DETECTION OF AN ATMOSPHERE AROUND THE SUPER-EARTH 55 CANCRI E

We downloaded the publicly available spectroscopic images of the transiting exoplanet 55 Cancri e (ID: 13665, PI: Björn Benneke) from the MAST Archive. The data set, obtained with the G141 grism, contains two visits of four HST orbits each. Each exposure is the result of three up-the-ramp samples with a size of 522 × 522 pixels in the SPARS10 mode, resulting in a total exposure time of 8.774724 s, a maximum signal level of 6.7 × 10⁴ electrons per pixel, and a total scanning length of approximately 350 pixels. Both scanning directions were used for these observations, and in the text we will refer to them as forward (increasing row number) and reverse (decreasing row number) scans. In addition, the data set contains, for calibration purposes, a non-dispersed (direct) image of the target with the F132N filter.

The configuration of this particular data set allows us to fully capitalize on our WFC3 scanning-mode pipeline, as the long scanning length and the high scanning speed intensify the effects of the geometrical distortions, as discussed in Tsiaras et al. (2015). In addition, we can study the coupling between the scanning speed and the reading process which are critical elements in fast scanning observations (Section 2.3).

In this section, we summarize the steps to extract the spectro-photometric light curves from the spatially scanned spectra. We refer the reader to Tsiaras et al. (2015) for a detailed discussion of our pipeline, which was conceived to reduce spatially scanned spectra.

The first step is the standard reduction of the raw scientific frames: bias drifts correction, zero read subtraction, nonlinearity correction, dark current subtraction, gain variations calibration, sky background subtraction, and finally bad pixel and cosmic-ray correction.

The next, fundamental, step is to calibrate the position of the frames, as this is required for wavelength calibration. In scanning-mode observations, position shifts are common. We measure the horizontal shifts by comparing the normalized sum across the columns of each frame to the first frame of the first visit. The forward and reverse scans are compared to the first forward or reverse scanned spectrum, respectively. This separation is necessary because the frames resulting from the two different scanning directions have slightly different positions on the detector and, consequently, slightly different structure, which could bias our measurement. For the vertical shifts, we make use of the first non-destructive read of each exposure. We fit an extended Gaussian function to each column profile because, due to the very fast scanning, even these spectra are elongated. Finally, we fit the central values of these extended Gaussians as a linear function of the column number, which indicates any possible vertical shifts. Again, we keep forward and reverse scans separated as their initial scanning positions are close to the two vertically opposite edges of the frame.

In the first visit, we find that the vertical shifts have an amplitude three times larger than the horizontal ones, while in the second visit they are five times larger (Figure 1). The behavior of the 55 Cancri e data set is not commonly observed and a plausible explanation is the high scanning speed used.

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We then proceed to wavelength calibration. Based on the direct image included in the data set, the calibration coefficients provided by Kuntschner et al. (2009), and the measured horizontal shifts, we calculate the wavelength-dependent photon trajectories for each frame. The wavelength-dependent photon trajectories indicate the position of the photons at each wavelength on the detector during the scan.

As we can see in Figure 2, the position of the photons at a particular wavelength is shifted toward the left part of the detector as the scan processes. This behavior is caused by dispersion variations that our approach accurately takes into account. The effect on a single spatially scanned spectrum is that a pixel at the bottom of a given column is probing a different part of the stellar spectrum compared to a pixel at the top of the same column. For a column at ∼1.2 μm, the wavelength difference between the lower and the upper edge of the spatially scanned spectrum is 62 Å, 33% of the total bin size of 185 Å. The effect is stronger at longer wavelengths (∼1.6 μm) where the difference is 140 Å, 57% of the total bin size of 230 Å. Given that the wavelength range inside one pixel is about 46 Å, in the first case the shift corresponds to 1.3 pixels, while in the second case to 3 pixels. We plan to further investigate how this bias propagates to the final planetary spectrum by using our WFC3 simulator, Wayne (Varley & Tsiaras 2015), in a future work.

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The photometric apertures are delimited by the wavelength-dependent photon trajectories of a selected binning grid and, as a result, they are of quadrangular shape. We take into account fractional pixels by using a second-order, two-dimensional (2D) polynomial distribution of the flux (based on the values of the surrounding pixels) and calculating the integral of this function inside the photometric aperture. By applying this process to all of the frames, we extract the white (Figure 3) and spectral light curves.

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Reading the IR detector of the WFC3 camera takes about 2.93 s in total and, as a result, while the exposure time is the same for all of the pixels, they are not all exposed simultaneously. The first and last rows of the detector are the first to be read, and then the process continues to the inner rows until the vertical mid-point is reached. The reading direction is, therefore, different for the two upper and the two lower quadrants, as the first are read downwards and the second upwards.

This process does not affect the staring-mode frames because the position of the spectrum is always the same. However, when the spatial scanning technique is used, there is a coupling between the scanning and reading directions, referred to as the down-stream/up-stream configuration, depending on whether the reading and scanning directions are the same/opposite. As a result, a down-stream configuration has a longer effective exposure time (McCullough & MacKenty 2012), which allows a longer total length for the scan and a higher total flux compared to an up-stream configuration.

Figure 3 clearly shows that the white light curves of the two different scanning directions have different long-term slopes. In particular, the reverse scans have an upward trend relative to the forward scans in the first visit, and a downward trend in the second visit. These trends are correlated with the vertical position shifts (Figure 1). Indeed, we find that the total length of the scans, i.e., the effective exposure time and therefore the total flux, changes with the vertical position shifts in a different way for the two scanning directions (Figure 4).

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In cases where the spectrum trace crosses the mid-point line, the scanning/reading configuration is down-stream at the beginning of the scanning process and up-stream at the end of it. We believe that this effect could cause a dependency between the vertical position of the spectrum on the detector and the effective exposure time. For this data set, the flux variation is about 0.7 × 10⁻³ for a vertical shift of one pixel.

We correct for this effect using the linear behavior of the scanning length with the vertical position shifts (Figure 4) and rescaling each data point to the first of each scanning direction. Figure 5 plots both scanning directions, which are fitted together with the same model, proving the consistency between them. Note that there is still a small, constant offset between them, and so we have to fit for two different normalization factors.

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The WFC3 infrared detector introduces time-dependent systematics, known as "ramps," both in staring mode (Berta et al. 2012; Swain et al. 2013; Wilkins et al. 2014) and scanning mode (Deming et al. 2013; Knutson et al. 2014a; Kreidberg et al. 2014b; Tsiaras et al. 2015) observations. The effect of these systematics is stronger with increasing flux and, since 55 Cancri is a very bright source, the presence of "ramps" is expected (Figure 3). We correct these systematics using an approach similar to that of Kreidberg et al. (2014b). We adopt an instrumental systematics function:

$$\begin{eqnarray}&&R(t)=(1-{r}_{a}(t-{t}_{{\rm{v}}}))(1-{r}_{b1}{e}^{-{r}_{b2}(t-{t}_{{\rm{o}}})})\end{eqnarray} \tag{ , 1 }$$

where t is the mid-time of each exposure, t_v is the time when the visit starts, t_o is the time when the orbit in which the frame belongs starts, r_a is the slop of the linear long-term "ramp," and (r_b1, r_b2) are the coefficients of the exponential short-term "ramp."

We use our transit light-curve model, which returns the relative flux, F(t), as a function of time, given the limb darkening coefficients, a_n, the ${R}_{{\rm{p}}}/{R}_{*}$ ratio, and all of the orbital parameters (${T}_{0},P,i,a/{R}_{*},e,\omega$). The model is based on the nonlinear limb darkening law (Claret 2000) for the host star:

$$\begin{eqnarray}&&I{({a}_{n},r)=1-\displaystyle \sum _{n=1}^{n=4}{a}_{n}(1-(1-{r}^{2})}^{n/4}).\end{eqnarray} \tag{ 2 }$$

We derive the limb darkening coefficients from the ATLAS stellar model (Kurucz 1970; Howarth 2011) of a star similar to 55 Cancri (Table 1), using the sensitivity curve of the G141 grism between 1.125 and 1.65 μm (Table 2) to avoid its sharp edges. Since the ingress and egress of the transit are not included in the light curve (Figure 3), it is impossible to fit for the orbital parameters. We therefore fix the inclination, the $a/{R}_{*}$ ratio, and the mid-transit point to the values listed in Table 1. We also assume a circular orbit.

Table 2.  White Light-curve Fitting Results

Limb Darkening Coefficients (1.125–1.650 μm)
a1	0.695623
a2	−0.268246
a3	0.357576
a4	−0.171548
${R}_{{\rm{p}}}/{R}_{*}$
visit 1	0.01894 ± 0.00023
visit 2	0.01892 ± 0.00023

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The models of the systematics, R(t), and the white transit light curve, ${F}_{{\rm{w}}}(t)$, are both fitted to the white light curve following two different approaches: (a) fitting the transit model multiplied by the instrumental systematics and a normalization factor, ${n}_{{\rm{w}}}^{\mathrm{scan}}R(t){F}_{{\rm{w}}}(t)$, and (b) fitting the instrumental systematics, R(t), on the out-of-transit points, correcting the light curve, and then fitting a normalized transit model, ${n}_{{\rm{w}}}^{\mathrm{scan}}{F}_{{\rm{w}}}(t)$. The normalization factor, ${n}_{{\rm{w}}}^{\mathrm{scan}}$, changes to ${n}_{{\rm{w}}}^{\mathrm{for}}$ when the scanning direction is upward and to ${n}_{{\rm{w}}}^{\mathrm{rev}}$ when it is downward to account for the offset between them. Figure 5 shows only the case of simultaneous fitting, as both approaches give the same result for each visit. The final ${R}_{{\rm{p}}}/{R}_{*}$ ratio is well consistent between the two visits (Table 2). Figure 6 plots the correlations between the fitted parameters, showing no correlation between the ${R}_{{\rm{p}}}/{R}_{*}$ ratio and any of the parameters describing the systematics.

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As we can see in Figure 3, the sky background is slightly different for the forward and reverse scans, indicating that the area from which the sky background level is estimated is contaminated by stellar flux. Since the area we are using is already at the left edge of the detector, this contamination is inevitable. To measure its effect on the final results, we repeat the whole process with an aperture that extends 10 pixels above and below the vertical edges of the spatially scanned spectrum (instead of the 20 used for the above results). We find a uniform shift of 3 ppm across the wavelength channels, while the uncertainty in the transit depth is, on average, 22 ppm for the relative spectral light curves. This result indicates that the relative structure of the spectrum is not affected, and the uncertainty in the ${R}_{{\rm{p}}}/{R}_{*}$ ratio includes this potential bias.

To calculate the wavelength-dependent transit depth, we use the spectral light curves divided by the white one. In this way, we minimize the effect of the systematics model not perfectly approximating the real systematics, as the residuals in Figure 5 do not follow a Gaussian distribution. The relative light curves appear to have an out-of-transit slope which we interpret as an effect caused either by the horizontal shifts (model 1) or by a wavelength-dependent, long-term "ramp" (model 2). In the first case, we fit for a factor which is linear with the horizontal shifts, as calculated in Section 2.2, while in the second case we fit for a factor which is linear with time. The models used for each of the above approaches are

$$\begin{eqnarray}\text{model 1:} & & {n}_{\lambda }^{\mathrm{scan}}(1+{\chi }_{\lambda }{\rm{\Delta }}x)({F}_{\lambda }/{F}_{{\rm{w}}})\\ \text{model 2:} & & {n}_{\lambda }^{\mathrm{scan}}(1+{\chi }_{\lambda }t)({F}_{\lambda }/{F}_{{\rm{w}}})\end{eqnarray} \tag{ 3 }$$

, where ${n}_{\lambda }^{\mathrm{scan}}$ is a normalization factor with the same behavior as in the white light curve, ${\chi }_{\lambda }$ is the linear factor in each case, ${\rm{\Delta }}x={\rm{\Delta }}x(t)$ is the horizontal shifts, ${F}_{{\rm{w}}}={F}_{{\rm{w}}}(t)$ is the white light-curve model, and is ${F}_{\lambda }={F}_{\lambda }(t)$ the spectral light-curve model. Fitting the normalization factor per wavelength channel is necessary, as the offset between the scanning directions varies with wavelength. The orbital parameters used are those from Table 2 and the white ${R}_{{\rm{p}}}/{R}_{*}$ ratio is taken from the fitting above.

For each spectral light curve, we fit the above models twice: the first time, using the uncertainties provided by the reduction and extraction process, and the second using the standard deviation of the residuals of the first fit. The final uncertainty reported is the maximum of the two and it is between 5% and 20% above the photon noise limit. In this way, we take into account possible scatter in the data points that is in addition to the photon noise and the noise introduced by the instrument.

The wavelength bins are selected within the limits of the white light curve and with a constant resolution of $\lambda /{\rm{\Delta }}\lambda =65$, which is half of the resolving power of the G141 grism, to keep an approximately uniform signal-to-noise ratio (S/N). We calculate the limb darkening coefficients for each spectral light curve using the ATLAS model, the stellar parameters in Table 1, and the sensitivity curve of the G141 grism inside the boundaries of each wavelength bin.

In order to fit the WFC3 spectrum, we use ${ \mathcal T }$-REx(Waldmann et al. 2015a, 2015b), a Bayesian spectral retrieval that fully maps the parameter space through a  nested sampling algorithm. The transmission spectra are generated using cross sections based on the line lists from ExoMol (Barber et al. 2006; Yurchenko et al. 2011; Tennyson & Yurchenko 2012; Barton et al. 2013; Barber et al. 2014; Yurchenko & Tennyson 2014), HITRAN (Rothman et al. 2009, 2013), and HITEMP (Rothman et al. 2010). The atmosphere is parametrized assuming an isothermal profile with constant molecular abundances as a function of pressure. We include a wide range of molecules in the fit, including H₂O, HCN, NH₃, CH₄, CO₂, CO, NO, SiO, TiO, VO, H₂S, and C₂H₂. The fitted parameters are the mixing ratios of these molecules, the atmospheric mean molecular weight, the surface pressure, and the planetary radius.

We use uniform priors for the gas mixing ratios ranging from 1 to 10⁻⁸. The mean molecular weight is coupled to the fitted composition in order to account for both the fitted trace gases and possible unseen absorbers with signatures outside the wavelength range probed here. The uniform prior assumed for the mean molecular weight ranges from 2 to 10 amu. Finally, we assume uniform priors for the surface radius, the surface pressure, and the mean atmospheric temperature in the range of 0.1–0.3 R_Jup, 10–10⁷ Pa, and 2100–2700 K, respectively. We do not include a separate parameterization for the cloud layer; the pressure at the surface could be the pressure at the top of a cloud deck.

In parallel to the spectral retrieval, we investigated the theoretical predictions for the chemical composition of an atmosphere enveloping 55 Cancri e. We assumed an atmosphere dominated by hydrogen and helium with a mean molecular weight of 2.3 amu. We used a thermal profile with a high-altitude atmospheric temperature of 1600 K. These parameters correspond to a scale height of 440 km, or 25 ppm, at the surface.

We used the same chemical scheme implemented in Venot et al. (2012) to produce vertical abundance profiles for 55 Cancri e, assuming a solar C/O ratio and a C/O ratio of 1.1. This chemical scheme can describe the kinetics of species with up to two carbon atoms. In Venot et al. (2015), it was shown that a more sophisticated chemical scheme including species with up to six carbon atoms produces comparable results, and that the simpler scheme can reliably model atmospheres with C/O ratios above 1. The scheme has been developed with combustion specialists and validated by experiments conducted in a wide range of temperatures (300–2500 K) and pressures (0.01–100 bar; e.g., Battin-Leclerc et al. 2006; Bounaceur et al. 2007, 2010; Anderlohr et al. 2010; Wang et al. 2010).

The stellar flux was calculated in the following manner. From 1 to 114 nm, we used the mean of the Sun spectra at maximum and minimum activity (Gueymard 2004), scaled to the radius and effective temperature of 55 Cancri. From 115 to 900 nm, we used the stellar flux of ε Eridani (HD 22049) from Segura et al. (2003), also scaled to the properties of 55 Cancri. ε Eridani is a K2V star (${T}_{\mathrm{eff}}=5084\;{\rm{K}}$ and $R=0.735\;{R}_{\mathrm{Sun}}$) quite close to 55 Cancri, which is a G8V star (${T}_{\mathrm{eff}}=5196\;{\rm{K}}$ and $R=0.943\;{R}_{\mathrm{Sun}}$), making ε Eridani a quite good proxy for 55 Cancri.

The absorbing features seen in the spectrum of 55 Cancri e are indicative of the presence of an atmosphere. Our spectral retrieval shows that the atmosphere is likely dominated by a mixture of hydrogen and helium, and suggests that the features seen are mainly due to HCN. No signature of water vapor is found.

If the features seen at 1.42 and 1.54 μm are due to hydrogen cyanide (HCN), then the implications for the chemistry of 55 Cancri e are considerable. Venot et al. (2015), using a new chemical scheme adapted to carbon-rich atmospheres, pointed out that the C/O ratio has a large influence on the C₂H₂ and HCN content in the exoplanet atmosphere, and that C₂H₂ and HCN can act as tracers of the C/O ratio. Indeed, in a large range of temperatures above 1000 K, at a transition threshold of about C/O = 0.9, the C₂H₂ and HCN abundances increase by several orders of magnitude, while the H₂O abundance decreases drastically, as sown in Figure 10.

We conclude that if the absorption feature is confirmed to be due to HCN, then the implications are that this atmosphere has a C/O ratio higher than solar. However, additional data in a broader spectral range are necessary to confirm this scenario. We also note that while there is a good line list available for the hot HCN/HNC system (Harris et al. 2002; Barber et al. 2014), there is no comprehensive line list available for hot C₂H₂; providing such a list is important for future studies of this interesting system.