Debris disks among Kepler solar rotational analog stars

Observations of circumstellar disks provide a powerful tool for our understanding of planetary systems dynamics. Analogs to the Solar System asteroid belts, debris disks result from the collision of the remaining solid material of the planet formation process. Even if the presence of disk is now reported for hundreds of stars, its detection around stars similar to the Sun is still very sparse. We report the results of a search for debris disks around Kepler stars with surface physical parameters close to solar values, including rotation period, using observations by the Wide-field infrared Survey Explorer (WISE). From the entire sample of Kepler stars, 881 targets were identified with these parameters and only six of them (KIC 1868785, 7267949, 7435796, 10533222, 11352643, and KIC 11666436) show unambiguous infrared excess, for which we determined debris disk physical parameters. Interestingly, the present study reveals traces of debris disks much more massive and brighter than the Solar System zodiacal dust, probably resulting from recent violent collisional events, orbiting stars with ages around the solar values.


INTRODUCTION
The asteroid belt in our Solar System is located between Mars and Jupiter, i.e., between the inner terrestrial planets and the outer giant planets, with components presenting a large compositional diversity in size and distance from the Sun (DeMeo & Carry 2014). It contains millions of irregularly shaped bodies composed of rocks, ices and metals with a total mass of approximately 4 percent of the Moon or 22 percent of that of Pluto. The presence of water vapor on Ceres, the largest body in the rodrigosobrinho@dfte.ufrn.br asteroid belt, and the identification of objects exhibiting apparently cometary activity yet orbiting completely within the main asteroid belt (Hsieh & Jewitt 2006) are the most outstanding recent discoveries related to this region of the Solar System. Observations indicate that at the planetesimal formation stage the location of the snow line, which denotes the radius outside of which ice forms, was within the asteroid belt (e.g., Martin & Livio 2012). Indeed, previous studies claimed that the inner asteroids, closest to Earth, at a radius of about 2.2 AU, were water devoid, whereas the outer asteroids, within a radius around 3.2 AU, were icy objects (Abe et al. 2000). However, more recent studies indicate that asteroids are less segregated by water content than previously believed (DeMeo & Carry 2014).
Although the presence of debris disks, with asteroid belt characteristics, is now well established for hundreds of stars (Chen et al. 2006;Cotten & Song 2016;Trilling et al. 2008;Weissman 1995;Aumann et al. 1984;Patel et al. 2014), the present day literature pints for a scarcity of asteroid belt signatures around Sun-like stars (Da Costa et al. 2017;Sibthorpe et al. 2018). For instance, a recent study has shown a null detection of warm debris around solar twin stars (Da Costa et al. 2017).
Given this reality, we report here a search for infrared (IR) excess, a well established diagnostic for circumstellar debris disks, in a sample of 881 Kepler main-sequence stars, using observations carried out with the Wide-field Infrared Survey Explorer (WISE) (Wright 2010). This space mission mapped the sky at wavelengths 3.4, 4.6, 12, and 22 µm, known as filters W1, W2, W3, and W4, offering a unique laboratory for the search for stellar mid-IR excess. The 12 and 22 µm wavelengths are very sensitive to thermal emissions from objects at temperatures comparable to the Earth, around 300 K, and to the Solar System asteroid belt and interior zodiacal cloud, around 150-250 K.
Indeed, thanks the high quality of the Kepler photometric data, we are now able to study a new type of solar analog stars, the solar rotational analogs, namely those stars presenting atmospheric solar parameters and rotation periods similar to the Sun. The stellar sample here analyzed presents these  Huber et al. (2014), rotation periods (P rot ) were taken from McQuillan et al. (2014). Disk properties (this work): temperature of the dust (T d ), radius of the debris disk (R d ), dust mass of the disk of circumstellar material (M d ), the fractional luminosity of the dust (f d ).  unique characteristics, surface physical properties similar to the Sun and rotation period ranging P rot from 23 to 33 days. In section 2 of this Letter, we describe the WISE and Kepler data used in this study. Section 3 describes the methods used in our analysis of these data. Finally, in Section 4, we present our results and discuss their implications. The Kepler coordinates of each target were then used to crosscheck with the 2MASS (Cutri et al. 2003) and full AllWISE (Cutri et al. 2013) catalogs. Assuming a positional accuracy of 5 arcsecond, we find 862 stars with photometry in the three bands of 2MASS (J, H, and K) and in the four WISE bands (W1, W2, W3 and W4). The values of W3 and W4 magnitudes, SNRW3 and SNRW4 signal-to-noise ratios, and the confusion condition flag (ccf), were used as criteria to assess the quality and reliability of WISE data. Checking these photometric properties, we identified 447 stars with fundamental problems such as artifacts contamination (ccf=H,h,P,p,D,d and O,o) (Cutri et al. 2013), high saturation levels (W 3 < 3.8 or W 4 < −0.4) and very low signal-to-noise ratio (SN RW 3/W 4 < 2.0). We have therefore disregarded these targets from our sample. Thus, a primary sample of 415 stars with non-saturated photometry, signal-to-noise greater than 2, and unaffected by known artifacts at one or both W3 and W4 bands was analyzed in the search for IR excess only in the band(s) in which no mentioned problem is found.

Searching for IR excess
Then, the observed spectral energy distribution (SEDs) and model-derived photospheric IR fluxes for each one of the referred 415 stars were compared using the Virtual Observatory Spectral Analyzer (VOSA, Bayo et al. 2008). The SEDs were constructed using the four IR bands W1-W4 from WISE (Cutri et al. 2013), the J, H, and Ks bands from 2MASS (Cutri et al. 2003), and when available, the UBV bands (Mermilliod 2006), the G-band from Gaia (van Leeuwen et al. 2017), and the color bands ugriz from SDSS (Abazajian et al. 2009). For increasing the reliability of IR excess measurements, the theoretical fluxes were computed using three grids of theoretical stellar spectra: Kurucz-ATLAS9 (Castelli et al. 1997), BT-DUSTY (Allard et al. 2012), and BT-NextGen (AGSS2009) (Allard et al. 2012). These models were used to determine the best-fitting line for the observed data by the χ 2 minimization. Only the stars presenting IR excess from the above three models were chosen as IR excess candidates, amounting to 47 stars (see Table 2 in the online data). We also adopted the estimation of interstellar extinction provided in the Kepler database.
For quantification of the observed IR excess, we used the excess significance parameter χ λ (Beichman et al. 2006;Moór et al. 2006), defined as follows: where F λ,obs is the observed flux density and F λ,phot is the expected photospheric flux density; σ λ,obs corresponds to the uncertainties of F λ,obs ; σ λ,cal refers to the calibration uncertainties of the WISE data of 4.5 % and 5.7 % in the W3 and W4 bands, respectively (Jarrett et al. 2011). Here, we consider as presenting IR excess only those stars for which χ λ ≥ 2 (Ribas et al. 2012), corresponding to at least 1.5σ or 87 % significance of deviation from photosphere IR emission (χ λ = 0.0). Based on this criterion, we find a total of 51 stars showing WISE mid-IR excess, although, only 47 stars present such excess in the three theoretical models, as explained before. The difference in significance between the Kurucz and the two other models fluctuates around 10% for the W3 band and 1% for the W4 band. This fluctuation gives us an order of magnitude of the systematic errors associated to the different physical ingredients considered in each model. Our criterion of selecting objects that present excess simultaneously using different models should avoid a bias associated to a particular one (e.g., Sinclair et al. 2010). Statistical errors due to the uncertainty in the fit with the models were not taken into consideration because they are negligible. Maldonado et al. (2017) Table 2 of the online data.

WISE image inspection
In order to identify which stars have a reliable IR excess, with no artificial artifacts or contamination, we applied to the sample of 47 stars the same procedure used by Da Costa et al. (2017) for a visual inspection of the WISE images, based on the identification of some significant problems as PSFs (Point Spread Function) deformed due to an object close to the source, an absent or no evident object, or even caused by nearby objects blended, leading to a misinterpretation of the image. The WISE images were obtained from IRSA (Infrared Science Archive), using 0-3σ linear scales around 1.7 ×1.7 of each IR excess candidate. In addition, we checked if the IR excess source is a punctual (circular) or elliptical (non-circular) or extensive object, we used a roundness criterion based on (Cotten & Song 2016), which consists on a comparison of bilateral symmetry of each source determined by a two-dimensional Gaussian adjustment defined by  shows that the detected disks are located between 0.33 and 1.07 AU, at smaller orbital radii than the Solar System asteroid belt, that is from 2.0 and 3.5 AU (Wyatt 2008). Computed temperatures indicate that the referred stars with IR excess present warm circumstellar dust with temperatures, in average, higher than the solar asteroid belt value. In effect, our finding may represent also an observational bias by considering that the presence of disks closer to the stars are hotter, and as a consequence, brighter if the IR excess is observed near the peak of their SEDs.
Circumstellar dust belts around main-sequence stars, as those reported in the present study, are composed of second-generation dust originated from the small-body population of planetary systems (Backman & Paresce 1993), which are mostly remnants of primordial protoplanetary disks (Hernández et al. 2007). These bodies can give fundamental informations about the chemistry and evolution of protoplanetary disk and the planetary systems they form. Despite a similar physical mechanism to be expected in the production of the reported debris disks, our findings show that stars with physical parameters similar to the Sun, as is the case of the whole sample here analyzed, can in fact be very different from the Sun once the star and its circumstellar environment are considered, confirming previous results by Da Costa et al. (2017). Among these physical parameters, age is an important one for determining the presence of debris disks. In the present work, based on gyrochronology estimations (e.g., Barnes et al. 2016;Ceillier et al. 2016), the stellar ages for our Kepler stars range around the solar age value, even though that range may be somewhat broad.
At the WISE wavelength bands, we are observing the Wien-edge of the energy distributions. In this sense, the lack of an excess for the large majority of the analyzed stars does not necessarily imply the absence of circumstellar material. Indeed, the detection of IR-excess, only in W3 band, is in agreement with Liu et al. (2014) assumption that the disk associated to this IR-excess are geometrically thin, that is, confined within a small radius range, with all the dust at the same temperature. The disks here reported may in fact be spatially extended and, by consequence, similar to the Solar System asteroid belt geometry. Their thin appearence may reflect the fact that only the inner edge of the disk can be detected with the present sensitivity. In addition, the abscence of detection in the W4 band may be explained by its considerably narrower range in comparison to W3. This fact would indicate that the fraction of solar rotational analog stars possessing debris disks could be higher than the fraction here observed. Nevertheless, the discovered debris disks are, by far, brighter and more massive than the Solar System zodiacal dust, a characteristic that allowed their detection. In this sense, the observation of solar debris disks at the distance of the refereed stars would be well below the WISE sensitivity level.
The present sample of debris disks has luminosity too high to be explained by a steady-state collisional cascade (Wyatt 2008;Gáspár et al. 2013) and a large amount of warm dust that cannot be sustained at the estimated stellar ages (Wyatt 2008). These unusual characteristics may reflect a possible disc-sculpting mechanism resulting from violent collisional events (e.g., Kral et al. 2015;Kenyon & Bromley 2005Raymond et al. 2009;Zappalà et al. 2002;Durda et al. 2007).
Dust belts cooler than those reported here have their imprints at longer wavelength bands, and slight or no excess in the mid-IR. Therefore, the null detection of IR excess, at WISE sensitivity level, for the remaining 875 solar rotational analogue stars will certainly motivate new observational studies at far-IR, submillimeter and millimeter wavebands for a better characterization of material around these stars with a rotation period similar to that of the Sun. Furthermore, the presence of other disks structures (Wyatt 2008), in particular cold components like the Kuiper belt, and water ice traces, can be determined from observations in longer IR wavebands. In this sense, further observational studies are mandatory for the stars with detected IR excess here announced.

Acknowledgments
Research