Abstract
Although thousands of exoplanets have now been discovered, there is still a significant lack of observations of young planets only a few Myr old. Thus there is little direct evidence available to differentiate between various models of planet formation. The detection of planets of this age would provide much-needed data that could help constrain the planet formation process. To explore what transit observations of such planets may look like, we model the effects of large starspots and dust clouds on the depths of exoplanet transits across multiple wavelengths. We apply this model to the candidate planet PTFO 8-8695b, whose depths vary significantly across optical and infrared wavelengths. Our model shows that, while large starspots can significantly increase the color dependence of planetary transits, a combination of starspots and a large cloud surrounding the planet is required to reproduce the observed transit depths across four wavelengths.
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1. Introduction
The 3 Myr old star PTFO 8-8695 is a weak-lined T Tauri star with a candidate transiting planet (van Eyken et al. 2012). Dimming events were observed in the infrared by Ciardi et al. (2015). Several authors have presented evidence both for and against the existence of the planet (Ciardi et al. 2015; Johns-Krull et al. 2016; Onitsuka et al. 2017; Bouma et al. 2020; Tanimoto et al. 2020). Onitsuka et al. (2017) found that simultaneous observations of the transit-like events across multiple wavelengths vary significantly in depth. They and Bouma et al. (2020) argue against the existence of the planet for this reason.
However, Ballerini et al. (2012) show that, in addition to limb darkening, starspots on a host star produce color-dependent transit depths. Also, Tanimoto et al. (2020) explain the color dependence of PTFO 8-8695 with a dust cloud surrounding the planet. We have modeled the light observed during a transit in order to determine the extent to which starspots and dust clouds affect transit depths in different bandpasses. To test the planetary explanation of PTFO 8-8695, we determine the conditions necessary to reproduce the wavelength-dependent observations of this object.
2. Model
Our model divides a stellar disk into a grid whose elements are each assigned a spectrum to represent the light produced by the star. The spectra come from NEXTGEN model atmospheres (Hauschildt et al. 1999), using the BT-NextGen low-resolution spectra of Allard et al. (2012) from http://svo2.cab.inta-csic.es/theory/newov2/. We use stellar parameters provided by van Eyken et al. (2012): an effective temperature of 3500 K, log g of 4.0, and solar metallicity. We apply linear limb darkening according to coefficients given by Claret (2004), Claret et al. (1995), and van Hamme (1993), interpolated over the wavelength ranges 3000–10,600 Å, 10,600–28,200 Å, and 28,200–52,500 Å, respectively. The planet is modeled as an opaque circle in a circular orbit at a distance of 1.685 stellar radii (van Eyken et al. 2012), with the inclination a free parameter of the model.
Light curves are created by summing all the spectra from grid elements which are not blocked by the planet at fixed intervals in the orbit, then applying bandpass transmission curves for the instruments used in observations. To reproduce the transit depths given by Onitsuka et al. (2017) and Ciardi et al. (2015), we modeled the 
, 
, and zs,2 filters on MuSCAT at OAO as well as Spitzer's 4.5 μm IRAC filter. The transmission curves were obtained from http://svo2.cab.inta-csic.es/theory/fps/.
Factors we considered which affect the depths of the transits include unocculted starspots and a translucent dust cloud surrounding the planet. We assume starspots are polar and that the stellar rotation axis is oriented 90° from the orbital plane. When modeling a starspot, we change the spectra within the spot to BT-NextGen spectra with an effective temperature between 2600 and 3500 K, and recalculate limb darkening to account for this temperature change.
Following the example of Tanimoto et al. (2020), we model a spherical dust cloud surrounding the planet by using the extinction law given by Cardelli et al. (1989), which depends on the optical depth of the cloud in the V -band and RV , the ratio of total to selective extinction. We assume a uniform cloud, so that optical depth per unit length remains constant for the entire cloud at each wavelength. For interstellar extinction, RV has been found to be near 3.1 (Cardelli et al. 1989), however we allow this value to vary.
3. Results and Discussion
To determine whether these factors are capable of reproducing observed transit depths, we run the model while varying the input parameters and minimize χ2 between the observed and model transit depths. Bouma et al. (2020) show that Gaia and TESS observations of PTFO 8-8695 are more consistent with two stars of similar temperature and radius than with a single star. A planet transiting one star in such a system would produce a transit half as deep as our model would predict; therefore we fit to twice the observed depths at each wavelength.
We consider eight different types of models: with or without a planet, starspot, and dust cloud, and with interstellar or best-fitting RV . The depths of the four modeled filters for each model are shown in Figure 1 with the factors the model includes indicated by a checkmark (✓) below. We allow spot radius and temperature, planet radius, orbital inclination, cloud radius, V -band optical depth per unit length in the cloud, and (for models 4, 5, 6, and 8) RV to vary, finding the best-fitting parameters for all eight models. Figure 1 also shows the observed depth of each filter, along with each model's root-mean-square deviation.
Figure 1. Modeled transit depths in four filters. Dashed horizontal lines indicate observed depths, and the same color vertical bars indicate the model depths. Factors included in each model are shown below the corresponding plots.
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The presence of a large starspot (model 2) does produce substantially more color dependence in the transit depths relative to a model with no spot (model 1) where the color dependence results entirely from color variations in limb darkening. However, the starspot alone is not able to reproduce the full spread of color dependence. Models without a planet but with a dust cloud (models 3–5) can reproduce the optical color variations fairly well, but are not able to produce an infrared transit of any significance. The best fitting model (model 8) includes a planet surrounded by a dust cloud as well as a large polar spot. This model has a spot with radius of 65° and temperature of 2900 K, planet orbital inclination of 71°, planet radius of 0.09 stellar radii (1.2 RJup, assuming a stellar radius of 1.39 R⊙ as in van Eyken et al. (2012)), cloud radius of 0.36 stellar radii, V-band optical depth of 0.1, and RV of 1.2. The optical depth of 0.1 is that corresponding to the distance between the surface of the planet and the top of the cloud. The product of the dust cloud's size and optical depth in our best fit is comparable to that found by Tanimoto et al. (2020).
The cloud in this model has radius around 5 RJup. The RV value of 1.2 is characteristic of Rayleigh scattering (Draine 2003), suggesting that the cloud is composed of very small particles. This appears consistent with observations of other hot Jupiters, as Wakeford & Sing (2015) show that the atmospheres of several hot Jupiters are dominated by Rayleigh scattering. Johns-Krull et al. (2016) suggest that PTFO 8-8695b is losing mass, which could be a source for such a large cloud surrounding the planet.
While not proving the existence of PTFO 8-8695b, our results show that color-dependent transit depths are not sufficient to reject a planet as the source of transit-like signals. The best explanation for all of PTFO 8-8695's transit-like signatures still appears to require a planet-like object approximately the size of Jupiter.