded signal-to-noise ratios of 50 and 43 per resolution element at 520 nm. We cross-correlated the two spectra with a suite of synthetic stellar template spectra from a library of synthetic spectra generated from Kurucz (1992) model atmospheres. These cross-correlations yielded an absolute radial velocity of −21.1 km s−1. Cross-correlating the two spectra against one another and averaging the results over many different echelle orders yielded a shift of only 400 m s− 1 between the two spectra. This is consistent with the photon-limited uncertainties for an F star with a rotational broadening of 57 km s−1 (at this SNR the precision would be at least an order of magnitude better for a slowly rotating solar-type star).
We estimated stellar parameters using the Stellar Parameter Classification code (‘SPC’; Buchhave et al. 2012). SPC cross-correlates a library of synthetic template spectra with varying temperature, metallicity, surface gravity and line broadening against the observed spectrum and interpolates the parameters from the best-matched template peaks to estimate the actual stellar parameters. SPC was designed to measure stellar parameters of slowly rotating stars close in effective temperature to the Sun and has been extensively tested and used for stars cooler than the Sun. For rapidly rotating stars hotter than the Sun (such as KIC 3542216), SPC has not been tested as fully and may have systematic errors, especially in the surface gravity and metallicity.
An SPC analysis of the TRES spectra of KIC 3542116 yields an effective temperature of 6900 ± 120 K and a projected rotational velocity of 57 km s− 1. This makes it fairly unusual for stars observed by Kepler, which mostly monitored sun-like dwarfs and smaller stars, which are more amenable for searches for small Earth-like planets. The properties of KIC 3542116 measured with, or inferred from, the TRES spectra are summarized in Table 1.
5.3 High-resolution imaging
We observed KIC 3542116 with the Near Infrared Camera 2 (NIRC2) instrument behind the Natural Guide Star (NGS) adaptive optic (AO) system on the Keck II telescope on the night of 2017 June 28. We obtained standard ‘AO’ images, both with and without a coronagraph in place. We also recorded interferograms produced by placing a sparsely sampled nine-hole non-redundant aperture mask (‘NRM’) in the pupil plane to re-sample the full telescope aperture into an interferometric array (Tuthill et al. 2006, 2010). This process makes it possible to detect companions closer to the target star than the traditional diffraction limit. We obtained four 20-s exposures in imaging mode in K΄ band, as well as four exposures of the same duration with the coronagraph. Six additional 20-s exposures were taken with the NRM in place. The imaging observations were reduced following Kraus et al. (2016), and detections and detection limits were assessed using the methods they described.
The summed set of the standard AO images is shown in the top panel of Fig. 7; it covers only the central 1 arcsec × 1 arcsec region of the field. The bottom panel in Fig. 7 shows the resultant image acquired with the coronagraphic disc in place, and it covers a wider 4 arcsec × 4 arcsec portion of the field. The images are colour coded so that roughly each contrast change of 1 mag is represented by a change of one colour. From the ordinary AO image we can estimate that there is no neighbouring star of comparable K΄ magnitude within 0.05 arcsec of the target star, and no star that is at most 4 mag fainter within 0.15 arcsec. With the AO-plus-coronagraph image, the sensitivities are comparable out to about 0.8 arcsec, beyond which the image goes 2 mag deeper than the plain AO image.
We can further constrain the magnitudes of any stars within ∼0.2 arcsec of the target, using the nine-hole mask interferogram. The analysis of those data shows that contrasts of <1.5, 4.2, 5.1 and 4.8 K΄ magnitudes can be rejected at the 99 per cent confidence limit at distances of 0.01–0.02, 0.02–0.04, 0.04–0.08 and 0.08-0.16 arcsec, respectively.
We summarize all of the constraints from the three different imaging modes in Fig. 8.
We now consider the constraints we can place on possible neighbouring stars in each of two different categories: (i) random interloping field stars and (ii) physically bound companions. For unbound field stars, we see from Fig. 8 that for angular separations greater than ≃0.4 arcsec there are no stars within 7 K΄ magnitudes of the target star. The significance of this latter limit is that stars fainter than Kp = 17th magnitude8 could not produce a dip as apparently deep as 0.0015 in the flux of KIC 3542116. It is possible, though most unlikely, that there could be a star accidentally aligned with the target to within ≲0.4 arcsec that is the source of the dips. We estimate the probability of a nearby interloper star with the requisite magnitude of Kp ≲ 17 randomly lying within 0.4 arcsec of KIC 3542116 as ≲ 0.1 per cent (see e.g. fig. 9 of Rappaport et al. 2014b).
Alternatively, the target star could have a physical binary companion that is the host of the dips. In this case, the companion star would be at the same distance and coeval with the target star. Since the target star is not significantly evolved (see Table 1) any fainter companion star would necessarily be redder in colour and lower in mass than the target star. For redder stars, the K΄-band is obviously more sensitive than the Kp band. From Fig. 8, we see that for any binary (projected) separation ≳0.04 arcsec all binary companions with ΔK΄ ≳ 4 are ruled out. That already suggests that any companion-star mass satisfying this requirement must be ≲0.8 M⊙. However, for main-sequence stars of this mass, and lower, the value of ΔKp to be expected in the Kepler band would be 2–3 mag greater. Thus, it is safe to say that for angular separations ≳0.04 arcsec there are no binary companion stars that could produce the observed dips. This translates to a binary orbital projected separation of ≲10 au. If we combine this with the constraint on the change in RVs over a 5-d interval (Section 5.2), this suggests that any viable binary companion star that could produce the dips would likely have an orbital separation of ∼0.5–10 au.
Of course very faint binary companions that are not the source of the dips are allowed. They must, however, still satisfy the constraints summarized in Fig. 8. In this regard, we note that the faint star, KIC 3542117 (see Fig. 6) has the colours (taken from the Sloan Digital Sky Survey images; Ahn et al. 2012) to be a ≃0.5 M⊙ (see also Dressing & Charbonneau 2013) companion star since it lies relatively close to the same photometric distance as KIC 3542116, and because it has only a ≲ 15 per cent chance of being found within 10 arcsec of the target star by chance (see e.g. fig. 9 of Rappaport et al. 2014b). We note, however, that the proper motion of KIC 3542117 is not consistent with comovement, though the Deacon et al. (2016) seeing-limited astrometry might be limited by the brightness of KIC 3542116. Any possible association should become clear in the upcoming Gaia Data Release 2.
5.4 Historical plate stacks
The available photometry of KIC 3542116 from the past century, taken from the ‘Digital Access Sky Century at Harvard’ (‘DASCH’; Grindlay et al. 2009) are shown in Fig. 9. The systematic drop in flux, by ∼10 per cent across the ‘Menzel gap’, is likely due to a change in the plate emulsion response. No other obvious dimmings or outbursts of the star are observed. A Fourier transform of these data show no clear periodicities in the range of 1–100 d over the past 100 yr down to a level of ≳2 per cent.
6 MODEL FITS TO THE TRANSITS
The repeatably asymmetric shape of the transits of KIC 3542116 is suggestive of an occulter with some sort of sustained or repeatable dust outflows causing the dimming. Here, we show that the observed asymmetry and the repeatable shape are consistent with, and what we might expect from, a large comet transiting the star with a dusty tail. We describe a simple model for the transit of a comet and show that the six transits detected in the light curve of KIC 3542116 are well fit by this model.
Almost all cometary dust tails will lag behind the direction in which the comet is moving. This is as opposed to the ion tails of comets that are driven out nearly radially by the stellar wind of the host star (see e.g. Reyes-Ruiz et al. 2010). When the dust is released from the immediate and gravitational environs of the comet, it finds itself in a reduced effective gravity due to the effects of radiation pressure on the dust grains. This, in turn, results in the dust moving too fast to remain in the same orbit as the parent comet. Somewhat paradoxically, the higher speed causes the dust to go into a higher orbit which, in turn, causes its mean orbital speed to decrease, and thus results in a trailing tail (in the sense of lagging in angular position).
Leading dust tails are also possible, but usually in the context of the dust overflowing the Roche lobe of the parent body, and with little subsequent radiation pressure (see e.g. Sanchis-Ojeda et al. 2015). However, Roche lobe overflow typically requires orbital periods of ≲1 d.
In this work, we assume that the orbital periods of the putative comets are substantially longer than the transit durations (∼1 d) and that the transverse velocity, vt, during the transit is essentially a constant. For lack of more detailed information, we further assume that the dust tail is narrow compared to the size of the host star and that its dust extinction profile is a simple exponential function of distance from the comet (see e.g. Brogi et al. 2012; Sanchis-Ojeda et al. 2015).
We utilize a Markov Chain Monte Carlo (‘MCMC’) code (Ford 2005; Madhusudhan & Winn 2009; Rappaport et al. 2017) to fit a comet-tail transit model to each of the six transits that we observe in KIC 3542116. There are six free parameters to be fit: t0, λ, C, vt, b and DC, where the final term is the DC background flux level away from the transit. For each choice of parameters, we generate a model light curve by integrating over the dust tail where it overlaps the stellar disc, and repeating this in increments of 6 min as the comet crosses the stellar disc. The model light curve is then convolved with the 30 min integration time of the Kepler long-cadence sampling. Each model is then evaluated via the χ2 value of the fit to the data, and the code then decides, via the Metropolis–Hastings jump condition, whether to accept the new set of parameters or to try again.
Each MCMC chain has 3 × 105 links, and we run a half-dozen chains. The results for the fitted parameters are given in Table 2 for each of the parameters and for each of the six transits. We show illustrative MCMC correlations among the three physically interesting parameters, λ, vt and b, graphically for the fit to transit D1268 in Fig. 10.
Parameter . | Dip 140 . | Dip 742 . | Dip 793 . | Dip 992 . | Dip 1176 . | Dip 1268 . |
---|---|---|---|---|---|---|
1. Depth (ppm) | 491 ± 38 | 524 ± 58 | 679 ± 125 | 1200 ± 100 | 1500 ± 130 | 1900 ± 150 |
2a. |$v_t^{a}$| (R* d−1) | 7.76 ± 0.31 | 6.55 ± 0.73 | 7.42 ± 0.42 | 3.04 ± 0.16 | 4.34 ± 0.39 | 3.70 ± 0.20 |
2b. vt (km s−1) | 89.8 ± 3.6 | 75.8 ± 8.5 | 85.9 ± 4.9 | 35.2 ± 1.8 | 50.2 ± 4.5 | 42.8 ± 2.3 |
3. λb (R*) | 0.44 ± 0.04 | 0.53 ± 0.09 | 0.85 ± 0.16 | 0.59 ± 0.10 | 0.76 ± 0.11 | 0.72 ± 0.08 |
4. bc (R*) | 0.66 ± 0.05 | 0.47 ± 0.18 | 0.63 ± 0.14 | 0.27 ± 0.13 | 0.44 ± 0.17 | 0.27 ± 0.14 |
5. |$t_0^{d}$| | 139.98 ± 0.02 | 742.45 ± 0.02 | 792.78 ± 0.02 | 991.95 ± 0.02 | 1175.62 ± 0.02 | 1268.10 ± 0.02 |
Parameter . | Dip 140 . | Dip 742 . | Dip 793 . | Dip 992 . | Dip 1176 . | Dip 1268 . |
---|---|---|---|---|---|---|
1. Depth (ppm) | 491 ± 38 | 524 ± 58 | 679 ± 125 | 1200 ± 100 | 1500 ± 130 | 1900 ± 150 |
2a. |$v_t^{a}$| (R* d−1) | 7.76 ± 0.31 | 6.55 ± 0.73 | 7.42 ± 0.42 | 3.04 ± 0.16 | 4.34 ± 0.39 | 3.70 ± 0.20 |
2b. vt (km s−1) | 89.8 ± 3.6 | 75.8 ± 8.5 | 85.9 ± 4.9 | 35.2 ± 1.8 | 50.2 ± 4.5 | 42.8 ± 2.3 |
3. λb (R*) | 0.44 ± 0.04 | 0.53 ± 0.09 | 0.85 ± 0.16 | 0.59 ± 0.10 | 0.76 ± 0.11 | 0.72 ± 0.08 |
4. bc (R*) | 0.66 ± 0.05 | 0.47 ± 0.18 | 0.63 ± 0.14 | 0.27 ± 0.13 | 0.44 ± 0.17 | 0.27 ± 0.14 |
5. |$t_0^{d}$| | 139.98 ± 0.02 | 742.45 ± 0.02 | 792.78 ± 0.02 | 991.95 ± 0.02 | 1175.62 ± 0.02 | 1268.10 ± 0.02 |
Note.aTransverse comet speed during the transit; bExponential tail length from equation (1); cImpact parameter; dTime when the comet head passes the centre of the stellar disc.
Parameter . | Dip 140 . | Dip 742 . | Dip 793 . | Dip 992 . | Dip 1176 . | Dip 1268 . |
---|---|---|---|---|---|---|
1. Depth (ppm) | 491 ± 38 | 524 ± 58 | 679 ± 125 | 1200 ± 100 | 1500 ± 130 | 1900 ± 150 |
2a. |$v_t^{a}$| (R* d−1) | 7.76 ± 0.31 | 6.55 ± 0.73 | 7.42 ± 0.42 | 3.04 ± 0.16 | 4.34 ± 0.39 | 3.70 ± 0.20 |
2b. vt (km s−1) | 89.8 ± 3.6 | 75.8 ± 8.5 | 85.9 ± 4.9 | 35.2 ± 1.8 | 50.2 ± 4.5 | 42.8 ± 2.3 |
3. λb (R*) | 0.44 ± 0.04 | 0.53 ± 0.09 | 0.85 ± 0.16 | 0.59 ± 0.10 | 0.76 ± 0.11 | 0.72 ± 0.08 |
4. bc (R*) | 0.66 ± 0.05 | 0.47 ± 0.18 | 0.63 ± 0.14 | 0.27 ± 0.13 | 0.44 ± 0.17 | 0.27 ± 0.14 |
5. |$t_0^{d}$| | 139.98 ± 0.02 | 742.45 ± 0.02 | 792.78 ± 0.02 | 991.95 ± 0.02 | 1175.62 ± 0.02 | 1268.10 ± 0.02 |
Parameter . | Dip 140 . | Dip 742 . | Dip 793 . | Dip 992 . | Dip 1176 . | Dip 1268 . |
---|---|---|---|---|---|---|
1. Depth (ppm) | 491 ± 38 | 524 ± 58 | 679 ± 125 | 1200 ± 100 | 1500 ± 130 | 1900 ± 150 |
2a. |$v_t^{a}$| (R* d−1) | 7.76 ± 0.31 | 6.55 ± 0.73 | 7.42 ± 0.42 | 3.04 ± 0.16 | 4.34 ± 0.39 | 3.70 ± 0.20 |
2b. vt (km s−1) | 89.8 ± 3.6 | 75.8 ± 8.5 | 85.9 ± 4.9 | 35.2 ± 1.8 | 50.2 ± 4.5 | 42.8 ± 2.3 |
3. λb (R*) | 0.44 ± 0.04 | 0.53 ± 0.09 | 0.85 ± 0.16 | 0.59 ± 0.10 | 0.76 ± 0.11 | 0.72 ± 0.08 |
4. bc (R*) | 0.66 ± 0.05 | 0.47 ± 0.18 | 0.63 ± 0.14 | 0.27 ± 0.13 | 0.44 ± 0.17 | 0.27 ± 0.14 |
5. |$t_0^{d}$| | 139.98 ± 0.02 | 742.45 ± 0.02 | 792.78 ± 0.02 | 991.95 ± 0.02 | 1175.62 ± 0.02 | 1268.10 ± 0.02 |
Note.aTransverse comet speed during the transit; bExponential tail length from equation (1); cImpact parameter; dTime when the comet head passes the centre of the stellar disc.
7 INTERPRETING THE TRANSITS
Now that we have shown that the shapes of the transits of KIC 3542116 are consistent with the shape caused by a dusty tailed comet, in this section, we will show that the parameters we derive from our fits correspond to plausible physical conditions.
7.1 Inferred comet orbital velocities
The first step in trying to understand what orbits the putative comets orbiting KIC 3542116 would be on, is to attempt to explain the observed transverse speeds of the bodies. This involves speeds of 35–50 km s−1 for the deeper transits and 75–90 km s−1 for the more narrow and shallow transits (see Table 2). To gain some insight into this problem, we carried out the following exercise. We chose random orbital periods from a distribution that is uniform in log Porb, and with a uniform distribution of eccentricities from e = 0 to 1. With respect to a fixed viewing direction, we also chose longitudes of periastron, ω, at random from 0 to 2π (ω is here defined as the angle from entering the plane of the sky to periastron). For simplicity, all orbits are taken to be in the same plane with an inclination angle of 90° with respect to the observer.
As discussed below in Section 7.3, comet dust tails are very unlikely to survive sublimation at distances from the host star of ≲0.1 au (see equation 5 and Fig. 12). Therefore, any systems with such close approaches during the transit are eliminated from the diagram. Equations (4) and (5) can be combined to yield analytic relations for the upper limit to vt and lower limit to Porb in Fig. 11 for a given minimum allowed star–comet separation during transit: |$v_t < 160 \, d_{0.1}^{-1/2}$| km s−1 and |$P_{\rm orb} > 3.5 \, d_{0.1}^{3/2}$| d, where the subscript on d indicates that it is normalized to 0.1 au. These boundaries are clearly evident in Fig. 11.
As we can see from Fig. 11, transverse speeds of 35–50 km s−1 would correspond to circular orbit periods of ∼100–300 d, but periods as short as ∼6 d are plausible. Note, especially from the right-hand panel in Fig. 11, that arbitrarily long orbital periods are quite possible. Similarly, the more narrow and shallow dips imply transverse orbital speeds during transit ranging between ∼75 and 90 km s−1. From Fig. 11, we see that such orbits would correspond to circular orbit periods of ∼20–35 d. However, periods as short as ∼6 d or arbitrarily long are also quite acceptable.
One possibility is that all three of the deeper transits arise from a single body in a periodic orbit (or nearly so). In that case, the orbital period would be 92 d, but would have to exhibit transit timing variations (‘TTVs’) of ∼1/3 d. Additionally, there would be the issue of why only three transits appear out of a possible ∼16 that potentially could have been detected during the Kepler main mission. Presumably, such an explanation requires highly and remarkably variable dust emission from the body. In this regard, we note that the dust-tail optical depths of some Solar system comets are highly variable (see e.g. Montalto et al. 2008; Sekanina & Chodas 2012; Knight & Schleicher 2015) and that the transit depths in the ‘disintegrating’ planets KIC 1255b and K2-22b are also highly and erratically variable (Rappaport et al. 2012; Sanchis-Ojeda et al. 2015). If the three deeper transits are indeed due to a single body orbiting with TTVs of up to ∼1/3 per cent of the orbital period, then only the discrete periods of 92/n, where n = 1, 2, 3,… are allowed.
Similarly, the three more shallow and narrow transits could be due to another distinct body orbiting KIC 3542116. The maximum such period consistent with these three transits is ∼51 d (the time interval between D742 and D793). If these three shallower transits are indeed due to a single body in a fixed orbit, then one must explain why only three of a possible 30 transits are detected. Again, this would require highly variable dust emission.
Alternatively, all six of the transits could each be due to a separate body in the system. In that case, one needs to explain why all three of the deeper transits are so remarkably similar in depth, shape and duration. And, to a somewhat lesser degree, the same argument applies to the three more shallow transits. We therefore tentatively adopt the working hypothesis that there are at least two distinct orbiting minor bodies in KIC 3542116 with cometary tails that produce transits.
7.2 Inferred dust mass-loss rates
Without knowing the specific properties of the dust or the comet orbit, it is difficult to know the speed of the dusty effluents with respect to the comet. However, if we assume a minimal value for β, the ratio of radiation pressure to gravity, of ∼0.05, the relative dust speed could be ∼0.1 times the orbital speed of the comet (see e.g. Rappaport et al. 2014a), or some 5 km s−1. At this rate, the dust tail at ∼2R* from the comet would be replenished every ∼5 d. This, in turn, corresponds to a minimum dust mass-loss rate of |$\dot{M}_d \gtrsim 2.5 \times 10^{10}$| g s−1.
Finally in this regard, if we assume that the comet emits dust at this rate for even half of the interval between the D992 and D1268 transits (276 d), during which time there were three of a possible four transits seen, then the minimum comet mass would be Mc ≳ 3 × 1017 g. This is just a little bit greater than the mass of Halley's comet.
7.3 Dust sublimation
In order for a dust-rich comet tail to exist, it should not be so close to the host star that the dust grains leading to most of the opacity quickly sublimate (i.e. on less than a time-scale of about a day). The equilibrium temperature of the dust, Tequil, depends mainly on the stellar flux at its location, the grain size, s, and the imaginary part of its index of refraction, k, at the wavelengths of interest. We have computed Tequil for three different characteristic grain sizes, s = 0.1, 1 and 10 μm as functions of their distance from KIC 3542116. In lieu of discussing any particular mineral composition for the grain size, we simply adopt three illustrative values for k equal to 1, 0.1 or 0.01, that are taken to be independent of wavelength, and are fairly representative of different refractory minerals (see e.g. Beust et al. 1998; van Lieshout, Min & Dominik 2014; fig. 13 of Croll et al. 2014; Xu et al. 2017; and references therein). The Mie scattering cross-sections were computed with the Bohren & Huffman (1983) code.
The bottom line of these calculations is that for many common minerals (e.g. obsidian, magnetite, fayalite, enstatite, forsterite, corundum and SiC), which commence rapid sublimation at Tequil ≳ 1200–1700 K,10 we can estimate that the dust tails begin to sublimate away at distances from KIC 3542116 of ≲0.1–0.3 au (see also Beust et al. 1998).
8 ANOTHER POTENTIAL EXOCOMET CANDIDATE KIC 11084727
Of all the Kepler target stars that were visually examined, the most compelling case for exocomet transits was KIC 3542116, discussed extensively above. However, there was one other target star, KIC 11084727, which exhibited a single transit event that was very similar to the three deeper transits found in KIC 3542116.
The transit event in KIC 11084727 is shown in Fig. 13 along with a model fit. As is evident from a casual visual inspection, and from the formal model fit (the red curve in Fig. 13), the transit properties are very similar in shape, depth and duration to those listed in Table 2 for the deeper dips in KIC 3542116.
The data validation process for this target was essentially the same as described in Section 4 for KIC 3542116. All indications are that this dip is astrophysical in origin and is associated with KIC 11084727.
The target star KIC 11084727 is a near twin to KIC 3542116 as can be seen from a compilation of their photometric properties in Table 1, with nearly identical magnitudes (at Kp = 9.99), similar Teff values, and comparable radii. The similarities between KIC 3542116 and KIC 11084727 are particularly striking given that the majority of Kepler targets were cooler, Sun-like stars and suggest that comet transits may preferentially happen around stars of this spectral type.
The fact that we have detected two individual stars with similar comet-like transit events also suggests that there may be more (perhaps shallower) comet-like transits hidden in the Kepler data set.
9 DISCUSSION
In this section, we discuss some possible follow-up observations of KIC 3542116 and KIC 11084727 that may connect these systems to other exocomet systems found with ground-based observations. We also attempt to understand the relative detection sensitivity of dusty transits using photometry and spectral line changes. A number of dynamical effects that might be responsible for driving comets into orbits close to the host star are briefly discussed. Finally, we compare our two systems with Boyajian's star (KIC 8462852).
It might be profitable to carry out follow-up ground-based spectroscopic studies of KIC 3542116 to see if any of the same type of spectral line changes such as are found in β Pic, 49 Ceti, HD 42111, HD 172555 and ϕ Leo can be discerned in KIC 3542116. Of the 16 stars listed by Welsh & Montgomery (2015) as exhibiting spectral line changes that are likely due to exocomets, the magnitudes range from 3.6 to 7.2 with a mean of 5.6. Moreover, the spectral types of these stars range from B9 to F6, with 2 of the 23 being stars of the F spectral type. Thus, aside from the fact that KIC 3542216 and KIC 11084727 are more than an order of magnitude fainter than these other stars, it may still be possible, even if challenging, to monitor the spectral line shapes of KIC 3542116 and KIC 11084727 for changes. We believe that connecting photometric transits to spectral transits in the same star could prove very rewarding.
Neither KIC 3542116 nor KIC 11084727 shows any particular evidence for being extremely young, e.g. via very rapid rotation or WISE excess flux. Nor is there any specific reason to believe that there is disc activity or populations of minor bodies at orbital separations much greater than these inferred for the comets in this work. Such debris might be expected to exhibit CO emission as is seen in HD 181327 (Marino et al. 2016), Eta Corvi (Marino et al. 2017) and Fomalhaut (Matrà et al. 2017). Nevertheless, the stars reported on herein are sufficiently unusual among the Kepler ensemble of 2 × 105 stars, so that it could be worth the gamble to use The Atacama Large Millimeter/submillimeter Array (ALMA) to search for CO emission around KIC 3542116 and KIC 11084727.
The observations of likely comets in two Kepler stars in this work raise some interesting questions by way of comparison with the comets (FEBs) inferred from spectral-line changes in a substantial number of primarily bright A stars (e.g. Beust et al. 1990; Welsh & Montgomery 2015). In particular, why are we not detecting ‘swarms’ of comets as are suggested by the papers on FEBs?
Of the 2 × 105Kepler stars studied continuously for approximately 4 yr, we have found only 6 comet-like dips in one star (KIC 3542116) and 1 dip in KIC 11084727. Presumably, Kepler is not as sensitive to small comets as the spectroscopic methods are. In the spectral approach, the comet is only blocking a small part of the light (a fraction of one spectral line), but which can be readily detectable in the line profile. By contrast, when looking at transits in Kepler data, we are collecting much of the bolometric flux from the star. Therefore, a much larger comet may be required to be detectable by Kepler than by a spectrograph on a large telescope.
The conclusion we draw from these expressions is that ground-based spectral observations of bright stars (magnitude 2–6) should be more sensitive, in terms of detecting a given |$\dot{M}$|, than are the Kepler observations, but with substantial uncertainties in the choice of parameter values. One caveat is in order, however, when interpreting equations (12) and (13). Presumably the dust will only survive rapid sublimation at distances beyond ∼0.1–0.3 au (see Fig. 12). By contrast, the atoms (in particular Ca ii, Mg ii and Fe ii) will mostly be present closer in where the dust, bearing many of the heavier elements, sublimates and the minerals become photodissociated and ionized.
With regard to the number of comets that should be seen crossing the disc of the host star, this rate should depend heavily on whether the infalling comet orbits are distributed roughly isotropically (lower rate) or if the reservoir of bodies producing the dusty tails has orbits that are coplanar with the angular momentum vector of the system (higher rate if the observer lies in this plane). We do have some limited information on the viewing inclination angle with respect to the spin axis of KIC 3542116. From Table 1, we find v sin i ≃ 57.3 ± 0.3 km s−1, R* ≃ 1.56 ± 0.15 R⊙ and a rotation frequency of 0.888 ± 0.04 cycle d−1. When we use this information to compute the inclination angle, i, we find that 45° ≲ i ≲ 80° with 95 per cent confidence. This is suggestive that we could be viewing the system from at least a partially favourable in-plane vantage point. It will be helpful to firm up these uncertainties in future work.
In Section 7.1, we made some initial assessments of the kinds of orbits that were most likely responsible for the exocomet transits we report (see, in particular, the right-hand panel of Fig. 11). There are basically two major dynamical mechanisms for generating potentially large numbers of transiting exocoments. These have been very well explored in the context of the best-studied FEB system – β Pictoris. However, we should keep in mind that in β Pic, there is a high preponderance of red-shifted FEB events, which implies a particular orientation for the comet trajectories. With this caveat in mind, we note that these dynamical mechanisms involve secular perturbations by a distant planet. First, they may be generated via the Kozai–Lidov mechanism (see e.g. Bailey, Chambers & Hahn 1992). The second mechanism involves resonances, either secular (Levison, Duncan & Wetherill. 1994) or mean-motion (Beust & Morbidelli 1996, 2000). In the former case, the exocomet orbits should be roughly isotropically distributed thanks to a rotational invariance of the Kozai Hamiltonian. Conversely, in the latter case, the longitude of periastron of the perturbing planet controls the geometry of the infall. Also, in this case, Beust & Valiron (2007) showed that the exocomets may have large inclination oscillations when reaching the FEB state even if they started out with only modest inclinations with respect to the orbit of the perturbing planet. We note that in the Solar system, most sun-grazers are thought to arise from the Kozai mechanism (e.g. Bailey et al. 1992). In the case of β Pic, the mean-motion-resonance mechanism was favoured to match the abundant statistics of the FEB events in that system. By contrast, for KIC 3542116, with only a few transit events detected, all of the above mechanisms are worthy of consideration.
Finally, the deep dips in the flux of KIC 8462852 (aka ‘Boyajian's Star’; Boyajian et al. 2016) are worth trying to relate to what is observed in KIC 3542116. By contrast, the largest flux dips in the former star reach 22 per cent that is more than two orders of magnitude greater than the transits we see in KIC 3542116. Furthermore, the dips in KIC 8462852 can last for between 5 and 50 d, depending on how the beginning and end points of the dip are defined. These are one to two orders of magnitude longer than for the transits in KIC 3542116. Finally, we note that none of the dips in KIC 8462852 has a particularly comet-shaped profile. There have been a number of speculations about the origin of the dips in KIC 8462852, including material resulting from collisions of large bodies and moving in quasi-regular orbits (Boyajian et al. 2016); swarms of very large comets (Boyajian et al. 2016); and even a ring of dusty debris in the outer Solar system (Katz 2017). However, there is currently no compelling evidence for any of these scenarios.
10 SUMMARY AND CONCLUSIONS
In this work, we reported the discovery of six apparent transits in KIC 3542116 that have the appearance of a trailing dust tail crossing the disc of the host star. We have tentatively postulated that these are due to between 2 and 6 distinct comet-like bodies in the system. We also found a single similarly shaped transit in KIC 11084727. Both of these host stars are of F2V spectral types.
We have carefully vetted the data from these target stars, including assessing the difference images in and out of transit, analysing potential video cross-talk, and inspecting the data quality flags associated with the dip events. The vetting also included deep high-resolution imaging studies of our prime target, KIC 3542116. No companion stars were found within an outer working angle of ρ ∼ 5 arcsec, though the nearby star KIC 3542117 (ρ = 10 arcsec) might plausibly be a bound companion.
The spot rotation period in KIC 3542116 is about as long as the durations of the deeper transits we see, and therefore it is difficult to imagine that they are caused by highly variable spots (which tend to produce dips at a fraction of the rotation period). Nonetheless, we cannot categorically rule out the possibility that the transit-like events are caused by some previously unknown type of stellar variability.
With this caveat in mind, we proceeded to study these systems under the assumption that the dips in flux are indeed due to dusty-tailed objects transiting the host stars. We then fit these transits with a model dust tail that is assumed to have an exponentially decaying extinction profile. The model profiles fit the transits remarkably well.
The inferred speeds of the underlying dust-emitting body during the transits are in the range of 35–50 km s−1 for the deeper transits in KIC 3542116 and for the single transit in KIC 11084727. For the more shallow and narrow transits in KIC 3542116, the inferred speeds are 75–90 km s−1. From these speeds, we can surmise that the corresponding orbital periods are ≳90 d (and most probably, much longer) for the deeper transits, and ≳50 d for the shorter events.
Solar system sun-grazing comets typically have extremely long orbital periods (e.g. ∼2300 yr for the members of the populous Kreutz group). Halley's comet, which has an apohelion distance of ∼125 R⊙, has a period of ≃75 yr, while the shortest known period for a bright comet is Comet Encke at 3.3 yr. The overall shortest period is Comet 311/Pan-STARRS with a period of 3.2 yr. Thus, if either the three deeper or the three more shallow transits in KIC 3542116 are from single orbiting bodies, then the maximum associated periods of 51–92 d would be considerably shorter than for Solar-system comets. The periods of the comets producing the FEB events are largely unknown. However, the characteristic infall velocities associated with the CaII FEB's (∼50 km s−1; e.g. Beust et al. 1990) are compatible with what we find for KIC 3542116 and KIC 11084727.
The fact that we find comet-like transits in two Kepler target stars holds out the promise that such events are not particularly rare. This is especially true when we note that the survey was made visually and without the aid of a computer search. In turn, the fact that the search was carried out visually raises the issue of its completeness. In this regard, we believe that there was no particular obstacle to finding asymmetric transits with depths of ≳0.1 per cent and lasting for ≳1/3 d, even in the presence of significant star-spot activity. Furthermore, we likewise found that data breaks and artefacts would also not have impeded the search.
We thus believe that we have found the majority of such comet-like transits in the Kepler data set, though we cannot preclude the possibility that there are many more such features with depths ≲0.1 per cent.
We reiterate that there are striking similarities between KIC 3542116 and KIC 11084727 in terms of both the stellar properties and the comet-like transit events. This is also noteworthy because the majority of Kepler targets were cooler, Sun-like stars. This might suggest that comet transits may preferentially happen around stars of this spectral type, and it would be instructive to try to understand why this might be.
One encouraging note in regard to finding more such comet-like transits in other stars is that dips in flux at the ≳0.1 per cent level and lasting for hours to days should not be particularly challenging for the photometry in the upcoming TESS mission (Ricker et al. 2015). Furthermore, the host stars are likely to be bright, plausibly even brighter than the 10th magnitude stars reported on here.
Note added in manuscript: After this manuscript was submitted we became aware of a remarkably prescient paper by Lecavelier des Etangs, Vidal-Madjar & Ferlet (1999) that predicted the photometric profiles of exocomet dust-tail transits of their host star (see also Lecavelier des Etangs 1999). The calculated profiles look rather remarkably like the ones we have found and reported on here. Therefore, it appears that this current work could help to confirm these earlier predictions, and similarly the predictions may help strengthen the case that we have indeed observed exocomet transits.
Acknowledgements
We are especially grateful to the referee, Hervé Beust, for a substantial number of very instructive suggestions leading to the improvement of the manuscript. We thank Tabetha Boyajian, Bradley Schaefer and Benjamin Montet for discussions of the long-term photometric variations in KIC 3542116. We also appreciate helpful discussions of comet properties with Nalin Samarasinha and Bruce Gary. A V was supported by the National Science Foundation (NSF) Graduate Research Fellowship, grant no. DGE 1144152, and also acknowledges partial support from NASA's Transiting Exoplanet Survey Satellite (TESS) mission under a subaward from the Massachusetts Institute of Technology to the Smithsonian Astrophysical Observatory, Sponsor Contract Number 5710003554. This work was performed in part under contract with the California Institute of Technology (Caltech)/Jet Propulsion Laboratory (JPL) funded by National Aeronautics and Space Administration (NASA) through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. This research has made use of NASA's Astrophysics Data System and the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). Space Telescope Science Institute (STScI) is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5–26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX13AC07G and by other grants and contracts. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France.
Facilities: Kepler/K2, FLWO:1.5 m (TRES), Keck Observatory
The Kepler data are downlinked and processed in approximately 90-d ‘quarters’.
We note that in many cases, for example when dealing with stellar variability in the presence of periodic transits, it is preferable to fit a model to the signal along with a Gaussian process to absorb the stellar variability (see e.g. Grunblatt et al. 2016, 2017). In our case, however, since we do not a priori know which models appropriately describe the transits around KIC 3542116, it is best to attempt to separate the stellar variability from the transits without making assumptions about the shape of the transits.
Stars observed by Kepler saturate at a magnitude of ∼11.5.
See Thompson et al. (2016b) for more information about anomalies flagged in the Kepler pixel and flux time series.
For neighbouring field stars cooler than Teff ≃ 7000 K the contrast limits in Kp are even more stringent than in K΄. However, we estimate that the contrast constraints obtained in K΄ are still good to within ≃1 mag in Kp for Teff of the hypothetical interloper star up to ≃15 000 K. For even higher Teff, the constraints weaken further only very slowly.
Δb is an undetermined parameter that is essentially degenerate with the normalization constant C.
An exception is magnetite which sublimates at a substantially lower temperature.
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