TRANSIT OBSERVATIONS OF THE HOT JUPITER HD 189733b AT X-RAY WAVELENGTHS

All previous observations of the HD 189733 system had been performed with XMM-Newton; due to the rather broad point-spread function (PSF) of the prime instrument PN (ca. 125 FWHM), the secondary HD 189733B was not properly resolved in those observations. Our Chandra observations with a PSF of ca. 05 (FWHM) fully resolve the stellar components for the first time; a soft X-ray image extracted from one single Chandra exposure with 20 ks duration is shown in Figure 1. The primary HD 189733A is shown in the center, the secondary HD 189733B to the lower right at an angular distance of 114 to the primary, and a background source at the bottom of the image at an angular distance of 117. The planetary orbit of HD 189733b is not resolved in these observations: if observed at quadrature, its angular distance to the host star would be ca. 1.6 mas.

To inspect the individual X-ray light curves of HD 189733A, HD 189733B, and the background source, we extracted X-ray photons from an extraction region centered on each source with 25 radius for the Chandra observations. We restricted the energy range to 0.1–2.0 keV for HD 189733A and HD 189733B, because practically no stellar flux at higher energies was present; we used an energy band of 0.1–10.0 keV for the background source. For the archival XMM-Newton observation, we chose an extraction radius 10'' to collect most of the source photons from HD 189733A while avoiding strong contamination from the other two sources. XMM-Newton EPIC/PN provides sensitivity down to 0.2 keV, so we restricted the energy range to 0.2–2.0 keV. In all Chandra observations, the background signal was negligibly low and constant (0.05% of the source count rate). For XMM-Newton, the background signal is weak and only slightly variable during times that are interesting for the transit analysis (ca. 2% of the source count rate); however, in the beginning of the observation the background is stronger, and we therefore followed the standard procedure and extracted photons from a large source-free area, scaled down this background signal to the source extraction area, and subtracted the background signal from the XMM-Newton source light curve.

For the light curves, we chose time bin sizes suited to obtain reasonable error bars; specifically, the chosen bin size is 200 s for HD 189733A, 1000 s for HD 189733B, and 500 s for the background source.

To test if a transit signal can be detected in the X-ray data, we also constructed a phase-folded, added-up X-ray light curve. We corrected all X-ray photon arrival times with respect to the solar system barycenter, using the ciao4.2 task axbary for the Chandra events and the SASv11.0 task barycen for the XMM-Newton events. Orbital phases were calculated using the mid-transit time and orbital period given in the Extrasolar Planet Encyclopaedia and are listed in Table 1. We first extracted light curves from the individual observations with a very small time binning (10 s). We normalized the light curves to an out-of-transit level of unity, chose the desired phase segments (0.005, corresponding to roughly 16 minutes), and added up the individual observations to form the binned phase-folded light curve, giving the same weight to each individual light curve. These 0.005 phase bins contain ≈500 X-ray photons each. The error bars of the individual light curves are dominated by Poissonian noise, which is close to Gaussian noise given the number of X-ray counts per 0.005 phase bin; these errors were propagated to the added-up light curve. Because of the intrinsic variability of the stellar corona, it is important to average over the individual transit observations. We therefore restrict our analysis to orbital phases at which at least six of the seven observations provide signal. Specifically, this is given at orbital phases between 0.9479 and 1.0470.

We extracted CCD spectra of all three sources from the Chandra ACIS-S exposures. We used a minimum binning of 15 counts per energy bin; for the secondary, we used smaller bins with ⩾5 counts per bin because of the low count rate. We fitted the resulting six spectra of each source simultaneously in Xpsec v12.0, therefore ignoring spectral changes in between the individual observations and focusing on the overall spectral properties of each object. We fit the spectra with thermal plasma models for HD 189733A and HD 189733B; since we do not know the exact nature of the third source a priori, we test a thermal plasma model and a power-law model for fitting those spectra. We use elemental abundances from Grevesse & Sauval (1998) for all spectral fits.

A detailed analysis of HD 189773A's spectrum observed with XMM-Newton (out of transit) was performed before (see Pillitteri et al. 2010, 2011).

The individual X-ray light curves of HD 189733A are shown in Figure 3. The mean count rate is at ≈0.07 counts s⁻¹ for Chandra's ACIS-S, and at ≈0.15 counts s⁻¹ for XMM-Newton's EPIC.

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An inspection of these light curves shows their intrinsic variability to be quite small for an active star with maximum count rate variations being less than a factor of two. Such small changes are often found to be the base level of variability in cool stars, and are referred to as "quasi-quiescence" (Robrade et al. 2010). Larger flares can be superimposed on this type of variability, but this is not the case for our observations of HD 189733A.

However, small flare-shaped variations are present, for example, in the second Chandra light curve at orbital phase 1.01. For the X-ray flares of HD 189733 which have been detected with XMM-Newton at other orbital phases, Pillitteri et al. (2010, 2011) show that changes in the hardness ratio do not always accompany the flares, so that we focus on the light curves as a primary flare indicator for our observations. We show the individual light curves split up into a hard and soft band (0.2–0.6 keV, 0.6–2 keV) together with the total band in Figure 4, using a bin size of 300 s to have reasonable photon statistics for the individual bands. We test for correlated intensity changes in both bands in detail in Section 3.5.3, finding that the second Chandra observation and the XMM-Newton observation likely contain small stellar flares.

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The source spectra of HD 189733A, extracted from the six Chandra ACIS-S pointings, are shown in Figure 5 (top panel). The dominant part of the emission is at energies below 2 keV, and all six observations display very similar energetic distributions and intensities. We fitted the spectra simultaneously with a thermal plasma model; two temperature components and variable abundances for the most prominent elements at soft X-ray energies (oxygen, neon, and iron) are necessary for a decent fit quality. We find a mean coronal temperature of ca. 4.5 MK, with a dominant temperature component at ca. 3 MK (see Table 3). Our spectral fit yields an X-ray flux of 2.63 × 10⁻¹³ erg cm⁻² s⁻¹ in the 0.25–2 keV energy band, corresponding to an X-ray luminosity of L_X = 1.1 × 10²⁸ erg s⁻¹. We calculate HD 189733A's bolometric luminosity, using bolometric corrections from Flower (1996), to be L_bol = 0.35 × L_bol, ☉ = 1.3 × 10³³ erg s⁻¹. The ratio of X-ray to bolometric luminosity is therefore R_X = L_X/L_bol = 10⁻⁵, characterizing HD 189733A as a moderately active star; the Sun, for comparison, emits varying X-ray flux fractions of about 10⁻⁶–10⁻⁷ during its activity cycle.

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Table 3. Thermal Plasma Models for the X-Ray Emission of the Primary and Secondary Stars

Object	HD 189733A	HD 189733B
T1 (keV)	0.25 ± 0.01	0.32 ± 0.02
norm1	(1.81 ± 0.1) × 10−4	(5.1 ± 0.5) × 10−6
EM1 (1050 cm−3)	7.7 ± 0.4	0.22 ± 0.02
T2 (keV)	0.62 ± 0.03	1.25 ± 0.5
norm2	(6.6 ± 0.5) × 10−5	(1.7 ± 0.5) × 10−6
EM2 (1050 cm−3)	2.8 ± 0.2	0.07 ± 0.02
O	0.31 ± 0.02	(Fixed at solar)
Ne	0.25 ± 0.13	(Fixed at solar)
Fe	0.64 ± 0.05	(Fixed at solar)
$\chi ^2_{{\rm red}}$ (dof)	1.43 (279)	1.12 (64)
FX (0.25–2 keV)	2.63 × 10−13	1.1 × 10−14
log LX (0.25–2 keV)	28.1	26.67

Notes. Flux is in units of erg s⁻¹ cm⁻², luminosity in units of erg s⁻¹. The emission measure is derived from Xspec's fitted normalization by multiplying it with 4π d² × 10¹⁴, with d being the distance to the two stars.

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The coronal abundances show a first ionization potential (FIP) bias, meaning that the abundances of elements with a high FIP (oxygen and neon) are lower than the abundances of low-FIP elements (iron); all abundances are given relative to solar photospheric values (Grevesse & Sauval 1998). This effect is observed in coronae of stars with low to moderate activity, while high-activity stars show an inverse FIP effect. Recently, a possible correlation of FIP bias with spectral type has been found for inactive and moderately active stars (Wood & Linsky 2010). Our measured abundances for HD 189733A fit into this pattern: the average logarithmic abundance of neon and oxygen relative to iron is −0.41 here, and Wood & Linsky (2010) predict similar values around −0.35 for stars of spectral type K0.

We detect the stellar companion HD 189733B in X-rays for the first time. It displays a mean count rate of ≈3 counts ks⁻¹, with considerable variability by up to a factor of five. The fourth light curve (Figure 6) displays a prominent flare-like variation which lasts for ca. 6 ks. Variability on shorter timescales is also implied by the other light curves, but individual small flares cannot be characterized properly due to the low count rate.

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The spectra of HD 189733B are well described by a thermal plasma with two temperature components, with a dominant temperature contribution at ca. 3.5 MK (see Table 3). The collected spectral counts are not sufficient to constrain elemental abundances in the corona, and therefore we fixed the abundances at solar values. The spectral fit yields an X-ray luminosity of log L_X = 26.67 erg s⁻¹ in an energy range of 0.25–2 keV. This is compatible with the upper limit of log L_X ⩽ 27 erg s⁻¹ derived from XMM-Newton observations by Pillitteri et al. (2010). In the context of late-type stars in the solar neighborhood, HD 189733B is slightly less X-ray luminous than the median value of log L_X = 26.86 erg s⁻¹ found for early M dwarfs (Schmitt et al. 1995). To calculate the bolometric luminosity of HD 189733B, we use the relations from Worthey & Lee (2011): the measured H−K color of 0.222 and a spectral type between M3.5V and M5V (Bakos et al. 2006) translate to a bolometric correction of BC_V = −2.05 to a V magnitude of 14.02, yielding L_bol = 1.8 × 10³¹ erg s⁻¹. The X-ray fraction of the total bolometric flux is therefore R_X = L_X/L_bol = 2.5 × 10⁻⁵, marking HD 189733B as a moderately active M star.

We detect X-ray emission from a source at the position R.A. = 300.1813, decl. = 22.7068, previously reported by Pillitteri et al. (2010). The projected distance to HD 189733A is 117, and the position angle is ca. 190°. The infrared Two Micron All Sky Survey data show a filter glint from HD 189733A at this position, so that the infrared magnitudes of the source are unknown; however, other surveys find two faint objects at the approximate position (see Bakos et al. 2006 and their Figure 1).

The X-ray emission from this source is at a mean level of 0.015 counts s⁻¹ and varies over time by factors of up to 2.5 (see Figure 7); the fifth light curve displays a variability feature that looks similar to a stellar flare. The X-ray spectra from the source show no significant flux at energies below 800 eV, as shown in Figure 5, but the flux at high energies (>2 keV) is larger than for HD 189733A and HD 189733B. A spectral feature is present at energies near 1.9 keV; additional smaller features may be present near 1.4 keV and 4 keV. The feature at 1.9 keV matches with emission lines of Si xiii/xiv between 1839 and 2005 eV; the 1.4 keV feature coincides with several strong Mg xi/xii lines between 1352 and 1472 eV, while the 4 keV feature falls into a spectral region where some weaker Ca xix/xx lines are present.

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The missing flux at soft X-ray energies and the spectral feature at 1.9 keV suggest that the object is a distant source which can be described as a thermal plasma with interstellar absorption. Indeed, the corresponding model yields a good fit to the data as shown in Table 4. The modeled temperature of ca. 70 MK is most likely biased toward high values, because plasma of lower temperatures is not seen due to the interstellar absorption and can thus not adequately be fitted. The peak formation temperatures of the Si xiii/xiv lines are at a range of 10–17 MK; we interpret this as an indication that the average plasma temperature is significantly lower than 70 MK. We assume from the fitted hydrogen absorption with a column density of n_H = 4.5 × 10²¹ cm⁻² that the source is located at a distance of roughly 1000 pc from the Sun, consistent with Pillitteri et al. (2010). With this distance, the measured flux converts to an intrinsic (unabsorbed) X-ray luminosity of log L_X = 31.4 erg s⁻¹.

Table 4. Spectral Fits for the X-Ray Emission of the Third Source

Model Parameters	Abs. Thermal Plasma	Abs. Power Law
nH	(4.5 ± 0.6) × 1021	(5.8 ± 0.7) × 1021
T (keV)	6.0 ± 0.9	⋅⋅⋅
Photon index	⋅⋅⋅	1.9 ± 0.1
Norm	(1.1 ± 0.06) × 10−4	(3.9 ± 0.5) × 10−5
$\chi ^2_{{\rm red}}$ (dof)	1.12 (99)	1.11 (99)
FX (0.25–10 keV)	1.44 × 10−13	1.47 × 10−13
$\log L_X^{{\rm abs}}$ (0.8–10 keV)	31.2	31.2
$\log L_X^{{\rm unabs}}$	31.4	31.4

Notes. An absorbed thermal plasma model and an absorbed power law both yield good fits. The absorbed and unabsorbed X-ray luminosities are calculated using a distance estimate of 1000 pc.

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So what is the nature of this source? Its position in galactic coordinates is l = 60.9623, b = −03.9227, meaning that it lies in the galactic plane in a viewing direction 60° off the galactic center, possibly on the Orion-Cygnus arm. Together with the rough distance estimate from hydrogen absorption, the emission feature in the spectra, and the flare-shaped variation in the light curves, we consider it likely that the source is an RS CVn or Algol system. Its X-ray luminosity is at the high end, but still in the range of observed values for such systems (Walter et al. 1980; White & Marshall 1983).

For completeness, we note that a model with an absorbed power law formally yields an equally good fit, but does not explain the observed feature at 1.9 keV. Adopting the power-law model, we find similar values for hydrogen absorption and X-ray luminosity (see Table 4).

We now turn to a detailed analysis of the phase-folded and added-up X-ray transit light curve of the Hot Jupiter HD 189733Ab.

As a first step, we test if the scatter in the observed individual and added-up light curves is sufficiently well described by white noise. If the sequence of measured count rates is not randomly distributed on timescales shorter than the transit, but is correlated in some way, this would require a more detailed treatment of the noise level. We have therefore tested for autocorrelation in the individual light curves, as well as for deviations from white noise in the added-up light curve, both with negative results. This analysis is presented in detail in the Appendix.

3.5.1. A Transit Detection in X-Rays

3.5.2. Deriving the Transit Depth

We have one observation that starts relatively late (Chandra light curve 3) and one that ends early (Chandra light curve 5). To increase our accuracy for a transit depth measurement, we therefore pre-normalized the individual transit light curves to an out-of-transit level of unity and use a larger orbital phase range between 0.9479 and 1.0470, as described in Section 2.3.

We used three different statistical methods to determine the depth of the X-ray transit in the phase-folded light curve; they are explained in the following, and their results are listed in Table 6.

• 1.  
  The mean normalized X-ray count rates in and out of transit were compared directly. We have defined data from orbital phases between second and third contacts as "in transit" and data from phases before first or after fourth contact as "out of transit." Since the total number of X-ray photons is large, differences between Poissonian and Gaussian errors are negligible, and we have used Gaussian error propagation to determine the error on the transit depth as $\sigma _{{\rm depth}} = \ssty \sqrt{ \sigma ^2_{{\rm in}} + \sigma ^2_{{\rm out}} }$.
• 2.  
  We have fitted the data to an analytical transit model as used for optical, limb-darkened transits (Mandel & Agol 2002). This will not be entirely correct, because coronae are limb-brightened, not limb-darkened like photospheres (see method 3). However, we give the fitting results to photospheric transit profiles for completeness. Specifically, we fixed the planetary orbital period, semimajor axis, mid-transit time, and inclination to the values given in the Extrasolar Planets Encyclopedia, used a quadratic limb-darkening law with coefficients u1 = 0.32 and u2 = 0.27 as used for the optical light curve (Winn et al. 2007) depicted in Figure 8(a), and performed a Markov chain Monte Carlo fit with the ratio of the planetary and stellar radius $R^{{\rm X-ray}}_P/R_\ast$ as a free parameter.
• 3.  
  The stellar corona is optically thin, so that it shows limb brightening instead of the limb darkening observed in the photosphere. We have taken this into account by fitting the data with a limb-brightened model (Schlawin et al. 2010) under the assumption that the corona is not significantly extended beyond the photospheric radius. This is a valid assumption: it is known that individual flaring loops in active stars may extend quite far over the photospheric radius, but the average corona of active stars apparently is not much extended. This was directly observed in the case of the binary α CrB, where the X-ray dark A star eclipses the active, X-ray bright G star without large differences in duration compared to the optical transit profile (Schmitt & Kuerster 1993). We again fixed the planetary orbital period, semimajor axis, mid-transit time, and inclination, and fitted the ratio of the planetary and stellar radius. The resulting transit profile is shown as a dashed line in Figure 8(a).

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Table 6. X-Ray Transit Depths, Derived from the Added-up, Pre-normalized X-ray Light Curves

	(a) All Seven Data	(b) Six Data Sets, Excluding	(c) Six Data Sets, Excluding	(d) Five Non-flaring
	Sets	Flaring Chandra Observation	Flaring XMM-Newton Observation	Data Sets
Transit depth derived from:
(1) Direct comparison	0.059 ± 0.026	0.080 ± 0.028	0.057 ± 0.030	0.081 ± 0.032
(2) Limb-darkened model	0.057 ± 0.028	0.082 ± 0.029	0.048 ± 0.030	0.077 ± 0.034
(3) Limb-brightened model	0.050 ± 0.025	0.073 ± 0.025	0.040 ± 0.027	0.067 ± 0.030

Notes. The results are given for the four different combinations of data sets discussed in Section 3.5.3. The transit depths are given with 1σ errors (statistical).

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3.5.3. Light Curve Selection

The stellar corona is much less homogeneous than the stellar photosphere. X-ray-emitting coronal loops are temporally variable, and solar observations show that its corona often displays several large, X-ray bright patches, while other parts are dimmer in X-rays. This is why it is unlikely to identify a planetary transit signal in a single X-ray light curve, even if the signal to noise is very high: it is possible that, given a specific configuration of X-ray bright patches of the corona, the planet happens to transit a mostly X-ray dim part. On the other hand, the planet may occult a large X-ray bright patch in a different coronal configuration, causing an atypically deep transit signal. One therefore needs to average over as many transits as possible to determine the transit depth with respect to the typical, average X-ray surface brightness of a corona.

To show the importance of the coronal averaging, we determined the observed transit depths (derived from the direct count rate comparison) for different combinations of the X-ray light curves. With a total of seven transit light curves, there is one combination which includes all light curves, and seven combinations which include six of the light curves. Given the relatively low overall number of X-ray photons, we do not use combinations of fewer light curves because the errors become quite large. We show the result in Figure 9. For better visibility, we symbolically show the mean transit depth without depicting any limb effects. The transit depths derived from only six X-ray light curves show some scatter; specifically, the depths range from 2.3% to 9.4%. Two out of seven (i.e., 29%) depth measurements lie outside the nominal error derived from all seven light curves (5.9% ± 2.6%). The differences we find by excluding single light curves reinforces our notion that we are likely dealing with a patchy stellar corona, and individual X-ray transit light curves may show strongly differing transit depths. It would therefore be desirable to average over a very large number of X-ray transits. However, we are limited to an analysis of the available seven light curves, in which the inhomogeneities of the stellar corona may not have been fully averaged out.

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There are a few combinations of six light curves that are worth investigating further. One is the combinations of all six Chandra light curves, excluding the XMM-Newton light curve. XMM-Newton and Chandra are very well cross-calibrated, so one does not expect systematic differences here. And indeed, the transit depth derived from the Chandra light curves alone is 5.7%.

Another combination that we want to look at in more detail is all light curves except the second Chandra light curve. From visual inspection of the light curves, it seems that there may be a small flare in the second Chandra light curve near phase 1.01–1.02. It is rather difficult to identify a flare unambiguously in light curves of this signal-to-noise level. Further, Pillitteri et al. (2011) have observed that small flares of HD 189733A are often not accompanied by a significant change in hardness ratio (which is often seen in larger flares on cool stars). Rather, they observed an almost simultaneous rise in both the hard and the soft X-ray band, with only a slightly earlier increase in hard X-rays. To test for such a behavior in our light curves, we calculate the Stetson index for 4 ks box car chunks for each light curve. The Stetson index measures correlated changes in two light curve bands, with positive values indicating correlated changes, negative values indicating anti-correlated changes, and values close to 0 indicating random changes (see Welch & Stetson 1993). Carpenter et al. (2001) showed that the 99% threshold for (anti)correlated variability is achieved near |S| = 0.55. A more conservative value of |S| > 1 is used to identify stronger variability (Rice et al. 2012).

We show the result of this analysis in Figure 10. All light curves display at least mildly correlated changes in the soft and hard X-ray bands, and two light curves display strongly significant correlated variability during part of the observations. Those light curves are from the XMM-Newton observations, shown as a dashed black line, and the second Chandra observation, shown as a solid green line. For the Chandra observation, the phase of significant correlated variability is the same as identified by visual inspection, namely, around 1.01–1.02. For the XMM-Newton light curve, one of the correlated phases coincides with a flare-shaped part of the light curve around phase 0.94 (outside the phase interval considered for the added-up light curve). No flare-like feature is seen for the other part of that light curve with correlated changes (phase 0.97–0.98), but a slight downward slope with small variability features is present. We interpret these findings as consistent with small flares occurring during the second Chandra observation and the first half of the XMM-Newton observation.

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We therefore identify four light curve combinations which are of interest: (a) all data sets (total: six observations from Chandra and one from XMM-Newton); (b) six data sets, excluding the Chandra observation with the assumed flare (total: five observations from Chandra and one from XMM-Newton); (c) only the six Chandra data sets, excluding the potentially flaring XMM-Newton observation; (d) only the five quiescent Chandra data sets, excluding the potentially flaring Chandra and XMM-Newton observations. This last combination will have rather large errors because two out of seven observations are ignored, but the flare analysis conducted above demonstrates the necessity to investigate this combination as well.

We list the transit depths derived for the three additional light curve combinations in Table 6 and show the limb-brightened fits to the data in Figures 8(b)–(d).

These results show that excluding the XMM-Newton data set has little consequence for the derived transit depth, but excluding the possibly flare-contaminated second Chandra light curve changes the depth by about 35%. This is still within the 1σ error range derived from Poissonian counting statistics. Given our flare analysis of the individual light curves above, we think that the true X-ray transit depth is closer to a value of 8% derived from the non-flaring observations than to 5.9% derived from all observations. We have therefore bold-faced two columns in Table 6: Column 1 represents the transit depth derived from all data sets, without selecting for stellar quiescence, and Column 4 represents the transit depth derived from only the quiescent data sets. We would like to remind the reader that our excess transit depths may be influenced by inhomogeneities of the stellar corona. We will discuss the possibility of latitudinal inhomogeneities in Section 4.1.1, which could be induced by activity belts. However, we have no means of testing for longitudinal inhomogeneities, i.e., testing whether the planet has occulted a typical number of coronal active regions during these specific seven observations. Additional X-ray observations are therefore necessary to confirm that the available X-ray data indeed sample a representative average of the stellar corona.

There are two possible explanations for the observed transit depth: in scenario A, the planet's X-ray and optical radii are more or less the same, but the planet occults parts of the stellar corona considerably brighter than the disk-averaged X-ray emission; in scenario B, the effective X-ray radius of the planet is significantly larger (by >50%) than its optical radius, and the occulted parts of the stellar corona have the same or a smaller X-ray brightness than the disk average.

4.1.1. Scenario A: An Inhomogeneous Corona

4.1.2. Scenario B: An Extended Planetary Atmosphere

Irradiation of exoplanets in the X-ray and EUV regime has been identified as the main driver for their atmospheric escape (Lecavelier Des Etangs 2007). The altitudes at which the high-energy irradiation is absorbed depend on the wavelength. Theoretical models show that the broadband (E)UV flux is absorbed close to the optical planetary surface, at R_UV ≈ 1.1 R_opt (Murray-Clay et al. 2009). In the far-UV hydrogen Lyα line, the opacity of the atmosphere is much larger, and transit depths between 2.7% and 7.6% have been inferred from individual observations, with a typical transit depth of ca. 5% (Lecavelier Des Etangs et al. 2010).⁴ Our X-ray observations have shown that the X-ray absorbing radius of the planet is likely even larger with about 1.75 R_P. This is consistent with our temperature estimate of ca. 20,000 K for the outer atmosphere, which means that hydrogen is mostly ionized and will not contribute to the EUV opacity at those altitudes. We show a qualitative representation of the different absorption altitudes in Figure 11. Note that the planetary atmosphere is likely distorted by the stellar wind, and may form a comet-like tail (Vidal-Madjar et al. 2003).

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Observations in the UV Lyα line of hydrogen yielded lower limits for mass-loss rates of the order of 10¹⁰ g s⁻¹ for transiting Hot Jupiters (Vidal-Madjar et al. 2003; Lecavelier Des Etangs et al. 2010). However, the dynamics of planetary mass loss are not well understood; the process is hydrodynamical (Tian et al. 2005; Murray-Clay et al. 2009) and therefore much more efficient than pure Jeans escape. Current models emphasize different aspects of the problem, such as extended absorption radii Roche-lobe overflow (Lammer et al. 2003; Erkaev et al. 2007). For an order-of-magnitude estimate of HD 189733b's mass loss, we choose to use an approximate formula which related the mass-loss rate to the stellar high-energy flux, the planetary absorption radius, and planetary mass:

$$\begin{equation} \dot{M_P} = \frac{\pi \epsilon F_{{\rm XUV}} R_P\, R^2_{P\,({\rm abs})}}{{GM}_P K}, \end{equation} \tag{ 1 }$$

with M_P being the planetary mass of 1.138 M_Jup (Triaud et al. 2010), R_P (abs) the relevant planetary radius for high-energy absorption, K a factor for including Roche-lobe overflow effects which we ignore here by assuming K = 1, F_XUV the incident high-energy flux at the planetary orbit, and a factor to account for heating efficiency of the planetary atmosphere. A choice of = 1 denotes that all incident energy is converted into particle escape, but several authors chose = 0.4 (Valencia et al. 2010; Jackson et al. 2010), inspired by observations of the evaporating Hot Jupiter HD 209458b, and we follow their approach.

Assuming that the broadband EUV flux is absorbed close to the optical planetary radius, while the X-ray flux is absorbed at altitudes of ≈1.75 R_P, we modify the formula to

$$\begin{equation} \dot{M_P} =\pi \epsilon R_P \frac{(1.75\, R_P)^2 F_{X} + R_P^2 F_{{\rm EUV}}}{{GM}_P K}. \end{equation} \tag{ 2 }$$

The broadband EUV flux of HD 189733A has not been directly measured, but scaling relations between the EUV and X-ray flux exist for main-sequence stars (Sanz-Forcada et al. 2011), using specific X-ray energy bands. We use WebPIMMS to extrapolate our measured X-ray luminosity of HD 189733A of log L_X (0.25–2 keV) = 28.08 to the required 0.12–2.5 keV band and find log L_{X (0.1–2.5)} = 28.15 for a mean coronal temperature of 4.5 MK. This yields an EUV luminosity of log L_EUV = 29.01 using formula (3) from Sanz-Forcada et al. (2011). Another way to estimate the EUV luminosity of HD 189733A is by extending its coronal emission measure distribution, derived from a single high-resolution X-ray spectrum, to EUV wavelengths. Sanz-Forcada et al. (2011) have done this and found log L_EUV = 28.5; given that the star displays some X-ray variability over time, we consider a range of EUV luminosities between those two values.

Converting these luminosities to flux at the planetary orbit with a semimajor axis of 0.03142 AU, we find a mass-loss rate between 1.2 and 2.3 × 10¹¹ g s⁻¹ for an energy efficiency of = 0.4, and a maximum mass loss of (3.0–5.8) × 10¹¹ g s⁻¹ for an energy efficiency of = 1. The contribution of the extended X-ray radius to the increased mass loss is 25%–65%, depending on the assumed high or low EUV flux which is absorbed at lower altitudes in the planetary atmosphere.

Other studies have tried to estimate the total mass lost by selected exoplanets over the planetary lifetime, by integrating over the age of the system and the likely activity evolution of the host star (Lammer et al. 2009; Sanz-Forcada et al. 2011; Poppenhaeger et al. 2012). For HD 189733A, however, the activity evolution is probably atypical, as shown in the next section.

Estimating ages of individual main-sequence stars is a thorny problem. Lithium abundances provide some leverage to derive ages of young stars, but this method loses its diagnostic power for ages larger than ca. 600 Myr. For older stars with outer convective zones, i.e., later than spectral type A, one can use the effect of magnetic braking to estimate their ages (Mamajek & Hillenbrand 2008); older stars rotate more slowly and are less magnetically active than younger stars. This has been successfully calibrated through comparisons of stellar clusters with different ages, using a variety of angular momentum proxies such as X-ray luminosity (Preibisch & Feigelson 2005; Lammer et al. 2009), fractional X-ray luminosity L_X/L_bol (Jackson et al. 2012), chromospheric Ca ii H and K line emission (Wright et al. 2004), and rotational periods (Cardini & Cassatella 2007).

All of these age–activity relationships assume that the stellar angular momentum is lost through magnetized stellar winds, and that there is no input of angular momentum through other physical processes. These age–activity relationships are violated by close binary stars because they are tidally locked; their stellar spin is locked to the orbital period and is therefore conserved over a long time, leading to X-ray luminosities which are orders of magnitude larger than for single stars of comparable age. It has been argued that Hot Jupiters might have similar but weaker activity-enhancing effects on their host stars (Cuntz et al. 2000). While initial observations found chromospheric and coronal activity enhancements (Shkolnik et al. 2005; Kashyap et al. 2008), later studies showed that such trends could not be disentangled from biases inherent to planet detection methods, and thus have to be regarded with care when testing for planet-induced effects (Poppenhaeger et al. 2010; Poppenhaeger & Schmitt 2011). It is therefore still under debate how strongly close-in exoplanets can influence the magnetic properties of their host stars.

The HD 189733 system provides a new angle to investigate the stellar activity level, because a physically bound stellar companion is present to which the planet-hosting star can be compared. The distance between the (planet-hosting) K dwarf and its M dwarf companion is large (projected orbital distance ≈216 AU; Bakos et al. 2006), so that the rotational history of each star is not influenced by the other. One would therefore expect both stars to display the appropriate activity level of their spectral class for a common age.

The relevant properties of HD 189733A in this context are log L_X = 28.1 erg s⁻¹, log (L_X/L_bol) = −5, chromospheric activity indicator $\log R^\prime _{{\rm HK}} = -4.537$ (Melo et al. 2006), and the rotational period was measured to be ≈12 days (Henry & Winn 2008). From the X-ray properties, we find age estimates of 1.2 Gyr and 1.5 Gyr (from Lammer et al. 2009; Jackson et al. 2012), the chromospheric activity yields 1.1 Gyr (from Wright et al. 2004), and the rotational period yields 1.7 Gyr (from Cardini & Cassatella 2007). All these estimates agree that HD 189733A displays the activity level of a star with an age around 1.5 Gyr.

HD 189733B's relevant properties are its X-ray luminosity log L_X = 26.67 erg s⁻¹and its fractional X-ray luminosity log (L_X/L_bol) = −4.6. This is in line with the X-ray upper limit previously reported by Pillitteri et al. (2011). Chromospheric activity indices or the rotational period are not available. Here, we find age estimates of 4 Gyr and 5.5 Gyr, respectively, from Jackson et al. (2012) and Lammer et al. (2009). This is consistent with the fact that HD 189733B's X-ray luminosity is slightly below the median value found for field M dwarfs by Schmitt et al. (1995).

This means that the Hot Jupiter host star HD 189733A is magnetically overactive when compared to its presumable coeval stellar companion. Interestingly, such a contradiction in activity-derived ages has also been observed for the CoRoT-2 system, where the Hot-Jupiter-hosting star is also overactive when compared to its stellar companion (Schröter et al. 2011). In the case of HD 189733A/B, the system has been observed multiple times over recent years, without large changes in the average X-ray luminosity. We can therefore exclude a stellar activity cycle to be the cause for the disagreement in activity levels. We consider it a more likely possibility that the stellar angular momentum of HD 189733A has been tidally influenced by the Hot Jupiter, which has inhibited the stellar spin-down enough to enable the star to maintain the relatively high magnetic activity we observe today.