The PFS view of TOI-677 b: A spin-orbit aligned warm Jupiter in a dynamically hot system¹¹1This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory (LCO), Chile.

In contrast to the alignment of the solar spin and the planetary orbits in our solar system (Souami & Souchay, 2012), exoplanets have been discovered on inclined, polar (e.g. Anderson et al., 2018; Addison et al., 2018; Bourrier et al., 2020; Albrecht et al., 2021; Watanabe et al., 2022) or even retrograde (e.g. Neveu-VanMalle et al., 2014; Temple et al., 2017, 2019) orbits around their host stars. The degree of the spin-orbit (mis)alignment of a planetary system is quantified by the "stellar obliquity", which is the angle between the planetary orbital angular momentum vector and the stellar spin angular momentum vector. The obliquity of a system is sculpted by both its degree of and mechanism for dynamical excitation, as well as subsequent tidal effects (see Ogilvie (2014) for a review of tidal dissipation). Obliquity excitation mechanisms fall into three categories (Albrecht et al., 2022): primordial misalignment of the proto-planetary disk (Matsakos & Königl, 2017; Takaishi et al., 2020; Romanova et al., 2021), post-formation misalignment (Anderson et al., 2016; Petrovich & Tremaine, 2016; Anderson & Lai, 2018; Teyssandier et al., 2019; Beaugé & Nesvorný, 2012), and changes in the stellar spin that are not related to planet formation (Rogers et al., 2012, 2013).

Stellar obliquities are commonly constrained using the Rossiter-McLaughlin effect (Rossiter, 1924; McLaughlin, 1924), which enables measurements of the sky-projected spin-orbit angle $\lambda$. A planet blocks out blue-shifted or red-shifted components of the rotating host star’s light at different phases during its transit, resulting in a deviation from the overarching Doppler reflex motion in the host star’s spectrum (Queloz et al., 2000). High-resolution spectroscopic observations across the transit can be leveraged to measure the Rossiter-McLaughlin effect.

To date, measurements of the stellar obliquity have been severely biased toward systems hosting a massive and close-orbiting ($a/R_{\star}\lesssim 11$) planet, which are referred to as “hot Jupiters”, due to their frequent, short, and deep transits (see Albrecht et al. (2022) for a review of existing constraints). Only a handful of wider-orbiting “warm Jupiter” systems ($a/R_{\star}\gtrsim 11$) have precise spin-orbit constraints due to their low transit probabilities, long transit durations, and infrequent transit events. However, the orbital configurations of warm-Jupiter systems can play an important role in constraining the prevalence of competing planet formation and evolution pathways (Winn & Fabrycky, 2015; Dawson & Johnson, 2018).

A comparison between the orbital configurations of close-orbiting hot Jupiters and wide-orbiting warm Jupiters (such as the orbital eccentricity distribution, the companion rate, and so on) can shed light on the prevalence of different formation mechanisms for these two types of planets. The possible formation channels for hot and warm Jupiters are directly comparable: each class of planets could potentially arise through in situ formation, disk migration, or high-eccentricity migration. Previous work has shown that high-eccentricity tidal migration triggered by planet-planet or planet-star Kozai-Lidov cycles (KL; von Zeipel, 1910; Lidov, 1962; Kozai, 1962; Wu & Murray, 2003; Naoz et al., 2011, 2012; Naoz, 2016) is a promising channel to account for the observed properties of hot Jupiters on a population level (Winn & Fabrycky, 2015; Dawson & Johnson, 2018; Rice et al., 2022).

However, it is not yet clear how warm Jupiters fit into this emerging picture. Warm Jupiters, by contrast to hot Jupiters, show a high occurrence rate of nearby planetary companions (Huang et al., 2016; Wu et al., 2023). Furthermore, previous work has proposed that the warm Jupiter eccentricity distribution contains both a low-eccentricity component and a roughly uniform component (Dawson & Johnson, 2018; Petrovich & Tremaine, 2016). In situ formation or disk migration could account for the low-eccentricity component of this distribution, producing warm Jupiters that cannot be excited by subsequent scattering (Petrovich et al., 2014). A separate mechanism is needed to reproduce the uniform eccentricity distribution component, which is also difficult to reproduce in the high-eccentricity migration framework as warm Jupiters are tidally detached from their host stars.

A comparison of the stellar obliquity distributions of hot and warm Jupiters, particularly around hot stars, can help to distinguish the prevalence of each mechanism by disentangling the stage at which misalignments arise (Triaud, A. H. M. J. et al., 2010; Hamer & Schlaufman, 2022; Attia et al., 2023). Hot Jupiters on tight orbits are strongly affected by tidal interactions with their host stars, such that the outer layer of the star may realign over time (Winn et al., 2010; Albrecht et al., 2012). Previous studies of hot Jupiter stellar obliquities exhibit evidence suggestive of tidal realignment (Albrecht et al., 2012): hot stars hosting hot Jupiters span a wider range of obliquities than their cool star counterparts (Schlaufman, 2010; Winn et al., 2010). The transition occurs at the Kraft break ($T_{\rm eff}\sim 6100$ K), the dividing point for whether the stellar envelope is convection-dominated or radiation-dominated (Kraft, 1967).

By contrast, warm Jupiters are expected to be “tidally detached” – that is, they are relatively unaffected by tidal dissipation within the age of the system, such that they offer valuable insights into the primordial obliquity distribution at the time of planet formation (Zhou et al., 2020; Rice et al., 2021). Rice et al. (2022a) suggests that small spin–orbit angles observed for warm Jupiters around single stars may indicate that protoplanetary disks tend to be aligned at the time of gas dispersal, while hot Jupiters are misaligned through dynamical interactions after the disk has dispersed. A larger sample of warm Jupiters with precisely measured spin-orbit orientations – particularly those around hot stars, which have relatively few such measurements to date – will enable us to examine the robustness of this preliminary statistical result and to further inform the key hot vs. warm Jupiter obliquity excitation mechanism(s).

The precise characterization of individual warm Jupiter orbital configurations is critical to inform competing models for the formation of warm Jupiters more generally. TOI-677 (TIC 280206394) was first identified as a planet-hosting candidate by the TESS mission (Ricker et al., 2015) and was then characterized by Jordán et al. (2020) as a bright ($V=9.8$), hot ($T_{\rm eff}=6295\pm 77$ K) late-F star hosting a wide-orbiting eccentric ($e=0.435\pm 0.024$) gas giant TOI-677 b. Recently, Sedaghati et al. (2023) reported a sky-projected obliquity measurement ($\lambda=0.3\pm 1.3^{\circ}$) for this target over a single transit with the ESPRESSO (Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations; Pepe et al., 2021) spectrograph.

We present a new, independent Rossiter–McLaughlin measurement across one transit of TOI-677 b with the Carnegie Planet Finder Spectrograph (PFS; Crane et al., 2006, 2008, 2010) on the 6.5m Magellan Clay telescope. This observation was obtained as part of the Stellar Obliquities in Long-period Exoplanet Systems (SOLES) survey (Rice et al., 2021; Wang et al., 2022; Rice et al., 2022b, 2023a; Hixenbaugh et al., 2023; Dong et al., 2023; Wright et al., 2023; Rice et al., 2023b; Lubin et al., 2023), and it represents the tenth published result from this program.

We examine our new measurement, together with archival observations and data from Jordán et al. (2020) and Sedaghati et al. (2023), to refine the orbital parameters and the stellar obliquity of the TOI-677 system. By combining two independent RM datasets, each from high-precision spectrographs on 6-8m class telescopes, we derive one of the most precisely constrained sky-projected spin-orbit measurements to date: an important advance toward inferring precise orbital geometries and understanding the true dispersion of exoplanet orbital distributions. We find that TOI-677 b is well aligned with its host star, with $\lambda={3.2^{+1.6}_{-1.5}}^{\circ}$.

We describe the newly analyzed observations in Section 2. In Section 3, we describe the joint analysis of photometry and RV data to get the projected stellar obliquity $\lambda$. We discuss the implications of this measurement in Section 4 and summarize our findings in Section 5.

We carried out three independent joint fits using in-transit RV data only from PFS, only from ESPRESSO, and from both telescopes together. Each of these fits included photometric data from TESS and LCO (see Section 2), as well as archival photometric data from SSMKO (see the second panel in Figure 1) and archival RV data from the FEROS, Coralie, CHIRON, NRES, and Minerva-Australis spectrographs. The in-transit PFS RV data are provided in Table 1, and the in-transit ESPRESSO RV data are adopted from Table 4 in Sedaghati et al. (2023). The SSMKO photometry data and all other archival RV data are drawn from Tables 2 and 4 in Jordán et al. (2020).

Our fits each used allesfitter (Günther & Daylan, 2021), which is a powerful tool for jointly modeling photometric and RV data. Allesfitter constructs a Bayesian inference framework that unites the ellc (light curve and RV models; Maxted (2016)) and emcee (Markov Chain Monte Carlo (MCMC) sampling; Foreman-Mackey et al. (2013a)) Python packages, building a joint model of photometry and radial velocities to fit the Rossiter-McLaughlin effect.

All fitted parameters listed in Table 4 were allowed to vary and were initialized with uniform priors $\mathcal{U}(a;b)$, with a lower bound $a$ and an upper bound $b$. $R_{\rm b}/R_{\star}$ is the planet-to-star radius ratio; $(R_{\star}+R_{\rm b})/a_{\rm b}$ is the sum of radii divided by orbital semimajor axis; $\cos{i_{\rm b}}$ is the cosine of the orbital inclination; $T_{\rm 0;b}$ is the mid-transit epoch; $P_{\rm b}$ is the orbital period; $K_{\rm b}$ is the RV semi-amplitude; $\sqrt{e}\cos{\omega}_{\rm b}$ and $\sqrt{e}\sin{\omega}_{\rm b}$ are the eccentricity parameters; $v\sin i_{\star}$ is the stellar rotation velocity projected on the line of sight; $\lambda$ is the sky-projected stellar obliquity; $q_{1}$ and $q_{2}$ are the quadratic limb darkening coefficients (Kipping, 2013) treated separately for all instruments that captured transit signals (TESS, SSMKO, LCO 1m, LCO 0.4m, PFS, and ESPRESSO). The initial values for $R_{\rm b}/R_{\star}$, $(R_{\star}+R_{\rm b})/a_{\rm b}$, $\cos{i_{\rm b}}$, $T_{\rm 0;b}$, $P_{\rm b}$, $K_{\rm b}$, $\sqrt{e}\cos{\omega}_{\rm b}$, and $\sqrt{e}\sin{\omega}_{\rm b}$ were adopted from Jordán et al. (2020).

The sky-projected spin-orbit angle $\lambda$ was initialized as $0^{\circ}$ and was allowed to vary between $-180^{\circ}$ and $180^{\circ}$. The two limb-darkening coefficients $q_{1}$ and $q_{2}$ were initialized with values of 0.5 and were only allowed to vary between 0 and 1. Jitter terms were modeled separately for each instrument and were added in quadrature to the formal uncertainties. The baseline model was evaluated separately for photometric and radial velocity data. We allowed for a constant offset with priors bounded between -0.1 and 0.1 in relative flux units for photometric data. For RV data, we adopted a linear baseline model, as previous work has identified a significant long-term trend in the radial velocities which could be caused by an outer companion (Jordán et al., 2020). We assigned a general linear slope for the archival radial velocities and different linear slopes for the PFS and ESPRESSO datasets. The constant RV offsets were different for individual spectrographs and were allowed to vary between -1 km/s and 1 km/s.

Stellar parameter priors are needed for the derived parameters, both listed in Table 4. We adopted Gaussian priors for the host star’s mass and radius drawn from Jordán et al. (2020), where they were derived from a combination of spectroscopy, spectral energy distribution (SED), and isochrone fits. The derived parameters are the planetary radius ($R_{\rm b}$), planetary mass ($M_{\rm b}$), planetary semi-major axis over host star radius ($a_{\rm b}/R_{\star}$), impact parameter ($b$), total transit duration ($T_{\rm 14}$), inclination of the planetary orbit ($i_{\rm b}$), eccentricity ($e_{\rm b}$), argument of periastron ($\omega_{\rm b}$), semi-major axis ($a_{\rm b}$), and the re-parameterized quadratic limb darkening coefficients $u_{1}$ and $u_{2}$ for TESS, SSMKO, LCO 1m, LCO 0.4m, PFS, and ESPRESSO.

We ran an affine-invariant MCMC analysis for each of our three joint fits, with 150 walkers to sample the posterior distributions of all model parameters. We ensured that each chain was fully converged by running all Markov chains to over 30 times their autocorrelation length, which corresponded to a minimum of 250,000 accepted steps per walker.

The values and 1-$\sigma$ uncertainties of fitted parameters are listed in Table 4. The best-fit joint models are shown in Figure 2, together with the values and uncertainties for each $\lambda$ measurement. The jitter term for each instrument has been incorporated into the error bar of the plotted data points.

The sky-projected spin-orbit angles derived from PFS, ESPRESSO, and the combined fit are $\lambda=7.9^{+2.4}_{-2.2}\,{}^{\circ}$, $\lambda=0.9^{+1.6}_{-1.5}\,{}^{\circ}$, and $\lambda=3.2^{+1.6}_{-1.5}\,{}^{\circ}$ respectively. These values are consistent with each other within 2-$\sigma$, and our final, combined fit measurement is also consistent with the result from Sedaghati et al. (2023) within 2-$\sigma$. TESS out-of-transit light curves of TOI-677 are nearly flat and bear no significant periodicities that could be attributed to the stellar spin, preventing a further derivation of the true 3D spin-orbit angle $\psi$.

While the PFS measurement alone is suggestive of a solar-system-like stellar obliquity ($6\,^{\circ}$ away from alignment; Souami & Souchay (2012)), the ESPRESSO measurement alone is more indicative of exact alignment. Our final result, which combines the two, lies at an intermediate value between these two possibilities. The 2-$\sigma$ discrepancy between $\lambda$ values from the PFS and ESPRESSO measurements is discussed in detail in Section 4.3.

We have presented a new Rossiter-McLaughlin measurement of the tidally-detached warm Jupiter TOI-677 b from PFS/Magellan. We combined this new measurement with archival data, including a recently published Rossiter-McLaughlin measurement from the ESPRESSO spectrograph (Sedaghati et al., 2023), to derive a self-consistent set of updated physical parameters for TOI-677 b. Our independent observation corroborates previous findings from Sedaghati et al. (2023) that TOI-677 b exhibits a high eccentricity and yet a surprisingly low sky-projected spin-orbit angle, with values $e=0.460^{+0.019}_{-0.018}$ and $\lambda=3.2^{+1.6}_{-1.5}\,{}^{\circ}$ from our combined fit.

Several formation pathways for TOI-677 b were examined through this work, each aiming to preserve the planet’s low observed sky-projected stellar obliquity while reproducing its high eccentricity. Ultimately, we find that CHEM is disfavored by the measured properties of the outer brown dwarf companion, and KL oscillations followed by tidal dissipation, while feasible, would require a low-likelihood chance alignment due to nodal precession from the outer companion. As a result, we conclude hat TOI-677 b most likely had its eccentricity excited through disk-planet interactions. Further monitoring of the outer companion – in particular, improved constraints on its mass and mutual inclination relative to TOI-677 b – would help to confirm this conjecture.

Our results expand upon previous findings from Rice et al. (2022b), showing that warm Jupiters in single-star systems continue to exhibit minimal deviation from spin-orbit alignment despite an emerging dispersion in orbital eccentricity and host star type. Ultimately, a larger population of warm Jupiters with precise spin-orbit measurements, spanning a wider range of orbital eccentricities and host star types, will be necessary to more fully demonstrate the range of orbital configurations spanned by warm Jupiters and the corresponding implications for their formation.

Q.H. is very grateful to Zhang Yisong at the Physics Department of Tsinghua University for his support in the discussion concerning the Kozai-Lidov oscillations. Q.H. thanks Prof. Zhu Wei from the Astronomy Department of Tsinghua University for his advice on the discussion sections. M.R. acknowledges support from Heising-Simons Foundation Grants #2023-4478 and #2023-4655, NASA grant GR122985/AWD0011072, and Oracle for Research grant No. CPQ-3033929. S.W. acknowledges support from Heising-Simons Foundation Grant #2023-4050.

This work has benefited from the use of the Grace computing cluster at the Yale Center for Research Computing (YCRC). This work makes use of observations from the Las Cumbres Observatory global telescope (LCOGT) network. Part of the LCOGT telescope time was granted by NOIRLab through the Mid-Scale Innovations Program (MSIP). MSIP is funded by NSF. This paper is based on observations made with the Las Cumbres Observatory’s education network telescopes that were upgraded through generous support from the Gordon and Betty Moore Foundation. This research has made use of the Exoplanet Follow-up Observation Program (ExoFOP; DOI: http://dx.doi.org/10.26134/ExoFOP5 (catalog 10.26134/ExoFOP5)) website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of the NASA Exoplanet Archive (2023) (DOI: http://dx.doi.org/10.26133/NEA12 (catalog 10.26133/NEA12)), which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This paper includes data collected by the TESS mission (MAST Team, 2021) (DOI: http://dx.doi.org/10.17909/t9-nmc8-f686 (catalog 10.17909/t9-nmc8-f686)). Funding for the TESS mission is provided by NASA’s Science Mission Directorate. K.A.C. acknowledges support from the TESS mission via subaward s3449 from MIT.

Magellan II: PFS, LCOGT CTIO 1m ($\times 2$) and 0.4m ($\times 2$), TEPCat