A DETECTION OF Hα IN AN EXOPLANETARY EXOSPHERE

We obtained observations of the planet-bearing systems HD 147506, HD 149026, HD 189733, and HD 209458 using the Hobby–Eberly Telescope (HET) from 2006 August to 2008 November. These data were used to make the first ground-based detection of an exoplanetary atmosphere by measuring Na i in HD 189733b (R2008). J2011 searched for Na i and K i in several targets and confirmed Na i absorption in HD 189733b in a semi-independent analysis of the same data set used by R2008. Recent HST observations have also confirmed the presence of Na i in HD 189733b (Huitson et al. 2012).

Details of the observations can be found in R2008 and J2011, but here we provide an overview. Observations were made with the High-Resolution Spectrograph (HRS) at a nominal resolution of R ∼ 60, 000. Individual exposures were limited to 10 minutes in length in order to avoid saturation (and are in some cases shorter due to observing constraints). Approximately 20% of the exposures for each target were taken while its respective planet was in transit. Specific details are provided in Tables 1 (observational statistics) and 2 (system and orbital parameters).

Table 1 also lists the telluric standard stars used for each observation. Telluric standard observations were made either immediately before or after primary science observations, thus limiting spatial and temporal variations in airmass and water vapor levels. Examples of the primary target and telluric standard spectra are shown in Figure 1.

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The HRS instrument on the HET is an echelle spectrograph. We used standard IRAF procedures to remove the bias level and scattered light, flatten the field, extract the apertures, and determine the wavelength calibration from the ThAr lamp exposures. We extracted to one-dimensional spectra the primary science observations, the telluric standard star observations, and the ThAr exposures.

In order to perform a proper telluric correction, we must remove the imprint of the strong Hα line in the telluric standard star. We model a high-order spline (see Figure 2) through the entire spectral order containing the Hα line in all of the telluric observations and then calculate an average model to be removed, via division, from these observations. When dividing this model from each telluric observation, we also add a low-order polynomial to account for wavelength shifts and differing scales between observations. After this division, we are left with a normalized telluric spectrum, free of the telluric standard's Hα imprint. The primary science observations are then corrected for telluric absorption using the normalized telluric spectra and standard IRAF procedures. We note that we find no apparent telluric residuals in the resulting transmission spectra (see Section 3.1).

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We separate the exposures by whether they are in- or out-of-transit, and we co-add spectra from a given group, leaving us with a master in-transit spectrum and a master out-of-transit spectrum. Two additional issues arise in the co-adding process. First, by measuring unsaturated lines in the ThAr lamp exposures, we note that the resolution varies slightly as a function of time. Second, we must apply small wavelength corrections, both an overall shift and a higher-order correction based on cross-correlating the stellar lines. These two steps were described in more detail in J2011. The final co-adding is weighted by the errors at each point in the spectrum, with the errors based on photon statistics and read noise.

With our master in- and out-of-transit spectra we derive a transmission spectrum. We perform a wavelength correction similar to that used in our co-adding process (an overall shift plus a higher-order correction from cross-correlating stellar lines). The spectrum is normalized, with the continuum defined several angstroms away from the line center. We then calculate the transmission spectrum,

$$\begin{equation} S_T=\left(\frac{F_{{\rm in}}}{F_{{\rm out}}}\right)-1 \; . \end{equation} \tag{ 1 }$$

We calculate a measurement of the absorption, M_abs, which we define as

$$\begin{equation} M_{{\rm abs}} = \langle S_T \rangle _{c} - \frac{\langle S_T \rangle _{b} + \langle S_T \rangle _{r}}{2}, \end{equation} \tag{ 2 }$$

where the subscripts c, b, and r represent the central primary integration region and the blue and red comparison integration regions, respectively.

Because of the many steps in our reduction process, we suspect that systematic errors may be larger than the formally propagated statistical errors. These systematic errors may come from either our reduction process or astrophysical sources. Systematic errors from our reduction process would include the telluric correction step, normalization of spectra, and our wavelength corrections. The dominant astrophysical source of systematic error would be stellar variability. To quantify the effect of these systematic errors, we use an "Empirical Monte Carlo" method (hereafter EMC). The details of this method can be found in R2008 and J2011, but we summarize here. We use our co-adding process described in Section 2.2 on various subsets of the in- and out-of-transit data (always of the same type) and compare them to the master in- or out-of-transit spectra using our procedure for calculating transmission spectra.

The three important combinations we examine are (1) in-transit subsets versus the out-of-transit master spectrum or "in–out," (2) in-transit subsets versus the in-transit master spectrum or "in–in," and (3) out-of-transit subsets versus the out-of-transit master spectrum or "out–out." Each method will have some characteristic distribution, but we expect that the "in–out" method will be centered around the master transmission spectrum measurement and the "in–in" and "out–out" methods will be centered around zero. Additionally, we expect that the distribution of the "out–out" method will provide the best estimate of the true systematic error (see R2008 and J2011 for more details).

Another important check on our results is to see whether they are the systematic result of our co-adding and transmission spectrum calculations near a strong stellar line. To check this, we performed the above procedures on a strong stellar line of Ca i at 6122 Å, which we do not expect to manifest in exoplanetary atmospheres (calcium should condense out at the temperatures implied by models, e.g., into CaTiO₃). If our method is robust even when performed on such a line, the results of the master measurement and the EMC distribution should be consistent with zero (see R2008 and J2011 for additional details). These calculations were performed by J2011, and we do not repeat them here (see Figures 2 and 5 of J2011). In J2011, we did indeed find the master measurements and EMC distributions to be consistent with zero for all four systems, an indication that any absorption results on other lines are not simply an inevitable, or even likely, consequence of our analysis procedures.

The transmission spectra of both HD 147506b and HD 149026b are relatively featureless compared to the noise level. Notably, the strongest "noise" feature is at approximately 6553 Å in HD 147506b, which, at our settings, corresponds to the known location of a large group of bad pixels (roughly a 3 × 3 square of pixels) on the CCD chip. Standard IRAF procedures and the telluric correction step largely take out the effects of these bad pixels in most individual exposures, but inspection here of the final transmission spectra shows that some residuals remain that are only obvious at high precision.

Though the transmission spectra for these two targets do not show any clear features that appear to be absorption or emission, the master integration measurements and corresponding EMC results show a slightly more complicated situation. The master integration measurement for HD 147506b results in an absorption level that is 2.8σ significant relative to the width of the "out–out" EMC, which we assume is the best estimation of the total systematic and statistical error (see Section 3.2 and similar discussions in R2008 and J2011). Notably, this master measurement is not well aligned with the "in–out" distribution, which is an exception in the 16 transmission spectra calculated between this work and J2011. The best-fit centroid of the "in–out" distribution is only 0.7σ away from zero, again using the Gaussian σ from the "out–out" distribution as the error. The "in–in" distribution is also not quite centered at zero (though it is only approximately 1.0σ away from zero using its own Gaussian width).

There are a few things we can say about the results for HD 147506b. First, based on the master transmission spectra, it appears to be the only one of the four targets where the aforementioned section of bad pixels, affecting data points near ∼6553 Å, comes into play in the final transmission spectrum. Second, as we noted in J2011, HD 147506 is the faintest star in our sample, with the resulting lowest signal-to-noise ratio (S/N; comparable to observations of HD 149026 but much lower than HD 189733 and HD 209458). It also has the broadest and shallowest stellar features of the four stars in our sample, due to its vsin i of 20.8 ± 0.3 km s⁻¹, which is ⩾3 × the other three stars (Pál et al. 2010; Butler et al. 2006). This complicates our process of cross-correlating stellar lines of different spectra in order to make additional corrections to the wavelength solution (note, for example, that there is also a small alignment artifact at ∼6575 Å in this target). Therefore, it would have been reasonable to identify this target a priori as the most qualitatively uncertain, a conclusion we also reached in J2011, where similar issues were seen in the transmission spectrum of this target. Finally, we note that we obtain different results when we integrate over a narrower bandpass. Our default bandpass is 16 Å; we also calculate a 6 Å bandpass, which is chosen so that the blue comparison band misses the ∼6553 Å noise feature. This results in the master transmission spectrum integration being reduced; note that this is an average value, so the two are already normalized despite the different bandpasses. The distribution of the "out–out" EMC is also wider, so the significance drops to 0.58σ. The consistency of the master measurement and the "in–out" distribution is slightly improved in an absolute sense and dramatically improved relative to the now-broader widths of both the "in–out" and "out–out" distributions. Furthermore, note that in both cases, the ∼6553 Å noise feature may affect the overall normalization of the transmission spectrum.

In the transmission spectrum of HD 149026b there is a slight "emission" bump just to the red of the stellar Hα line center. This turns out to be significant at the 2.0σ level. Unlike the unusual EMC distributions (in that there are apparent internal inconsistencies) of HD 147506b described above, in this case the "in–in" and "out–out" distributions are both consistent with zero, and the "in–out" distribution is consistent with the master integration measurement. Changing the bandpass also does not affect these results in the same way that we described above for HD 147506b. The feature is visually subtle and only 2.0σ, so we are disinclined to associate this with a real feature. However, if the feature is real, the primary way that an emission feature could be observed in a transmission spectrum is by induced stellar activity from a star–planet interaction (SPI), which might occur on the portion of the stellar surface facing the planet. We discuss this more in Sections 5.2.1 and 5.3.3.

We detect a dramatic absorption-like feature in the transmission spectrum of HD 189733b, with a value of M_abs = (− 1.06 ± 0.24) × 10⁻³ (integrated over 16 Å and M_abs defined as in Equation (2) and using the standard deviation of the "out–out" EMC distribution as our error). This detection is significant at a 4.4σ level. The EMC results place important constraints on any otherwise undetected systematic errors, including any remaining atmospheric residuals of our telluric correction and planet-independent stellar variability. The statistical significance of this result argues strongly that this is a real, transit-dependent feature rather than a reduction or analysis artifact. We also note that when we inspect the transmission spectra of the several thousand EMC iterations visually, the results are qualitatively consistent with the measurements: all "in–out" iterations consistently show an absorption feature in transmission, whereas the "in–in" and "out–out" iterations show variation in the residuals of emission or absorption in the Hα line, but the variation is centered about zero and smaller in magnitude than the average magnitude of the "in–out" absorption. The variation in the "in–in" and "out–out" iterations is probably due to stellar variability, which we discuss below. Another qualitative argument in favor of the HD 189733b result being a real phenomenon associated with transit is the null results in HD 147506b and HD 149026b. Similar to the Ca i control line in these targets, this shows that an artificial feature is not an inevitable result due to some effect of our transmission spectrum procedure performed on a strong stellar line.

However, the level of variability in the "in–in" and "out–out"—which we noted above was less than the magnitude of the absorption feature in the master transmission spectrum—is worth further inspection. The EMC takes a random sample of the observations and is unlikely to sample all observations from a given night. Therefore, if there is significant stellar variability on timescales greater than the length of the individual observations but shorter than the time spanned by different sets of observations (e.g., nights), then the EMC as initially constructed may not adequately characterize the variability. Therefore, we make an additional attempt to do so by calculating a transmission spectrum and integrated absorption measurement for each individual out-of-transit observation relative to the master out-of-transit spectrum. This assumes that the master out-of-transit spectrum sufficiently samples any variability and averages it out; using only out-of-transit observations explicitly removes the dependence of planetary transit from the calculation. This provides us with a time series representation of the variability on which we can perform period analysis.

We used a Lomb–Scargle periodogram to analyze this time series, which is shown in Figure 5, along with the window function associated with our data. There are many periods with power spectral density (PSD) of greater than 3σ significance, according to both analytic determination and white-noise simulation estimations of the false alarm probability. The strongest group of peaks in the periodogram, in terms of PSD, is at high frequency (∼1 day); the second strongest set of peaks is near ∼12 days; the third strongest set of peaks is at ∼8.5 days; and more are found at one-half of the ∼12 day group, as well as lower frequencies of ≳16 days. In contrast, similar periodograms for HD 147506 and HD 149026 do not show any variability that exceeds the 3σ false alarm threshold (we deal with HD 209458 in Section 4.3). Given that HD 189733 is the most chromospherically active star in our small sample (see the discussion in Section 5.2.5), this might be expected. Of the periods just described, the ∼12 day period is the one with a clear physical interpretation. Bouchy et al. (2005) estimated a rotational period of ∼11 days, based on the vsin i and the assumption that we are viewing the star along its plane of rotation. Similarly, Hébrard & Lecavelier Des Etangs (2006) found microvariability at several periods, with the dominant period to be at 11.8 days, which they interpreted as the rotation period. "Quasi-periodic" flux variations were measured by Winn et al. (2007a) with a period of 13.4 days. Fares et al. (2010) suggest that the discrepancy between the latter two results may be due to the temporal variation in stellar spots coupled to differential rotation and find an equatorial period of 11.94 ± 0.16 days.

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Fares et al. (2010) observed Ca ii and Hα and found significant variability. For each line, they observe over three epochs and calculate a best-fit period. The Hα best-fit periods are 11.6^+0.3_{− 0.2}, 14.4^+1.5_{− 1.3}, and 13.8^2.2_{− 2.3} days for observations in 2006 June and August, 2007 June, and 2008 July (though the authors note that the phase coverage is poor for the 2006 data). Note that all three best-fit Hα periods are consistent with our period of 12.077 days (the period with the largest PSD between 10 and 15 days) to within 2σ; 12.077 days is also consistent to within 1σ with their derived equatorial period.

Notably, there is also a straightforward explanation for the high-frequency peaks. The window function peaks at 0.9967 days, which is expected because the timing of the HET observations is correlated with the length of the sidereal day, which is 0.9972 civil days. The two peaks in the periodogram that are closest to this peak in the window function are also the two most powerful peaks in the periodogram, at 1.086 and 0.920 days. These peaks are, to high precision, plus and minus one 12.077 day period in frequency space away from the window function peak. This strongly suggests that these peaks are due to aliasing of the longer period in conjunction with the window function peak of 1 sidereal day, and therefore the power in these peaks should be disregarded.

We attempt to remove the variability from our master transmission measurement by making a fit based on only the out-of-transit variability. Then we can estimate an additive calibration term for any observation (in- or out-of-transit) by phasing it to this function. These calibration terms are then averaged for all in-transit observations in order to calculate a calibrated master transmission spectrum integration, as well as for each iteration of the EMC. We show a fit to data phased to the 12.077 day period in Figure 6, using a low-order Fourier series. In Figure 7 we show this same fit as a function of absolute time. Both Figures 6 and 7 show the general tendency of the in-transit residuals to be below the out-of-transit residuals. When we calculate a new periodogram with the residuals, the PSD of the ∼1 day high-frequency peaks is greatly reduced—the two highest-power peaks disappear and the highest remaining ∼1 day period with the largest PSD is at the peak of the window function. The other significant peaks of higher frequency than the 12.077 day period that we noted above are also significantly reduced. We limit the fit to two terms in the Fourier series (i.e., the function is a linear combination of sines and cosines with periods of P and P/2, where P is the 12.077 day period) based on what we see in the periodogram; if more terms are allowed, the function begins to fit for some of the periodicity caused by our sampling frequency as characterized by the window function.

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The calibrated EMC and master measurement gives us a new result of (− 8.72 ± 1.48) × 10⁻⁴. The error from the EMC in this case has gone down significantly because we are explicitly fitting for the dominant source of astrophysical noise. HD 189733 is the brightest star in our sample with the greatest number of observations and therefore should have the highest S/N and lowest corresponding error if astrophysical noise is removed. Prior to calibrating the error, it was largest for HD 189733b. The calibrated error is smaller than for HD 147506b and HD 149026b with their fainter central stars, but larger than for HD 209458b and its comparably bright star. Using the uncalibrated measurements, our result was significant at a 4.4σ level; the calibrated result is significant to 5.9σ, and the EMC results behave as we expect—the widths of the three EMC distributions are each reduced by a reasonably consistent fraction of between 39% and 46%: the master "in–out" measurement is consistent with the "in–out" EMC, and the "in–in" and "out–out" EMCs are consistent with zero.

HD 209458 is equally intriguing for different reasons. We do not detect an overall absorption or "emission" signal, as the master integration measurement over the 16 Å band is consistent with zero. All three variations of the EMCs are centered on zero, although the "in–in" and "in–out" distributions are slightly asymmetric. However, the transmission spectrum shows a dramatic feature with a "spike" to the blue of stellar line center and a "dip" to the red. Both features peak at roughly 0.5% absolute deviation from zero and are several angstroms wide. The feature is roughly symmetric if a reflection is applied about the zero point and line center. When we use our EMC process and shift the integration bands to correspond to these features, the EMCs confirm that these are consistent features that are highly significant. In order to explore these features that appear to reflect about the stellar Hα line center, we examined 〈S_T〉 in two 5 Å bands with their edges centered on the stellar line center (unlike the 16 Å and 6 Å bandpasses of Table 3, which are centered on the stellar line); 5 Å is the approximate width of the spike and dip. We find that in the blueward spike, 〈S_T〉 (omitting the comparison bands) is a 6.6σ "emission" feature, and in the redward dip, 〈S_T〉 is a 6.1σ absorption feature. The corresponding "in–in" and "out–out" distributions are consistent with zero to within better than 0.5σ. Visual inspection of the EMC iterations qualitatively confirms these results—i.e., these features are consistently seen in the various "in–out" iterations and not present in the "in–in" and "out–out" iterations. We also note that if we integrate over the range of −130 to +100 km s⁻¹—the range over which Vidal-Madjar et al. (2003) detected significant Lyα absorption, and the range over which Winn et al. (2004) search for Hα absorption—we arrive at a value for 〈S_T〉 of 1.27 × 10⁻³. The positive value is due to the asymmetry of the velocity limits favoring the blueward spike; over a similar range, Winn et al. (2004) placed an upper limit of 0.1%. We suggest an explanation for the discrepancy later in this section.

It is difficult to explain apparent "emission" features in a transmission spectrum. However, it is not impossible for such features to occur. Because of the nature of normalizing S_T to zero, an "emission" feature indicates a wavelength-dependent apparent planetary radius (R_λ/R_P) of less than one. However, this assumes a constant stellar disk intensity. If the stellar disk intensity changes as a function of both wavelength and time, wavelength-dependent features may be observed in the cumulative transmission spectrum. For example, in the Rossiter–McLaughlin effect (RME), the exoplanetary disk blocks different portions of the stellar disk, and each portion of block stellar surface has a different radial velocity relative to the observer due to stellar rotation. This creates wavelength-dependent variations in the disk intensity. The apparent symmetry of the HD 209458b feature also indicates the possibility that it is due to some sort of velocity misalignment between two absorption features that is not fully corrected in our transmission spectrum calculation (cf. the artifact at ∼6575 Å in the transmission spectrum of HD 147506b). In the case of HD 209458b, this would have been a very broad feature that is misaligned between the in- and out-of-transit spectra. The misalignment would also need to be relative to the core of the stellar Hα line, as there is no residual indicating that the strong central Hα cores are misaligned in our spectra. While we cannot completely rule out a reduction artifact, if such a misalignment is responsible for this feature, its consistency in the various "in–out" EMC iterations argues for a genuine physical origin. This could perhaps be due to SPI-related stellar variability. Another hypothesis is that the "broad" component of the stellar Hα line actually includes absorption from excited hydrogen that has been lost by the planet, remains around the star in some sort of toroidal shape, and is influenced by the planet's orbit. We discuss potential interpretations more in Section 5.3.

As with HD 189733b, we investigated whether or not there is variability beyond just transit that is not picked up by the EMCs. This is represented in Figure 8, using the 5 Å integration band to the blue of the Hα line as the measure of M_abs. Positive measurements therefore mean that there is a blue spike and a red dip relative to Hα; negative measurements would indicate an inverted feature. Notably, there does seem to be a phase correlation, as the blue spike is prominent during transit and near secondary eclipse (orbital phase ϕ ∼ 0.5), but at intermediate values (ϕ ∼ 0.25 and ϕ ∼ 0.75), there is either no feature or an inverted feature (we examined the spectra and confirmed visually that these descriptions are the correct interpretation of M_abs, which again, in this case, refers to the offset measurement centered on the blue spike). Such features apparently do not show up as readily in the "in–in" and "out–out" EMCs due to the fact that observations are selected individually and there are very few, if any, iterations that are dominated by a single night. If the phase correlation seen in Figure 8 is real and the effect seen in the master transmission spectrum is not strictly a transit effect but a broader phase effect, then it also explains the fact that Winn et al. (2004) did not note this feature, as they made observations over only ∼5 hr on one night, through a single transit, and did not have the wide range of phase coverage that we present here.

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As described in Section 4.1, in neither HD 147506b nor HD 149026b do we detect clear Hα absorption. The atmospheres of these planets are not well studied, with no Lyα detections (or null results)⁷ and comparatively little IR work. No Spitzer observations have been taken of HD 147506b (Seager & Deming 2010), and only 8 μm Spitzer observations have been taken of HD 149026b (Harrington et al. 2007; Knutson et al. 2009). In an analysis of the potential connection between stellar activity and the presence or lack of atmospheric temperature inversions, Knutson et al. (2010) categorized these two planets' atmospheres as "unknown" with respect to temperature inversions.

In J2011 we examined these spectra for absorption at Na i λλ5889, 5895 and K i λ7698. We did not find clear evidence of absorption from either species, though we reported the suggestion of Na i absorption in HD 149026b, significant at the 1.7σ level, with a self-consistent EMC and plausible features in the transmission spectrum. The measured strength of this possible absorption would very tentatively predict no temperature inversion, as the extra opacity source(s) needed to produce temperature inversions may tend to suppress the observability of atmospheric features, e.g., the suppressed Na i absorption in HD 209458b (Charbonneau et al. 2002; Snellen et al. 2008) compared to HD 189733b (R2008; Huitson et al. 2012).

The lack of Hα detections in these two targets, as well as the lack of comparison points in their atmospheric spectra in the literature of these planets, severely limits our ability to draw firm conclusions about their atmospheres. In Section 5.2, we discuss limits on the excitation temperature, T_exc, of hydrogen due to the now-available combination of Lyα and Hα measurements for HD 189733b and HD 209458b. With Lyα detections, we could in principle put similar constraints on T_exc in these two targets.

We also note here that the a priori expectation of detectable atmospheric absorption in HD 147506b is by far the lowest, and also lower for HD 149026b than the remaining two targets. This is primarily based on S/N limitations due to the fact that both central stars are fainter than HD 189733 and HD 209458, which have similar apparent magnitudes—HD 149026 is fainter by ∼0.5 mag and HD 147506 by ∼1 mag. In addition, HD 147506b also has by far the smallest scale height of our four targets due to its very high mass even though its radius is comparable to the other planets. In terms of scale height, HD 149026b is comparable to HD 189733b, but the prospect of detecting absorption is made more difficult due to the lower S/N resulting from the respective apparent brightness of their central stars. Despite these relative limitations, these systems have bright enough central stars that if Lyα absorption exists in their exospheres, it should be detectable with a reasonable amount of observing time. Furthermore, we note that our upper limits on Hα are a factor of a few smaller with respect to the HD 189733b detection and the HD 209458b feature. HD 147506b's scale height is much smaller but its Roche lobe is much larger than the other targets; this reduces the possibility that a true, unbound exosphere exists. Our non-detection of Hα does not confirm this but is certainly consistent with it and therefore not unexpected. HD 149026b is different in that its scale height and Roche lobe are comparable to HD 189733b (slightly larger in both cases). Therefore, our non-detection of Hα in this target is arguably indicative of a more interesting difference between this target and HD 189733b and HD 209458b. Whatever processes that create the features seen in these two targets (see Sections 5.2 and 5.3) are apparently not present, or significantly weaker, in HD 149026b.

5.2.1. Identification and Description

5.2.2. Velocity Range

The narrow velocity range over which we detect this absorption is also interesting because, at least superficially, it raises the question of whether or not we are detecting hydrogen in the exosphere. With R_HD 189733b = 1.14 R_Jupiter and M_HD 189733b = 1.138 M_Jupiter, the escape velocity,

$$\begin{equation} v_{{\rm esc}}=\sqrt{\frac{2{\it GM}}{R}} \; , \end{equation} \tag{ 3 }$$

is 59.5 km s⁻¹ (at the planetary surface). With the Lecavelier Des Etangs et al. (2010) detection of Lyα, the absorption was not resolved over the 150 km s⁻¹ FWHM of the Lyα line in the ACS spectrum.⁸ Lecavelier Des Etangs et al. (2010) argue that under any scenario, the hydrogen must be escaping—though unresolved, the total amount of absorption demands that either some of the gas is at a velocity greater than the escape velocity or some of it is beyond the planet's Roche lobe.

Our detection of Hα is not as clear in this respect. The maximum absolute velocity at which we detect clearly Hα absorption, ∼25 km s⁻¹, is significantly smaller than the escape velocity at the planetary surface of ∼59.5 km s⁻¹. The escape velocity is equivalent to 25 km s⁻¹ at approximately 5.7R_HD 189733b or 6.4 R_Jupiter (which would also be outside HD 189733b's Roche lobe). The maximum apparent planetary radius implied by the Hα absorption is 1.35R_HD 189733b,⁹ which is not outside the Roche lobe. Note, though, that calculating this apparent planetary radius assumes optically thick absorption; if the Hα absorption is optically thin, it could be physically present at much greater radii. Assuming that the hydrogen responsible for the Hα absorption has the same physical extent as the hydrogen responsible for the Lyα absorption, our result argues for the former case of lower-velocity hydrogen that overfills the Roche lobe rather than gas within the Roche lobe that exists at speeds greater than the escape velocity.

Due to the low resolution of the Lecavelier Des Etangs et al. (2010) ACS spectra, we cannot directly compare the velocity ranges of the Lyα and Hα absorption in HD 189733b. However, we note that the interstellar Lyα absorption is probably saturated over the velocity range of our Hα detection (see Figure 10 and the corresponding discussion in Lecavelier Des Etangs et al. 2010). Therefore, in order for there to be any detectable Lyα absorption in HD 189733b, it must indeed cover a wider velocity range than our Hα detection, and any attempt to understand how hydrogen in the n = 2 state is formed and sustained in the HD 189733b exosphere must recognize that Lyα is absorbed by hydrogen over a larger velocity range. This also complicates the calculation of column density and excitation temperature that we perform below in Sections 5.2.3 and 5.2.4.

5.2.3. Column Density

If we assume that the Hα absorption is optically thin, we can calculate an estimated column density from our absorption measurements by the equation

$$\begin{equation} {W_{\lambda }}\left(\frac{\Delta A}{A}\right)=\frac{\pi e^2}{mc^2}f_{23}\lambda _{{\rm H\alpha }}^2 N_2, \end{equation} \tag{ 4 }$$

where (ΔA/A) is the fractional area of the stellar disk covered by the absorbing material, f₂₃ is the oscillator strength of the Hα transition, and N₂ is the column density of hydrogen in the n = 2 state. W_λ is the equivalent width of the absorption, defined as

$$\begin{equation} {W_{\lambda }}= \int { \left[ \frac{F_{{\rm out}}-F_{{\rm in}}}{F_{{\rm out}}} \right] d\lambda }. \end{equation} \tag{ 5 }$$

However, we earlier defined the "transmission spectrum," S_T, in Equation (1), such that we can substitute and get

$$\begin{equation} {W_{\lambda }}= \int\!\! {-}{S_T d\lambda }, \end{equation} \tag{ 6 }$$

which for approximately equally spaced points in S_T, and substituting Equation (2), means that

$$\begin{equation} {W_{\lambda }}\approx -M_{{\rm abs}}\Delta \lambda. \end{equation} \tag{ 7 }$$

Note that the substitution from Equation (2) is not exact in that M_abs only approximates 〈S_T〉 because the former also includes normalization from the comparison bands. In Table 4, we show the values of M_abs for HD 189733b in three additional integration bands beyond those shown in Table 3. Table 4 also shows the resulting W_λ of these three values of M_abs. As should be the case, the W_λ is constant to within the errors because the additional integration region of the wider bands is only adding, in principle, 〈S_T〉 ≈ 0.

Table 4. Additional HD 189733b Hα Absorption Results

Velocity Range	$\frac{M_{{\rm abs}}}{10^{-4}}$a	Wλ	Physical Significance
(km s−1)		(Å)a
[ − 24.1, 26.6]	−143 (− 118)	0.0155 (0.0128)	Range of Hα detection, this work
[ − 59.5, 59.5]	−61.6 (− 50.7)	0.0159 (0.0131)	±vesc at HD 189733b surface
[ − 150, 150]	−27.5 (− 22.6)	0.0180 (0.0148)	Range (FWHM) of unresolved Lyα emission
[ − 365, 365]	−10.7 (− 8.8)	0.0171 (0.0141)	Initial integration band of 16 Å centered on Hα

Note. ^aCalibrated values in parentheses; see Section 4.2.

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To calculate N₂ is fairly straightforward with the exception of calculating (ΔA/A), because, as we have previously noted, the Lyα absorption—which would be our best indicator of the extent of the hydrogen envelope—is not resolved. Using an equivalent width of 0.0128 Å from the top row of Table 4 implies a column density of 6.4 × 10¹⁰ cm² (ΔA/A). Lecavelier Des Etangs et al. (2010) quote values for the absorption, which is equivalent to (ΔA/A), as small as 5% over the entire unresolved Lyα line, and as large as 30% if restricted to the velocity range of ±49 km s⁻¹ (the escape velocity at 1.65 R_Jupiter, the minimum size of the hydrogen cloud allowable by the absorption). Thus, our effective n = 2 hydrogen column density, N₂, could be anywhere from 3.2 × 10⁹ cm² to 1.9 × 10¹⁰ cm². Notably, there are still strong assumptions in these values. The 30% figure could be even larger if the velocity range of Lyα is even more restricted than ±49 km s⁻¹, meaning that these calculations are upper limits. We have also argued that Hα absorption occurs over a smaller velocity range than Lyα and therefore may not share its physical extent. This means that (ΔA/A)_Hα ⩽ (ΔA/A)_Lyα, and the prior calculations are instead lower limits for a given (ΔA/A)_Lyα.

5.2.4. Excitation Temperature

The excitation, or population, temperature of an atomic or molecular species is defined as

$$\begin{equation} \frac{N_2}{N_1} = \frac{g_2}{g_1}\exp {\left[-\frac{\Delta E_{21}}{k_{B}T_{{\rm exc}}}\right]}. \end{equation} \tag{ 8 }$$

Solving for T_exc and plugging in constants, we obtain the relationship

$$\begin{equation} T_{{\rm exc}} = \frac{1.18\times 10^5 \rm \; K}{\ln {\left[4\frac{N_1}{N_2}\right]}} \; . \end{equation} \tag{ 9 }$$

We have already seen above how many assumptions are in the calculation of N₂, but we can simplify the calculation in our approximation for N₁. The resolution of the ACS in spectroscopic mode as used by Lecavelier Des Etangs et al. (2010) is R ∼ 100 (FWHM) or ∼12 Å. They detect 5.05% absorption over this line, but if normalized to the baseline transit depth of 2.4%, the differential absorption is only 2.65%. Therefore, the equivalent width is 0.32 Å. If the b-value¹⁰ of the exospheric hydrogen is large enough that the absorption is not saturated, then we can approximate N₁/N₂ with W_λ, Lyα/W_λ, Hα. This results in a temperature of 2.6 × 10⁴ K. Of course, we are again violating our previous conclusion that Lyα and Hα are not fully spatially coincident. We can explicitly state this assumption and write the excitation temperature as

$$\begin{equation} T_{{\rm exc}} = \frac{1.18\times 10^5 \rm \; K}{4.61+\ln {\left[\frac{\Delta A_{\rm Ly\alpha }}{\Delta A_{\rm H\alpha }}\right]}} \; . \end{equation} \tag{ 10 }$$

In this case, even a spatial discrepancy of a factor of three between Lyα and Hα changes the excitation temperature by <25%.

It is very likely that the Lyα absorption is indeed saturated, which would make N₁ larger, and therefore our calculation of T_exc is an upper limit. To quantify this would require another additive term of ln (N_1, actual/N_{1, unsaturated}) in the denominator of Equation (10). Figure 9 shows the dependence of T_exc on N₁ (and implicitly on b-value) as well as ΔA_Lyα/ΔA_Hα. However, there are two important fixed assumptions in Figure 9: one is that the Lyα W_λ is not corrected for ISM absorption and the other is that the Hα absorption is unsaturated. Both assumptions mean that the N₁ and N₂ column densities are lower limits, which would respectively decrease or increase the calculated T_exc. Notably, Ballester et al. (2007) argue that any Hα absorption in HD 209458b would be optically thick and in a thin layer (or ΔA_Lyα/ΔA_Hα ≫ 1 in our discussion here); if this is true of HD 189733b, these two facts would have competing effects on T_exc relative to our assumptions.

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5.2.5. Physical Interpretation

5.3.1. Identification and Description

5.3.2. Rossiter-McLaughlin Effect?

5.3.3. Broad Stellar Hα Component Shifting?

5.3.4. Shifting due to an Existing Hydrogen Torus?

We thank the anonymous referee, Jeffrey Linsky, and Thomas Ayres for providing several helpful comments on the manuscript. A.G.J. and S.R. acknowledge support by the National Science Foundation through Astronomy and Astrophysics Research Grant AST-0903573 (PI: S.R.). The Hobby–Eberly Telescope is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen and is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. This work made use of IDL, the Interactive Data Language;¹² IRAF, the Image Reduction and Analysis Facility;¹³ the SIMBAD Database;¹⁴ the Exoplanet Data Explorer (Wright et al. 2011);¹⁵ and the Exoplanet Transit Database.¹⁶