The stellar obliquity distribution of warmJupiter systems is crucial for constraining the dynamical history of Jovian exoplanets as the warm Jupiters tidal detachment likely preserves their primordial obliquity. However the sample size of warmJupiter systems with measured stellar obliquities has historically been limited compared to that of hot Jupiters particularly in hotstar systems. In this work we present newly obtained skyprojected stellar obliquity measurements for the warmJupiter systems TOI559 TOI2025 TOI2031 TOI2485 TOI2524 and TOI3972 derived from the RossiterMcLaughlin effect and show that all six systems display alignment with a median measurement uncertainty of 13. Combining these new measurements with the set of previously reported stellar obliquity measurements our analysis reveals that singlestar warmJupiter systems tend to be aligned even around hot stellar hosts. This alignment exhibits a 3.4 deviation from the T SUBeffSUB dependency observed in hotJupiter systems where planets around cool stars tend to be aligned while those orbiting hot stars show considerable misalignment. The current distribution of spinorbit measurements for Jovian exoplanets indicates that misalignments are neither universal nor primordial phenomena affecting all types of planets. The absence of misalignments in singlestar warmJupiter systems further implies that many hot Jupiters by contrast have experienced a dynamically violent history. This Letter includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory Chile.
['Planetary alignment', 'Exoplanet dynamics', 'Exoplanet evolution', 'Star-planet interactions', 'Exoplanets', 'Planetary theory', 'Exoplanet systems', 'Exoplanet astronomy', 'Planetary dynamics', 'Hot Jupiters', '1243', '490', '491', '2177', '498', '1258', '484', '486', '2173', '753', 'Astrophysics - Earth and Planetary Astrophysics']
Singlestar WarmJupiter Systems Tend to Be Aligned Even around Hot Stellar Hosts No T SUBeffSUB Dependency
{'Single-Star Warm-Jupiter Systems Tend to Be Aligned, Even Around Hot Stellar Hosts: No T eff -λ Dependency ∗': "Xian-Yu Wang , 1 Malena Rice , 2 Songhu Wang , 1 Shubham Kanodia , 3 Fei Dai , 4 Sarah E. Logsdon , 5 Heidi Schweiker , 5 Johanna K. Teske , 3, 6 R. Paul Butler , 3 Jeffrey D. Crane , 6 Stephen Shectman , 6 Samuel N. Quinn , 7 Veselin Kostov, 8, 9 Hugh P. Osborn , 10, 11 Robert F. Goeke , 10 Jason D. Eastman , 7 Avi Shporer , 10 David Rapetti , 12, 13 Karen A. Collins , 7 Cristilyn N. Watkins , 14 Howard M. Relles , 14 George R. Ricker , 10 Sara Seager , 10, 15, 16 Joshua N. Winn , 17 and Jon M. Jenkins 12  \n1  \nDepartment of Astronomy, Indiana University, 727 East 3rd Street, Bloomington, IN 47405-7105, USA  \n2  \nDepartment of Astronomy, Yale University, 219 Prospect Street, New Haven, CT 06511, USA  \nCarnegie Institution for Science, Earth & Planets Laboratory, 5241 Broad Branch Road NW, Washington, DC 20015, USA  \n4 Institute for Astronomy, University of Hawai'i, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA  \n5 NSF's National Optical-Infrared Astronomy Research Laboratory, 950 N. Cherry Ave., Tucson, AZ 85719, USA  \n6 The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA  \n7 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  \n8  \nNASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA  \n9 SETI Institute, 189 Bernardo Ave, Suite 200, Mountain View, CA 94043, USA  \n10 Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  \n11 Physics Institute, Universitat Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland  \n12 NASA Ames Research Center, Moffett Field, CA 94035, USA  \n13 Research Institute for Advanced Computer Science, Universities Space Research Association, Washington, DC 20024, USA 14 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA 15 Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 16 Department of Aeronautics and Astronautics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 17 Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA", 'ABSTRACT': "The stellar obliquity distribution of warm-Jupiter systems is crucial for constraining the dynamical history of Jovian exoplanets, as the warm Jupiters' tidal detachment likely preserves their primordial obliquity. However, the sample size of warm-Jupiter systems with measured stellar obliquities has historically been limited compared to that of hot Jupiters, particularly in hot-star systems. In this work, we present newly obtained sky-projected stellar obliquity measurements for warmJupiter systems, TOI-559, TOI-2025, TOI-2031, TOI-2485, TOI-2524, and TOI-3972, derived from the Rossiter-McLaughlin effect, and show that all six systems display alignment with a median measurement uncertainty of 13 · . Combining these new measurements with the set of previously reported stellar obliquity measurements, our analysis reveals that single-star warm-Jupiter systems tend to be aligned, even around hot stellar hosts. This alignment exhibits a 3.4σ deviation from the T eff -λ dependency observed in hot-Jupiter systems, where planets around cool stars tend to be aligned, while those orbiting hot stars show considerable misalignment. The current distribution of spin-orbit measurements for Jovian exoplanets indicates that misalignments are neither universal nor primordial phenomena affecting all types of planets. The absence of misalignments in single-star warm-Jupiter systems further implies that many hot Jupiters, by contrast, have experienced a dynamically violent history.  \nCorresponding author: Songhu Wang  \nsw121@iu.edu  \n- ∗ This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile.  \n3  \nKeywords: planetary alignment (1243), exoplanet dynamics (490), star-planet interactions (2177), exoplanets (498), planetary theory (1258), exoplanet systems (484)", '1. INTRODUCTION': "The Solar System planets lie on near-coplanar orbits that are close to alignment (within ∼ 6 · ) with the Sun's equator, offering a seemingly coherent framework for planetary formation (Kant 1755; de Laplace 1796). In contrast, the landscape of exoplanetary systems is remarkably varied, showing a puzzling range of spinorbit orientations for hot Jupiters (see Winn & Fabrycky 2015; Triaud 2018; Albrecht et al. 2022 and references within). The origins of these orbital misalignments have sparked a contentious debate: are misalignments a unique feature of hot-Jupiter systems due to their specific formation processes and dynamical histories, including planet-planet scattering (Rasio & Ford 1996; Beaug'e & Nesvorn'y 2012), Kozai-Lidov oscillations (Wu &Murray 2003; Fabrycky & Tremaine 2007; Naoz 2016), and secular interactions (Wu & Lithwick 2011; Petrovich 2015a)? Or, do they instead hint at more ubiquitous processes, such as chaotic accretion (Bate et al. 2010; Thies et al. 2011; Fielding et al. 2015; Bate 2018), magnetic warping (Foucart & Lai 2011; Lai et al. 2011; Romanova et al. 2013, 2021), tilting by a companion star (Borderies et al. 1984; Lubow & Ogilvie 2000; Batygin 2012; Matsakos & Konigl 2017), or internal-gravitywave-induced tumbling (Lai 2012; Lin & Ogilvie 2017; Damiani & Mathis 2018), that may affect a wide array of planetary systems?  \nThe relationship between the spin-orbit orientation of a system and the stellar host's properties adds another layer to the mystery. Previous studies have demonstrated that hot Jupiters around hot stars, which possess thin convective envelopes and experience rapid rotation, span a wide range of spin-orbit angles, while those around cool stars tend to be aligned (Schlaufman 2010; Winn et al. 2010). Could this trend indicate that tidal interactions have played a significant role in realigning the cool-star systems (Albrecht et al. 2012; Rogers & Lin 2013; Xue et al. 2014; Valsecchi & Rasio 2014; Li & Winn 2016; Anderson et al. 2021; Wang et al. 2021; Rice et al. 2022a; Spalding & Winn 2022; Zanazzi et al. 2024)? Or, could this trend arise due to hot-star systems being dynamically 'hotter' - that is, could it be that these systems are more likely to form multi-giant planet systems, subsequently leading to inclination excitation from post-disk dynamical interactions (Wu et al. 2023)?  \nWarm Jupiters, defined in this work as wide-orbiting (11 ≤ a/R ∗ ≤ 200) Jovian-mass (0 . 3 M J ≤ M P ≤ 13 M J ) planets 1 , offer a compelling lens through which to scrutinize these questions. The comparatively wider orbital separations of warm Jupiters make them less prone to tidal realignment than hot Jupiters - which fall within the same mass range, but lie within a/R ∗ < 11 - such that they do not suffer from the same tidal realignment degeneracy that plagues interpretations of aligned hot Jupiters (Rice et al. 2021). Additionally, warm Jupiters seem less likely to have undergone high-eccentricity migration - a leading theory for hot Jupiter migration (see Dawson & Johnson 2018 and references within) making them even more valuable for teasing apart the origins and evolution of spin-orbit misalignment.  \nHistorically, the scarcity of spin-orbit measurements for warm Jupiters has stemmed from observational challenges, including the day/night cycle and weather limitations of ground-based transit surveys (e.g., SuperWASP, Pollacco et al. 2006; HATNet, Bakos et al. 2004; HATSouth, Bakos et al. 2013; TrES, Alonso et al. 2004; KELT, Pepper et al. 2007; XO, McCullough et al. 2005 and, CSTAR, Wang et al. 2014) and the Kepler mission's 'long stare' observing strategy that identified transiting planets primarily around fainter host stars (Borucki et al. 2010), which are not conducive to precise follow-up studies of wide-orbiting planets with long transits. However, this landscape has been transformed by the advent of the K2 (Howell et al. 2014) and TESS (Ricker et al. 2015) missions, which have successfully identified warm Jupiters around brighter host stars across the sky (e.g., K2-99 b, Smith et al. 2017; K2-114 b and K2-115 b, Shporer et al. 2017; K2-140 b, Giles et al. 2018; K2-232 b, Brahm et al. 2018; TOI481 b and TOI-892 b, Brahm et al. 2020; TOI-558 b and TOI-559 b, Ikwut-Ukwa et al. 2022, TOI-1478 b,  \nTable 1. Log of Observations", 'Ground-Based Photometric Follow-Up Observations': 'Rodriguez et al. 2021, and 55 warm Jupiter candidates listed in Dong et al. 2021).  \nIn this context, 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; Hu et al. 2024; Radzom et al. 2024; Ferreira et al. 2024) was initiated to broaden the sample of Rossiter-McLaughlin (RM) measurements, especially for planets with wide orbital separations. This paper represents the most recent contributions from the SOLES survey, adding six new spinorbit angle measurements for warm Jupiters (TOI-559 b, TOI-2025 b, TOI-2031 b, TOI-2485 b, TOI-2524 b, and TOI-3972 b 2 ) that orbit hosts spanning a range of stellar types. Our findings reinforce the recent evidence that warm Jupiters in single-star systems are preferentially aligned relative to hot Jupiters, as first demonstrated by Rice et al. (2022b). We crucially extend this observation to demonstrate the same trend for warm Jupiters around hot stars, showing a 3.4σ confidence difference with the T eff -λ dependency observed in hotJupiter systems.', '2.1. Spectroscopy Observation': "2.1.1. PFS observation  \nThe transit spectroscopy sequence across the transit of TOI-559 b was conducted during UT September 26, 2023, using the Carnegie Planet Finder Spectrograph (PFS, Crane et al. 2006; Crane et al. 2008, 2010) on the 6.5 m Magellan Clay telescope at Las Campanas Observatory (LCO), Chile. PFS, which has been on-sky since 2010, covers wavelengths from 391 to 734 nm with a default resolving power of ∼ 127,000 (1 × 2 binning and 0.3 '' slit). In our case, due to the faint magnitude of the star, we used 3 × 3 binning, resulting in a resolving power of ∼ 110,000. Our observing sequence provided a total of 15 RVs each with an exposure time of 1520 seconds, obtained with a moon phase of 79% and a 76 · separation between the moon and TOI-559. Seeing ranged from 1 . 4 -2 '' . We also obtained an iodine-free template observation with PFS, which consisted of three 1000second exposures during UT November 11, 2023 with seeing 0 . 55 '' .  \nThe spectral data reduction and radial velocity (RV) extraction for PFS spectra were performed using a customized pipeline described in Butler et al. (1996).", '2.1.2. NEID observation': 'The transit spectroscopy observations of TOI-2025 b, TOI-2031 b, TOI-2485 b, TOI-2524 b and TOI-3972 b were conducted using the High-Resolution mode ( R ∼ 110 , 000) of the NEID spectrograph (Schwab et al. 2016; Halverson et al. 2016) on the WIYN 3.5m telescope at Kitt Peak National Observatory in Arizona, USA. The fiber-fed (Kanodia et al. 2018, 2023) and ultra-stable (Stefansson et al. 2016; Robertson et al. 2019) NEID spectrograph has been operational since 2022, covering a wavelength range of 380 to 930 nm. Observations of these five targets were conducted on the following dates: UT June 14, 2023; October 17, 2023; April 6, 2023; March 20, 2024; and December 21, 2023, respectively, yielding a total of 88 measurements. Apart from the in-transit RVs, for TOI-3972, we collected 13 additional out-of-transit RVs from UT October 18, 2023 to January 29, 2024 using NEID. We also collected an additional six RVs for TOI-2025 on April 4, 2023, using NEID.  \nThe NEID spectra were analyzed using version 1.3.0 of the NEID Data Reduction Pipeline ( NEID-DRP ) 3 . The DRP adopted the cross-correlation function (CCF) method to derive the radial velocities. Barycentriccorrected radial velocities for re-weighted orders ( CCFRVMOD ) were extracted from the NExScI NEID Archive 4 .  \nA comprehensive summary of the observations conducted by PFS and NEID is presented in Table 1. The resulting RVs, available through the Data behind the Figure program (see caption of Figure 1), are displayed in Figure 1.', '3. PHOTOMETRY': 'The TESS data used in this analysis were reduced by the TESS Science Processing Operations Center (SPOC; Jenkins et al. 2016) at NASA Ames Research Center to obtain Presearch Data Conditioning simple aperture photometry (PDCSAP; Smith et al. 2012; Stumpe et al. 2012, 2014) light curves. Table 1 indicates the cadence at which data were acquired for each TOI and for each sector. The SPOC light curves were obtained at 2-min cadence and the TESS-SPOC light curves from Full Frame Images (FFIs; Caldwell et al. 2020). The transit signatures of TOIs 559 b, 2031 b,  \nFigure 1. Rossiter-McLaughlin measurements for TOI-559 b, TOI-2025 b, TOI-2031 b, TOI-2485 b, TOI-2524 b and TOI-3972 b are shown as a function of hours from mid-transit. The RM data, with the Keplerian signal subtracted, are represented as blue dots. The median RM models are each depicted using red dashed lines. The 1 σ credible intervals are indicated by grey areas. In the lower-left corner, a schematic diagram illustrates the sky-projected stellar obliquity. Orange arrows indicate the projected stellar spin axis, while black arrows represent the planetary orbital axis, with its uncertainty shown in grey. Black lines illustrate the planetary orbital plane. Residuals are displayed beneath each panel. The RV data used in this work are available via this link.  \n<!-- image -->  \n2485 b, and 3972 b were all initially detected by the TESS Quick Look Pipeline (QLP; Huang et al. 2020a,b) and alerted by the TESS project to the community (Guerrero et al. 2021). Note that TESS Year 2 sectors (14-26) are affected by a sky background bias which starting in Sector 27 was addressed by the algorithm documented in the associated TESS Data Release Note DR38 5 . We thus analyzed the target pixel and light curve files of the affected targets and sectors (TOI-2031, Sectors 18, 19, 24, 25, 26; TOI-3972, Sectors 17, 18, 24; and TOI-2485, Sector 23) to determine whether there was a significant effect in these cases. We found that the bias induced on the planetary radii for TOI-2031 ( < 1%) and TOI-2485 ( ∼ 0.3%) was small compared to the respective overall errors ( ∼ 3.2% and ∼ 5%; see Table 2). However, for TOI-3972 since this bias was higher, we  \naccounted for it in the fits, reducing the overall error on the planetary radius from ∼ 3.4% to ∼ 2.4% (see Table 2 for the latter). All TESS data used in this paper can be found in MAST: 10.17909/r8dh-5j34.  \nIn this work, we also incorporated two new sets of ground-based photometry for TOI-2025 b and TOI-2031 b. Details on the observations and data reduction are provided in Appendix A.', '4.1. Synthetic spectral fitting by iSpec': "Co-added NEID spectra and iodine-free PFS spectra were adopted to determine the star's spectroscopic parameters, including stellar effective temperature ( T eff ), surface gravity (log g ∗ ), metallicity ([Fe / H]), and projected rotational velocity ( v sin i ∗ ). We used the synthetic spectral fitting technique provided by the Python package iSpec (Blanco-Cuaresma et al. 2014; BlancoCuaresma 2019) to measure these parameters.  \nWe employed the SPECTRUM radiative transfer code (Gray & Corbally 1994), the MARCS atmosphere model (Gustafsson et al. 2008), and the sixth version of the GES atomic line list (Heiter et al. 2021), all incorporated within iSpec , to create a synthetic model for the iodineimprinted PFS spectra and the co-added NEID spectra (S/N: TOI-559, 188; TOI-2025, 83; TOI-2031, 88; TOI2485, 151; TOI-2524, 41; TOI-3972, 96). We treated micro-turbulent velocities as a variable in our fitting process, allowing us to accurately represent the small-scale turbulent motions in the stellar atmosphere. Macroturbulent velocities were determined using an empirical relationship that leverages established correlations with various stellar attributes (Doyle et al. 2014). We selected specific spectral regions to streamline the fitting process, focusing on the wings of the H α , H β , and Mg I triplet lines, which are tracers of T eff and log g ∗ , as well as Fe I and Fe II lines that are crucial for constraining [Fe / H] and v sin i ∗ . Spectroscopic parameters were refined using the Levenberg-Marquardt nonlinear least-squares fitting algorithm (Markwardt 2009), which iteratively minimizes the χ 2 value between the synthetic and observed spectra. The final spectroscopic parameters are detailed in Table 2.", '4.2. SED+MIST fit by EXOFASTv2': 'To derive additional stellar parameters, such as stellar mass ( M ∗ ) and radius ( R ∗ ), we utilized the MESA Isochrones & Stellar Tracks (MIST) model (Choi et al. 2016; Dotter 2016) in combination with a spectral energy distribution (SED) fitting approach. Photometry was compiled from various catalogs, including 2MASS (Cutri et al. 2003), WISE (Cutri et al. 2021), TESS (Ricker et al. 2015), and Gaia DR3 (Gaia Collaboration et al. 2023). Gaussian priors based on our synthetic spectral fitting were applied to T eff and [Fe / H], along with the parallax from Gaia DR3 and an upper limit for the V -band extinction from (Schlafly & Finkbeiner 2011) 6 . A 2.4% systematic uncertainty floor in T eff was adopted, as suggested by Tayar et al. (2022).  \nThe SED fitting was performed using the Differential Evolution Markov Chain Monte Carlo (DE-MCMC) technique, integrated within EXOFASTv2 (Eastman 2017; Eastman et al. 2019) to evaluate uncertainties. The MCMC procedure was considered converged when the Gelman-Rubin diagnostic ( ˆ R ; Gelman & Rubin 1992) fell below 1.01 and the count of independent draws surpassed 1000. The resulting stellar parameters are listed in Table 2.', '5. OBLIQUITY MODELING': "To derive the sky-projected spin-orbit angles, a modified version of allesfitter (Gunther & Daylan 2021, 2019) was adopted to conduct simultaneous fits to transits, radial velocities, and Rossiter-McLaughlin measurements. The transit and radial velocity models were integrated using PyTransit (Parviainen 2015) and RadVel (Fulton et al. 2018), respectively. The RM model, grounded in Hirano et al. (2011), was implemented in tracit (Hjorth et al. 2021; Knudstrup & Albrecht 2022).  \nThe RM, ground-based photometric, and TESS data included within our fits are listed in Table 1. We also incorporated out-of-transit RVs for TOI-559, TOI-2025, TOI-2524, and, TOI-3972. The RVs of TOI-559, as presented by Ikwut-Ukwa et al. (2022), were obtained using the 1.5m Tillinghast Reflector Echelle Spectrograph (TRES, Fur'esz et al. 2008) on the 1.5m Tillinghast Reflector and CTIO High-Resolution spectrometer (CHIRON, Tokovinin et al. 2013) on the CTIO 1.5meter telescope. The out-of-transit RVs for TOI-2025 include 16 from TRES, 6 from WIYN, and 39 from the Fiber-fed Echelle Spectrograph (FIES; Telting et al. 2014; Telting et al. 2014) on the Nordic Optical Telescope (NOT; Djupvik & Andersen 2010). For TOI-2025, we included an additional RM observation drawn from Knudstrup et al. (2022), which consists of 16 RVs from FIES from which Knudstrup et al. (2022) previously derived λ = 9 +36 -34 · . For TOI-2524, an additional eight out-of-transit RVs from CHIRON were adopted. For TOI-3972, 13 additional out-of-transit RVs from NEID were also adopted.  \nWe drew initial guesses for the orbital period ( P ), the reference transit mid-time ( T 0 ), the cosine of the planet's orbital inclination (cos i ), the radius ratio of the planet to host ( R p /R ⋆ ), the sum of the stellar and planetary radii divided by the semimajor axis (( R ⋆ + R p ) /a ), and the radial velocity semi-amplitude ( K ) from the values derived from the Exoplanet Follow-up Observing Program (ExoFOP) website 7 . All fitted parameters were allowed to vary and were initialized with uniform priors. For TOI-559, TOI-2025, TOI-2524, and TOI-3972, which each included out-of-transit RVs in their models, the two eccentricity parameters √ e sin ω and √ e cos ω were each initialized with a value of 0. Because no out-of-transit RVs were included within our models of TOI-2031 and TOI-2485, we fixed their eccentricities to zero. The two transformed quadratic limb-darkening co-  \nFigure 2. Upper panel : the distribution of sky-projected stellar obliquity ( | λ | ) for Jovian planets around hot and cool stars as a function of stellar effective temperature. The obliquity measurements conducted by this work are shown as red stars. Lower panel : Left : The greater alignment of hot-star warm-Jupiter systems compared to hot-star hot-Jupiter systems is shown, with the number of misaligned systems for each type represented in orange and blue, respectively. The black line represents the fitted Gaussian function profile. Right : significance levels as a function of T eff and a/R ∗ . The brighter regions have higher significance levels. Black lines indicate significance levels, with inline numbers showing the values. The 3 σ significance level lines are shown in red. The dataset used to create this figure is available via this link.  \n<!-- image -->  \nq 1 and q 2 8 for each in-transit dataset (including each photometric band and each instrument used for the RM observation) were initialized with a value of 0.5. Uniform priors ranging from 0 to 1 were applied to cos i . The sky-projected spin-orbit angle λ was initialized with a value of 0 · and allowed to vary between ± 180 · . Furthermore, we incorporated Gaussian priors for macro-turbulence ( ζ ) and micro-turbulence ( ξ ) to reflect stellar surface motion. These priors were from Doyle et al. (2014) for macro-turbulence and Jofr'e et al. (2014) for micro-turbulence, with a standard deviation of 1 km/s applied.  \nThe TESS light curves were detrended using Gaussian Processes with a Matern 3/2 kernel, implemented in wotan (Hippke et al. 2019). For each ground-based transit, a third-order polynomial function was employed to model potential trends. To accommodate the RV offset in the out-of-transit RVs, both a constant baseline and a jitter term were incorporated. For each RM fit, a polynomial was utilized to address short-term overnight instrumental systematics and stellar variability. To determine the optimal degree of the polynomial, we conducted RM-only fits in which only the v sin i ∗ , λ , and polynomial parameters were allowed to vary, with polynomial degrees ranging from 0 to 3. The best fits were obtained through global optimization using differential evolution, implemented in PyDE (Storn & Price 1997). The polynomial yielding the lowest Bayesian Information Criterion was ultimately selected. Furthermore, to account for potential distortions caused by the long ex-  \nure times ( > 1000 s) of our RM observations, we performed exposure interpolation during the fitting process to produce 2-minute sampling for each RM fit.  \nTo sample the posterior distributions of all fitted parameters, we employed the affine-invariant Markov Chain Monte Carlo (MCMC) method as implemented in the emcee (Foreman-Mackey et al. 2013) Python package, using 100 walkers. The total number of accepted steps exceeded 200,000, and we discarded the initial 20% of these steps as burn-in. The chains were deemed to have converged only if all chains were longer than 50 times their autocorrelation lengths. The derived parameters are tabulated in Table 2.  \nFor all six targets, we applied the autocorrelation function as implemented in SpinSpotter (Holcomb et al. 2022) and the Generalized Lomb-Scargle periodogram (Zechmeister & Kurster 2009) to the TESS light curve. This process did not yield a confident identification of the rotation period in any of the six systems, preventing us from establishing limits on their true obliquity.", '6. STATISTICAL ANALYSIS': "In the past several years, the number of warm Jupiters with Rossiter-McLaughlin measurements has increased significantly (e.g., Kepler-448 b/KOI-12 b, Bourrier et al. 2015; Johnson et al. 2017; K2-140 b, Rice et al. 2021; K2-232 b, Wang et al. 2021; Qatar-6 b, Rice et al. 2023a; TOI-1478 b, Rice et al. 2022b; TOI-1670 c, Lubin et al. 2023; TOI-1859 b, Dong et al. 2023; TOI-2202 b, Rice et al. 2023b; TOI-677 b, Sedaghati et al. 2023; Hu et al. 2024; TOI-3362 b, Espinoza-Retamal et al. 2023; TOI-4201 b, Gan et al. 2024; TOI-4641 b, Bieryla et al. 2024; and WASP-106 b, Wright et al. 2023; Harre et al. 2023; Prinoth et al. 2024). By combining newly collected RM data with literature RMs and following the procedure described in Appendix B, we obtained a sample of 78 Jovian-planet systems without known stellar companions. This includes 55 hot-Jupiter systems and 23 warm-Jupiter systems, providing a valuable opportunity to explore the connection between stellar obliquity and the dynamical histories of warm Jupiters. Notably, to date, SOLES has contributed 14 of these 23 RM measurements to the warm-Jupiter sample.  \n6.1. Statistical Significance of the Aligned Single-Star Warm-Jupiter System Trend  \nWe subsequently utilized this sample to examine whether warm-Jupiter and hot-Jupiter systems exhibit similar or distinct misalignment distributions. In this  \nwork, we define a 'misaligned' system as one in which the angle | λ | exceeds 10 · and differs from 0 · at the 3 σ level (Wang et al. 2022; Rice et al. 2022b). All other systems are considered 'aligned'.  \nPrevious studies have shown that hot-Jupiter systems are often misaligned in the presence of host stars with high stellar effective temperatures (above the Kraft break, T eff ≈ 6100 K, Kraft 1967). However, due to a previously small sample size, it has so far been unclear whether this host star temperature trend extends to warm-Jupiter systems. The larger, clean sample of hot- and warm-Jupiter systems constructed within this work provides the necessary context for a comparative study examining the dependence of stellar obliquities on host star temperature.  \nSingle-cool-star systems with giants tend to be aligned:  \nIn systems with cool stars ( T eff < 6100 K), there are 19 hot-Jupiter systems and 14 warm-Jupiter systems with RM measurements, all of which are aligned. Consequently, to date, no robust observational evidence suggests that Jupiters around single cool stars can be spinorbit misaligned.  \nTo compare if the projected stellar obliquity distributions of cool-star hot-Jupiter and cool-star warm-Jupiter systems are identical, we applied the KolmogorovSmirnov (K-S, Hodges 1958) and Anderson-Darling (AD, Scholz & Stephens 1987) tests, implemented in scipy (Virtanen et al. 2020). The null hypothesis is that these distributions are the same. We resampled the | λ | values with associated uncertainties and conducted 10,000 trials to derive the distribution of the p-values for the K-S and A-D tests. To be conservative, we adopted the larger value between the lower and upper uncertainties for each | λ | . The resulting distribution of pvalues for the K-S and A-D tests showed that merely 4.3% and 1.6% of the values, respectively, fell below the 0.05 threshold, failing to reject the null hypothesis. This indicates that the alignment tendency of cool-star hotJupiter systems are similar to those of cool-star warmJupiter systems.  \nSingle-hot-star warm-Jupiter systems tend to be aligned:  \nOur sample includes 36 hot Jupiters and 9 warm Jupiters around hot stars ( T eff ≥ 6100 K), with all of these warm Jupiters exhibiting spin-orbit alignment. To determine the misalignment probability in hot-Jupiter systems, we iteratively draw random samples of 9 | λ | values from the hot-star hot-Jupiter sample without replacement to see how many of them are misaligned. This process was repeated until the distribution of the number of misaligned systems stabilized, which occurred after 100,000 iterations. Since all nine warm Jupiters around hot stars are aligned, we found a 3.4 -σ differ-  \nTable 2. Stellar and Planetary Parameters  \nT eff : effective temperature (K), [Fe / H]: metallicity (dex), log g ∗ : surface gravity (log 10 (cm/s 2 )), v sin i ∗ : projected stellar rotational velocity (km/s), M ∗ : stellar mass ( M ⊙ ), R ∗ : stellar radius ( R ⊙ ), T eff : effective temperature (K), [Fe / H]: metallicity (dex), log g ∗ : surface gravity (log 10 (cm/s 2 )), Age: age (Gyr), ϖ : parallax (mas), d: distance (pc), λ : sky-projected spin-orbit angle (deg), v sin i ⋆ : projected stellar rotational velocity (km/s), ξ : micro-turbulent velocity (km/s), ζ : macro-turbulent velocity (km/s), R b /R ⋆ : planet-to-star radius ratio, ( R ⋆ + R b ) /a b : ratio of the sum of star and planet radii to semi-major axis, cos i b : cosine of inclination, T 0; b : mid-transit time - 2450000 (BJD TDB ), P b : orbital period (days), K b : radial velocity semi-amplitude (m/s), √ e b cos ω b and √ e b sin ω b : eccentricity vector components, q 1 and q 2 : transformed limb-darkening coefficients, M b : planetary mass (M jup ), R b : planetary radius (R jup ), a b /R ⋆ : semi-major axis scaled by stellar radius, a b : semi-major axis (AU), i b : inclination (deg), e b : eccentricity, ω b : argument of periastron, T 14; b : total transit duration (hours), T 23; b : full transit duration (hours).  \nence between the hot-star hot-Jupiter systems and the hot-star warm-Jupiter systems, as shown in the lower left panel of Figure 2. Furthermore, we examine the dependency of statistical significance on the choice of the difference criteria, varying a/R ∗ from 10 to 20 and T eff from 6100 to 6300 K (see the lower right panel of Figure 2). For 98% of the area where 6000 ≤ T eff ≤ 6300 K and 10 ≤ a/R ∗ ≤ 12, the significance level is ≥ 3 σ . A more straightforward approach to verify this result is as follows: among 36 hot-star hot-Jupiter systems, 18 are misaligned, corresponding to a misalignment rate of 50%. The probability of randomly drawing nine systems and finding that all are aligned is 0 . 50 9 ≈ 0 . 2%, indicating a 3.1σ occurrence.  \nAdditionally, we treat hot-Jupiter and warm-Jupiter systems as two groups without distinguishing between aligned and misaligned. We applied the K-S and AD tests utilizing the aforementioned approach to study whether the projected stellar obliquity distribution of hot-star hot-Jupiter and hot-star warm-Jupiter systems is identical. The null hypothesis is that they are identical. The analysis of the p-value distributions demonstrated that 70% of the p-values from the K-S test and 85% of the p-values from the A-D test fell below the 0.05 threshold, allowing us to reject the null hypothesis and highlighting the significant disparity between the two samples.", '7. THEORETICAL IMPLICATIONS': "In our analysis of Rossiter-McLaughlin measurements, we identified a 3.4σ trend 9 : single-star warm-Jupiter systems consistently exhibit no spin-orbit misalignments, even above the Kraft break, demonstrating a 3.4σ confidence difference when compared to the T eff -λ dependency found in hot-Jupiter systems. This trend presents intriguing contrasts with the orbital orientations of hot Jupiters, which typically align with cooler stars but often show misalignment around hotter ones.  \nOne explanation for these contrasting alignment trends is that hot and warm Jupiters might originate from different formation processes. Warm Jupiters could form directly from well-aligned protoplanetary disks, leading to an initial alignment (albeit with some lowlevel, ≲ 20 · range of expected primordial misalignments; see Rice et al. 2023b). This interpretation is in agreement with findings from Morgan et al. (2024), which found that giant planets around cool stars out to ∼ 2 AU  \nare preferentially aligned. It is also supported by a growing body of evidence for primordial alignment from direct imaging observations of giant planets around young stars (Kraus et al. 2020; Bowler et al. 2023; Franson et al. 2023; Sepulveda et al. 2024) and from both protoplanetary (Davies 2019) and debris disk (Hurt & MacGregor 2023) spin-orbit constraints. By contrast, hot Jupiters, irrespective of stellar host temperature, may emerge from more violent evolutionary processes - often associated with high-eccentricity migration - after protoplanetary disk dispersal, resulting in initial misalignment. Subsequently, only cooler stars with hot Jupiters undergo tidal realignment, shaping the observed obliquity distribution in hot-Jupiter systems (Albrecht et al. 2012; Rice et al. 2022a; Zanazzi et al. 2024).  \nThe observed sharp transitions near the Kraft break in the relationship between a star's effective temperature and the alignment of hot Jupiter orbits strongly support tidal realignment mechanisms. However, these observations do not preclude the possibility that hot Jupiters around both cool and hot stars might initially have different obliquity distributions. Hot Jupiters around cooler stars, which may have formed and evolved quiescently, tend to be aligned (Wu et al. 2023; Hixenbaugh et al. 2023). By contrast, hot Jupiters around hot stars may often experience violent formation histories that lead to significant spin-orbit misalignments (Wu et al. 2023).  \nThis scenario may arise if, for example, higher-mass stellar hosts preferentially form multiple Jupiter-mass planets. Following the dispersal of the protoplanetary disk, planet-planet interactions would naturally increase eccentricities and excite spin-orbit misalignments. As these orbits circularize, the initially eccentric and misaligned warm and cold Jupiters evolve into misaligned hot Jupiters around hotter stars. This explanation also accounts for why current observations show warm Jupiters around hot stars as aligned.  \nThe fundamental factor here is the relative ease of exciting eccentricities over inducing inclinations (Petrovich 2015b; Espinoza-Retamal et al. 2023; Sedaghati et al. 2023), suggesting that warm Jupiters with significant initial misalignments likely underwent high eccentricities that drove their inward migration, transforming them into misaligned hot Jupiters. The persistent misalignment in resulting hot Jupiters, even though their orbital eccentricity has been damped, can primarily be attributed to differences in tidal damping timescales between orbital circularization and spin-orbit realignment. The timescale for circularization, dominated by tides raised by the star on the planet, is typically much shorter than the timescale for realignment, driven by  \ntides the planet induces on the star (Hut 1981; Ogilvie &Lin 2007). This disparity in timescales between damping eccentricity and realigning the host star effectively maintains the observed spin-orbit misalignment in these tidally circularized resulting hot Jupiters.", 'ACKNOWLEDGMENTS': "We appreciate the valuable comments from our anonymous reviewer, which have significantly improved this manuscript. We thank Simon Albrecht, Emil Knudstrup, and Cristobal Petrovich for insightful discussions. We acknowledge support from the NASA Exoplanets Research Program NNH23ZDA001N-XRP (Grant No. 80NSSC24K0153). Additionally, M.R. and S.W. acknowledge support from the Heising-Simons Foundation, with M.R. supported by Grant #2023-4478, and S.W. supported by Grant #2023-4050. This research was supported in part by Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute. The work of HPO has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation under grants 51NF40 182901 and 51NF40 205606. DR was supported by NASA under award number NNA16BD14C for NASA Academic Mission Services. This paper contains data taken with the NEID instrument, which was funded by the NASA-NSF Exoplanet Observational Research (NN-EXPLORE) partnership and built by Pennsylvania State University. NEID is installed on the WIYN telescope, which is operated by the National Optical Astronomy Observatory, and the NEID archive is operated by the NASA Exoplanet Science Institute at the California Institute of Technology. NN-EXPLORE is managed by the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. Funding for the TESS mission is provided by NASA's Science Mission Directorate. We acknowledge the use of public TESS data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. This research has made use of the Exoplanet Follow-up Observation Program 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 paper includes data collected by the TESS mission that are publicly available from the Mikulski Archive for Space Telescopes (MAST). KAC  \nand CNW acknowledge support from the TESS mission via subaward s3449 from MIT. This work makes use of observations from the 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: 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.  \nFacilities: WIYN/NEID, PFS/Magellan, LCOGT  \nSoftware: allesfitter (Gunther & Daylan 2021, 2019), AstroImageJ (Collins et al. 2017), emcee (Foreman-Mackey et al. 2013), EXOFASTv2 (Eastman 2017; Eastman et al. 2019), iSpec (Blanco-Cuaresma et al. 2014; Blanco-Cuaresma 2019), matplotlib  \n(Hunter 2007), numpy (Oliphant 2006; Walt et al. 2011; Harris et al. 2020), pandas (McKinney 2010), PyDE (Storn & Price 1997), PyTransit (Parviainen 2015), scipy (Virtanen et al. 2020), TAPIR (Jensen 2013a), wotan (Hippke et al. 2019).", 'A. GROUND-BASED PHOTOMETRY': 'To measure the transit times near the epoch of our spectroscopic time series observations, we acquired ground-based time-series photometry of the fields around TOI-2025 and TOI-2031 as part of the TESS Follow-up Observing Program (TFOP; Collins 2019) 10 . We used the TESS Transit Finder , which is a customized version of the Tapir software package (Jensen 2013b), to schedule our transit observations.', 'A.1. TOI-2025': "We observed a full transit window of TOI-2025 b in Pan-STARRS z -short band on UT 2023 June 14 from the Las Cumbres Observatory Global Telescope (LCOGT, Brown et al. 2013) 1 m network node at McDonald Observatory near Fort Davis, Texas, United States. The 1 m telescope is equipped with a 4096 × 4096 SINISTRO camera having an image scale of 0 . '' 389 per pixel, resulting in a 26 ' × 26 ' field of view. The images were calibrated by the standard LCOGT BANZAI pipeline (McCully et al. 2018), and differential photometric data were extracted using AstroImageJ (Collins et al. 2017). We used circular photometric apertures with radius 4 . '' 3. The target star aperture excluded all of the flux from the nearest known neighbor in the Gaia DR3 catalog (Gaia DR3 2296342644635200512), which is ∼ 80 '' north of TOI-2025. The light curve data are available on the EXOFOP-TESS website 11 and are included in the global modeling described in Section 5.", 'A.2. TOI-2031': "We observed a full transit window of TOI-2031.01 in Sloan i ' band on UT 2023 July 06 from the LCOGT 1m network node at McDonald Observatory. The images were calibrated by the standard LCOGT BANZAI pipeline, and differential photometric data were extracted using AstroImageJ . We used circular photometric apertures with radius 6 . '' 6. The target star aperture excluded all of the flux from the nearest known neighbor in the Gaia DR3 catalog (Gaia DR3 2296342644635200512), which is ∼ 45 '' southwest of TOI-2031. The light curve data are available on the EXOFOP-TESS website 12 and are included in the global modeling described in Section 5.", 'B. SAMPLE CONSTRUCTION': 'We began with the set of systems listed in the TEPCat orbital obliquity catalog 13 (Southworth 2011) as of July 25, 2024. We adopted the preferred values for λ and T eff from the TEPCat catalog for each system. Other parameters were drawn from the Planetary Systems Composite Data table of the NASA Exoplanet Archive 14 . Note that the parameters for WASP-109 and WASP-111 were from Anderson et al. (2014). We followed the steps outlined below to define our sample.  \n- 1. Minimize biases introduced by nonuniform measurement techniques. We only included results derived from Rossiter-McLaughlin and Doppler tomography measurements to avoid the biases caused by other methods. For example, spot-crossing is particularly sensitive to systems that are either aligned or anti-aligned, whereas gravity darkening is most sensitive to misaligned systems (Siegel et al. 2023; Dong & Foreman-Mackey 2023; see Albrecht et al. 2022 for a review of stellar obliquity measurement methods). When selecting stellar obliquity measurements,  \nwe prioritize the most recent results, with Rossiter-McLaughlin measurements receiving higher precedence than Doppler tomography measurements.  \n- 2. Remove low-quality and contested measurements. We removed the systems with low-quality or contested measurements as suggested by Albrecht et al. (2022), including CoRoT-1 (Bouchy et al. 2008; Pont et al. 2010), CoRoT-19 (Guenther et al. 2012), HATS-14 (Zhou et al. 2015), HAT-P-27 (Brown et al. 2012), WASP-1 (Simpson et al. 2011; Albrecht et al. 2011), WASP-2 (Triaud et al. 2010; Albrecht et al. 2011), WASP-23 (Triaud et al. 2011), WASP-49 (Wyttenbach et al. 2017), and WASP-134 (Anderson et al. 2018). Note that we also excluded HAT-P-17 considering the disagreement between its two measurements (Fulton et al. 2013, 19 +14 -16 · ; Mancini et al. 2022, -27 . 5 ± 6 . 7 · )\n- 3. Remove binary and multi-star systems. Apart from the relatively confined gravitational interactions within a single-star system, stellar obliquity can also be strongly influenced by stellar companions (e.g., Wu & Murray 2003; Fabrycky & Tremaine 2007; Naoz et al. 2012; Naoz 2016). Therefore, in this work, we have excluded stars with bound companions identified in Gaia DR3. Following the methods described in El-Badry et al. (2021) and Rice et al. (2022b), we checked for bound companions to each system, determining whether candidate companions meet the following criteria: 1) their proper motion is within 5 km/s of the planet-hosting star, and 2) their parallax is consistent with that of the planet-hosting star within 5 σ . Candidates satisfying both criteria were identified as stellar companions and subsequently removed from our sample. Moreover, systems listed in the Binary and Multiple Star systems catalog 15 (Schwarz et al. 2016), the catalog of Exoplanets in Visual Binaries (Fontanive & Bardalez Gagliuffi 2021), or flagged as having more than one star in NASA Exoplanet Archive were also excluded.\n- 4. Remove systems with the T eff of host stars < 3500 K or > 7000 K. To ensure uniformity in the effective temperature ( T eff ) range across both warm- and hot-Jupiter systems, exclusion criteria were applied where T eff exceeds 7000 K or falls below 3500 K.  \nThis procedure yielded 78 Jovian planets ( M pl ≥ 0 . 3 M J ) around single-star systems with stellar obliquity measurements, including 55 hot-Jupiter systems ( a/R ∗ < 11) and 23 warm-Jupiter systems ( a/R ∗ ≥ 11). A 0.1 M J uncertainty was assumed for planetary measurements with only upper-limit values.', 'REFERENCES': "Albrecht, S., Winn, J. N., Johnson, J. A., et al. 2011, ApJ, 738, 50, doi: 10.1088/0004-637X/738/1/50 -. 2012, ApJ, 757, 18, doi: 10.1088/0004-637X/757/1/18 Albrecht, S. H., Dawson, R. I., & Winn, J. N. 2022, PASP, 134, 082001, doi: 10.1088/1538-3873/ac6c09 Alonso, R., Brown, T. M., Torres, G., et al. 2004, ApJL, 613, L153, doi: 10.1086/425256 Anderson, D. R., Brown, D. J. A., Collier Cameron, A., et al. 2014, arXiv e-prints, arXiv:1410.3449, doi: 10.48550/arXiv.1410.3449 Anderson, D. R., Bouchy, F., Brown, D. J. A., et al. 2018, arXiv e-prints, arXiv:1812.09264, doi: 10.48550/arXiv.1812.09264 Anderson, K. R., Winn, J. N., & Penev, K. 2021, ApJ, 914, 56, doi: 10.3847/1538-4357/abf8af Bakos, G., Noyes, R. W., Kov'acs, G., et al. 2004, PASP, 116, 266, doi: 10.1086/382735  \n```\nBakos, G. ' A., Csubry, Z., Penev, K., et al. 2013, PASP, 125, 154, doi: 10.1086/669529 Bashi, D., Helled, R., Zucker, S., & Mordasini, C. 2017, A&A, 604, A83, doi: 10.1051/0004-6361/201629922 Bate, M. R. 2018, MNRAS, 475, 5618, doi: 10.1093/mnras/sty169 Bate, M. R., Lodato, G., & Pringle, J. E. 2010, MNRAS, 401, 1505, doi: 10.1111/j.1365-2966.2009.15773.x Batygin, K. 2012, Nature, 491, 418, doi: 10.1038/nature11560 Beaug'e, C., & Nesvorn'y, D. 2012, ApJ, 751, 119, doi: 10.1088/0004-637X/751/2/119 Bieryla, A., Zhou, G., Garc'ıa-Mej'ıa, J., et al. 2024, MNRAS, 527, 10955, doi: 10.1093/mnras/stad3785 Blanco-Cuaresma, S. 2019, MNRAS, 486, 2075, doi: 10.1093/mnras/stz549 Blanco-Cuaresma, S., Soubiran, C., Heiter, U., & Jofr'e, P. 2014, A&A, 569, A111, doi: 10.1051/0004-6361/201423945\n```  \n- Xue, Y., Suto, Y., Taruya, A., et al. 2014, ApJ, 784, 66, doi: 10.1088/0004-637X/784/1/66\n- Yee, S. W., Winn, J., Hartman, J., et al. 2024, in prep Zanazzi, J. J., Dewberry, J., & Chiang, E. 2024, ApJL, 967, L29, doi: 10.3847/2041-8213/ad4644\n- Zechmeister, M., & Kurster, M. 2009, A&A, 496, 577, doi: 10.1051/0004-6361:200811296\n- Zhou, G., Bayliss, D., Hartman, J. D., et al. 2015, ApJL, 814, L16, doi: 10.1088/2041-8205/814/1/L16"}