MULTI-BAND, MULTI-EPOCH OBSERVATIONS OF THE TRANSITING WARM JUPITER WASP-80b

We observed three primary transits of WASP-80b with the Simultaneous Infrared Imager for Unbiased Survey (SIRIUS; Nagayama et al. 2003) camera mounted on the Infrared Survey Facility (IRSF) 1.4 m telescope at the South African Astronomical Observatory on 2013 July 16, August 22, and October 7 (UT). SIRIUS has three detectors, each consisting of 1k × 1k pixels with a pixel scale of 045 pixel⁻¹, enabling us to obtain J-, H-, and K_s-band images simultaneously with a field of view (FOV) of 77 × 77. During each observation, we defocused stellar images so that the FWHM of stellar point-spread function (PSF) was 14–17 pixels on July 16 and October 7, and 9.5–12 pixels on August 22, in order to improve photometric precision. In addition, we activated a software that corrects tracking errors by calculating the stellar positional shift on the newly obtained J-band image and feeding it back to the telescope. The exposure time was set to 10 s on July 16 and August 22, and 15 s on October 7. The weather was photometric without any thin cloud passing for the three nights. We observed full transit including pre- and post-transit parts on July 16 and October 7; however, we discarded the data before 22:47 on July 16 (UT) because of an accidental drift of the stellar position on the detector that causes uncorrectable systematic errors on photometry. The pre-transit part on August 22 was not observed due to interference with another observational program. In the lower left panel in Figures 1–3, we show the air-mass change (top) and stellar positional change along x and y directions on the J-band detector (bottom) during the respective observations. An observing log is shown in Table 1.

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We observed two primary transits of WASP-80b by simultaneously using two instruments at Okayama Astrophysical Observatory (OAO) on 2013 August 13 and September 22 (UT); one is the NIR imaging and spectroscopic instrument ISLE (Yanagisawa et al. 2006, 2008) mounted on the 188 cm telescope and the other is a multi-color imager mounted on the 50 cm telescope which is one of Multicolor Imaging Telescopes for Survey and Monstrous Explosions (MITSuME; Kotani et al. 2005; Yanagisawa et al. 2010).

ISLE has a 1k × 1k HAWAII-1 array having a pixel scale of 025 pixel⁻¹ and a FOV of 45 on a side. We used J-band filter and set the exposure time to 45 s on both nights. We defocused stellar images so that the FWHM of stellar PSF was 23–27 pixels. In addition, we activated a hybrid auto-guiding system (Fukui et al. 2013), which consists of an off-axis auto-guiding camera to correct telescope's tracking errors in real time, and a software that corrects a gradual drift of the origin of the auto-guiding camera with respect to the ISLE detector by calculating the shift of stellar positions on the ISLE images.

The multi-color imager mounted on the MITSuME telescope consists of three 1k × 1k CCDs, enabling us to obtain g'-, R_c-, and I_c-band images simultaneously. Each CCD has a pixel scale of 15 pixel⁻¹, providing a FOV of 26' on a side. We slightly defocused the stellar images so that the FWHM of PSF was 1.2–2.5 pixels. We also activated a software that corrects the stellar positional shift on the I_c-band detector soon after each exposure. The exposure time was set to 30 s on both nights.

The weather was mostly photometric on both nights, while some thin clouds passed at the beginning of the observation on September 22, which results in large flux drops especially in the optical bands; we discarded these data from the analysis in the remainder of this paper. In the lower left panel of Figures 4 and 5, we show air-mass change (top) and stellar positional change along x and y directions on the ISLE (middle) and MITSuME/I_c-band (bottom) detectors during the respective observations. An observing log is compiled in Table 1.

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In order to check the intrinsic variability of the host star WASP-80 around the period of our transit observations, we conducted out-of-transit observations on 14 nights spanning 43 days from 2013 August 10 to 2013 September 22, by using the 50 cm MITSuME telescope in g', I_c, and R_c bands. All the settings were the same as the transit observations described in the previous section. The observations were conducted for one to two hours on each night, and in total about 1700 images were gathered for each band.

All the observed images are dark-subtracted and flat-fielded in a standard manner. The flat-field images are created from dozens of twilight flat images that were obtained before and after each observation for the SIRIUS and MITSuME data, and from 100 dome-flat images that were taken on each observing night for the ISLE data. After that, aperture photometry is performed for the target and several (for SIRIUS and ISLE) or dozens (for MITSuME) of bright stars spread on the reduced images, by using a customized tool with constant-aperture-radius mode (Fukui et al. 2011). The target flux is divided by the sum of the fluxes of a selected number of bright stars (comparison stars) to produce a relative light curve.

The time for each data point is assigned as the mid-time of exposure in the Barycentric Julian Day (BJD) time system based on Barycentric Dynamical Time (TDB), which is converted from Julian Day (JD) based on Coordinated Universal Time (UTC), recorded on the FITS header, via the code of Eastman et al. (2010).

In order to optimize the set of comparison stars and aperture radius for each instrument, filter, and transit (each data set), we produce a number of trial light curves for each data set by changing the combination of comparison stars, as well as changing the aperture radius with a step size of 0.5 pixel (for MITSuME) or 1 pixel (for others). Then, we fit the individual trial light curves with a transit-plus-baseline model to select the best light curve so that the root mean square (rms) of the residual light curve is minimum. For the light curve model, we use the following functions:

$$\begin{equation} F= k_0 \times 10^{-0.4 \Delta m_\mathrm{corr}} \times F_\mathrm{tr}, \end{equation} \tag{ 1 }$$

$$\begin{equation} \Delta m_\mathrm{corr} = \sum _{i=1} k_i X_i, \end{equation} \tag{ 2 }$$

where F is the relative flux, F_tr is the transit light-curve model, {X} are variables for the baseline function, and {k} are coefficients. For the variables {X}, we tentatively use {t, z}, where t is time and z is air mass. For the transit model F_tr, we use the analytic formula given by Ohta et al. (2009), which is equivalent to that of Mandel & Agol (2002) when using the quadratic limb-darkening raw. The transit parameters we use are the mid-transit time T_c, the planet-star radius ratio R_p/R_s, the semi-major axis normalized by the stellar radius a/R_s, the orbital inclination i_orb, and the quadratic limb-darkening coefficients u₁ and u₂. Among these parameters, T_c, R_p/R_s, and u₁ are let free, while a/R_s and i_orb are fixed at the values derived from Mancini et al. (2014), namely, 12.6119 and 88.91 deg, respectively. We also fix u₂ at the theoretical values for a star with logg = 4.5 and T_eff = 4100 K for respective filters, adopted from Claret et al. (2012), namely, 0.109, 0.191, 0.225, 0.223, 0.267, 0.241 for g', R_c, I_c, J, H, and K_s, respectively. A circular orbit, with an orbital period of P = 3.06786144 days adopted from Mancini et al. (2014), is assumed. The individual light curves are fitted by the AMOEBA algorithm (Press et al. 1992) to find the one that gives the minimum rms value by iteratively eliminating >4σ outliers. In Table 2, we summarize the number of selected comparison stars and the selected aperture radius for all data sets. The selected light curves are shown in the upper left panels in Figures 1–5, where 10 minute binned data are also shown as a visual guide. We note that there exists a fainter neighboring star (ΔB = 2.8 and ΔK_s = 4.0) that is separated from WASP-80 by 89; we confirm that with the selected aperture radii the flux contamination from the fainter star is negligible for all the data sets.

After preparing the light curves, we select the best-describing baseline model, i.e., which variables should be included in {X} in Equation (2), for each light curve. To do so, we first fit each light curve with Equations (1) and (2), letting T_c, R_p/R_s, u₁, and a/R_s be free while fixing others, by changing the set of variables {X}. The set of variables are chosen from t, z, t², Δx, and Δy, where Δx and Δy are the relative stellar displacement along the x and y directions, respectively, on the detectors. Next, we evaluate the Bayesian information criteria (BIC; Schwarz 1978) for each baseline model; the BIC value is given by BIC = χ² + kln N, where k is the number of free parameters and N is the number of data points. Finally, we select the best baseline model such that the BIC value is minimum.

This procedure works well for all the light curves except for the J- and H-band light curves obtained on 2013 August 22. For these two light curves, we find that the fittings with the minimum-BIC models, namely {X} = {t, t²} for both, derive inconsistent a/R_s values with that derived from Mancini et al. (2014), although for all the other light curves the comparable fittings derive consistent a/R_s values, largely within their uncertainties (see Figure 6). The two exceptional light curves lack a pre-transit part; in such a case, incorrect baseline models can incidentally fit the data well. If this is the case, the derived R_p/R_s value, which is what we want to measure, could be shifted from the true value. In fact, the respective R_p/R_s values for the J- and H-band light curves on August 22 are significantly larger than those for the light curves from the same band on October 7 (see the corresponding panels in Figure 6), which depict both before and after the transit. For the two exceptions, we alternatively find that a simpler baseline model of {X} = {z} can fit them giving consistent a/R_s values with those from Mancini et al. as well as consistent R_p/R_s values with the light curves from the same band on October 7 (denoted as open circles in Figure 6), while the BIC differences between {X} = {z} and {t, t²} for the J- and H-band light curves are 18.8 and 34.1, respectively. For the above reasons, we choose {X} = {z} as the best for baseline model these two light curves. We note that it is not likely that a/R_s and R_p/R_s have changed over time, because fitting to the K_s-band light curve on the same night by the minimum-BIC model gives a a/R_s value that is consistent with that of Mancini et al. In Table 2, we summarize the selected sets of variables {X} for the respective light curves.

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We also note that even for the other light curves, there can be several baseline models that give BIC values similar to the minimum one, potentially causing systematic errors on R_p/R_s depending on which baseline we select. To see the impact of this possibility, we also plot in Figure 6 the R_p/R_s and a/R_s values for the baseline models that give the BIC difference with respect to the minimum-BIC model (ΔBIC) of less than five. As a result, the R_p/R_s and a/R_s values for similar-BIC models (the filled circle, triangle, and square are for the minimum, second-, and third-minimum BIC models, respectively) are close to each other compared to their uncertainties, implying that the systematics on R_p/R_s due to different baseline models are small.

After the baseline-selection process, we rescale the flux uncertainties in each light curve such that the reduced χ² of the transit-plus-baseline-model fit becomes unity. In addition, we further rescale these uncertainties by the so-called β factor (Winn et al. 2008) taking red noises into account. The β factor is defined as σ_{N, obs}/σ_{N, exp}, where σ_{N, obs} is the standard deviation of the residual light curve binned by N data points into M bins, and $\sigma _{N, \mathrm{exp}} \equiv \sigma _1 \sqrt{M/N(M-1)}$ is the expected standard deviation for the binned residual light curve assuming that the unbinned residuals with the standard deviation of σ₁ are dispersed in a Gaussian distribution. We take the median value of β calculated for N = 4 to 15 for each light curve. The calculated β values are summarized in Table 2.

To properly derive the R_p/R_s values and their uncertainties for the respective data sets, we perform the Markov Chain Monte Carlo (MCMC) analysis for each transit by using a customized code (Narita et al. 2007, 2013). In this analysis, all the light curves involved in one transit are analyzed simultaneously, treating i_orb, a/R_s, and T_c as common parameters, whereas R_p/R_s, u₁, u₂, and {k} are treated as independent parameters for the respective light curves. Here, {k} are the coefficients corresponding to the variables {X} selected in the previous section. In the same way as in Section 3.2, we fix i_orb and a/R_s at the values from Mancini et al. (2014), and fix u₂ at the theoretical values for the respective filters; we let the other adjustable parameters be free. The reason for fixing the i_orb and a/R_s values to those of Mancini et al. is that these parameters are correlated with R_p/R_s, and varying them would cause systematic offset on measured R_p/R_s, which is what we aim to compare between different bands among the data including the ones from Mancini et al. (see Section 4.1).

We start the MCMC procedure with the best-fit parameters determined by the AMOEBA algorithm, using their 1σ uncertainties as the widths of Gaussian jump functions for updating MCMC steps. We perform 10 sequential MCMC runs with 10⁶ chained steps in each run, updating the best-fit parameters and their 1σ uncertainties. To wait for convergence, we discard the first five MCMC runs. The final median values and 1σ uncertainties of the respective parameters are calculated from the merged posterior-probability distributions from the last five MCMC runs.

The resultant parameters are summarized in Table 3. The final light curve models are displayed as solid lines in the upper left panels in Figures 1–5, as well as the baseline-corrected light curves and residual light curves are shown in the upper right and lower right panels, respectively, in the same figures. We note that no apparent spot-crossing event is seen in any of the five transits.

Table 3. MCMC Results^a

Parameter	2013 Jul 16	2013 Aug 13	Value	2013 Sep 22	2013 Oct 7	Mancini et al. (2014)
			2013 Aug 22
Tc	6490.492507	6518.10335	6527.30758	6557.98585	6573.32468	...
[BJDTDB-2450000]	±0.000091	±0.00012	±0.00016	±0.00018	±0.000088
u1 (g')	...	0.842 ± 0.087	...	0.642 $^{0.095}_{-0.097}$	...	...
u1 (Rc)	...	0.624 $^{0.042}_{-0.043}$	...	0.551 $^{0.056}_{-0.059}$	...	...
u1 (Ic)	...	0.407 $^{0.048}_{-0.050}$	...	0.353 $^{0.052}_{-0.054}$	...	...
u1 (J)	0.270 ± 0.026	0.254 ± 0.032	0.265 $^{0.035}_{-0.037}$	0.258 $^{0.038}_{-0.040}$	0.204 ± 0.027	...
u1 (H)	0.213 ± 0.023	...	0.126 $^{0.033}_{-0.031}$	...	0.133 $^{0.033}_{-0.038}$	...
u1 (Ks)	0.153 ± 0.029	...	0.159 ± 0.038	...	0.048 $^{0.048}_{-0.053}$	...
Rp/Rs (g')	...	0.1743 $^{0.0045}_{-0.0047}$	...	0.1787 ± 0.0064	...	0.17033 ± 0.00217
Rp/Rs (Rc)	...	0.1736 ± 0.0017	...	0.1711 $^{0.0040}_{-0.0037}$	...	0.17041 ± 0.00175
Rp/Rs (Ic)	...	0.1741 ± 0.0015	...	0.1778 ± 0.0039	...	0.17183 ± 0.00161
Rp/Rs (J)	0.1697 ± 0.0015	0.1704 ± 0.00092	0.1690 ± 0.0014	0.1686 ± 0.0016	0.17234 $^{0.00089}_{-0.00081}$	0.1695 ± 0.0028
Rp/Rs (H)	0.1688 ± 0.0014	...	0.1709 ± 0.0012	...	0.1702 ± 0.0017	...
Rp/Rs (Ks)	0.1708 ± 0.0016	...	0.1672 ± 0.0022	...	0.1679 ± 0.0023	...

Note. ^aThe MCMC analysis in this work is performed by fixing i_orb = 88.91 deg and a/R_s = 12.612, which are obtained from Mancini et al. (2014).

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For the 43 day long photometric monitoring data gathered by the MITSuME telescope, we perform aperture photometry in the same way as in Sections 3.1 and 3.2. After eliminating the data points fallen in any transit events, we correct the systematics on the respective light curves by fitting them with Equations (1) and (2) fixing F_tr = 1 and using {X} = {z, Δx, Δy}. The resultant light curves with nightly binned data points are shown in Figure 7, in which the error bars are calculated as rms of the unbinned data on each night divided by the square of the number of data points.

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In this section, we discuss the dependence of R_p/R_s on wavelength that could arise from the atmospheric properties of WASP-80b. In Figure 8, we plot the observed R_p/R_s values derived in Section 3.4 as a function of wavelength, along with those derived by Mancini et al. (2014). At each band, the measured values from different transits are consistent with each other within 2σ uncertainties. Especially in the J band, we have now a total of six observations of R_p/R_s, including the one from Mancini et al. (2014), and they are mostly consistent with each other, indicating the correctness of our methodology and the smallness of systematics. We note that the effect of stellar intrinsic variability on measured R_p/R_s is negligible, as will be discussed in Section 4.3.

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In order to search for atmospheric features in the observed R_p/R_s spectrum, we first compare the overall observed data with two possible model spectra; one is from an atmospheric model with the solar abundances and the other is from an atmospheric model with opaque clouds. For the former model, we simulate the model spectrum assuming a solar abundance atmosphere and a temperature of 800 K, which corresponds to the equilibrium temperature with albedo of 0.1 (Triaud et al. 2013), as described in the Appendix; for the latter model, we approximate it simply as a flat line assuming that the atmosphere is thoroughly opaque in the wavelength range from optical to NIR. Note that our motivations for comparing with the cloudy model come from the fact that flat transmission spectra compatible with the presence of thick cloud layers have been recently observed for several other low-temperature exoplanets such as GJ1214b (Kreidberg et al. 2014) and GJ436b (Knutson et al. 2014b), as well as the fact that Mancini et al. (2014) reported that their observed spectrum of WASP-80b is consistent with a flat line. We then fit the two model spectra to the data; for both cases, the number of free parameters is one: the radius of the planetary disk that blocks the incident stellar radiation completely, R₀. In the fitting process, we create a theoretical R_p/R_s spectrum for each R₀ using Equation (A2) and the fixed R_s value of 0.63 R_☉ (Triaud et al. 2013), and integrate the spectrum over each filter's pass band to compare it with the observational data. The best-fitted models for the solar abundance atmosphere and the cloudy atmosphere are shown, respectively, by the solid cyan and dashed gray lines in Figure 8. As a result, we find that the solar abundance and cloudy models give the minimum-χ² values of 35.4 and 34.7, respectively, for the degrees of freedom (dof) of 25. These values indicate that the two models are both largely consistent with the data at the discrepancy level of 1.7σ. When we discard the MITSuME data, which were obtained with a relatively small-aperture telescope and might contain relatively large unknown systematics, the solar abundance and cloudy models fit the remaining data with χ²/dof = 24.3/19 and 22.7/19, respectively, reducing the discrepancy levels to 1.3 and 1.1σ. Therefore, we cannot rule out these two models from the current observational data.

On the other hand, we also find that the observed R_p/R_s in the optical region is marginally larger than that in the NIR region; the weighted mean of the observed R_p/R_s in the optical (λ < 1 μm) and NIR (λ > 1 μm) regions are 0.17193 ± 0.00041 and 0.17029 ± 0.00039, respectively, having a 2.9σ discrepancy. As discussed in Section 1, because the equilibrium temperature of WASP-80b is about 800 K or less, a photochemically produced hydro-carbon haze like tholin may exist in the atmosphere (e.g., Fortney et al. 2013). If so, the observed spectral rise in the optical region could be explained by the existence of tholin haze in the planetary atmosphere.

Motivated by this possibility, we model the transmission spectrum of a hazy atmosphere with the solar abundances and compare it with the observed data. The haze layer is characterized by four parameters that include the particle size a_haze, the number density n_haze, and the pressures at the top and bottom of the haze layer, which are denoted by P_top and P_bot, respectively. Values of P_top and P_bot are chosen as described in the Appendix; in the case of GJ1214b, the method of choice is confirmed to yield values of P_top and P_bot that are consistent with the result from Morley et al. (2013). We assume a_haze = 0.04 μm, which is the typical size of haze particles in Titan's atmosphere (Tomasko et al. 2009). We then search for the best-fit hazy model by changing n_haze every one order of magnitude from 10 to 1 × 10⁶ cm⁻³, as well as letting R₀ be free. As a result, we find that n_haze = 1 × 10⁴ cm⁻³ gives a minimum-χ² value of 29.3 with dof = 24 (in this case, the number of free parameters is two) for temperature of 800 K, which means that the discrepancy level is 1.3σ. A comparable fit to the data without the MITSuME data gives χ²/dof = 22.7/18, or 0.99σ. These values are slightly better than those for the above two models of the haze-free solar-abundance atmosphere and the cloudy atmosphere.

In reality, however, we may have to consider temperature lower than 800 K. The 800 K corresponds to the globally averaged equilibrium temperature of WASP-80b with an albedo of 0.1. Since WASP-80b is likely to be tidally locked, the limb of the planetary disk that we observe may be much cooler than 800 K, provided the atmospheric heat redistribution is inefficient. Also, the high-altitude haze may block incident stellar flux from reaching the deep atmosphere. Thus, we consider 600 K, as an example of a moderately warm atmosphere to simulate the transmission spectrum which is shown by the dotted magenta line in Figure 8. In this case, the best-fit model (with n_haze = 1 × 10⁴ cm⁻³) results in a χ²/dof of 26.8/24, giving a discrepancy level of only 1.0σ. These statistical values decrease to χ²/dof = 19.5/18 and 0.92σ for the case without the MITSuME data. These results indicate that the hazy atmosphere model with temperature of 600 K is rather consistent with the observed data, relative to the above three models. In contrast, we also find that the haze-free solar abundance atmosphere of 600 K yields a large χ²/dof of 44.2/25 and 29.7/19 for the data with and without the MITSuME data, respectively. In Table 4, we summarize the statistical results of the model fittings discussed above.

A more extensive search for the best-fit model is beyond the scope of this study because the observed data have uncertainties that are too large and wavelength resolutions that are too low. Also, we need more detailed treatment concerning the role of haze on the atmospheric temperature and the heat redistribution in the atmosphere, which will be left to future studies. Nevertheless, we confirm that at least one atmospheric model with haze can explain the observed data well. Thus, the relatively large R_p/R_s in the optical region detected by our observation has raised another possibility of the presence of haze in the atmosphere. Higher-precision and higher-wavelength-resolution observations are desired to further shed light on this possibility.

Due to the multi-epoch observations, we are able to refine the transit ephemeris as well as search for transit timing variations (TTVs) that would be caused by additional perturbing planets (e.g., Holman et al. 2010). The latter is particularly of interest because warm Jupiters may have a higher probability of having TTV-causing neighboring planets compared to hot Jupiters, most of which are known to be solitary (e.g., Steffen et al. 2012).

Using the mid-transit times of the five transits measured in Section 3.4 as well as those from the previous works, we refine the transit ephemeris of WASP-80b as T_c (BJD_TDB) = 2456125.417574 (86) + 3.06785952 (77) × E, where E is the relative transit epoch and the numbers in parentheses indicate the uncertainties written to the last two significant digits. The residuals of the observed transit timings from the above ephemeris are shown in Figure 9. The χ² value for the linear fit is 59.0 for 11 degrees of freedom, indicating that a liner function does not fit the data well. This in principle could be due to perturbations from an additional object in the planetary system, however, it could also be due to small-number statistics and/or unknown systematics as well (e.g., Maciejewski et al. 2013; Barros et al. 2013; Southworth et al. 2012; Hoyer et al. 2012). In addition, we cannot see any plausible periodicity nor large amplitude exceeding ∼50 s that are usually seen in the detection cases (e.g., Mazeh et al. 2013). Therefore, we do not claim a detection of TTVs due to a third body at this time.

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To check for the existence/absence of stellar intrinsic variability that causes systematic offsets on the observed R_p/R_s, we investigate the 43 day long light curves created in Section 3.5. The χ² values of the 14 nightly binned data with respect to a constant fit are 212.7, 181.8, and 137.4 for g', R_c, and I_c bands, respectively, suggesting that the host star's brightness could significantly vary over time. However, the data points in different bands are not correlated each other, with the correlation coefficients between I_c and R_c, R_c and g', and g' and I_c are −0.26, 0.29, −0.32, respectively. This fact indicates that the observed dispersions are due to systematics rather than astrophysical origin. In addition, no periodic variation or linear trend can be seen in any of the three light curves. Therefore, we do not detect any star-spot-induced periodic variability with the semi-amplitude larger than 0.25%, 0.3%, and 0.7% for I_c, R_c, and g' bands, respectively, during the observed period range of 43 days. Even if the observed dispersions were of astrophysical origins, the maximum variability of 0.7% in the g' band would change the observed R_p/R_s values by only 0.07%, or 0.0001 in units of R_p/R_s, which is negligible compared to the uncertainties of R_p/R_s.

The non-detection of significant stellar variability is in line with the report of Triaud et al. (2013), who did not detect >1 mmag rotational variability from wide-band (V+R) photometric data of the WASP transit survey, as well as from multi-epoch observations with a 60 cm telescope. We therefore confirm from the multi-band observations that the host star WASP-80 does not show spot-induced large (> a few mmag) periodic variations. In addition, so far no spot-crossing event has been observed during any of the transits observed in this work or in previous works (nine transits in total), implying that there are not many or large spots distributed on the stellar surface. On the other hand, Triaud et al. (2013) pointed out that the star could be young because of its high projected stellar rotational velocity (v sin i_s = 3.55 ± 0.33 km s⁻¹), depletion of lithium, and the presence of Ca H+K emission, although there is also counter-evidence that the galactic dynamical velocities are low. In addition, Mancini et al. (2014) also detected strong Ca H+K emission lines, indicating that the star has strong magnetic activity. If the star is truly young and active, the star is expected to be heavily spotted. If so, a possible scenario would be that either many small spots are widely distributed on the stellar surface (Mancini et al. 2014), or the stellar inclination i_s is very small such that the polar region of the stellar surface is always facing us. The latter idea is particularly consistent with the fact that the projected spin-orbit angle β was measured as a significantly non-zero value (±75°  ±  4), assuming V sin i_s = v sin i_s, where V sin i_s and v sin i_s are the projected stellar rotation velocities measured from the Rossiter–McLaughlin effect and spectral equivalent width, respectively (Triaud et al. 2013). In this case, the star should be rotating very fast, possibly less than a few days. Photometric monitoring of the star with much higher precision may help to measure the rotational period and test this possibility.