MNRAS 527, 10955-10964 (2024) interactions experienced by the system. In particular, warm Jupiters, planets with a / R ⋆ > 10 and R p > 8 R e , offer an opportunity to study the primordial obliquities of their host stars (Albrecht, Dawson & Winn 2022 ) without having to account for planet-star tidal interactions that may have modified the orbital architecture.

There exists clear trends in the hot Jupiter spin-orbit obliquity distribution as a function of stellar temperature (e.g. Albrecht et al. 2012 ). The dependence between the observed obliquity distribution and stellar temperature for longer period planets is less clear due to observational biases that make such observations more difficult. Close-in giant planets around cool stars ( T eff < 6250 K) are generally observed to have well-aligned orbits (Albrecht, Dawson & Winn 2022 ). In contrast, more distantly orbiting giant planets about cool stars with a / R ⋆ > 10 show a wider range of spin-orbit angles, as in systems like WASP-8 (Queloz et al. 2010 ;Bourrier et al. 2017 ), Kepler-420 (Santerne et al. 2014 ), and HD 80 606 (Pont et al. 2009 ;Winn et al. 2009 ). Such a dependence is expected if the close-in planet obliquity distribution is strongly shaped by planet-star tidal interactions.

Short-period Jovian planets around early-type stars exhibit a wide distribution of orbital obliquities. Few long-period planets around hot stars have had their spin-orbit angles mapped. Kepler-448b is the only Jovian planet around an early-type star with an spin-orbit angle measured spectroscopically found to reside in a well-aligned orbit (Bourrier et al. 2015 ;Johnson et al. 2017 ).

The lack of well-characterized long-period planets around earlytype stars prohibits informative tests on the mechanisms thought to induce misalignments in planet orbits. Early-type stars with radiativ e env elopes e xperience weaker planet-star tidal interactions and offer the opportunity of exploring the primordial period obliquity relationship for giant planets. Each mechanism that induces planetstar misalignments have their own expected dependencies on orbital distance. Warps in the protoplanet disc lead to preferentially longer period planets being found in misaligned orbits (Heller 1993 ;Wijnen et al. 2017 ). The spin-axis of stars hotter than the Kraft break (Kraft 1967 ) may also evolv e o v er time by itself. Gra vity-wa ve instabilities induced at the radiativ e-conv ectiv e boundary of early-type stars may result in their outer envelopes changing in spin-axis o v er time (Rogers, Lin & Lau 2012 ), leading to a wide range of spin-orbit obliquites for planets around such stars. Such instabilities are not dependent on the planetary system, and as such no period-spin-orbit obliquity dependencies should be expected.

In this paper we report the planetary confirmation of TOI-4641b, a warm Jupiter on a 22-d orbit that is well aligned with the equatorial plane of a rapidly rotating F-star. In Section 2 , we describe the photometric data from TESS and the Tierras Observatory, high-resolution speckle imaging, and Tillinghast Reflector Echelle Spectrograph (TRES) spectroscopic observations to measure the stellar obliquity. Section 3 describes the global modelling of the system and Section 4 describes the stellar variability. We conclude with a discussion in Section 5 .

The Transiting Exoplanet Survey Satellite ( TESS ; Ricker et al. 2015 ) is an all-sky survey searching for transiting exoplanets around nearby bright host stars. The satellite uses four cameras to stare at 24 × 96 deg sectors of the sky for approximately 27 d at a time. TOI-4641 (TIC 436873727) was observed by TESS during Sector 18 of the primary mission and then again in Sectors 42, 43, 44, and 58 of the extended mission, in all cases with 2-min cadence. The data were processed by the NASA Science Processing Operations Center pipeline (SPOC; Jenkins et al. 2016 ) and the light curves were downloaded from the Mikulski Archive for Space Telescopes (MAST)foot_0 using the Lightkurve package (Lightkurve Collaboration 2018 ). The Presearch Data Conditioning Simple Aperture Photometry [PDCSAP; (Smith et al. 2012 ;Stumpe et al. 2012Stumpe et al. , 2014 ) )] light curves were employed in our analysis and are plotted in Fig. 1 . Sector 44 was excluded from our planet analysis because the transit occurred at the edge of a gap in the light curve.

A candidate exoplanet orbiting TOI-4641 with a period of 22.1d was identified in light curves including data through Sector 43 in both SPOC (Jenkins et al. 2016 ) and QLP (Huang et al. 2020 ;Kunimoto et al. 2022 ) pipelines. The SPOC performed a transit search with an adaptive, noise-compensating matched filter (Jenkins 2002 ;Jenkins et al. 2010Jenkins et al. , 2020 ) ), producing a Threshold Crossing Event (TCE) for which an initial limb-darkened transit model was fitted (Li et al. 2019 ) and a suite of diagnostic tests were conducted to help assess the planetary nature of the signal (Twicken et al. 2018 ). The QLP performed its transit search with the Box Least Squares Algorithm (Kov ács, Zucker & Mazeh 2002 ). The transit signature passed all SPOC data validation diagnostic tests, and the TESS Science Office issued an alert (Guerrero et al. 2021 ) for TOI 4641.01 on 2021 No v ember 19. The difference image centroid offsets localized the transit source for TOI 4641.01 within 2.4 ± 2.5 arcsec; all TIC v8 (Stassun et al. 2019 ) objects other than TOI-4641 were excluded as potential sources of the transit signature.

To check the field for nearby eclipsing binaries that could potentially be contaminating the TESS photometry and to confirm the transit was on the target star, we used the TESS TRANSIT FINDER , a customized version of the TAPIR software package (Jensen 2013 ), to schedule ground-based transit observ ations. Follo w-up observ ations were done using the Tierras Observatory (Garcia-Mejia et al. 2020 ) at the Fred Lawrence Whipple Observatory atop Mount Hopkins in AZ, USA. Tierras is a 1.3m telescope with a Teledyne e2v 4K × 4K NIR-optimized deep-depletion CCD. It has a 0.48 × 0.25 deg field of view and a 0.43 arcsec per pixel scale. The camera was designed to have a custom narrow (40 nm full width at half-maximum) bandpass filter centred around 863.5 nm to minimize precipitable water vapor errors known to limit ground-based photometry of M dwarfs.

The data were reduced using a custom pipeline based on similar procedures as outlined in Irwin et al. ( 2015 ) and aperture photometry was performed using ASTR OIMA GEJ (AIJ, Collins et al. 2017 ). Two partial transits were observed on UT 2022 December 17 (egress) and UT 2023 January 30 (ingress). A full transit was observed on UT 2023 January 8. The transits on the nights UT 2022 December 17 and UT 2023 January 8 coincided with the spectroscopic observations described in more detail in Section 2.2.1 . We extracted the photometry using an aperture radius of 12 pixels (5.16 arcsec) from the data on UT 2022 December 17 to determine that the target star was the source of the transit events and we excluded any star more distant than 5 arscec as the source of the dips observed by TESS . That light curve is shown in Fig. 2 along with the phase-folded TESS light curve. We note ∼6 h variation in the ground-based light curve at TOI-4641b 10957 MNRAS 527, 10955-10964 (2024) the ∼1 mmag lev el. The light-curv e variability is discussed in more detail in Section 4 . Data from the nights of UT 2023 January 8 and 30 were not of sufficient quality to add any value to the fit due to poor observing conditions and experimental exposure times leading to occasional saturation and were not included in the global analysis. The photometric analysis files from AIJ are all available publicly on the Exoplanet Follow-up Observing Program (ExoFOP) 2 website.

2 https:// exofop.ipac.caltech.edu/ tess/

We observed TOI-4641 on UT 2023 February 5 using NESSI (Scott et al. 2018 ), a speckle imager at the WIYN 3.5m telescope. The observations consisted of taking speckle sequence data in two filters with central wavelengths of 562 and 832 nm. We reduced these data using the standard speckle pipeline (Howell et al. 2011 ) to obtain reconstructed images of the focal plane as well as a contrast curve centred on the target star and extending out to a radius of 1.2 arcsec. No secondary sources were detected surrounding TOI-4641. The background limit plots are shown in Fig. 3 . two filters centred at 562 nm (blue curve) and 832 nm (red curve). Speckle imaging analysis was confined to the inner 1.2 arcsec of the full 4.6 × 4.6 arcsec field of view. Speckle reconstructed images centred on the star are inset at the top of the figure. We find no companions to TOI-4641 in these high-resolution imaging observations. element (SNRe) of 113. The quick-look classification showed that the host star was rapidly rotating. Despite the rapid rotation which w ould mak e precise radial v elocities v ery challenging, a second TRES spectrum (SNRe of 131) at opposite orbital quadrature was obtained on UT 2021 December 21 to check for a large velocity variation that would be indicative of a stellar companion. The velocity offset between the two spectra was ∼275 m s -1 based on the standard TRES pipeline which derives velocities using a single order of the spectrum centred on the Mg b features as described in Buchhave et al. ( 2010 ). An additional 13 TRES observations were obtained between UT 2022 December 10 and 31 with longer exposures than the original reconnaissance spectra in an attempt to gain high enough SNRe to detect an orbital solution. The average SNRe of the new observations was 195.

In an attempt to get the best velocity precision, we used a least squares deconvolution technique (Zhou et al. 2016 ) based on the methods of Donati et al. ( 1997 ) andCollier Cameron et al. ( 2010 ) to extract radial velocities. Due to the rapid rotation of the host star, we were unable to detect an orbital signal of the planet. We also tried a multispectral order analysis of the available spectra. Each spectrum was cross-correlated order-by-order against the highest SNRe observed spectrum to derive relative multi-order velocities. While we again were unable to detect a clear orbital signal, we were able to determine a 3 σ upper limit planetary mass of 3.87 M Jup . The least squares deconvolution velocities are presented in Table 1 , and were adopted for further analysis in Section 3 . In addition, we also modelled the line profile determined from each spectrum to derive rotational and macroturbulent broadening velocities for the host star. The line profile is modelled as per Gray & Corbally ( 1994 ), with the macroturbulent broadening component described via a radial-tangential model. We find the best-fitting rotational broadening velocity of 86.3 ± 1.0 km s -1 , and a macroturbulent velocity of 4.00 + 0 . 62 -0 . 66 km s -1 for TOI-4641.

As a planet transits across its host star's stellar disc, a portion of the stellar blue-and red-shifted light is blocked, which produces a shift in the radial velocity measurements. This ef fect, kno wn as the Rossiter-McLaughlin (Rossiter 1924 andMcLaughlin 1924 ) effect, allows us to measure the projected spin-orbit angle of a transiting system.

To determine the projected spin-orbit angle, spectra were obtained during two transits on UT 2022 December 17 and UT 2023 January 8 using the TRES spectrograph. Spectra were acquired in the standard way by obtaining a set of three 300 s exposures surrounded on either side by Thorium-Argon calibration spectra. The three spectra were then combined using cosmic ray rejection and run through the standard TRES pipeline as described in Section 2.2.1 . We observed a partial ingress on the night of UT 2022 December 17 collecting 18 sets of three spectra and a full transit on UT 2023 January 8 of 39 sets of three spectra with an average SNRe of 147 and 195, respectively.

To extract the planetary Doppler shadow, we derived the linebroadening profiles for each observation in an analysis similar to that described abo v e. We performed a least squares deconvolution between the observed spectra and a synthetic ATLAS9 stellar template (Castelli & Kurucz 2004 ), generated at the atmospheric parameters of the host star, with no rotational broadening incorporated. We then modelled the differences between each derived line profile and the median combined line profile measured o v er the transit night as part of our global modelling analysis as per Zhou et al. ( 2019 ). Briefly, for each observation, we calculated the integrated line profile of the portion of the star blocked by the planet. This incorporates the effects of local limb darkening, macroturbulent broadening, and rotation. This is modelled simultaneously with the system parameters as part of the global modelling process (Section 3 ). The line profile residuals for each transit observation, and for the combined observations, are shown in Fig. 4 . The dark trail from bottom left to top right represents the shadow of the planet during the transit in the line profile residuals.

We used the Stellar Parameter Classification (SPC; Buchhave et al. 2012 ) tool to derive stellar parameters using the TRES spectra. SPC cross-correlates an observed spectrum against a library grid of synthetic spectra calculated using the Kurucz ( 1992 ) atmospheric models. A ∼310 Å region of the spectrum surrounding the Mg b lines is used to derive effective temperature, T eff , surface gravity, log g , rotational velocity, vsin i , and metallicity, [m/H]. Metallicity is derived using all available metal lines rather than just the Fe lines and therefore reported as [m/H] but is closely related to [Fe/H] values. Downloaded from https://academic.oup.com/mnras/article/527/4/10955/7464053 by guest on 18 September 2024 TOI-4641b 10959 MNRAS 527, 10955-10964 (2024) We recently developed a quality flag (QF) metric -Excellent, Good, Fair, and Poor -for SPC results based on the known limitations of SPC. Each spectrum is run through an algorithm (shown in Fig. 5 ) to determine the reliability of the result using stellar ef fecti ve temperature, rotational velocity, SNRe, and the cross-correlation function (CCF) peak value as quality indicators. As a service to the community, SPC stellar parameters for all TRES spectra of TESS targets are uploaded to the ExoFOP website when the QF is Excellent or Good. If the QF is determined to be Fair, as in the case of TOI-4641 due to the high stellar rotational velocity, the stellar parameters are not considered reliable and only the rotational velocity of the star is uploaded. Stellar parameters are not uploaded when a QF of Poor is determined.

SPC reports a vsin i of 91.60 ± 0.50 km s -1 for TOI-4641 but because SPC does not solve for macroturbulence and the Least Squares Deconvolution analysis does, we chose to use the Least Squares Deconvolution reported value as determined in Section 2.2.1 (86.3 ± 1.0 km s -1 ) as a prior for our global analysis. The SPC uncertainty reported is the floor error and should be inflated due to the star's rapid rotation.

We used all available broad-band photometry, including Hipparcos B and V bands (Perryman et al. 1997 ), Gaia DR3 G , Bp , Rp (Gaia Collaboration 2023 ), 2MASS J , H , K (Skrutskie et al. 2006 ), and WISE W 1 , W 2 , W 3 , W 4 bands (Cutri et al. ), as well as Gaia DR3 parallaxes to model the spectral energy distribution of TOI-4641. The spectral energy distribution is modelled simultaneously with the photometric and spectroscopic observations of the system, such that the stellar properties derived are jointly constrained by the transit and the photometric properties of the star. At each iteration of the global model (Section 3 ), we compute the interpolated isochrone magnitudes for each tested stellar mass, age, and metallicity. We then compute the log likelihood between the isochrone magnitudes and the observed values and associated uncertainties for each band. We adopt the MIST isochrones (Dotter 2016 ), interpolated via the MINIMINT package (Koposov 2020 ), for our stellar models. The bestfitting model, as per Table 2 , is shown in Fig. 6 .

To determine the stellar and planetary parameters of the system holistically, we performed a joint analysis of all available photometric, spectroscopic, and catalogue observations. This included photometric transit observations from TESS and Tierras (Sections 2.1.1 and 2.1.2 ), two spectroscopic transit observations from TRES (Section 2.2.2 ), the TRES out-of-transit radial velocities (Section 2.2.1 ), and available catalogue observations (Section 2.3 ). Free parameters largely describing the transit include the orbital period P , reference time of transit centre T 0 , planet-to-star radius ratio R p / R ⋆ , lineof-sight inclination i , and orbital eccentricity parameters √ e cos ω and √ e sin ω. In addition, the radial velocity orbit is modelled by including the free parameter describing the mass of the planetary companion M p . The spectroscopic transit is modelled as per Zhou et al. ( 2019 ), with free parameters including the projected spinorbit angle λ, rotational broadening vsin I ⋆ , and macroturbulent broadening velocity. Simultaneous with the transit models, we also interpolate the stellar isochrones as per Section 2.3 . At each step, we model the spectral energy distribution to constrain the stellar A number of parameters are constrained by informed priors in the global modelling. Parallax is tightly constrained by a Gaussian prior about its Gaia DR3 value and associated uncertainties. Rotational and macroturbulent broadening velocities are constrained by Gaussian priors about their spectroscopically determined values. Stellar metal-licity is constrained by a Gaussian prior about the SPC-determined value. Uniform priors about reasonable physical parameter spaces are adopted for all other free parameters. The adopted priors are noted in Table 3 . Gaussian priors are noted as G( µ, σ ), while uniform priors and their adopted ranges are noted by U( min , max ).

The photometric transits are modelled as per Mandel & Agol ( 2002 ) via the BATMAN package (Kreidberg 2015 ). Limb darkening parameters are interpolated and fixed to their values as per Claret & Bloemen ( 2011), Claret ( 2017 ), and Eastman, Gaudi & Agol ( 2013 ). The spectroscopic transit is modelled as per Section 2.2.2 , via a disc integration of the portion of the stellar surface occulted by the planet, incorporating the effect of local macroturbulence and rotational broadening.

The best-fitting parameters are presented in Tables 2 and 3 . A number of additional parameters are derived from the posterior chains and reported in Table 3 for completeness. These are marked as 'inferred' in the table. Stellar parameters for luminosity, ef fecti ve temperature, surface gravity, and age are rederived from MIST isochrones interpolations for each given link in the MCMC chain subsequent to the global modelling. Planet properties, including radius, orbital semimajor axis, eccentricity, and transit impact parameter are subsequently derived from the posteriors. In addition to the global model, we also propagate the posteriors and follow Masuda & Winn ( 2020 ) to derive the 3D spin-orbit obliquity of the system. We use the rotational period (see Section 4 ), line broadening, and projected spin-orbit angle to derive a 3D orbital obliquity of 2.4 ± 1.3 • .

TOI-4641 exhibits short time-scale stellar variability at the 1 mmag level during all five sectors of TESS observations and is also noticed in the ground-based observations. The variability is likely consistent with changing rotational spot modulation on the stellar surface.

The top left panel of Fig. 7 shows the sector-by-sector frequency power spectrum of TOI-4641. Sectors 18 and 58 exhibit variability at the 0.96 ± 0.02 c ycles d -1 frequenc y, while the 3.93 ± 0.02 cycles d -1 peak is strongest for Sectors 42, 43, and 44. The variability does not exhibit equal period spacing as is expected for γ Dor variables, and the frequency is too low for δ Scuti pulsations. We suggest the variability is most consistent with rotational modulation. The rotational broadening velocity v sin I ⋆ = 86 . 3 ± 1 . 0 km s -1 propagates to an expected rotation period of 1.06 ± 0.04 d assuming sin I ⋆ = 1, corresponding to 0.94 ± 0.04 cycles d -1 , which is consistent with the peak variability frequency in the light curve in Sectors 18 and 58. The 1 cycle d -1 periodicity is the second most dominant peak in Sectors 42, 43, and 44, with the 4 cycles d -1 peak likely due to the specific spot configuration during this timeframe. Low-amplitude spot variability is seen in early-type stars in the Kepler sample. Sikora, Wade & Rowe ( 2020 ) note that 10-30 per cent of A and B stars exhibit spot-induced variability, despite not showing spectroscopic signatures of chemical peculiarity. Using all TESS sectors of data, we derive a 3 σ lower limit on the stellar inclination

To check if the variability is on target, we used the LIGHTKURVE code (Lightkurve Collaboration 2018 ) to extract light curves from multiple target and background apertures, and found no changes in the amplitude and shape of the variability. Fig. 8 shows a set of example target apertures and resulting light curves. The target is in a sparse field and there are no stars within a 1 arcmin field that are bright enough to cause the 1 mmag variability seen on target after dilution. We also note that the rotational modulation was similarly identified in the SPOC transit search of the combined TOI-4641 light curves. Note. Gaussian priors are listed as G(median,width) and uniform priors are listed as U (lower bound, upper bound). Inferred parameters are calculated from the posterior distribution. TRES spectra were used to derive a metallicity prior using the SPC analysis (Buchhave et al. 2012 ) and the project rotational velocity and macroturbulent velocity using a least squares deconvolution analysis (Zhou et al. 2016 ). Parallax was obtained from the Gaia DR3 release (Gaia Collaboration 2023 ).

These TCEs attributed to the rotational modulation were subjected to the same diagnostic tests as would any TCE triggered by a transiting planet. The difference image centroid offsets (Twicken et al. 2018 ) showed that the source of the modulation was consistent with TOI-4641 at the 3 σ level and inconsistent at that level with all other TIC v8.2 objects.

TOI-4641 is a warm Jupiter in a 22 d orbit around a bright ( V = 7.5), rapidly rotating (86.3 + 1 . 00 -0 . 99 km s -1 ) F-star. The orbit is nearly circular with eccentricity constrained at the 3 σ level to less than 0.074. This target was observed in five TESS sectors and was photometrically followed up by the Tierras ground-based Observatory to rule out the false positive scenario of a nearby eclipsing binary contaminating the aperture. Additionally, we obtained high-resolution images from the Speckle imager on the WIYN 3.5m telescope and detected no secondary sources out to a radius of 1.2 arcsec. TRES spectra allowed us to detect a 3 σ upper limit planetary mass of 3.87 M Jup . We also obtained two nights of TRES in-transit spectroscopic data to measure the projected spin-orbit angle of 1 . 41 + 0 . 76 -0 . 76

• . TOI-4641b is amongst the longest period planets to be thoroughly characterized about a hot rapidly rotating star (Fig. 9 ). Longperiod planets provide tests for mechanisms that induce primordial misalignment in planetary systems. At such orbital distances, starplanet tidal interactions are too weak to modify the orbital obliquity.

Chaotic accretion is one proposed method of primordial misalignments where neighbouring protostar material interacts or arrives at different times during the accretion process, potentially causing the protostar disc to tilt with respect to the star (Bate, Lodato & Pringle MNRAS 527, 10955-10964 ( 2024) 2010 ; Thies et al. 2011 ;Fielding et al. 2015 ;Bate 2018 ;Kuffmeier et al. 2021 ). Another proposed mechanism for misalignment is magnetic warping. In young stars, in particular, the twisting of magnetic field lines between the ionized disc and the differential rotation of the young star can cause misalignment (Foucart & Lai 2011 ;Lai 2012 ). In this scenario, the misalignment torque must o v ercome the realignment torque from accretion, magnetic braking, disc winds, and viscosity. Stellar or planetary companions can also cause misalignment during the primordial phase of formation (Borderies, Goldreich & Tremaine 1984 ;Lubow & Ogilvie 2000 ;Batygin 2012 ;Matsakos & K önigl 2017 ). Rogers, Lin & Lau ( 2012 ) proposed that internal gravity waves excited at the radiati ve-convecti ve boundary of early-type stars can induce their surface layers to change in spin direction. Changes to the spin axes of early-type stars will also lead to an apparent spin-orbit misalignment, potentially contributing to the temperature-obliquity gradient seen in the hot Jupiter population.

Critically, most of these proposed mechanisms do not have a strong dependence on the host star properties beyond planet-star tidal interactions. We should not observe strong differences in the obliquity distributions of longer period Jovian planets as a function of stellar mass. Should internal gravity waves (Rogers, Lin & Lau 2012 ) play a major role in shaping the spin axes of early-type stars, no orbital distance trends should be observed in that population.

Testing these predictions moti v ate full characterizations of planets in long-period orbits about early-type stars. TOI-4641b is the second such Jovian-sized planet around a rapidly rotating early-type star, preceded only by Kepler-448b (Bourrier et al. 2015 ;Johnson et al. 2017 ). Both planets have been found in well-aligned geometries, whereas early-type stars with closer orbiting giant planets tend to show a broad range of obliquities including nearly polar and retrograde orbits.