ON THE DETECTABILITY OF STAR–PLANET INTERACTION

We identified WASP-18 as the potentially most strongly interacting system among currently discovered exoplanets, a distinction it retains as of 2012 April. We obtained a list of all confirmed planets with M_P > 0.1 M_J (i.e., planetary mass greater than 10% that of Jupiter), orbital period P < 100 days, and V < 15 from the Exoplanet Orbit Database⁷ (Wright et al. 2011). As may be seen in Figure 1, WASP-18b (Hellier et al. 2009; Southworth et al. 2009), with M_P = 10.4 M_J, P = 0.941 days, and a = 0.020 AU, has the largest value of the interaction strength proxy M_P/a² within this sample (and would also rank first for other plausible parameterizations of interaction strength). More specifically, after excluding brown dwarfs (with M_P > 13 M_Jup), of the 551 entries in the Exoplanet Orbit Database, the M_P/a² ≃ 25,000 M_Jup AU⁻² for WASP-18 is nearly 2.5 times greater than the next largest value (CoRoT-14b), and only five systems have M_P/a² > 5000 M_Jup AU⁻². Because WASP-18 is a transiting system, the planetary properties are securely established by light curve and radial velocity measurements. The values of M_P/a² are also labeled for several systems described in Section 1; for example, HD 179949 has M_P/a² ≃ 500 M_Jup AU⁻².

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The stellar and planetary properties for the WASP-18 system are given in Table 1, as are those for previously identified star–planet interaction candidates HD 179949, υ And, and τ Boo (but recall τ Boo is tidally locked, with stellar and orbital periods of ∼3.2 days, which may suppress magnetic interaction). The value of M_P/a² for WASP-18b exceeds that for the other candidate systems by one to two orders of magnitude. Such extreme planetary systems are difficult to maintain, and WASP-18b itself is expected to have a short lifetime against infall from tidal drag (Hellier et al. 2009). The star WASP-18 has spectral type F6, effective temperature T_eff = 6400 ± 100 K, and stellar mass M_* = 1.22 ± 0.03 M_☉ (values from the Exoplanet Orbit Database, from which original references may be obtained); conveniently, these are similar to the properties of HD 179949 (F8, 6170 K, 1.18 M_☉), υ And (F8, 6210 K, 1.31 M_☉), and τ Boo (F7, 6390 K, 1.34 M_☉). WASP-18 is slightly hotter than HD 179949 and υ And, and consequently likely possesses a slightly shallower outer convection zone. On the other hand, the stellar rotation period is shorter, at ∼5.6 days, estimated from vsin i = 11 km s⁻¹; the orbit and stellar rotation are aligned⁸ (Triaud et al. 2010). HD 179949 and υ And have rotational periods of 7.6 days (Fares et al. 2012) and ∼12 days (Shkolnik et al. 2008), respectively. Further, WASP-18 appears to be a younger star, with an age of ∼500–700 Myr (Hellier et al. 2009; Brown et al. 2011). The age–rotation-activity relation would then predict relatively greater intrinsic activity in WASP-18, apart from any planet-induced modulation or enhancement (but see Section 3.2 for caveats). Observationally, WASP-18 has other appealing features: the star is among the brighter transit-detected systems, and the short planetary period facilitates rapid accumulation of phase coverage across multiple orbits. Due to its extreme properties, WASP-18 has been studied at a range of frequencies; for example, Nymeyer et al. (2011) used Spitzer observations of secondary eclipse to infer that the planet has T ≃ 3100 K with near-zero values for both albedo and day/night side energy redistribution. However, high-resolution, high signal-to-noise Ca ii H and K spectroscopy, and sensitive X-ray observations have not been published prior to the observations presented here.

Table 1. Candidates for Star–Planet Interaction

	Star				Planet			Activity
Name	Type	V	B−V	d	MP	P	a	Age	MP/a2	R'HK	log LX	$\log {\left(\frac{L_{\rm X}}{L_{\rm bol}}\right)}$
				(pc)	(MJ)	(days)	(AU)	(Gyr)	(MJ/AU2)		(erg s−1)
WASP-18	F6	9.39	0.49	100	10.4	0.94	0.0201	0.6	25700	< −5.0a	<27.6	<−6.2
τ Boob	F7	4.50	0.51	15.62	4.1	3.31	0.0480	2.5	1780	−4.73	28.8	−5.3
HD 179949	F8	6.25	0.55	27.5	0.95	3.09	0.0439	2.1	490	−4.80	28.6	−5.3
υ And	F8	4.10	0.54	13.49	0.69	4.62	0.0594	3.8	200	−5.07	27.6	−6.5

Notes. Data are taken from the Exoplanet Orbit Database (http://www.exoplanets.org), except for planetary mass and system age which are from the Extrasolar Planets Encyclopedia (http://www.exoplanet.eu), and log L_X which is from this work, Poppenhaeger et al. (2012), Kashyap et al. (2008), and Poppenhäger et al. (2010) for WASP-18, τ Boo, HD 179949, and υ And, respectively; log (L_X/L_bol) is calculated. ^aEstimated from our measured log L_X < 27.5 erg s⁻¹ and the R'_HK − log (L_X/L_bol) correlation in Mamajek & Hillenbrand (2008). See also footnote 15. ^bThe potential strength of magnetic star–planet interaction in the τ Boo system is reduced due to the apparent tidal locking of the star to the planet; see Section 1.

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Optical spectroscopy was carried out with the 6.5 m Clay Telescope on 2011 November 6–7 and 10–13 using the Magellan Inamori Kyocera Echelle (MIKE), a high-throughput double echelle spectrograph. A 07 × 5'' slit was used throughout, providing a resolution of R ≃ 40,000 near the Ca ii H and K lines. A communication board failure prevented use of the blue-side CCD on November 10 and bad weather limited observing on November 11. In total, 13 visits to WASP-18 were obtained, with combined exposure times of 20–40 minutes per visit. The planetary orbital phase coverage (Figure 2) spans 0.7–1.4 and includes one visit at central planetary transit.

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The spectra were reduced using the IDL MIKE Redux⁹ package. Briefly, milky flats (taken of δ Ori with the diffuser) were combined and normalized to correct pixel response variations; trace flats (from internal lamps) were combined for order and slit tracing; arc images (including one associated with each science exposure) were processed and used to derive two-dimensional wavelength maps, using a fifth-degree polynomial fit along the orders which was found to give generally structureless residuals; the slit profile was determined for each order; science exposures were processed (bias-subtracted from overscan and flat-corrected), the object was traced and the sky subtracted, and the object flux was optimally extracted. Flux is retained in relative units (i.e., no spectrophotometric standard star calibration was conducted) as we are interested in normalized spectra. Automated cosmic-ray correction was not performed due to concern about potential introduction of spurious variability; two science frames with an obvious cosmic ray located near the two-dimensional center of the Ca ii K line were discarded.

Contemporaneous monitoring was obtained with the Swift satellite from November 1–17 (Target ID 32149), notably with the X-ray Telescope (XRT) through 58 snapshots of 500–1500 s each. The XRT observations were reduced using HEASARC version 6.11.1. An exposure map was generated for each sequence, including a vignetting correction and with time-dependent instrument maps used whenever attitude variations exceeded 24. Images were extracted in both the full (0.3–10 keV) and soft (0.3–2 keV) bands. The stacked XRT effective exposure from all sequences at the position of WASP-18 reached ∼50 ks. The UV/Optical Telescope was also used to obtain both photometry (with the U, UVW1, UVM2, and UVW2 filters) and UV grism spectroscopy, with coverage of the Mg ii h and k lines which are also chromospheric activity indicators (Buccino & Mauas 2008).

We checked for phase-dependent variability, as from one-sided-enhanced chromospheric activity, within the cores of the Ca ii H and K lines, focusing primarily upon the latter. The Ca ii K line and nearby stellar continuum were isolated through selecting wavelengths spanning 3920–3950 Å, which included contributions from two orders. For each visit, the flux from individual exposures was summed, and the wavelength scale was adjusted through subtraction of a center-of-mass velocity of 3.1961 km s⁻¹ and a stellar reflex velocity with an amplitude of 1.8183 km s⁻¹, using the values and ephemeris from Hellier et al. (2009). Continuum normalization near the Ca ii H and K regions is difficult because the absorption lines are quite broad relative to the blaze function; there are a large number of nearby metal lines, and the Wien tail is falling off steeply. We used a similar normalization method to that conducted and detailed by Shkolnik et al. (2005, 2008), removing a slight linear trend over ≃7 Å centered near the line cores, such that unity represents approximately one-third of the local stellar continuum. The normalized Ca ii H and K spectra for all 13 visits are plotted in Figure 3 (top).

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Residuals from median-normalized Ca ii H and K spectra were calculated for each visit, and then stacked (weighted by exposure times corrected for seeing) within orbital phase bins of 0.70–0.93, 0.99–1.19, and 1.21–1.41; these bins then contain spectra from four, five, and four visits, respectively. The residuals were boxcar smoothed with a width of 0.4 Å and then any remaining slight linear trend was subtracted to avoid influencing comparison of the line core. There is no obvious difference in the residual spectra within the three separate phase bins, to an amplitude of 0.003 of the normalized continuum (Figure 3, bottom). Integrating the normalized flux over the 1 Å line cores within phase bins of 0.70–0.93, 0.99–1.19, and 1.21–1.41 gives nearly identical values: 0.252 ± 0.001, 0.251 ± 0.002, and 0.253 ± 0.003 for K and 0.225 ± 0.001, 0.227 ± 0.001, and 0.228 ± 0.003 for H, where the 1σ uncertainties have been estimated as the standard deviation of the component flux measurements within each phase bin. The 3σ limit on the relative flux variability is <3.2% and <3.4% for the K and H line cores, respectively. The apparent marginal tendency for the 1.21–1.41 K bin to show relatively more red-side emission is within the noise level¹⁰ but in any case this slight profile variation is not present in H, is lopsided rather than symmetric about the core, and lags rather than leads the subplanetary point; these effects are inconsistent with planetary magnetic interaction.

The XRT observations were initially planned for similar phase-resolved analysis, but the star proved to be unexpectedly X-ray faint (see also Section 3.2) and so all sequences were combined for an effective exposure of ∼50 ks. WASP-18 is not detected by XRT in the stacked exposure, in either the soft (Figure 4) or the full bands. Specifically, within an aperture of 20'' centered on the SIMBAD optical position of WASP-18, there are 3.8 counts in the 0.3–2 keV band, where the expected background is 3.7 counts. The 95% upper limit on the source counts within 20'' is <5.9 net counts (from Kraft et al. 1991), corresponding to <8.1 total net counts after accounting for the XRT point-spread function (Moretti et al. 2005). For a coronal model with kT = 1 keV and solar abundances, the unabsorbed 0.3–2 keV X-ray flux is <3.3 × 10⁻¹⁵ erg s⁻¹, calculated using the Portable Interactive Multi-Mission Simulator¹¹ for a plasma/APEC model presuming an intervening column of N_H = 10¹⁸–10¹⁹ cm⁻²; other plausible models give similar results to within ≲30% (or 0.1 dex). At the Hipparcos distance to WASP-18 of 100 ± 10.6 pc, this corresponds to a limiting X-ray luminosity of log L_X < 27.6 erg s⁻¹ (0.3–2 keV).

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Past work would seem to suggest that the degree of planet-induced Ca ii H and K variability expected for WASP-18 could be substantial. For example, Shkolnik et al. (2005, 2008) report "on/off" Ca ii H and K variability phased with the planetary orbital period in HD 179949 and υ And (see also Poppenhäger et al. 2011), which have stellar types of F8 and do not show obvious core emission within the deep photospheric absorption (similar to WASP-18). The amplitude of residual flux associated by Shkolnik et al. (2008, Figure 3; Shkolnik et al. 2005, Figure 6) with star–planet activity in HD 179949 (υ And) is ≃0.017 (≃0.008).¹² The value of M_P/a² for WASP-18 could suggest an effect 50 (130) times greater than for HD 179949 (υ And).¹³ In contrast to such predictions, the level of phase-binned variability observed for WASP-18 is ≲0.003 (Figure 3; Section 2.2), below the levels detected in HD 179949 and υ And.

The degree of X-ray variability expected in WASP-18 is more difficult to estimate, as only a handful of X-ray-brightening events have been attributed to potential star–planet interaction. For example, HD 179949 displayed an increase in X-ray emission by ∼30% near the phase associated with the Ca ii H and K enhancement (Saar et al. 2008); with a stellar X-ray luminosity of log L_X = 28.6 erg s⁻¹ (Kashyap et al. 2008), this is an increase of log L_X = 28.1 erg s⁻¹. HD 189733 showed two X-ray flares near phase 0.53 (i.e., shortly after occultation), peaking at twice the baseline count rate (Pillitteri et al. 2011); with a stellar X-ray luminosity of log L_X = 28.4 erg s⁻¹ (Kashyap et al. 2008), this is an increase of log L_X = 28.4 erg s⁻¹. Cohen et al. (2011) used their MHD modeling of the HD 189733 system to estimate that the energy available from magnetic reconnection to accelerate particles into the stellar corona is ∼10²⁸ erg s⁻¹ (after applying conservative efficiency assumptions). From these examples, WASP-18 might be expected, taking into account its exceptional value of M_P/a², to possess interaction energy available for coronal activity enhancement sufficient to generate absolute increases in its X-ray luminosity by several times 10²⁸ erg s⁻¹. However, the observed XRT upper limit of log L_X < 27.6 erg s⁻¹ indicates that the X-ray luminosity did not achieve this level for any more than ≲10% of the Swift coverage. Without even a stacked X-ray detection it is not possible to evaluate the relative amplitude of phase-dependent X-ray variability, if any, in WASP-18.

The scaling of star–planet interaction strength with M_P/a² that we (and others; Section 1) have adopted approximately holds for otherwise similar systems. We briefly consider the impact upon the energy available for star–planet interaction due to potentially differing planetary or stellar magnetic field strengths in WASP-18 compared to HD 179949 and υ And. The planetary magnetic field strength depends most relevantly upon M_P but also scales inversely with the planetary rotational period. For tidally locked planets, as all these are believed to be (out to ∼0.15 AU; Bodenheimer et al. 2001), the planetary rotation period is identical to the orbital period, and both are substantially shorter for WASP-18 than for HD 179949 or υ And. This suggests (Arge et al. 1995; Sánchez-Lavega 2004; Stevens 2005) an increase in baseline planetary magnetic field strength by a factor of a few, which would enhance any star–planet interaction. The relative velocity between magnetic field lines, which is governed by the difference between the planetary and stellar rotation rates, is v_rel = K(R_*/a) − v_rot for tidally locked planets, where K is the orbital velocity and v_rot is the equatorial stellar rotational velocity (Cuntz et al. 2000). This would suggest a further increase in interaction strength by a factor of a few. On the other hand, the interaction strength approximately scales with the stellar magnetic field, B_* (Cuntz et al. 2000; Kashyap et al. 2008; see Lanza 2009 and Scharf 2010 for slightly different formulations), which appears to be substantially weaker in WASP-18 than in at least HD 179949 and perhaps also υ And. This is evident by the X-ray nondetection of WASP-18, as B_* is observed to depend approximately linearly upon L_X (Pevtsov et al. 2003). That log (L_X/L_bol) is at least one order of magnitude lower in WASP-18 than HD 179949 possibly offsets any gains in interaction strength due to faster planetary rotation, although the difference in inferred stellar magnetic field strengths is less between WASP-18 and υ And. However, since the observed amplitude of Ca ii H and K variability in WASP-18 is already ≳5 times lower than that suggested to arise from star–planet interaction in HD 179949, B_* would need to be ≳50 times lower in WASP-18 than in HD 179949 to explain our nondetection for a similar interaction efficiency, which seems implausible given their similar stellar spectral types.

The lack of evidence for star–planet interaction in WASP-18 is unexpected given that we selected it as the system with the greatest predicted interaction strength (based on planetary mass and semimajor axis) and given the broad similarity in stellar properties between WASP-18 and other systems (notably HD 179949 and υ And) for which star–planet interaction has been claimed. Star–planet interaction in WASP-18 would seem to be at best highly transient as it was not demonstrably present during our observations. For reference, Ca ii H and K variability has been described as phased with the planetary orbit in ≲50% of the epochs at which HD 179949 and υ And have been observed. Further, the timescale for a magnetic reconnection event in the simulations of Cohen et al. (2011) is short, ∼0.25 orbits. On the other hand, our spectroscopic coverage of WASP-18 extends over eight complete planetary orbits, and the X-ray observations cover many more (albeit at a lower sensitivity per orbit). To the extent that star–planet interactions are transient, they should intuitively occur with greater frequency in extreme systems such as WASP-18, which contrasts (if not definitively) with our findings. It might be alternatively suggested that, if our observations did not simply happen to take place within a period of relative quiescence, the efficiency of star–planet interaction for WASP-18 could be lower than has been identified in the past for less extreme systems. However, we emphasize again that WASP-18 is not notably distinctive in terms of stellar properties from HD 179949 and υ And. (Below, we explore the possibility that the particularly massive and close-in planet in WASP-18 actually acts to suppress stellar activity.)

Regardless of its underlying cause, this lack of observed variability in WASP-18 demonstrates that even extreme systems, arguably the best candidates to display planet-induced activity enhancements, challenge prevailing ideas concerning star–planet interaction. The appealing prospect of calibrating star–planet interactions to estimate exoplanet magnetic field strengths would currently appear to require additional unambiguous evidence of such interactions occurring.

We next consider the overall baseline level of chromospheric and coronal activity in WASP-18, to provide context for the nondetection of planet-induced variability. WASP-18 shows atypically low Ca ii H and K core emission for its spectral class and inferred age (contrast with, e.g., HD 111456; Freire Ferrero et al. 2004). When stellar age is calculated from Ca ii activity, main-sequence F, G, K, or M stars with inferred ages of 340–740 Myr (i.e., similar to the age of WASP-18, which is not based on Ca ii activity¹⁴) are chromospherically "active" (following the definition of Henry et al. 1996), with characteristic values of −4.5 < R'_HK < −4.4 (from data in Wright et al. 2004). While stars with 0.48 < B − V < 0.52, as for WASP-18, display a wide range of activity, they are significantly less likely to have R'_HK < −5.0 (19%, versus 37% for F, G, K, and M stars; from data in Wright et al. 2004). However, R'_HK in WASP-18 is low; if estimated indirectly based on the R'_HK − log (L_X/L_bol) correlation presented in Mamajek & Hillenbrand (2008), the measured X-ray limit for WASP-18 suggests R'_HK ≲ −5.0.¹⁵

The X-ray luminosity for WASP-18 is also lower than predicted. Nine nearby stars of spectral class F5V–F7V (i.e., matched to WASP-18) in a volume-limited ROSAT sample have X-ray luminosities of 27.5 erg s⁻¹ < log L_X < 29.0 erg s⁻¹, with mean and median values of log L_X ≃ 28.3 erg s⁻¹ (from data in Schmitt & Liefke 2004). However, WASP-18 is younger than typical main-sequence stars and should consequently be more X-ray luminous. While we are not aware of a specific comprehensive study of young F stars, in general the X-ray luminosity of F5+ stars modestly exceeds that of G stars (Schmitt 1997), and Hyades G stars (hence of a similar age to WASP-18) have mean log L_X ≃ 28.8 erg s⁻¹ (Stelzer & Neuhäuser 2001; Preibisch & Feigelson 2005). Consequently, the XRT-derived limit of log L_X ≲ 27.6 erg s⁻¹ marks WASP-18 as notably X-ray faint relative to comparable stars, with a log (L_X/L_bol) ≲ −6.2, similar to that of the Sun.

In summary, not only is there no apparent enhancement in chromospheric or coronal activity in WASP-18 that might be linked to interaction with the planet, but rather, the above results, taken together, suggest that WASP-18 is unusually quiet for a young F6 star. It is possible that the stellar age is incorrect; the 1σ error bars on the measurement given by Hellier et al. (2009) encompass ≳1 Gyr, and the Brown et al. (2011) estimate depends upon complicated planet–star interactions. If the planet has acted to spin up the star (recall the orbital plane and the stellar rotation axis are aligned), the current relatively rapid stellar rotation rate would not be reflective of true age. Stellar age has proven difficult to determine in some other hot Jupiter systems; for example, Schröter et al. (2011) find that CoRoT-2a is X-ray bright and young but a late-K companion is X-ray undetected, inconsistent with the inferred system age, and a similar situation may apply for HD 189733 (Pillitteri et al. 2011). If WASP-18 were two to three times older than current estimates, the intrinsic activity would still be somewhat low but to a much less unusual degree. If the age is indeed correct, it is natural to consider whether the extremely massive and close-in planet could act to suppress, rather than enhance, stellar activity. The tidal force exerted by WASP-18 upon its parent star is much greater than is typical even for hot Jupiter systems, and in fact Arras et al. (2012) note that the small but apparently non-zero eccentricity indicated by radial velocity data is likely due to tidal fluid motion on the star. Mid-type F stars have shallow outer convective zones; perhaps the tidal pull is sufficient to repress dynamo activity in WASP-18 or comparably extreme systems (of which none are, however, currently known). This possibility could be assessed through magnetohydrodynamic simulations.

Here, we explore the possibility that a hotspot rotating upon the stellar surface can potentially mimic a shorter-period signature of star–planet interaction if only observed over a small fraction of the stellar rotation. Figure 5 shows simulated examples for HD 179949 and υ And, which have stellar/planetary periods of 7/3.09 and 14/4.618 days, respectively (Shkolnik et al. 2008). The half and full sinusoid models for planet-induced activity chosen for these examples are similar to those applied by Shkolnik et al. (2005, 2008) to these systems, but here for an edge-on inclination and with arbitrary normalizations. (By construction the stellar hotspot amplitude is taken as unity, and the relative amplitude of the interaction model is then greater for HD 179949 than for υ And, also qualitatively similar to the published models.) The probability of the stellar and planetary phases co-aligning to mimic star–planet interaction for these particular models is not very large (e.g., ≃3% of 10,000 random phase offsets for each example yield total squared residuals less than 0.1), but with additional freedom to adjust the relative amplitudes, or to consider additional parameters (such as spot latitude or system inclination, within a limited range) or to choose from alternative model functional forms, or with a greater tolerance for (apparent) outliers, this effect could potentially present a significant source of contamination within a large sample of tested stars. For the particular cases of HD 179949 and υ And, it must be emphasized that several observing runs were conducted, and in some (but not all) of those runs variability of similar amplitude similarly phased with the planetary orbit was observed (Shkolnik et al. 2005, 2008; Poppenhäger et al. 2011), which clearly decreases the probability of mistaking a stellar hotspot for one corotating with the planet.

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We note that, in general, searches for star–planet interaction based on Ca ii core variability can guard against this type of false positive at a given epoch through obtaining coverage over at least one complete stellar rotation and over multiple planetary orbits (as was done with our coverage of WASP-18). If searches over multiple epochs find some instances in which core variability phases with the stellar rotation and others in which it apparently matches the orbital period, a comparison of the amplitudes can also check whether the observed activity is likely to arise from distinct (intrinsic versus planet-induced) sources. It would be odd if the activity in the "off" state (phased with stellar rotation rather than orbital period) had a similar amplitude to that seen in the "on" state, during which there is no obvious physical reason that the star should otherwise go silent. It is not clear to us that the current data for HD 179949 and υ And can definitively pass this test, but see, e.g., Fares et al. (2012). In any case, the conclusion is that complete and extended coverage, preferably across multiple epochs and multiple orbits per epoch, is essential for high-confidence detections of star–planet interaction.