Planet-Induced Stellar Pulsations in HAT-P-2's Eccentric System

TL;DR

This study uses extensive space telescope observations to detect star pulsations in the HAT-P-2 system, revealing tidal interactions that challenge current stellar models and deepen understanding of planet-star dynamics.

Contribution

First detection of tidally induced stellar pulsations in an exoplanet host star with an eccentric orbit, providing new insights into star-planet tidal interactions.

Findings

No orbit-to-orbit variability observed in HAT-P-2 b

Detected stellar pulsations at harmonics of orbital frequency

Current stellar models cannot explain the observed pulsations

Abstract

Extrasolar planets on eccentric short-period orbits provide a laboratory in which to study radiative and tidal interactions between a planet and its host star under extreme forcing conditions. Studying such systems probes how the planet's atmosphere redistributes the time-varying heat flux from its host and how the host star responds to transient tidal distortion. Here, we report the insights into the planet-star interactions in HAT-P-2's eccentric planetary system gained from the analysis of 350 hr of 4.5 micron observations with the Spitzer Space Telescope. The observations show no sign of orbit-to-orbit variability nor of orbital evolution of the eccentric planetary companion, HAT-P-2 b. The extensive coverage allows us to better differentiate instrumental systematics from the transient heating of HAT-P-2 b's 4.5 micron photosphere and yields the detection of stellar pulsations with an amplitude of approximately 40 ppm. These pulsation modes correspond to exact harmonics of the planet's orbital frequency, indicative of a tidal origin. Transient tidal effects can excite pulsation modes in the envelope of a star, but, to date, such pulsations had only been detected in highly eccentric stellar binaries. Current stellar models are unable to reproduce HAT-P-2's pulsations, suggesting that our understanding of the interactions at play in this system is incomplete.

Tables

Table 1. Table 1 Description of HAT-P-2’s AOR a at 4.5 μ 𝜇 \mu m

AORKEY(${⨁}^b$)	Start time [UT]	Eclipse time [BJD-2455000]	Eclipse depth [p.p.m]	Pulsation amplitude [p.p.m.]	Aperturec [px]	${\beta }_{red}$ d
42789632(O)	7/9/2011 1:51	5751.8763$\pm$0.0012	1120$\pm$83	36$\pm$90	$\sqrt{\tilde{\beta }}$-0.6 (2.1)	1.55
42789888(P)	7/10/2011 1:36				$\sqrt{\tilde{\beta }}$-0.6 (1.9)	1.4
43962624(P)	7/11/2011 3:16				$\sqrt{\tilde{\beta }}$-0.6 (1.9)	1.2
43962880(P)	7/12/2011 3:01				$\sqrt{\tilde{\beta }}$-0.6 (2.1)	1.5
43963136(T)	7/13/2011 2:12	5756.42696$\pm$0.00047	4961$\pm$72	12$\pm$42	$\sqrt{\tilde{\beta }}$-0.6 (1.9)	1.4
43963392(O)	7/14/2011 1:56	5757.5081$\pm$0.0013	1116$\pm$117	32$\pm$83	$\sqrt{\tilde{\beta }}$-0.6 (1.8)	1.45
46473216(O)	10/31/2013 4:49	6394.0922$\pm$0.0014	839$\pm$93	-56$\pm$56	$\sqrt{\tilde{\beta }}$-0.5 (1.7)	1.15
46473472(O)	10/19/2013 22:45	6422.2591$\pm$0.0016	858$\pm$97	76$\pm$46	$\sqrt{\tilde{\beta }}$-0.5 (1.6)	1.6
46473728(O)	10/14/2013 7:21	6427.8928$\pm$0.0011	854$\pm$83	78$\pm$45	$\sqrt{\tilde{\beta }}$-0.5 (1.5)	1.05
46474496(O)	9/21/2013 18:24	6489.8599$\pm$0.0013	887$\pm$96	-16$\pm$45	$\sqrt{\tilde{\beta }}$-0.4 (2.1)	1.55
46474752(O)	9/16/2013 3:11	6495.4952$\pm$0.0015	899$\pm$110	39$\pm$49	$\sqrt{\tilde{\beta }}$-0.6 (1.8)	1.2
46475008(O)	8/30/2013 5:55	6529.2941$\pm$0.0014	1002$\pm$96	99$\pm$42	$\sqrt{\tilde{\beta }}$-0.5 (1.55)	1.3
46475264(O)	8/24/2013 14:26	6534.9295$\pm$0.0013	959$\pm$86	20$\pm$41	$\sqrt{\tilde{\beta }}$-0.6 (1.45)	1.4
46475520(O)	7/21/2013 19:19	6540.5602$\pm$0.0010	802$\pm$97	96$\pm$49	$\sqrt{\tilde{\beta }}$-0.7 (1.6)	1.3
46475776(O)	7/16/2013 4:21	6551.8272$\pm$0.0012	974$\pm$84	7$\pm$43	$\sqrt{\tilde{\beta }}$-0.5 (1.5)	1.15
46476032(O)	5/15/2013 4:55	6557.4625$\pm$0.0011	987$\pm$90	37$\pm$41	$\sqrt{\tilde{\beta }}$-0.6 (1.45)	1.2
46476288(O)	5/9/2013 13:53	6579.9946$\pm$0.0010	901$\pm$88	69$\pm$39	$\sqrt{\tilde{\beta }}$-0.5 (1.55)	1.45
46476544(O)	4/11/2013 9:42	6585.6294$\pm$0.0013	750$\pm$83	18$\pm$48	$\sqrt{\tilde{\beta }}$-0.5 (1.55)	1.35
46477312(P)	9/5/2013 21:46				$\sqrt{\tilde{\beta }}$-0.6 (1.55)	1.6
46477568(P)	9/5/2013 9:46				$\sqrt{\tilde{\beta }}$-0.6 (1.45)	1.3
46477824(O)	9/4/2013 21:45	6591.2611$\pm$0.0010	890$\pm$80	94$\pm$40	$\sqrt{\tilde{\beta }}$-0.5 (1.55)	1.2
46478336(P)	10/26/2013 14:45				$\sqrt{\tilde{\beta }}$-0.5 (1.5)	1.2
46478592(P)	10/26/2013 2:45				$\sqrt{\tilde{\beta }}$-0.4 (1.6)	1.2
46478848(O)	10/25/2013 14:44	6596.8941$\pm$0.0012	918$\pm$76	-20$\pm$38	$\sqrt{\tilde{\beta }}$-0.5 (1.55)	1.4
57787136(T)	10/21/2015 13:20	7316.89688$\pm$0.00047	4923$\pm$66	-40$\pm$74	$\sqrt{\tilde{\beta }}$-0.7 (1.35)	1.1
57786880(T)	11/18/2015 17:39	7345.06511$\pm$0.00051	4948$\pm$71	15$\pm$71	$\sqrt{\tilde{\beta }}$-0.7 (1.4)	1.05
57787648(O)	11/19/2015 19:28	7346.1474$\pm$0.0012	102$\pm$99	19$\pm$68	$\sqrt{\tilde{\beta }}$-0.5 (1.6)	1.45
57787392(O)	11/25/2015 10:49	7351.7813$\pm$0.0011	864$\pm$87	33$\pm$85	$\sqrt{\tilde{\beta }}$-0.6 (1.4)	1.35

Equations

$$\left.\begin{array}[]{l c l}P&=&5.6334675\pm 1.3\times 10^{-6}\mbox{days}\\ T_{c,0}&=&2455288.84969\pm 0.00039\mbox{ BJD}\\ e&=&0.51023\pm 0.00042\\ \omega&=&188.44\pm 0.43^{\circ}\\ \end{array}.\right.$$

Full text

1. Introduction

Owing to its large mass (8 $M_{\rm Jup}$), short orbital period ($P\sim$5.63 d), and eccentricity ($e\sim 0.5$), the hot Jupiter HAT-P-2 b (Bakos et al., 2007) is a favored target for the study of planet-star interactions (Fortney et al., 2008; Jordan & Bakos, 2008; Langton & Laughlin, 2008; Fabrycky & Winn, 2009; Levrard et al., 2009; Hartman, 2010; Cowan & Agol, 2011; Cébron et al., 2013; Kataria et al., 2013; Lewis et al., 2013, 2014; Salz et al., 2016). Measurements of the flux variations caused by its transient heating obtained at 3.6, 4.5, and 8.0 $\mu$m with Spitzer yielded the first insights into the planet’s response to transient heating (Lewis et al., 2013) but were not reproducible by atmospheric models (Lewis et al., 2014), in particular at 4.5 $\mu$m. Here, we present the analysis of all the observations of HAT-P-2 b obtained at 4.5 $\mu$m with Spitzer—including two new primary and sixteen new secondary eclipses—whose extensive coverage allows us to better differentiate instrumental systematics from the transient heating of HAT-P-2 b’s 4.5 $\mu$m photosphere and yields the detection of unexpected pulsations with an amplitude of 40 ppm.

2. Observations & Analysis

The observations total 350 hours (2.9 million 32x32-pixels subarray images with a 0.4 sec exposure time) and include (1) a full-orbit phase curve obtained between 2011 July 9 and 2011 July 15 (Lewis et al., 2013), (2) sixteen new secondary eclipses—including two partial phase curves each covering 30 hrs post periastron passage—obtained between April 2013 and October 2013 (PI: H. Knutson), and (3) two new primary and two new secondary eclipses obtained between October 2015 and November 2015 (PI: N. Lewis).

We extract the photometry following the method detailed in de Wit et al. (2016). While Lewis et al. (2013) used a fixed aperture of 2.25 pixels to minimize the scatter in the final solution, we use here for all the Astronomical Observation Requests (AORs) time-varying apertures with a radius equal to the square root of the noise pixel parameter $\tilde{\beta}$ (see, e.g., Mighell, 2005; Lewis et al., 2013) with an AOR-dependent constant offset estimated to minimize the relative amount of red noise in the final time series of each AOR (see Online Table). The resulting aperture radius has an average across all AORs of 1.75 pixels. We trim outliers from the resulting time series for each visit, discarding 0.8% of the images overall.

As for the photometry extraction, we follow the standard procedures described in de Wit et al. (2016) to analyze the photometry, allowing us to reach photometric precisions of 75 ppm per 1-hr bin. We update the combined instrumental and astrophysical model to include functional forms to account for the transient heating of the planet’s atmosphere due to its eccentric orbit and the stellar pulsations. The resulting phase-folded photometry is shown in Figure 1.

2.1. Nominal Model

We model transits and occultations following Mandel & Agol (2002) and allow the eclipse times to vary to search for possible orbital evolution. We model HAT-P-2’s transient heating using the functional forms introduced in Lewis et al. (2013). We find that the asymmetric Lorentzian function is favored over the function based on harmonics in orbital phase ($\Delta BIC$ = -7). This difference is due to two new partial phase curves obtained after periastron passage together with sixteen new occultations that provide a stronger leverage on HAT-P-2 b’s flux modulation around occultation allowing a better disentanglement from the instrumental systematics.

2.2. Pixelation Effect and Intrapixel Sensitivity Variations

The change in position of the target’s point-spread function (PSF) over a detector with non-uniform intrapixel sensitivity leads to apparent flux variations that are strongly correlated with the PSF position. We account for this effect using the same implementation of the pixel-mapping method as in Lewis et al. (2013)—see, e.g., Wong et al. (2015b) and Ingalls et al. (2016) for detailed method comparisons.

2.3. Detector Ramp

IRAC observations often display an exponential increase in flux at the beginning of a new observation. The standard procedure for 4.5 $\mu$m observations is to trim the first hour at the start of each observation and subsequent downlinks which reduces the complexity of fits with minimal loss of information on the eclipse shape and time (Lewis et al., 2013). However, we find here that the photometry around the primary and secondary eclipses shows a positive trend. Individual primary and secondary eclipse fits allowing for the correction of a linear trend in the photometry show that the trend is consistent across all epochs and has a slope of $65\pm 6$ ppm/hr (see Online Table). Similarly to Stevenson et al. (2012), we find that this trend is best accounted for with a simple exponential function.

2.4. Pulsations

While fitting HAT-P-2’s photometry with the standard models introduced above, we observed additional signals in the photometry in the forms of oscillations (Figure 1). We account for the oscillations by including sine functions in our global fit—details in Sections 3.4 and 4.1.

2.5. Time-Correlated Noise and Uncertainty Estimates

We find that the standard deviation of our best-fit residuals is a factor of 1.11 higher than the predicted photon noise limit at 4.5 $\mu$m. We expect that this noise is most likely instrumental in nature, and account for it in our error estimates using a scaling factor $\beta_{red}$ for the measurement errobars (Gillon et al., 2010). We find that the average $\beta_{\rm red}$ is 1.3, the maximum values corresponding to a timescale of $\sim$50 minutes.

3. Results

3.1. Orbit-to-Orbit Variability

We find no sign of variability across the eighteen occultations obtained with Spitzer at 4.5 $\mu$m. The occultation depths estimated via individual fits are shown in Figure 2(A) and are all consistent with the global-fit estimate within $\sim 1\sigma$. This implies that the thermal structure of HAT-P-2 b’s 4.5 $\mu$m photosphere around occultation shows no sign of orbit-to-orbit variability. This lack of significant orbit-to-orbit variability is consistent with the predictions presented in Lewis et al. (2014).

The reproductibility of the parameter estimates across eighteen occultations obtained over four years also further emphasizes the reliability of current techniques used for the acquisition and analysis of Warm Spitzer measurements (see also e.g., Wong et al., 2015b, a; Ingalls et al., 2016).

3.2. HAT-P-2’s Orbital Parameters and Ephemeris

We find no sign of orbital evolution from the estimated times of primary and secondary eclipses (Online Table). We derive a new ephemeris from a simultaneous fit of our measured primary and secondary eclipse times, those from the literature (all but the 4.5 $\mu$m eclipse times gathered in Lewis et al., 2013) and HAT-P-2’s radial velocity (RV) measurements111RV measurements obtained by the California Planet Search (CPS) team with the HIRES instrument (Vogt et al., 1994) on Keck using the CPS pipeline (Howard et al., 2009). (Online Table). Our new observations extend the previous baseline by a factor of two and the number of occultations by a factor of five yielding ultra-precise estimates of HAT-P-2 b’s orbital period, midtransit time, orbital eccentricity, and argument of periastron:

[TABLE]

Our global fit of HAT-P-2’s photometry also yield improved constraints on the transit depth (4941$\pm$39 ppm), the occultation depth (971$\pm$21 ppm, which translates into an hemisphere-averaged brightness temperature of 2182$\pm$27 K), the orbital inclination (86.16$\pm$0.26∘), and stellar density (0.434$\pm$0.020 g/cm3). We also derive from the ultra-precise eclipse times the 3-$\sigma$ upper limit on the variation of HAT-P-2 b’s orbital eccentricity and argument of periastron, respectively 0.0012 and 0.90*∘* per year.

3.3. HAT-P-2 b’s Transient Heating

The extensive coverage of HAT-P-2 b’s occultation and post-periastron passage allows us to disentangle further systematics from the planetary flux modulation. The result is a phase curve (Figure 1) whose main difference with Lewis et al. (2013) is a lower minimum—322$\pm$69 ppm, which translates into a hemisphere-averaged temperature of 1327$\pm$106 K. We find an excellent agreement on the timing and amplitude of the planetary flux peak, 5.40$\pm$0.57 hr after periastron passage and 1178$\pm$34 ppm—which translates into a hemisphere-averaged temperature of 2425$\pm$40 K. The timescales for the planetary flux increase and decrease are respectively 5.5$\pm$1.1 hr and 10.3$\pm$1.5 hr. Because of the orbital geometry of HAT-P-2 b with periastron passage occurring midway between transit and occultation, the measured flux increase and decrease timescales are likely an overestimate of the true radiative timescale of HAT-P-2 b’s atmosphere near the 4.5 $\mu$m photosphere, but are consistent with a short atmospheric radiative timescale of a few hours. The results presented here are in excellent agreement with the predictions from three-dimensional general circulation models presented in Lewis et al. (2014).

3.4. HAT-P-2’s Pulsations

Our analysis also reveals distinct pulsations with a period of approximately 87 minutes in HAT-P-2’s photometry (Figure 1). The oscillations are observed during the occultations, which implies that if they are astrophysical in nature they must originate from the host star and not the planet. We verify that the pulsations are not due to a strong instrumental signal in a subset of the AORs which would then be diluted by the inclusion of additional observations without this signal. We first explore this possibility by showing that the oscillations are consistently visible across subsets of AORs. To do so, we randomly picked off the eighteen occultation AORs 25 random sets of 9 AORs, 25 random sets of 5 AORs, and 25 random sets of 3 AORs and included in our model a sine function. We found that all but two of the sets of 3 AORs and one of 5 AORs yield a consistent detection of the pulsation. The consistency of the retrieved pulsation implies that, although the pulsation is not detectable from an individual AOR, the SNR of 5 AORs combined is sufficient to yield a $>2\sigma$ detection. Furthermore, its consistency over these different AOR subsets indicates its coherence. We explore this further by including a sine curve function in the model and allowing its amplitude to vary individually for each occultation AOR. We find that the individual amplitudes scatter around 40 p.p.m., while the significance of the pulsation detection in each individual visit is less than 1 $\sigma$ (Figure 2.(B)). The pulsations are hence present in each individual occultation AORs but its study requires fitting multiple AORs.

The transit photometry, however, shows no sign of such short-period oscillations (Figure 1.(B) and Online Table). Similar individual fits lead to an oscillation amplitude of 3$\pm$15 ppm in transit. The pulsations build coherently when we combine eighteen distinct epochs of data, which implies that the pulsation is a harmonic of the planet orbital frequency, as shown by the periodogram of the residuals (Figure 3). The two most significant peaks correspond to HAT-P-2 b’s 79th and 91st orbital harmonics, which are found to interfer constructively around occultations but destructively around transits as a result of the relative phase of the two harmonics. The pulsations are therefore astrophysical in nature unless the instrumental systematics appear to be harmonics of HAT-P-2 b’s orbital frequency phased in such a way that they build coherently over all the different epochs. This scenario would require the modulation of the detector gain/noise or the PSF position/shape222The PSF shape can be affected by structural changes of the instrument (e.g., due to heating). follows a repeated pattern of oscillatory changes that are not only harmonics of the planet’s orbital frequency, but also constructively phased. We use the noise pixel parameter Mighell (2005); Lewis et al. (2013) as a proxy for any changes in the PSF position and shape. We use the “sky” background as a proxy for gain variations and electronic noise. We find that the periodograms of the PSF position (Figures 4(B) and (C)) and of the noise-pixel parameter (Figure 4(D)) show no significant peak in the period range related to the pulsations while showing a significant signal at Spitzer’s pointing oscillation period. Similarly, the periodogram of the “sky” background shows no specific peak around the 79th and 91st planetary harmonics as revealed in the photometry, ruling out the scenario of constructively-phased and adequately-modulated instrumental systematics.

We therefore conclude that the pulsations are stellar and not instrumental in nature, and we account for them by including two sine functions in the final version of our global fits. We find that the pulsations have respective amplitudes and frequencies of 35$\pm$7 and 28$\pm$6ppm and 162.335$\pm$0.015 and 186.976$\pm$0.013 $\mu$Hz—respectively 79.006$\pm$0.007 and 91.006$\pm$0.007 times the orbital frequency.

3.5. HAT-P-2’s Radial Velocity

HAT-P-2’s radial velocity (RV) measurements provide a complementary perspective to Spitzer’s. In addition to showing a high level of stellar jitter ($\sim 36$m/s, discussed in Section 4.2), the RV measurements suggest that HAT-P-2 b’s orbit is evolving in a way that is inconsistent with our previous fits to the photometry alone. Figure 5 shows that an independent analysis of the first half of HAT-P-2’s RV data (obtained prior to BJD 2454604) yields values for $e$ and $\omega$ that are inconsistent at the 4.5-$\sigma$ level with those from a fit of the second half of the data (obtained after BJD 2455466). This translates into respective variations of $e$ and $\omega$ of 8.9$\pm$2.8E*-4* and 0.91$\pm$0.31*∘* per year, which is inconsistent with the limits derived from the primary and secondary eclipse times alone.

4. Discussion

4.1. The Origin of HAT-P-2’s Pulsations

The exact correspondence of the stellar pulsation frequencies with harmonics of the planet’s orbital frequency implies a connection between the two. Two scenarios are possible; either the pulsations are altering the planet’s orbit or the planet is causing the pulsation. Mode-planet gravitational interactions could synchronize the planet’s orbital frequency to an integer harmonic of a mode oscillation period, analogous to two weakly coupled oscillators that synchronize in the presence of weak damping. However, the detection of multiple harmonics of the planet’s orbital frequency rules out this scenario.

We next consider the hypothesis that the observed stellar pulsations are induced by the orbiting planet. Tidally excited pulsations have been previously observed in several eccentric stellar binaries (Welsh et al., 2011; Thompson et al., 2012; Beck et al., 2014) known as “heartbeat” stars. The characteristic feature of a tidally excited pulsation is that its frequency is an exact integer harmonic of the orbital frequency, because it arises from a resonantly forced stellar pulsation mode (Derekas et al., 2011; Fuller & Lai, 2012; Burkart et al., 2012; O’Leary & Burkart, 2014; Smullen & Kobulnicky, 2015).

In order to understand the nature of the detected pulsations, we calculate the stellar response to tidal forcing. We first calculate the non-adiabatic stellar pulsation mode spectrum of HAT-P-2 using the MESA evolution code (Paxton et al., 2011, 2013) to describe the stellar evolution and the GYRE pulsation code (Townsend & Teitler, 2013) to compute the pulsation modes. We then calculate the response of each pulsation mode to the tidal forcing, and compute the amplitude and frequencies of each tidally excited pulsation. Our models indicate that although HAT-P-2 b can in principle create luminosity fluctuations of this amplitude in its host, we expect these pulsations to have much lower frequencies, in the vicinity of twice the periastron orbital frequency (Hut, 1981)—approximately $10~{}\mu$Hz (period of approximately 28 hrs). Our models are unable to reproduce a tidally excited pulsation at the 79th or 91th orbital harmonics at the observed amplitude; the strength of the forcing at these harmonics is many orders of magnitude weaker than at the tidal forcing peak near the 6th orbital harmonic.

Although HAT-P-2 lies near the extreme cool ends of the $\gamma$-Doradus and $\delta$-Scuti instability strips ($T_{eff}\sim$ 6300K, log10g$\sim$4.16, $R\sim$ 1.54 $R_{Sun}$, Uytterhoeven et al., 2011; Balona et al., 2015), it shows no evidence for the large amplitude ($\sim$mmag) pulsations typically observed in these pulsators. Nonetheless, it is possible that the observed pulsations correspond to low-amplitude $\delta$-Scuti pulsation modes, as our non-adiabatic pulsation calculations indicate that $l\!=\!1$ and $l\!=\!2$ pulsation modes are unstable near the observed frequencies of $f\!\sim$175 $\mu$Hz, although we caution that mode growth rates–the parameter indicating stability of a pulsation mode–may be altered by a more realistic treatment of convective flux perturbations. In our models, the unstable modes correspond to low-order ($n\!<\!3$) mixed pressure-gravity modes. In principle, these modes can couple strongly with HAT-P-2 b because they produce relatively large gravitational perturbations (i.e., they are similar to fundamental modes). However, our models suggest that they have frequencies that are too large to resonantly interact with the planet.

The failure of our models to explain the observed high frequency pulsations suggests that current tidal theories may be incomplete. One tentative possibility is that non-linear effects are important. The difference between the observed pulsations is $\simeq$12 times the orbital frequency where resonant interactions with the planet can occur. This sort of non-linear mode splitting at orbital harmonics has been observed in stellar systems (see e.g., Hambleton et al., 2013) and could occur in the HAT-P-2 system as well.

4.2. Tidally-Induced Pulsations and RV Measurements

Stellar pulsations cause RV variations of the stellar photosphere (e.g., Willems & Aerts, 2002; Welsh et al., 2011). The RV amplitude of the photospheric motion due to a pressure mode is $\Delta v\sim 2\pi f\Delta R$, where $\Delta R$ is the mode surface displacement. Our non-adiabatic pulsation calculations indicate that the stellar surface displacements and luminosity variations are approximately related by $\Delta R/R\sim 2\Delta L/L$ for modes near the observed frequencies. The observed photometric amplitudes imply $\Delta v\sim 60\,{\rm m/s}$, consistent with HAT-P-2’s RV jitter. Mode identification would be required for a more precise calculation, but we posit that HAT-P-2’s RV jitter and HAT-P-2 b’s apparent orbital evolution in the RV data is mainly produced by the pulsations.

5. Conclusion

Our study provides a new perspective on the planet-star interactions in HAT-P-2’s system. The extensive coverage of the system at 4.5 $\mu$m allows us to better disentangle the instrumental systematic from the planet’s transient heating, reconciling observations and atmospheric models. The photometric observations also show no sign of orbit-to-orbit variability nor of orbital evolution but reveals high-frequency low-amplitude stellar pulsations that correspond to harmonics of the planet’s orbital frequency, supporting their tidal origin. Current stellar models are however unable to reproduce these pulsations. HAT-P-2’s RV measurements exhibit a high level of jitter and support the orbital evolution of HAT-P-2 b inconsistent with the ultra-precise eclipse times. The inability of current stellar models to reproduce the observed pulsations and the exotic behavior of HAT-P-2’s RV indicate that additional observations and theoretical developments are required to understand the processes at play in this system.

Future missions such as TESS, PLATO, and CHEOPS will provide further insights into the nature of HAT-P-2’s pulsations and its interaction with its eccentric companion. The detection of multiple unexpected high-frequency pulsations as HAT-P-2’s could be used to indirectly hint at the presence of a companion–regardless of their orbital inclination, to be later confirmed with traditional techniques such as direct imaging or RV.

This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA. Support for this work was provided by JPL/Caltech. J.d.W. was further supported by the WBI (Wallonie-Bruxelles International) under the WBI-World Excellence Fellowship Program. A.S. performed this work in part under contract with the California Institute of Technology (Caltech) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. V.A. is funded by the Stellar Astrophysics Centre via the Danish National Research Foundation (Grant DNRF106). The research was supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler) funded by the European Research Council (Grant agreement no.: 267864). Radial velocity data presented herein were obtained at the W. M. Keck Observatory using time granted by the California Institute of Technology, UC Berkeley, and the University of Hawaii. We thank the observers who contributed to the measurements reported here and acknowledge the efforts of the Keck Observatory staff. We extend special thanks to those of Hawaiian ancestry on whose sacred mountain of Mauna Kea we are privileged to be guests. J.d.W. thanks T. Rogers, V. Stamenković, A. Zsom, B.-O. Demory, M. Gillon, S. Seager, and V. Van Grootel for useful discussions during the preparation of this manuscript.

6. Online Table