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Open Access
Issue
A&A
Volume 688, August 2024
Article Number L34
Number of page(s) 9
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202451332
Published online 23 August 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. Subscribe to A&A to support open access publication.

1. Introduction

On planets with ultra-short period (≲1 d) orbits (USPs) and equilibrium temperatures > 2000 K, the constitutive elements of silicate minerals (e.g., Si, Mg, Fe) are volatile and can contribute to an atmosphere (Fegley 2023). Rocky planets that are depleted of highly volatile light elements (H, He, C, O, N) due to their proximity to the host star could instead have rock-vapour atmospheres in equilibrium with magma oceans (Kite et al. 2016; Chao et al. 2021). The escape of these atmospheres over billions of years lowers planet mass and surface gravity, and can lead to catastrophic runaway evaporation of the entire planet (Perez-Becker & Chiang 2013; Curry et al. 2024).

Scattering by dust that condenses in the escaping rock-vapour atmosphere of such objects has been invoked to explain the rare quasi-periodic transit-like signals discovered in Kepler and K2 time-series photometry of three main-sequence stars: KIC 12557548 (Kepler-1520), KOI-2700, and K2-22 (Rappaport et al. 2012, 2014; Sanchis-Ojeda et al. 2015). While these objects dim at strictly periodic intervals, the events vary significantly and stochastically in depth and are sometimes absent. The duration and shape of the light curves also deviate from those of a transiting planet, suggesting an extended dust cloud with a trailing (and sometimes leading) tail (van Lieshout et al. 2016). The progenitor planets are presumably transiting but the absence of a detectable signal at some epochs indicates that they are smaller than Mercury (Perez-Becker & Chiang 2013). These light curves are analogous to those of so-called “dipper” stars, but the latter phenomenon is more pronounced and is invariably associated with T Tauri disks (e.g., Ansdell et al. 2016), with rare exceptions (Gaidos et al. 2019a, 2022).

Observations of evaporating rocky planets can probe their otherwise inaccessible interior composition (Bodman et al. 2018; Okuya et al. 2020; Zilinskas et al. 2022) and test theories of planet formation and migration under extreme conditions close to the star (Winn et al. 2018; Adams et al. 2021). Monitoring of the variation in transit depth can test models of chaotic evaporation and dust-production feedbacks (Bromley & Chiang 2023; Booth et al. 2023). Since Mie-like scattering by dust is wavelength dependent, multi-band photometry can constrain the dust grain size (Croll et al. 2014; Bochinski et al. 2015; Sanchis-Ojeda et al. 2015; Colón et al. 2018; Ridden-Harper et al. 2019; Schlawin et al. 2021), which is a key parameter of outflow models that are used to calculate light curves and mass-loss rates (Perez-Becker & Chiang 2013; Campos Estrada et al. 2024).

We describe long-term multi-band optical monitoring from ground and space of the evaporating planet K2-22b, which was discovered in data obtained by K2 during Campaign 1 in 2014 (Sanchis-Ojeda et al. 2015). The (unseen) object is on a 9.14 hr orbit around a K7-type main-sequence dwarf star. Using ground-based monitoring, Colón et al. (2018) found that transits persisted for at least several years after the discovery. Sanchis-Ojeda et al. (2015), Colón et al. (2018), and Schlawin et al. (2021) found no wavelength dependence in the depth and duration of most events, but a greater depth at shorter wavelengths for the deepest transits. This resembles the lack of wavelength dependence seen in the transits of Kepler-1520b (Croll et al. 2014). Spectroscopic searches for accompanying gas, specifically volatilised neutral sodium, have not yielded detections (Gaidos et al. 2019b; Ridden-Harper et al. 2019).

2. Observations and data reduction

Between December 2021 and April 2023 we observed 33 predicted transits of K2-22b with the MuSCAT3 imager (Narita et al. 2020) installed at the 2 m Faulkes Telescope North at Haleakala Observatory on Maui, Hawai’i operated by the Las Cumbres Observatory Global Telescope (LCOGT), and 7 transits with the MuSCAT2 imager (Narita et al. 2019) on the 1.5 m Telescopio Carlos Sánchez at the Teide Observatory, Spain (Table 1). MuSCAT2 and MuSCAT3 observe simultaneously and either synchronously (same cadence) or asynchronously in gri and zs (short) bands. The star was typically observed for 3 hr centred on the predicted 46-minute-long transit with a cadence between 0.5 and 2 min, depending on the observing mode and filter. The window for 16 observations was 1.5 h early due to an error in the ephemeris, but most of these included whole or partial transit intervals. Nine observations were rendered useless due to weather, a tenth due to guiding problems, and two other observations missed the transit completely. MuSCAT2 data were analysed using a dedicated pipeline that performs image processing and standard aperture photometry and calibration as described in Parviainen et al. (2020), while the MuSCAT3 observations were first processed using the LCOGT BANZAI pipeline (McCully et al. 2018), after which photometry was extracted using the MuSCAT2 pipeline.

Table 1.

MuSCAT observations of K2-22.

3. Analysis and numerical methods

To set limits on individual transit depths ΔF, we fitted a transit light-curve model constructed with PYTRANSIT (Parviainen 2015; Parviainen & Korth 2020; Parviainen 2020) to our MuSCAT photometry. The model used different limb-darkening parameters for each bandpass, but assumed a wavelength-independent transit depth. The Bayesian fit adopted normal priors based on the values of Sanchis-Ojeda et al. (2015) for the orbital parameters (time of inferior conjunction, orbital period, inclination, and stellar density), and LDTK (Parviainen & Aigrain 2015) with the stellar parameters of Sanchis-Ojeda et al. (2015) for the two limb-darkening coefficients in each passband.

Observations with a significant transit detection were jointly analysed with a model in which orbital and limb-darkening parameters are the same for all transits, but the transit depth at a reference wavelength and the wavelength dependence were allowed to vary. The transit depth and effective planet-to-star area ratio k2 for transit i and passband j is defined as

Δ F ij ≈ k ij 2 = ∫ T j ( λ ) k i 0 2 e − α i ( λ − λ 0 ) d λ ∫ T j ( λ ) d λ , $$ \begin{aligned} \Delta F_\mathrm{ij} \approx k^2_\mathrm{ij} = \frac{\int T_\mathrm{j} (\lambda )\; k^2_\mathrm{i0} \; e^{-\alpha _\mathrm{i} (\lambda - \lambda _0)}\; \mathrm{d}\lambda }{\int T_\mathrm{j} (\lambda )\;\mathrm{d}\lambda }, \end{aligned} $$(1)

where T is the bandpass response function, k i0 2 $ k^2_\mathrm{i0} $ is the star-to-planet area ratio at a reference wavelength λ0, and α is the Ångström exponent describing the wavelength dependence of k2.

4. Results

Five MuSCAT3 observations and two MuSCAT2 observations revealed a significant transit-like signal around the predicted times (Table 1 and Fig. 1). We combined these detections with previous measurements (Sanchis-Ojeda et al. 2015; Colón et al. 2018; Schlawin et al. 2021) to revise the ephemeris: Tc = 2456811.1207 ± 0.0006 (BJD) and P = 0.38107710 ± 1 × 10−7 d.

thumbnail Fig. 1.

MuSCAT3 and MuSCAT2 photometry of seven K2-22b transits (UT dates at right) binned to 10-min intervals for visualisation (black points), along with the median of the posterior model fits (black line) and 16th and 84th percentiles (blue shading). The posteriors of the reference band transit depth k0 = Rp/R* and Ångström coefficient α estimates are reported in the rightmost panels.

thumbnail Fig. 2.

Compilation of the depths of detections and upper limits of transits of K2-22b. K2 values are as re-derived in this work and the Sanchis-Ojeda et al. (2015) values are from ground-based follow-up. The TESS and ATLAS values are p = 0.01 upper limits derived from an entire sector or survey (see Fig. 2 for ATLAS light curve).

We retrieved values of the Ångström coefficient α for each detected transit. Figure 3 plots these with values for three transits in 2015 from Sanchis-Ojeda et al. (2015). We also estimated an α of 0.30 ± 0.08 from the synthetic photometry that Colón et al. (2018) constructed from GTC-OSIRIS time-series spectroscopy (top panel of their Fig. 7). To estimate the transit depth, we averaged the values around the deepest part of the transit and used the mean wavelengths in the blue and red OSIRIS intervals (623 and 808 nm, respectively). We estimated the uncertainty using 1000 Monte Carlo simulations of the data, adopting the standard deviations in the transit intervals as the errors. Only the original deep transit analysed by Sanchis-Ojeda et al. (2015) has a significantly positive value of α. When compared to models of single Mie scattering, these values of α suggest grains larger than 0.3 μm (Appendix A).

thumbnail Fig. 3.

Ångström coefficients of the transits of K2-22b from MuSCAT photometry plus previously published values. The value from Colón et al. (2018) was determined from blue and red synthetic photometry (their Fig. 7a) derived from GTC-OSIRIS time-series spectra.

The light curves of K2-22 from Sectors 45, 46, and 72 of the Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2015) covering 80 days (Fig. B.1), phased to the ephemeris of the planet, exhibit no significant indication of transits (Fig. B.2). We established upper limits (p = 0.01 significance) of 0.03, 0.09, and 0.15% for the respective sectors (Fig. 2 and Appendix B). Likewise, 6 years of photometry from the Asteroid Terrestrial-impact Last Alert System (ATLAS, Tonry et al. 2018) phased to the period of K2-22b (Fig. B.3) contain no significant signal at inferior conjunction (Appendix B). The upper limits are less restrictive than those of TESS (2% and 0.3% in c and o bands, respectively) but the baseline is much longer (Fig. 2 and Appendix B).

The absence of a detectable average signal in TESS or ATLAS is not due to ephemeris error since over 6.5 yr, the period error of 1 × 10−7 d amounts to an ephemeris error of only 1 min or 0.004 in phase. Since the TESS (but not the ATLAS) passband is somewhat redder than that of Kepler, scattering by a dust cloud should be weaker. However, calculations of this effect using the constraint on the grain size from our MuSCAT photometry limit this to ≲10% (Appendix A). Our new ephemeris agrees with that of Schlawin et al. (2021) and is more accurate than but consistent with the value from Sanchis-Ojeda et al. (2015). The use of the latter would not appreciably change the TESS or ATLAS phased light curves.

To statistically assess the decline in transits of K2-22b, we computed the expected number of MuSCAT detections based on the distribution of transit depths in the K2 discovery light curve. Because Sanchis-Ojeda et al. (2015) reported a subset of events with satisfactory light-curve fits we performed a fit of the entire K2 PDC-SAP light curve using PyTransit (Parviainen 2015). The light curve was detrended using a linearly interpolated median in a 25-point (12.5-h) window, where the upper and lower 16% of the points in each bin were excluded. The central transit times were computed using our revised ephemeris, and model light curves were computed using the limb-darkening parameters from the LDTk toolkit (Parviainen & Aigrain 2015) based on the stellar parameters of Sanchis-Ojeda et al. (2015). These calculations adopted a circular orbit with a/R* = 3.3 (Sanchis-Ojeda et al. 2015) and accounted for the 30-minute integration time of K2. These models were fitted to the data, allowing only Rp/R* and the impact parameter (i.e. orbital inclination) to vary. Using the best-fit parameter values, we re-evaluated the transit depth for the shorter integration times of the MuSCAT observations (few minutes). In the minority of cases where the fit failed (inclinations > 90 deg or less than the value for unit impact parameter, or transit depths > 0.02), we set the transit depth to one minus the minimum in the light curve immediately around the predicted central time. The depth distribution of 171 transits resembles that reported by Sanchis-Ojeda et al. (2015) and has a mean of 0.56% (Fig. 2). We performed 104 Monte-Carlo simulations of our MuSCAT campaign. Each observation in the campaign was assigned a transit depth drawn from the interpolated K2 distribution. We flagged simulated detections as those with depths that exceeded either the upper limit (for actual non-detections) or the lower bound (for actual detections). Figure 4 shows the distribution of the number of simulated detections in our Monte Carlo campaigns. Compared to 28 possible detections, the predicted minimum, median and mode are 22, 26.5, and 27. The actual number is 7, and this distribution rules out the possibility that the intrinsic depth distribution is unchanged and we had few detections by chance. Moreover, the upper limits from the three TESS sectors and ATLAS o-band photometry are all below the mean K2 transit depth.

thumbnail Fig. 4.

Fractional distribution of the predicted number of detections with MuSCAT (of 28 possible) in 104 Monte Carlo simulations based on the distribution of transit depths observed with K2 in 2014. The actual number of MuSCAT detections is seven.

5. Conclusions and discussion

5.1. Dust properties

The absence of a significant wavelength dependence (α > 0) in our transit-depth measurements agrees with previous findings (Sanchis-Ojeda et al. 2015; Colón et al. 2015; Schlawin et al. 2021). When compared to single Mie-scattering models, our MuSCAT-based Ångström coefficients suggest grain sizes > 0.3 μm (see Appendix A). Alternatively, multiple scattering occurs in an optically thick cloud. The existence of a leading dust tail in the orbit of K2-22b also indicates that radiation pressure is lower than the gravitational force, implying either very small or very large dust grains (Sanchis-Ojeda et al. 2015). Campos Estrada et al. (2024) predicted that that the K2-22b dust cloud has an optical depth τ ∼ 1 − 10 along lines of sight near the planet, and thus appreciable vertical optical depth. The latter – and commensurate surface cooling – has been invoked to explain the variability between transit events as a limit cycle between dust formation and magma-pool evaporation (Booth et al. 2023; Bromley & Chiang 2023). A μm size for dust raises the question of how these grains are lofted in the expected vapour wind (Perez-Becker & Chiang 2013), and it challenges a model of chaotic behaviour that assumes very small dust (Bromley & Chiang 2023).

5.2. Intermittency of the K2-22b transit signal

A change in the dust cloud over the past decade, distinct from the inter-transit variability modelled by Booth et al. (2023), Bromley & Chiang (2023), is analogous to the years-long variation in the signal of Kepler-1520b reported by Rappaport et al. (2012), Schlawin et al. (2018). We consider two scenarios to explain this change: Variability in the host star, or intrinsic changes on the planet.

One mechanism that involve the star is based on the effect of its magnetic activity and wind on the dust tail from the planet. Kawahara et al. (2013) found an anti-correlation between the transit depth of Kepler-1520b and stellar rotational variability (derived from the same Kepler light curve). This might be evidence for a link, although the effect of spots on the apparent transit depth may play a role (Croll et al. 2015; Schlawin et al. 2018). For μm-size dust, the stellar wind pressure is predicted to be much lower than the radiation pressure, but if grains are charged, Lorenz forces could be important (Price et al. 2019, 2023). The majority of M dwarfs (K2-22 has a K7 spectral type) exhibit cycle-like variability in their magnetic activity (Mignon et al. 2023). Where magnetic cycles on cool dwarfs are detected, their periods range from some years to over a decade, with a positive correlation with rotation period (Saar & Brandenburg 1999; Suárez Mascareño et al. 2016) but no discernible trend with spectral type (Suárez Mascareño et al. 2016; Mignon et al. 2023).

As has been suggested for Kepler-1520b (Kite et al. 2016), long-term change in the behaviour of K2-22b might reflect variability in the surface composition of the substellar magma pool thought to be the source of the dust-forming wind. Kite et al. (2016) described four regimes for magma pool coupled to such a wind depending on the stellar irradiance and the Fe content of the silicate mantle. On relatively Fe-poor (including Earth-like) planets, the vaporisation of the magma pool produces a negatively buoyant chemical boundary layer or lag. At the same time, the thermal gradient between the substellar point and the edge of the pool is expected to drive a global-scale overturning flow. If the timescale for lag formation is much shorter than the overturn timescale then the magma pool will be patchy and the observable average of many such patches would change little. If the reverse is true, the magma pool will be chemically uniform. However, if the timescales are comparable then the surface of the magma pool might vary chemically on the overturning timescale. This variation could be amplified by the sensitivity of dust grain opacity to Fe content and equilibrium vapour pressure to temperature (Bromley & Chiang 2023). Kite et al. (2016) related the overturning circulation to thermal buoyancy forces and estimated the timescale to be about a decade (their Eq. 5), consistent with the timescale of the observed change for K2-22b. If indeed the magma pool circulates, this means that its depth is very shallow (a multiple of the thermal boundary layer) and its chemistry is not representative of the bulk crust or mantle (Kite et al. 2016; Curry et al. 2024).

A third explanation is that the source of dust is not a planet but a much smaller body that is in terminal decline. The stability of the transit phase over a decade (∼104 orbits) unambiguously rules out scenarios in which dust is temporarily trapped in the stellar magnetic field (Sanderson et al. 2023; Bouma et al. 2024). Moreover, it limits drift in phase due to non-gravitational acceleration to < 5 × 10−3, corresponding to 4 × 104 km, over a decade. This places an upper limit on the acceleration (of < 10−12 km sec−2) and a lower limit on its mass. This logic was used to estimate the masses of comet nuclei (Sosa & Fernández 2009, and references therein). For a mass-loss rate of ∼2 M⊕ Gyr−1 (Schlawin et al. 2021; Campos Estrada et al. 2024) and a net velocity (averaged over the surface) equal to ξvth where vth is the thermal speed (∼2 km s−1) and ξ is a dimensionless factor that is ∼0.5 for comets (Sosa & Fernández 2009, but here conservatively taken to be 0.1), the mass of K2-22b must be > 1.5 × 10−5M⊕ or 10% the mass of Ceres. At the current mass-loss rate, a body of this size ould not evaporate for ≳104 yr and it is highly unlikely that we would observe it right at its demise.

More long-term monitoring of K2-22b is needed to conclusively test these scenarios. If the variation is due to stellar activity or overturn of a surface magma ocean, the transits of K2-22b will eventually become more frequent. If it is the continuous disintegration of a much smaller dust source, dimming events will disappear and will not return. Since TESS will not re-observe K2-22 in the foreseeable future, and it is not in either of the PLATO long-stare fields (Nascimbeni et al. 2022), monitoring from the ground, for example by ATLAS, is key. Any correlation with the magnetic activity of the star could be elucidated by spectroscopy of the chromospheric emission lines.

If objects such as K2-22b only produce dust clouds with a finite duty cycle, then their intrinsic occurrence is higher than previously estimated. This aggravates the possible discrepancy between the occurrence of evaporating planets and the USP population that is presumed to be their progenitors (Curry et al. 2024). A long-term variation in the behaviour of K2-22b (and that of other evaporating planets) could also impact the planning for follow-up campaigns with major observatories.

Acknowledgments

EG was supported by NASA Astrophysics Data Analysis award 80NSSC19K0587 and US National Science Foundation Astronomy & Astrophysics Grant 2106927, and was a visiting scientist at the International Space Sciences Institute in Bern during a portion of this work. HP acknowledges support from the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC2021-031798-I, and funding from the University of La Laguna and the Spanish Ministry of Universities. This work is partly supported by JSPS KAKENHI Grant Numbers JP21K13955, JP24H00017, JP24K00689, JP24K17083 and JSPS Bilateral Program Number JPJSBP120249910. This article is partly based on observations made with the MuSCAT2 and MuSCAT3 instruments, developed by the AstroBiology Center (ABC) under the National Institutes of Natural Sciences of Japan with support by ABC, JSPS KAKENHI (JP18H05439), and JST PRESTO (JPMJPR1775). MuSCAT2 is operated by the IAC in the Spanish Observatorio del Teide, while MuSCAT3 on the Faulkes Telescope North, is operated by the LCOGT network Part of the LCOGT telescope time was granted by NOIRLab through the Mid-Scale Innovations Program (MSIP). MSIP is funded by NSF. This work has made use of data from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project. The ATLAS project is primarily funded to search for near earth asteroids through NASA grants NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search include images and catalogues from the survey area. This paper includes data collected by the TESS mission, funding of which is provided by the NASA’s Science Mission Directorate. This work used the SciPy and AstroPy packages (Virtanen et al. 2020; Astropy Collaboration 2022).

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Appendix A: Comparison of Ångström coefficients to a Mie scattering model

We compared the estimated Ångström coefficients to those predicted by a model of single Mie scattering by spherical dust grains (Budaj et al. 2015). We adopted a power-law dust size distribution with a minimum size cutoff where the power-law index and cutoff are varied. We adopted a dwarf K7 spectral type template from Kesseli et al. (2016) for K2-22 and computed single-scattering opacities over the MuSCAT passbands using profiles from the Spanish Virtual Observatory filter service. We considered several compositions (Mg-Fe olivine, enstatite, forsterite) and found similar results because the opacity at these wavelengths is dominated by scattering. Figure A.1a show the case for olivine; for non-flat distributions the minimum size is constrained to ∼0.3μm. Smaller grains are allowed if there is multiple scattering within an optically thick cloud. We used the same approach to calculate the ratio of the opacities of dust in the TESS to Kepler passbands. For grain size distributions that are consistent with the MuSCAT data, that ratio is ≳0.9 (Fig. A.1b).

thumbnail Fig. A.1.

Left (a): Predicted Ångström coefficient for griz wavelengths as a function of minimum dust size and power-law index. Grey regions indicate the range of values derived from each of five transit observations. Right (b): Predicted ratio of TESS to Kepler transit depth due to scattering by dust.

Appendix B: TESS and ATLAS photometry of K2-22

K2-22 appears as TIC 363445338 in the Input Catalogue (Pepper et al. 2007) of the Transiting Exoplanet Survey Satellite(TESS, Ricker et al. 2015) and was observed during three 27-day sectors (45, 46, and 72) from 6 Nov to 30 Dec 2021, and from 11 Nov to 7 Dec 2023. Two-minute cadence Pre-search Data Conditioning Simple Aperture Photometry (PDC-SAP) light curves generated by the TESS SPOC pipeline were retrieved from the Mikulski Archive of Space Telescopes (MAST). These were generated by the TESS-Science Processing Operations Centre (SPOC) pipeline using 3-4 pixel (i.e. 42" across) apertures centred on the star.

While a Lomb-Scargle periodogram analysis did not return significant signals at the orbital period of K2-22b, in all three there was a significant signal at ∼5 days. The rotation period of the primary star has already been established as ≈15 days (Sanchis-Ojeda et al. 2015), and Gaidos et al. (2023) estimate a rotation-based age of 1.1 ± 0.2 Gyr at which mid-to late M-type dwarfs may be still rapidly rotating (Agüeros et al. 2018). Thus we speculate that the 5-day signal is from the M4 dwarf companion. While the RMS of the light curves (1.6%) is larger than the expected transit depth (∼0.5%), the RMS of the median of binned, phased light curves (red curves in Fig. B.3) is < 0.1% and does not contain any obvious trend (χ2 of 30-34 for 19 degrees of freedom). Based on the statistics of the photometry between predicted ingress and egress (vertical dotted lines in Fig. B.2), in no sector is a significant (p = 0.01) mean signal detected and 99% upper limits for the three sectors are 0.03, 0.09, and 0.15%.

Since 2018, K2-22 has also been monitored by the Asteroid Terrestrial-impact Last Alert System (ATLAS, Tonry et al. 2018; Heinze et al. 2018). light curves in the survey’s broad (Δλ > 210 nm) “cyan" (c) and“orange" (o) passbands (respective effective wavelengths of ∼520 and 660 nm) were generated by “forced" photometry on ATLAS images. After filtering points with error codes or errors exceeding 0.1 mag, there were 593 and 2100 measurements spanning 6.5 years in the respective filters.

Both light curves contain apparent dimming events, including a 0.6-mag drop in o-band near the end of the 2023 season (Fig. 2). These could be systematics but there is no correlation with either sky brightness or the FHWM of the point spread function for the forced photometry. The o-band light curve (but not the c-band light curve) also contains numerous positive excursions, which we speculate to be due to flares from the mid M-type companion of K2-22 (separation 2", Sanchis-Ojeda et al. 2015). Such stars are often rapidly rotating and very active, especially if the system age is ∼1 Gyr (Gaidos et al. 2023). The o filter but not the c filter includes the Hα line that intensifies during flares. There are also long term (months) variation of ∼0.04 mag in the o-band (but not c-band) which are correlated with PSF FWHM ( 3" or more) and are undoubtedly variable contamination from this very red star.

thumbnail Fig. B.1.

ATLAS light curves of K2-22 through "o" (orange, left y axis) and "c" (blue, right y axis) filters. Vertical grey bars mark observations by TESS during Sectors 45-46 and 72. Inverted red triangles mark MuSCAT observations, sequentially displaced for clarity. (K2-22 was discovered in mid-2014.)

thumbnail Fig. B.2.

TESS light curves of K2-22 for Sectors 45, 46, and 72 phased to the orbital period of “b". The red curve is the median in 20 bins and the shaded region is the 68% confidence range based on 1000 re-samples with replacement. The vertical dotted lines are the predicted phases of ingress and egress based on a 46-min transit duration (Sanchis-Ojeda et al. 2015). Many individual data points outside the range are not shown.

thumbnail Fig. B.3.

Phased light curves of K2-22 from forced photometry in ATLAS images through “cyan" (left) and “orange" (right) filters. The curves are the medians in 20 bins and the shaded regions are the 68% confidence range based on 1000 samples with replacement. The vertical dotted lines are the predicted phases of ingress and egress based on a 46-min transit duration (Sanchis-Ojeda et al. 2015).

All Tables

Table 1.

MuSCAT observations of K2-22.

In the text

All Figures

thumbnail Fig. 1.

MuSCAT3 and MuSCAT2 photometry of seven K2-22b transits (UT dates at right) binned to 10-min intervals for visualisation (black points), along with the median of the posterior model fits (black line) and 16th and 84th percentiles (blue shading). The posteriors of the reference band transit depth k0 = Rp/R* and Ångström coefficient α estimates are reported in the rightmost panels.
In the text
thumbnail Fig. 2.

Compilation of the depths of detections and upper limits of transits of K2-22b. K2 values are as re-derived in this work and the Sanchis-Ojeda et al. (2015) values are from ground-based follow-up. The TESS and ATLAS values are p = 0.01 upper limits derived from an entire sector or survey (see Fig. 2 for ATLAS light curve).
In the text
thumbnail Fig. 3.

Ångström coefficients of the transits of K2-22b from MuSCAT photometry plus previously published values. The value from Colón et al. (2018) was determined from blue and red synthetic photometry (their Fig. 7a) derived from GTC-OSIRIS time-series spectra.
In the text
thumbnail Fig. 4.

Fractional distribution of the predicted number of detections with MuSCAT (of 28 possible) in 104 Monte Carlo simulations based on the distribution of transit depths observed with K2 in 2014. The actual number of MuSCAT detections is seven.
In the text
thumbnail Fig. A.1.

Left (a): Predicted Ångström coefficient for griz wavelengths as a function of minimum dust size and power-law index. Grey regions indicate the range of values derived from each of five transit observations. Right (b): Predicted ratio of TESS to Kepler transit depth due to scattering by dust.
In the text
thumbnail Fig. B.1.

ATLAS light curves of K2-22 through "o" (orange, left y axis) and "c" (blue, right y axis) filters. Vertical grey bars mark observations by TESS during Sectors 45-46 and 72. Inverted red triangles mark MuSCAT observations, sequentially displaced for clarity. (K2-22 was discovered in mid-2014.)
In the text
thumbnail Fig. B.2.

TESS light curves of K2-22 for Sectors 45, 46, and 72 phased to the orbital period of “b". The red curve is the median in 20 bins and the shaded region is the 68% confidence range based on 1000 re-samples with replacement. The vertical dotted lines are the predicted phases of ingress and egress based on a 46-min transit duration (Sanchis-Ojeda et al. 2015). Many individual data points outside the range are not shown.
In the text
thumbnail Fig. B.3.

Phased light curves of K2-22 from forced photometry in ATLAS images through “cyan" (left) and “orange" (right) filters. The curves are the medians in 20 bins and the shaded regions are the 68% confidence range based on 1000 samples with replacement. The vertical dotted lines are the predicted phases of ingress and egress based on a 46-min transit duration (Sanchis-Ojeda et al. 2015).
In the text

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