A Decade of Hα Transits for HD 189733 b: Stellar Activity versus Absorption in the Extended Atmosphere

As discussed in Cauley et al. (2015, 2016), changes in stellar activity from one observation to another can mimic absorption by circumplanetary material. We note that this is separate from the in-transit contrast effect, which is discussed in Section 6. One method of distinguishing absorption from stellar variability is to compare the ${W}_{{\rm{H}}\alpha }$ values with simultaneous measurements of an independent measure of the stellar activity level. Changes in ${W}_{{\rm{H}}\alpha }$ can be more confidently attributed to absorption if there is no correlation with the independent stellar activity measure.

Figure 3 shows the values of ${W}_{{\rm{H}}\alpha }$ versus ${\eta }_{\mathrm{HK}}$ for each epoch. In-transit observations are shown in dark red while out-of-transit observations are shown in dark blue. We calculate Spearman's ρ rank correlation coefficients for each date. The ${\rho }_{S}$ value and corresponding two-sided significance p are shown in green in the upper-right of each panel. Only the dates of 2013 June 3, 2013 July 4, and 2015 August 4 show significant ($p\lesssim 0.05$) correlations between ${W}_{{\rm{H}}\alpha }$ and ${\eta }_{\mathrm{HK}}$. The 2015 August 4 correlation is largely driven by the distinct in- and out-of-transit groupings, i.e., there is no correlation within the in-transit points or within the out-of-transit points. The clumping of the points from 2013 June 3 likely prevents the correlation from being stronger but ${\eta }_{\mathrm{HK}}$ clearly changes at the same time as ${W}_{{\rm{H}}\alpha }$ near $t-{t}_{\mathrm{mid}}=0$ min. We discuss the relationship between ${W}_{{\rm{H}}\alpha }$ and ${\eta }_{\mathrm{HK}}$ for the uniform ${W}_{{\rm{H}}\alpha }$ transits in the next section.

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For the non-uniform transits of 2006 August 21, 2007 August 29, and 2013 June 3, the interpretation of the ${\eta }_{\mathrm{HK}}$ and ${W}_{{\rm{H}}\alpha }$ relationship is uncertain. The small number of comparison points and low S/N of the 2007 August 29 data make this transit especially difficult to interpret. The 2006 August 21 and 2013 June 3 transits both feature abrupt changes in ${W}_{{\rm{H}}\alpha }$ at mid-transit, producing strong absorption in the case of 2006 August 21 and filling in the absorption in the case of 2013 June 3. The clear change in ${\eta }_{\mathrm{HK}}$ at a similar time in the 2013 June 3 transit suggests that this may be entirely attributable to changes in the stellar activity level. This is not the case for 2006 August 21.

It seems unlikely that such abrupt changes can be due to physical variations in the planetary atmosphere. However, transiting gas (e.g., previously evaporated material) not associated with the atmosphere could cause such changes. In this case, the atmosphere would show no absorption and the external feature (e.g., a condensation or accretion stream; Lai et al. 2010; Lanza 2014) would be orbiting ahead of the planet in the case of 2013 June 3 and behind the planet for the 2006 August 21 data. The feature would have to be ∼5 R_p ahead of or behind HD 189733 b for the transit to end or begin halfway through the planet's transit. Although it is unclear as to the exact nature of these short-term ${W}_{{\rm{H}}\alpha }$ variations, which are present in all of the transits, we showed in Cauley et al. (2017) that changes of the magnitudes seen, for example, in the 2013 June 3 and 2006 August 21 data, are rare when the planet is out-of-transit, suggesting that they occur preferentially when the planet is in- or near-transit. We find it more likely that these changes are due to variable absorption in the circumplanetary environment since stochastic changes in the stellar activity level, as a result of star–planet interactions, should be observable at orbital phases not associated with the transit.

Although Ca ii emission is a widely examined indicator of chromospheric activity, it is possible that Ca ii atoms in the extended atmosphere of HD 189733 b might have enough opacity to absorb stellar photons (Turner et al. 2016). Lanza (2014) posited that Ca ii absorption in stellar prominences fed by planetary mass loss could be responsible for the correlation between planetary surface gravity and log${R}_{\mathrm{HK}}^{\prime }$ found by Hartman (2010) (see also Fossati et al. 2015). Indeed, detections of multiple transitions of neutral calcium have been claimed in the atmosphere of HD 209458 b (Astudillo-Defru & Rojo 2013). If there is significant Ca ii absorption by the planet, the measured in-transit core flux is no longer directly tracing the short-term stellar activity level, especially when comparing in-transit to out-of-transit observations. This is hinted at by the fact that five of seven transits have lower mean in-transit ${\eta }_{\mathrm{HK}}$ values compared to the comparison spectrum ${\eta }_{\mathrm{HK}}$ value (see Table 2). We note, however, that the probability of measuring a decrease in ${\eta }_{\mathrm{HK}}$ in at least five of the seven transits is ∼22%, assuming that there is an equal probability of measuring either an increase or decrease. Thus we cannot say with any statistical certainty that the in-transit Ca ii measurements show a preference for absorption. Increasing the number of transits at Ca ii would help clarify whether the observed statistics are representative of a real effect.

Planetary Ca ii absorption may explain the data for the dates showing lower in-transit $-{\eta }_{\mathrm{HK}}$ values and fairly smooth ${W}_{{\rm{H}}\alpha }$ transits. For the 2006 September 8, 2007 July 20, 2013 July 4, and 2015 August 4 transits the mean ${\eta }_{\mathrm{HK}}$ value for the comparison spectra is more negative (meaning more core flux) than the mean in-transit ${\eta }_{\mathrm{HK}}$ value. We find significant correlations between ${W}_{{\rm{H}}\alpha }$ and ${\eta }_{\mathrm{HK}}$ for 2013 July 4 and 2015 August 4. The 2013 July 4 correlation is driven by a correlation within the out-of-transit points (${\rho }_{S}=0.71$, p = 0.002); none of the other dates shows correlations within only the in- or out-of-transit points. However, the 2013 July 4 out-of-transit correlation is itself driven by strong differences between the pre-transit points and the post-transit comparison points (see Figure 1). Thus we do not see strong evidence of correlated changes between ${W}_{{\rm{H}}\alpha }$ and ${\eta }_{\mathrm{HK}}$ from one exposure to another. This tentatively suggests that the lower in-transit ${\eta }_{\mathrm{HK}}$ differences are not due to changes in the stellar activity level.

An alternative to absorption in the planetary atmosphere producing the lower in-transit ${\eta }_{\mathrm{HK}}$ values is the transiting of bright active regions (Llama & Shkolnik 2015). If the planet happens to transit an especially active latitudinal band that is bright in Ca ii compared to the rest of the star, the Ca ii core emission will be preferentially blocked by the planet's disk, resulting in lower in-transit ${\eta }_{\mathrm{HK}}$ values. Unless the active latitude is fairly uniform in brightness, the transit tends to be choppy and uneven (Llama & Shkolnik 2015). Although the Ca ii light curves in Figure 1 do show some significant exposure-to-exposure variations, the epochs with lower in-transit versus out-of-transit ${\eta }_{\mathrm{HK}}$ values (e.g., 2007 July 20 and 2013 July 4) exhibit fairly smooth time series. Thus we tentatively favor the atmospheric absorption scenario over active region transits, although a thorough investigation of the contrast effect at Ca ii H and K would be informative.

If Ca ii in the planetary atmosphere is indeed absorbing, it cannot be considered a reliable independent measure of the stellar activity level near (i.e., immediately pre- or post-transit) or during the planet's transit. Detailed theoretical modeling of the Ca ii population in the extended atmospheres of hot exoplanets would be useful in determining whether Ca ii should be specifically targeted in these systems. A possible alternative is simultaneous monitoring of FUV activity diagnostics (e.g., France et al. 2016) that are not expected to be present in the extended atmospheres of hot planets.

Here we provide a brief overview of the steps involved in creating the model transmission spectra. The stellar and planetary parameters used in the model are given in Table 3. The model has eleven input parameters which are listed in Table 4 along with the range of parameter values we explored with the contrast model, but most of the examples presented below focus on a much smaller range or even specific values. This is due to the fact that some parameters have little influence on the contrast effect.

Table 3.  Stellar and Planetary Parameters

Parameter	Symbol	Valuea	Units
(1)	(2)	(3)	(4)
Stellar radius	R*	0.756	${R}_{\odot }$
Stellar rotational velocity	vsini	3.10	km s−1
Impact parameters	b	0.680	R*
Orbital period	Porb	2.218573	days
Orbital velocity	vorb	151.96	km s−1
Orbital semimajor axis	a	0.03099	au
Planetary radius	Rp	1.138	RJ

Note.

^aWith the exception of vsini, all stellar and planetary parameters taken from Torres et al. (2008). The vsini value is taken from Collier Cameron et al. (2010).

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Table 4.  Contrast Model Parameters and Explored Values

Parameter Description	Symbol	Value Range
(1)	(2)	(3)
Spot coverage fraction	Asp	0.005–0.10
Ratio of spots to faculae	Q	2.0–0.2
Filament coverage fraction	Afil	0.005–0.03
Ratio of facular to photosphere core Hα	qfac	0.1–6.0
FWHM of facular emission	${\sigma }_{\mathrm{fac}}$	10–50 km s−1
Central latitude of active region distribution	${\theta }_{\mathrm{act}}$	0°–45°
Temperature difference between spots and photosphere	${\rm{\Delta }}{T}_{\mathrm{sp}}$	300–800 K
Temperature difference between faculae and photosphere	${\rm{\Delta }}{T}_{\mathrm{fac}}$	20–50 K
Filament Hα core contrast	cfil	0.2–0.8
Minimum spot radius	rspmin	0.1–0.5 Rp
Maximum spot radius	rspmax	0.3–1.0 Rp

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We first simulate the location of spots and faculae on the stellar disk. We assume that each spot has some concentric associated facular region that has an area equal to 60% of the spot area. After all spot locations have been determined, additional facular regions are added to match the desired spot-to-facular ratio $Q={A}_{\mathrm{sp}}/{A}_{\mathrm{fac}}$. The location of a spot is determined by randomly selecting from a normal distribution in latitude centered on the latitude input parameter. The full width at half maximum (FWHM) of the distribution is kept fixed at 10°. The size of the spot is then determined by randomly selecting from a uniform distribution with boundaries specified by r_sp^min and r_sp^max, the minimum and maximum allowed spot radii in units of R_p. We do not allow overlap of spots. Finally, the projected boundaries, which are ellipses, of the spot and surrounding faculae are determined based on the central spot location. The additional facular regions are added in an identical procedure except the edges of the ellipses may overlap to allow potentially more irregular patterns.

We also include filaments which appear in absorption against the stellar disk (e.g., Heinzel & Anzer 2006; Kuckein et al. 2016). The filaments have a fixed width of 0.2 R_p and their length is defined by the total filament coverage fraction. Filaments are constructed by choosing a random starting point and direction and then letting the filament grow in that direction with a narrow cone defining the directions in which each new piece of the filament is allowed to move toward. The filament is allowed to grow until the desired coverage fraction is achieved to within 0.1%.

To simulate the transmission spectrum, we first calculate the out-of-transit spectrum by summing the spectra from individual grid points across the entire stellar surface. The grid resolution is 0.02 R_p which results in a 647 × 647 Cartesian grid. The surface feature spectra are PHOENIX model spectra with the addition of a Gaussian emission profile or extinction of the photospheric spectrum, assuming a Gaussian profile shape, depending on the type of feature (e.g., a plage or filament). The emission and absorption profiles are assumed to be Gaussian due to the approximately Gaussian shape of the observed Hα transmission spectra. In addition, the exact line shape is less important than the magnitude of the effect, which will not change significantly if a Lorentzian or Voight profile is assumed. The spectrum at each point on the stellar disk is shifted by the appropriate stellar rotational velocity, for which we assume rigid rotation. We also compute the radial velocity of the star relative to the observer (see Equation (11) of Logis & Fischer 2010) and apply this velocity shift to each of the stellar spectra. We then calculate the stellar spectrum blocked by the planet at five minute intervals across the transit. The out-of-transit spectrum is subtracted from the blocked spectrum and then the result is divided by the out-of-transit spectrum to generate synthetic transmission spectra according to Equation (1). An example of the stellar surface for the parameters ${A}_{\mathrm{sp}}=0.02$, Q = 0.7, and ${A}_{\mathrm{fil}}=0.005$ is shown in Figure 5.

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Each distinct surface feature contributes a different Hα spectrum. We include four separate surface components: (1) the naked photosphere; (2) star spots; (3) faculae; (4) filaments. Below we discuss each spectrum in detail, as well as the other parameters associated with that specific surface feature. Example Hα spectra of the four surface components at $\mu =\cos \theta =1.0$, where θ is the angle between the normal vector to the stellar surface and the line-of-sight, are shown in Figure 6 for a model with T_sp = 4300 K, q_fac = 1.5, T_fac = 5040 K, and c_fil = 0.6. The faculae are approximately the same brightness as the photosphere at μ = 1.0 (see Equation (4)). The normalized continuum flux for the spot spectrum is reduced by a factor of ${({T}_{\mathrm{sp}}/{T}_{\mathrm{eff}})}^{4}$. We ignore all small-scale velocity effects in the spectra, such as photospheric convective blueshifts, since we are only concerned with the overall contrast between the different regions. The contrast is weakly affected by these velocity shifts, which are of the order ∼200–300 m s⁻¹ (e.g., Meunier et al. 2010b; Lanza et al. 2011).

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6.2.1. Photospheric Spectra

6.2.2. Spot Spectra

6.2.3. Filament Spectra

6.2.4. Facular Spectra

Facular spectra consist of the intensity-weighted sum of the underlying photosphere and overlying emission region. During small solar flares, the ratio of Hα line core emission to the underlying photospheric spectrum can reach ∼2.0–4.0 (Johns-Krull et al. 1997; Xu et al. 2016). The ratios measured for non-flaring faculae are closer to ∼1.2 (Ahn et al. 2014) and very weak flares show ratios of ∼1.1–1.6, or ${q}_{\mathrm{fac}}=0.1\mbox{--}0.6$ (Deng et al. 2013). For the contrast models, we are only interested in the low-level stellar activity that does not change dramatically over the course of a single night. This implies values for ${q}_{\mathrm{fac}}\sim 0.1\mbox{--}2.0$. Larger ratios than this likely do not apply to non-flaring regions. However, we explore larger values of q_fac since larger values are needed to reproduce the observed ${W}_{{\rm{H}}\alpha }$ values. Whether or not these large values for the Hα core emission are physical will be discussed below.

Facular and plage regions are limb-brightened relative to the underlying photosphere. We adopt the limb-brightening law of Meunier et al. (2010a) and Herrero et al. (2016):

$$\begin{eqnarray}&&{c}_{\mathrm{fac}}(\mu )={\left(\displaystyle \frac{{T}_{\mathrm{eff}}+{\rm{\Delta }}T(\mu )}{{T}_{\mathrm{eff}}+{\rm{\Delta }}{T}_{\mathrm{fac}}}\right)}^{4}\end{eqnarray} \tag{ 4 }$$

where ${\rm{\Delta }}{T}_{\mathrm{fac}}$ is the temperature difference between the photosphere and faculae and ${\rm{\Delta }}T(\mu )=250.9\mbox{--}407.4\mu +190.9{\mu }^{2}$.

Czesla et al. (2015) calculated differential center-to-limb variations (CLVs), or differences in the limb-darkening or brightening as a function of wavelength across a specific spectral line, for the Ca ii H and K and Na i D lines for HD 189733. They demonstrated that the Na i lines show limb-brightening in the wings of the line compared with the line core or neighboring continuum. This is important since a transiting planet with no atmosphere can produce a transmission signal, even if there are no active regions present on the stellar surface, due to the fact that the ratio of the line core to the continuum changes as a function of the transit (see Figures 1–5 of Czesla et al. 2015). This effect was recently included in Na i transit modeling by Khalafinejad et al. (2017).

Such CLVs will also affect the in-transit Hα measurements. In order to account for this effect, we have calculated high-resolution Hα spectra using the program SPECTRUM⁶ by Gray & Corbally (1994) and an ATLAS9 model atmosphere⁷ with T_eff = 5000 K, log g = 4.5, and [Fe/H] = 0.0. The spectra were computed at fourteen values of $\mu =\cos (\theta )$ between 0.01 and 1.0. To avoid interpolation during the contrast model calculations, we fit the following limb-darkening law from Hestroffer & Magnan (1998) to each wavelength across the spectrum:

$$\begin{eqnarray}&&I(\mu )=1-u(1-{\mu }^{\alpha }).\end{eqnarray} \tag{ 5 }$$

The parameters from Equation (5) are then used to compute $I(\mu )$ as a function of wavelength across the line for a densely sampled grid of μ across the stellar disk. Examples of the $I(\mu )$/$I(\mu =1)$ versus μ curves and the corresponding Equation (5) fits are shown in Figure 7. There is a significant difference between the limb-darkening in the core of the line versus the line wing which can impact the measured ${W}_{{\rm{H}}\alpha }$ values.

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Figure 8 shows a transit example for a pure photosphere, i.e., no spots, faculae, or filaments. The only mechanism affecting the transmission spectrum or, in the absence of a planetary atmosphere, the contrast spectrum, is the CLVs described above. Five representative in-transit times are shown in the left panel of Figure 8 and their corresponding S_T profiles are shown in the middle panel. The deepest contrast profiles are seen when the planet is near the stellar limb, but still almost completely covers the disk, since this is where the limb-darkening curves in the line wing and line core differ the most. The ${W}_{{\rm{H}}\alpha }$ values for the entire in-transit calculation are shown in the right panel of Figure 8 which explicitly shows the "absorption" effect near the stellar limb.

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An important take-away from the example shown in Figure 8 is that the signal induced by CLVs at Hα is well below the measured ${W}_{{\rm{H}}\alpha }$ values for most of the transit presented here. This is especially true for values of ${W}_{{\rm{H}}\alpha }$ near mid-transit where the CLV effect is weakest. Although HD 189733 is an active star and thus it is unlikely that the visible hemisphere is ever pure photosphere, this baseline demonstrates that the observed Hα transit signals cannot be caused by only CLVs in this specific case. However, the magnitude of the CLV effect is significant upon ingress and egress and must be included in any model of the in-transit absorption. It is also important to highlight the velocities of the S_T profiles in the middle panel of Figure 8: upon ingress, S_T shows redshifted velocities near maximum absorption while upon egress it shows blueshifted velocities. This contrast signal will have an important effect on the ${v}_{{\rm{H}}\alpha }$ models presented in Section 7.

Specifying unique spectra and a unique spatial configuration for active regions on the stellar disk requires all of the parameters in Table 4. However, some of these parameters are much more important than others in determining changes in the contrast spectra. In addition, we can look to the observed Hα transmission spectra and previous HD 189733 studies for guidance on other parameter values. For example, the spot radii actually govern the distribution of spots since larger spot radii means fewer spots for a constant A_sp. But A_sp is more important for determining the relative weights between spotted spectra and the photosphere, which in turn is more important for the contrast spectrum. The distribution of active regions is a strong determinant of the time series but does not strongly affect the contrast spectrum if the planet is not occulting a large fraction of the active regions. Another example is ${\sigma }_{\mathrm{fac}}$ of the active region emission. With the assumption of the spectra being produced by the contrast effect, we can infer that ${\sigma }_{\mathrm{fac}}\approx 40$ km s⁻¹. This suggests that we do not need to explore a large range of values for ${\sigma }_{\mathrm{fac}}$ since most values will not be able to reproduce the line profile shape. For these reasons, although we have investigated the full range of parameters given in Table 4, we do not present details of the full extent of these efforts and instead focus on illuminating cases that are most relevant to the measurements.

In this section we present various illustrative examples of the contrast effect for an active stellar surface. These examples are not meant to be exhaustive but rather representative of how general configurations affect the contrast spectrum and which parameters are most important in producing a significant contrast spectrum. We do not explore scenarios where the active regions are isolated to a small portion of the stellar disk since transits of these isolated regions have short durations. Instead, we explore scenarios that might produce absorption across the entire transit.

6.5.1. Transiting a Photospheric Chord

The planet can either transit active regions or the photosphere. Either way, the in-transit spectrum will be altered relative to the out-of-transit spectrum. Figure 9 shows an example of the planet transiting a chord with no active regions for the parameter values ${A}_{\mathrm{sp}}=0.02$, Q = 0.7, ${A}_{\mathrm{fil}}=0.0$, ${\theta }_{\mathrm{act}}=10^\circ$, and ${q}_{\mathrm{fac}}=1.5$. The CLVs can still be seen in the contrast profiles (middle panel) but since the in-transit spectra are weighted toward active regions, S_T shows emission in the line core at most $t\mbox{--}{t}_{\mathrm{mid}}$ rather than absorption. This also shifts the $-{W}_{{\rm{H}}\alpha }$ curve up toward less absorption.

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One important thing to reiterate in this example is that strong absorption lines are not produced in the contrast spectra. This occurs for two reasons: (1) the facular core emission dominates the contrast spectrum; (2) the spot spectrum actually has a smaller core-to-continuum contrast compared with the photospheric spectrum. This reflects the fact that the Hα line strength decreases for cooler stellar spectra. In this example, ${\rm{\Delta }}{T}_{\mathrm{sp}}=700$ K so the spot spectrum is identical to that in Figure 6. This has important consequences for the pure-spot scenario, which we do not show: even without the core emission from the facular/plage regions, the contrast spectrum would still show core emission instead of absorption since the spot spectrum shows less core absorption than the photosphere. As a result, spots have little effect on the Hα transmission spectrum.

We also show the filament-only case in Figure 10 for ${A}_{\mathrm{fil}}=0.01$. Filaments do not produce strong contrast spectra for reasonable values of A_fil, although we note that the average transmission spectrum (not shown) for an entire transit is seen in weak absorption for the case of the photospheric chord transit. Individual transmission spectra are seen in emission for transits of filaments. Since their contribution to the contrast effect is minor, even when the planet transits filaments, we do not focus on them further.

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6.5.2. Transiting an Active Latitude

The photospheric transit examples demonstrate that ${W}_{{\rm{H}}\alpha }$ cannot be measured in absorption if the planet does not consistently occult facular regions. Thus in order to produce the strongest ${W}_{{\rm{H}}\alpha }$ curves shown in Figure 1 HD 189733 b must be transiting a chord that is densely covered with faculae and plage regions. Furthermore, as we demonstrate below, the emission strength in these facular regions must be similar to what is seen in flaring regions on the Sun.

Here we present examples of the planet transiting chords that contain active regions. The first scenario is shown in Figure 11 for uniformly distributed active regions with ${A}_{\mathrm{sp}}=0.01$, Q = 0.13, ${A}_{\mathrm{fil}}=0.0$, and ${q}_{\mathrm{fac}}=4.0$. The ${W}_{{\rm{H}}\alpha }$ time-series in the right panel is erratic; there is no trend. We have chosen the large value of ${q}_{\mathrm{fac}}=4.0$ to demonstrate that even very strong core emission cannot produce strong contrast spectra (center panel) if the planet never occults significant areas of active regions.

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Figures 12 and 13 show examples of the planet transiting an active latitude. The active region configuration is identical in both cases. The only difference is in the value of q_fac: in Figure 12 ${q}_{\mathrm{fac}}=0.5$, while in Figure 13 ${q}_{\mathrm{fac}}=1.5$. The mid-transit times where the planet occults the largest area of facular regions show significant differences in the strength of the transmission spectrum: for the larger q_fac the absorption line is ∼2× stronger. Furthermore, the ${W}_{{\rm{H}}\alpha }$ values consistently show absorption across the entire transit whereas in the ${q}_{\mathrm{fac}}=0.5$ case ${W}_{{\rm{H}}\alpha }$ approaches zero near mid-transit. These examples illustrate the important point that the strength of q_fac is the dominant factor in determining the magnitude of the contrast effect for any given transit snapshot. For the ${W}_{{\rm{H}}\alpha }$ time-series, Q, and therefore the facular coverage fraction, is also important. But q_fac is the main determinant of the depth of the contrast spectrum. In neither case does the contrast effect produce absorption similar to what is observed.

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The previous two examples demonstrate the need for greater contrast at Hα in order to reproduce the observations. Figures 14 and 15 show scenarios with very high surface coverage fractions (${A}_{\mathrm{sp}}=0.03$ and Q = 0.15 in both cases) and very strong facular/plage emission (${q}_{\mathrm{fac}}=4.0$). The only difference is that the active region distribution in Figure 14 is centered at ${\theta }_{\mathrm{act}}=\pm 40^\circ$ while in Figure 15 it is centered at ${\theta }_{\mathrm{act}}=\pm 30^\circ$. In Figure 14 the planet transits an almost constant area of active regions and the strength of the facular emission produces strong contrast absorption lines (center panel) and a relatively uniform ${W}_{{\rm{H}}\alpha }$ timeseries (right panel). Although q_fac is the same in Figure 15 the contrast profiles are weaker and ${W}_{{\rm{H}}\alpha }$ is $\sim 3\times$ shallower. This is the result of the planet transiting the edge of the active region distribution where, at any in-transit snapshot, the planet occults a relatively smaller area of facular/plage regions compared to the distribution in Figure 14. This suggests that the active regions on HD 189733's surface must be centered very near the planet's transit chord in order to produce a relatively uniform ${W}_{{\rm{H}}\alpha }$ time-series.

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The value of Q in the above examples, which equates to a 20% surface coverage of facular/plage regions, does not necessarily need to be so low, i.e., the active region surface coverage does not need to be so large. Figure 16 shows the case for ${A}_{\mathrm{sp}}=0.02$, Q = 0.4, ${A}_{\mathrm{fil}}=0.0$, and ${q}_{\mathrm{fac}}=4.0$. While ${W}_{{\rm{H}}\alpha }$ is not as uniform, the values during the first half of the transit approach the largest observed values from Figure 1. We note that moving the center of the active region distribution to $\pm 30^\circ$ latitude results in essentially no contrast for the entire transit. This again illustrates the need for the active regions to be concentrated near the transit chord and to be uniformly distributed in longitude. It also shows that if Q increases, q_fac must remain high or even increase in order to get close to the observed values; decreasing q_fac from 4.0 to ∼2.0 produces a very weak contrast effect.

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We demonstrated above that it is possible under some conditions to reproduce even the strongest observed ${W}_{{\rm{H}}\alpha }$ in-transit signals using the contrast effect. However, the only parameter configurations that are able to produce these ${W}_{{\rm{H}}\alpha }$ values involve modest to large facular coverage fractions and ${q}_{\mathrm{fac}}\sim 4\mbox{--}5$. Although we do not know exactly how the active regions are distributed on HD 189733 or the strength of the facular/plage Hα core emission, we can attempt to roughly constrain the combination of these parameters by comparing HD 189733 with less active main sequence templates of similar T_eff.

We have downloaded archived Keck HIRES data for the three template stars listed in Table 5. HD 189733 is also listed for comparison. We use these templates to find parameter combinations of q_fac and A_fac, where A_fac is the fractional surface area covered by facular regions, that can fill in the Hα absorption of the less-active template and match the line profile of HD 189733. Note that A_fac is just another way of specifying Q in the contrast models, where $Q={A}_{\mathrm{sp}}/{A}_{\mathrm{fac}}$. The HD 189733 spectrum is an average of the comparison spectra used in all of the Keck transits (purple circles in Figure 1). The facular spectrum S_fac is constructed in the same manner as the contrast model facular spectrum except now q_fac refers to the core flux of the template spectrum. The final spectrum is the weighted average of the photospheric spectrum S_phot, which is the observed template spectrum, and S_fac:

$$\begin{eqnarray}&&{S}_{\mathrm{tot}}=(1-{A}_{\mathrm{fac}}){S}_{\mathrm{phot}}+{A}_{\mathrm{fac}}{S}_{\mathrm{fac}}.\end{eqnarray} \tag{ 6 }$$

Table 5.  Less-active Comparison Stars

	Teff	M*	R*
ID	(K)	(${M}_{\odot }$)	(${R}_{\odot }$)	SHK
(1)	(2)	(3)	(4)	(5)
HD 189733	5040	0.81	0.76	0.51
HD 192263	4975	0.83	0.75	0.47
HD 104067	4956	0.91	0.75	0.34
HD 87883	4958	0.78	0.77	0.28

Note. HD 189733 parameters taken from Torres et al. (2008). All template stellar parameters are taken from Valenti & Fischer (2005). Values of S_HK are taken from Isaacson & Fischer (2010).

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While all of the observed template spectra are rotationally broadened according to the vsini value of HD 189733, we do not account for the CLVs discussed previously. Thus we are only exploring first-order approximations for which q_fac and A_fac values are needed to reproduce the HD 189733 Hα core. Since we do not have spatially resolved spectra of these stars we cannot build up the spectrum across the stellar disk as is done in the contrast model case.

Three different parameter combinations are shown for each template in Figure 17. A ${\chi }^{2}$ minimization routine is used to produce the fits for various initial parameter combinations that correspond roughly to the parameter space explored in each column. The first column shows a direct comparison between HD 189733 (dark gray line) and the templates (orange lines). Column 2 shows the case of high A_fac and low q_fac, i.e., weak facular emission but distributed across much of the stellar disk. Column 3 shows slightly stronger q_fac but reduced A_fac. Finally, column 4 shows large q_fac and small A_fac. We note that the HD 189733 spectrum is also plotted in columns 2–4 but is obscured by the model fits.

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For all three templates, a crucial trend is seen: as q_fac increases, A_fac must decrease for a given photospheric spectrum. This is not surprising but has important consequences for which parameter combinations in the contrast model are likely to be representative of HD 189733's active surface. For example, the very low Q and very high q_fac case shown in Figure 14 is unlikely to accurately represent the stellar surface since the same parameter combination would drastically overestimate the line core emission in Figure 17. However, the less active case in Figure 16 seems plausible: similar values of q_fac and Q, or a facular coverage fraction of ∼8%, are seen in the low A_fac, high q_fac case for HD 87883 in Figure 17.

One important caveat to the template comparison is that the template spectra themselves contain some contribution from active regions. Thus we are not comparing pure photospheres to HD 189733's active surface. However, this does not affect the relationship between q_fac and A_fac; one must decrease as the other increases for a specific template spectrum, pure photosphere or not. On the other hand, the value of the parameters in Figure 17 may be affected. For example, instead of ${A}_{\mathrm{fac}}=0.08$ and ${q}_{\mathrm{fac}}=4.06$ in the lower right panel of Figure 17, one or both values would need to be larger if HD 87883's spectrum contained no contributions from active regions. Thus the parameter combinations shown in Figure 17 are likely lower limits to the true values.

We have presented transit models for a planet with no atmosphere in order to explore the contrast effect in Hα that is produced when in-transit spectra, for which a portion of the stellar disk is occulted, are compared with out-of-transit spectra. We find the following.

• 1.  
  Spots and filaments, for the physically reasonable surface coverage fractions and spot/filament parameters explored here, are unimportant in the Hα contrast spectrum. The main contribution to the contrast effect comes from strong facular or plage emission.
• 2.  
  Transits of the photosphere do not produce Hα contrast in absorption; active regions that include strong faculae/plage emission must be transited to produce S_T in absorption.
• 3.  
  The facular coverage fraction must be $\gtrsim 5 \% \mbox{--}10$% and these facular regions must be concentrated around the transit chord in order for the strongest observed Hα transits to be reproduced. Large coverage fractions, no matter the value of q_fac, cannot reproduce the observed Hα line profiles if the distribution is uniform across the stellar disk. This holds true even for very large coverage fractions of $\gt 50$% since the contrast spectrum then begins to be weighted back toward the active region spectra, producing emission instead of absorption.
• 4.  
  Certain configurations of facular regions combined with values of ${q}_{\mathrm{fac}}\sim 4.0$ are able to produce relatively uniform transits with depths of ${W}_{{\rm{H}}\alpha }\approx 0.007\mbox{--}0.015$, similar to the observed transits shown in Figure 1.
• 5.  
  The comparison of less active template stars to HD 189733 suggests that for ${q}_{\mathrm{fac}}\sim 4$ the facular coverage fraction must be $\gtrsim 5 \% \mbox{--}10$%. This is similar to what is needed to reproduce the observed transits, although these are lower limits since the templates do not represent pure stellar photospheres.

While our simulations show that the contrast effect is able to reproduce the observed in-transit ${W}_{{\rm{H}}\alpha }$ values, it is unclear whether the necessary parameters are physically realistic. We believe facular coverage fractions of ∼10%, and possibly higher, are not unreasonable considering the stronger activity level of HD 189733 compared with the Sun. Solar facular coverage can reach ∼5% during solar active periods (Shapiro et al. 2015) and plage coverage can reach ∼8% (Foukal 1998). On the other hand, Shapiro et al. (2015) (see also Foukal 1998; Lockwood et al. 2007) find that photometric variations for more active stars are spot-dominated and that the ratio of facular/plage coverage to spot coverage decreases with increasing activity level. Lanza et al. (2011) find that RV modulations in HD 189733's spectrum are best modeled with values of $Q={A}_{\mathrm{fac}}/{A}_{\mathrm{spot}}\sim 0$, i.e., they find no evidence of facular/plage effects on the measured RV values. Furthermore, Lanza et al. (2011) find spot filling factors of ∼1% are able to reproduce HD 189733's photometric variations across roughly four weeks of nightly observations. Similar spot coverages are found by Herrero et al. (2016) for the same data set. This would suggest values of Q = 0.1 for the contrast model in order to produce ∼8% facular/plage coverage.

The larger question for Hα contrast models is what constitutes a reasonable value of q_fac. We have shown that ${q}_{\mathrm{fac}}\gtrsim 4.0$ is needed in order to produce values of ${W}_{{\rm{H}}\alpha }$ similar to what is observed. If this is the case, then the normal or quiescent facular/plage regions on HD 189733 have Hα emission line strengths similar to moderate flaring regions on the Sun. Magnetic fields play an important role in heating the chromosphere and producing bright regions in the atmosphere (e.g., Hansteen et al. 2007). Indeed, simulations of Hα brightness in solar active regions show that the brightest regions correspond to the strongest local magnetic field strengths (Leenaarts et al. 2012). HD 189733 has a much stronger global magnetic field than the Sun, with radial field values reaching 30–40 G across much of the stellar surface (Fares et al. 2010). Thus the larger field values, and consequently heating rates, could have a significant effect on the emission strength of Hα in active regions.

A final consideration is the requirement that the facular/plage regions be concentrated very close to the planetary transit chord, or a latitude very near $+40^\circ$. Active latitudes are known features of the solar surface (e.g., Vecchio et al. 2012) and have been inferred via photometric transits for other stars as well (Sanchis-Ojeda & Winn 2011; Kirk et al. 2016). Lanza et al. (2011) find that spots near $\approx 30^\circ \mbox{--}40^\circ$ are able to best reproduce the measured RV variations. Thus it is not unreasonable that the facular/plage regions are located near the transit chord. The specificity required, however, to reproduce any of the observed ${W}_{{\rm{H}}\alpha }$ transits is a concern, especially if active latitudes migrate as a function of time.

Although we cannot conclusively distinguish between models in which the observed ${W}_{{\rm{H}}\alpha }$ transits are due to absorption by the planet or from the contrast effect, we believe the parameter values required to reproduce the observations are specific and likely do not represent the average stellar disk of HD 189733. Furthermore, the contrast effect cannot explain the ${W}_{{\rm{H}}\alpha }$ values seen in absorption immediately before the 2013 July 4 transit, before and after the 2015 August 4 transit, and immediately after the 2006 August 21 transit, i.e., these extended transits are suggestive of absorbing circumplanetary material. In addition, we demonstrated in Cauley et al. (2017) that these pre- and post-transit signatures are abnormal and must be related to the planetary transit, further making the case for a circumplanetary origin. More detailed modeling of Hα spectral line profiles in faculae and plages for active stars are needed to determine if the large core strengths used here are realistic. For now, however, we favor the planetary interpretation.

In order to explore physical scenarios for the Hα line velocities presented above, we have simulated transmission spectra through a rotating planetary atmosphere. We use the same stellar and planetary parameters that were presented in Section 6 and the same PHOENIX model spectra are used as the intrinsic stellar spectra. We neglect active regions on the stellar surface and assume a pure photosphere (see Section 7.2). The stellar radial velocity as a function of in-transit time is included in the line profile calculations.

The planetary atmosphere is assumed to be of uniform density. This choice is motivated by the models of Christie et al. (2013) who found that the number density of n = 2 hydrogen was approximately constant across 3–4 orders of magnitude in atmospheric pressure. Assuming a hydrostatic versus uniform density atmosphere has little effect on the simulations. The planetary Hα absorption profile is approximated as a velocity-broadened delta function where the broadening parameter is labeled b (Draine 2011; Cauley et al. 2015, 2016). The planet is assumed to rotate rigidly throughout the atmosphere.

We have also investigated the effects of superrotating equatorial jets (Showman et al. 2008; Rauscher & Menou 2010) and find that they produce similar effects as rigid rotation, although the jet velocities required to produce the same line profiles are larger than the rotational velocities since the jets occupy a smaller portion of the atmosphere. We do not include jets explicitly in the rest of the model discussion but we will discuss them as part of the general effect of large rotational velocities.

Figure 19 shows the effect of a rotating atmosphere on the transmission spectrum for a prograde planetary orbit. Upon ingress (left panel) the portion of the planet's atmosphere dominating the transmission spectrum is moving away from the observer while the planet's bulk motion is toward the observer. The net effect is to produce a measured centroid velocity, or in our case ${v}_{{\rm{H}}\alpha }$, that is significantly less than the bulk planetary velocity. This was first demonstrated by Miller-Ricci Kempton & Rauscher (2012, their Figure 8) and reiterated in Louden & Wheatley (2015, their Figure 2). The same effect is seen upon egress (right panel).

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Simulated ${v}_{{\rm{H}}\alpha }$ curves for the entire transit are shown in Figure 20 where the effect of higher rotational velocities can be seen in the suppression of ${v}_{{\rm{H}}\alpha }$ relative to the line-of-sight orbital velocity upon ingress and egress. For the highest rotational velocities, the atmosphere is moving fast enough to cause ${v}_{{\rm{H}}\alpha }$ to have the opposite sign compared to the planet's bulk motion. We note that for strong atomic lines, even the case of no rotation, produces suppressed line velocities due to the CLVs discussed in Section 6. For transits that are sampled asymmetrically in time, CLVs could produce velocity shifts in the average transmission spectrum (e.g., see Louden & Wheatley 2015; Wyttenbach et al. 2015).

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Figure 20 shows that for sufficiently large v_rot the measured ${v}_{{\rm{H}}\alpha }$ values can be very small or even have the opposite sign relative to the planetary bulk velocity. While these transit curves cannot explain the erratic velocities of the HARPS data or the 2006 August 21 Keck data, they may provide evidence for what we are seeing in the 2013 July 4 and 2015 August 4 Keck transits and perhaps the first half of the 2013 June 3 transit.

Figure 21 shows three different rotation models plotted against the 2015 August 4 ${v}_{{\rm{H}}\alpha }$ values. Rotational velocities $\lesssim \,9$ km s⁻¹ do not match the data well; velocities between 10 and 12 km s⁻¹ are required to produce the small ${v}_{{\rm{H}}\alpha }$ values between first and second and third and fourth contact. Values of ${v}_{\mathrm{rot}}\gtrsim 12$ km s⁻¹ begin to produce ${v}_{{\rm{H}}\alpha }$ values that are too small, i.e., of the wrong sign. The models do not do a good job of reproducing ${v}_{{\rm{H}}\alpha }$ near −20 and +20 minutes; all of the models produce ${v}_{{\rm{H}}\alpha }$ larger than the measured values. Overall, however, these models demonstrate that large velocities in the extended atmosphere can produce the small observed velocities.

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It is possible for certain contrast model scenarios to produce ${v}_{{\rm{H}}\alpha }$ values similar to what is observed for the 2013 July 4 and 2015 August 4 transits. We have calculated ${v}_{{\rm{H}}\alpha }$ for the contrast model line profiles. The ${v}_{{\rm{H}}\alpha }$ values for the contrast models from Figure 16 (left panel), Figure 14 (middle panel), and Figure 15 (right panel) are shown in Figure 22. The contrast model line profiles show trends similar to the 2015 August 4 data, although only the very active case (middle panel) shows the blueshifted to redshifted pattern from the first half of the transit to the second half. Although not shown here, all of the other cases explored in Section 6 show something similar to the left panel of Figure 22: large redshifted velocities during the first half of the transit and blueshifted velocities during the second half. More active cases than the middle panel tend to move in the other direction: larger and larger blueshifted velocities and then redshifted velocities during the second half.

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Overall, the velocities from the contrast models do not reproduce the observed 2015 August 4 velocities except for the case of a very active stellar surface with the active regions centered very near the planet's transit chord (see Figure 14). For this reason, and those given concerning the planetary rotation models, we do not believe the contrast velocities represent a convincing explanation for the observations. However, further in-transit observations should be conducted to strengthen or reject this argument.

The rotation models presented here are meant to demonstrate that the low velocities, i.e., much less than the in-transit planetary line-of-sight velocity, observed in the Hα transits are not necessarily intrinsic to the star because of their magnitude. While very hot Jupiters such as HD 189733 b are generally assumed to be synchronously rotating, there are no measurements of hot Jupiter rotation rates outside of the studies done by Brogi et al. (2016) and Louden & Wheatley (2015), who  both found evidence for a synchronously rotating HD 189733 b. However, these measurements were made in CO⁸ (Brogi et al. 2016) and Na i (Louden & Wheatley 2015). The CO measurements probe much higher pressures deeper in the atmosphere than Hα and Na i, which probe pressures of 10⁻⁶–10⁻⁹ bar (Christie et al. 2013; Wyttenbach et al. 2015). The Na i measurements by Louden & Wheatley (2015) do not examine the velocities of individual observations and instead fit the average in-transit line profile. Louden & Wheatley (2015) also do not include differential limb darkening, opting to use a broadband limb-darkening law. This could significantly affect the velocities of the model line profile (Czesla et al. 2015) and should be investigated.

Even if a hot Jupiter is synchronously rotating, velocities larger than the equatorial rotational velocity may be present in the extended atmosphere. Rauscher & Kempton (2014) find wind speeds of ∼7–11 km s⁻¹ in the upper atmospheres of both a synchronously and a quickly rotating HD 189733 b. Their models were calculated at pressures of 10⁰–10⁻⁶ bar, which begins to probe the potential Hα formation region. Thus it is not implausible that even stronger winds may form at higher altitudes or that unexplored atmospheric dynamics are contributing to the Hα transmission spectra.

While the most active contrast model is able to produce ${v}_{{\rm{H}}\alpha }$ values similar to what is observed for the 2015 August 4 transit, we do not believe this is the correct model due to required specificity of the model parameters. In other words, matching the velocities requires all of the most active contrast model parameters to be accurate whereas matching only the ${W}_{{\rm{H}}\alpha }$ observations provides more leeway in the active region coverage fraction and facular emission line strength. On the other hand, the 2015 August 4 transit does seem to be unique in that it shows the largest ${W}_{{\rm{H}}\alpha }$ signal and the strongest out-of-transit Ca ii emission. Although it seems unlikely, we cannot definitively rule out the most active case as an explanation for the both ${W}_{{\rm{H}}\alpha }$ and ${v}_{{\rm{H}}\alpha }$.

We emphasize that the Hα transits do not show a consistent velocity signal across epochs, and as a result no firm conclusions can be reached concerning their origin. The individual HARPS spectra are especially noisy and the velocity uncertainties derived here are large, making them even less useful for understanding the in-transit signal. Further short-cadence Hα transit observations are needed to work toward clarifying the velocity signal and, by extension, the in-transit Hα absorption line profiles.