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Evidence for Misalignment Between Debris Disks and Their Host Stars

Spencer A. Hurt Department of Physics and Astronomy, University of Wyoming, Laramie, WY 82071, USA Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA Meredith A. MacGregor Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA
Abstract

We place lower limits on the obliquities between debris disks and their host stars for 31 systems by comparing their disk and stellar inclinations. While previous studies did not find evidence for misalignment, we identify 6 systems with minimum obliquities falling between ∼​30​°−60​°\mathord{\sim}30\degree-60\degree, indicating that debris disks can be significantly misaligned with their stars. These high-obliquity systems span a wide range of stellar parameters with spectral types K through A. Previous works have argued that stars with masses below 1.2 M⊙M_{\odot} (spectral types of ∼\mathord{\sim}F6) have magnetic fields strong enough to realign their rotation axes with the surrounding disk via magnetic warping; given that we observe high obliquities for relatively low-mass stars, magnetic warping alone is likely not responsible for the observed misalignment. Yet, chaotic accretion is expected to result in misalignments of ∼​20​°\mathord{\sim}20\degree at most and cannot explain the larger obliquities found in this work. While it remains unclear how primordial misalignment might occur and what role it plays in determining the spin-orbit alignment of planets, future work expanding this sample is critical towards understanding the mechanisms that shape these high-obliquity systems.

††software: astropy (Astropy Collaboration et al., 2018), exoplanet (Foreman-Mackey et al., 2021), matplotlib (Hunter, 2007), numpy (Harris et al., 2020), PyMC3 (Salvatier et al., 2016), SciPy (Virtanen et al., 2020)

1 Introduction

The Sun’s equatorial plane is well-aligned with the ecliptic, having an obliquity of 7.155±0.002​°7.155\pm 0.002\degree (Beck & Giles, 2005). Most of the major solar system bodies move in nearly the same plane, suggesting that the planets formed from a protoplanetary disk that was rotating in the same direction as the early Sun. It has commonly been thought that other planetary systems form similarly and that exoplanet orbital axes should be closely aligned with their stars’ spin axes. However, observational techniques such as the Rossiter-McLaughlin effect (Queloz et al., 2000; Shporer & Brown, 2011; Triaud, 2018), Doppler shadows (Albrecht et al., 2007; Zhou et al., 2016), and gravity darkened transits (Barnes, 2009; Ahlers et al., 2020) have measured large spin-orbit angles for many extra-solar systems (Albrecht et al., 2022).

Possible mechanisms responsible for spin-orbit misalignment generally fall into three categories: primordial misalignment, post-formation misalignment, and changes in the stellar spin axis that are independent of planet formation. The first, primordial misalignment, suggests that a protoplanetary disk is misaligned with its star’s rotation axis and that planets with large spin-orbit angles form in situ. Processes that could misalign the disk include chaotic accretion (where the late arrival of material from the molecular cloud warps or tilts the disk; Bate et al. 2010; Thies et al. 2011; Fielding et al. 2015; Bate 2018; Takaishi et al. 2020), magnetic warping (when the Lorentz force between a young star and ionized inner disk magnifies any initial misalignments; Lai et al. 2011; Foucart & Lai 2011), and secular processes involving an inclined stellar or planetary companion (Borderies et al., 1984; Lubow & Ogilvie, 2000; Batygin, 2012; Matsakos & Königl, 2017). Post-formation misalignment implies that after formation, gravitational interactions alter a planet’s orbit. This could occur via planet-planet scattering (Malmberg et al., 2011; Beaugé & Nesvorný, 2012) or secular processes like Kozai-Lidov cycles (Naoz, 2016) or disk-driven resonance (Petrovich et al., 2020). Both primordial and post-formation misalignment could also occur via stellar clustering, which appears to have a strong influence on the architecture of planetary systems (Tristan & Isella, 2019; Winter et al., 2020; Rodet & Lai, 2022) and may be commonplace (Yep & White, 2022). Thirdly, it has been proposed that stars with convective cores and radiative envelopes can reorient themselves without an external torque due to internal gravity waves generated at the radiative-convective boundary (Rogers et al., 2012, 2013).

Hot Jupiters—massive planets on very short orbits—frequently appear misaligned with hot, rapidly-rotating stars that generally fall above the Kraft break (∼​6200\mathord{\sim}6200 K; Kraft, 1967) while low-mass planets appear misaligned with both cool and hot stars (Winn et al., 2010; Schlaufman, 2010; Albrecht et al., 2022). It has been suggested that hot Jupiters first enter high-obliquity orbits regardless of their host stars’ properties; however, tidal interactions between the massive, close-orbiting planets and the relatively thick convective envelopes found in stars below the Kraft break realign the stellar spin axes with the hot Jupiters’ orbits. The mechanisms responsible for spin-orbit misalignment may help reveal how these exotic planets form. While formation in situ through core accretion may be possible (Batygin et al., 2016), it would be challenging for enough material to accumulate and develop into a planet that close to a star. Instead, if a massive planet formed far from its star, it could move to a short orbit via disk-driven migration or high-eccentricity tidal migration (Dawson & Johnson, 2018). If the hot Jupiter were primordially misaligned, this would indicate disk-driven migration, whereas post-formation misalignment could result from high-eccentricity tidal migration.

Constraints on which mechanisms actually contribute to spin-orbit misalignment can be placed using the observed distribution of obliquities and trends across system parameters. Additional constraints on primordial misalignment can be placed using observations of circumstellar disks and their stars. Watson et al. (2011) first compared stellar inclinations to disk inclinations for 8 systems with spatially resolved debris disks, while Greaves et al. (2014) later did the same for 10 systems imaged by the Herschel satellite. Neither found evidence for misalignment, but both had limited samples and predate many spatially resolved images of disks taken by the Atacama Large Millimeter/submillimeter Array (ALMA), Hubble Space Telescope (HST), and Gemini Planet Imager (GPI) that can robustly measure disk inclinations. Davies (2019) compared inclinations for resolved disks (mostly protoplanetary) in the ρ\rho Ophiuchus and Upper Scorpius star forming regions, finding that a third of systems are potentially misaligned. Davies (2019) used these contrasting results to raise the additional question of whether or not debris disks preserve the preceding protoplanetary disks’ geometry and if star-disk-planet interactions or the formation of a debris disk can change the star-disk obliquity.

In this work, we study the star-disk alignment for an expanded sample of 31 resolved debris disks. In Section 2, we outline our methods, including the sample selection and measurements made. We then discuss our results in Section 3. Finally, in Section 4, we conclude our findings.

2 Methods

We assembled a list of spatially resolved debris disks from the literature, excluding circumbinary and circumtriple disks to simplify our analysis. We then identified systems with published stellar inclinations (isi_{s}) or the data necessary to measure the inclination available, leaving a sample of 31 targets that can be found in Table 4.

Effective temperatures (TeffT_{\mathrm{eff}}), masses (MM), and radii (RR) were taken from the TESS Input Catalog (TIC; Stassun et al. 2018; Paegert et al. 2021) for most stars in our sample. Given the majority resolved debris disks are located around nearby, bright stars, the TIC adopted most of these parameters from large spectroscopic catalogs, avoiding the challenges of color-temperature relationships discussed in Stassun et al. (2018), particularly for the coolest stars (Teff<3800T_{\mathrm{eff}}<3800 K). Parallaxes are known for all objects in our sample, providing precise measurements of radius in the TIC. 4 targets (AU Mic, Vega, β\beta Leonis, and β\beta Pictoris) that were either missing measurements or were reported without uncertainties were supplemented using values found elsewhere in the literature. The number of confirmed planets in each system was additionally determined by searching the NASA Exoplanet Archive Confirmed Planets Table (NASA Exoplanet Archive, 2019). 8 out of the 31 systems have at least one confirmed planet.

To determine the projected rotational velocities (v​sin⁡iv\sin i) of our sample, we adopted published values for each target. If multiple values were found, we adopted the measurement made using the highest-resolution spectrograph. Only 1 object (β\beta Leonis) had a v​sin⁡iv\sin i reported without uncertainties; we assume 10%10\% error bars on this measurement, typical for the uncertainties in our sample. 2 objects (GJ 581 and HD 23484) had upper limits on their projected rotational velocities and were treated as such in our analysis. We note that spectral line broadening from rotation is degenerate with turbulence in the stellar atmosphere and the v​sin⁡iv\sin i measurements in this work use a variety of modeling frameworks to account for macroturbulence, possibly introducing unknown systematics to our analysis.

Refer to caption
Figure 1: Disk inclinations plotted against the stellar inclinations for each system in our sample. The color of each point corresponds to the absolute value of the median of Δ​i=id−is\Delta i=i_{d}-i_{s}, where blue indicates a well-aligned system and red indicates a large misalignment. Capped error bars represent the range of values that a parameter falls within (assuming a uniform distribution) while the rest represent the 68%68\% credibility interval.

Archival rotation periods were gathered for 26 objects in our sample. We also directly measured the rotation period for stars that displayed quasiperiodic variations in the Pre-Search Data Conditioned Simple Aperture Photometry (PDCSAP) light curves produced by the TESS Science Processing Operations Center (SPOC), which have been corrected for instrumental systematics (Stumpe et al., 2012; Smith et al., 2012; Stumpe et al., 2014). Each photometric time series was modeled using a Gaussian process (GP), which are commonly used to represent rotational modulation induced by active regions rotating in and out of view (Haywood et al., 2014; Rajpaul et al., 2015). We used the rotation kernel implemented in celerite2 that combines two dampened simple harmonic oscillators with periods of PP and P/2P/2 to capture the stochastic variability in a star’s rotation signal (Foreman-Mackey et al., 2017; Foreman-Mackey, 2018). Using TESS data, we measured the rotation period of 18 stars, 5 of which had no previously published measurements; all of these measurements agree with either our archival values or the rotation period relationship in Noyes et al. (1984). For each of these 18 targets, we used the rotation periods and uncertainties determined using TESS data as they are well-constrained and measured under a standard framework. These periods, along with the projected rotational velocities and the corresponding uncertainties, can be found in Table 4 while the TESS light curves, GP models, and rotation period posteriors are shown in Appendix A.

We then determined the stellar inclination for each target with a known radius, rotation period, and v​sin⁡iv\sin i using the projected rotational velocity method, where the inclination is given by

i=arcsin⁡(v​sin⁡iv)=arcsin⁡(v​sin⁡i2​π​R/P).i=\arcsin\left(\frac{v\sin i}{v}\right)=\arcsin\left(\frac{v\sin i}{2\pi R/P}\right). (1)

As discussed by Masuda & Winn (2020), v​sin⁡iv\sin i and vv are not independent from each other, complicating the statistical inference of ii. A simple technique accounting for this is to to use a Markov chain Monte Carlo (MCMC) process with a uniform prior on cos⁡i\cos i and measurement informed priors on RR, PP, and (2​π​R/P)​1−cos2⁡i\left(2\pi R/P\right)\sqrt{1-\cos^{2}i} (Albrecht et al., 2022). This approach is also advantageous because it easily accounts for uncertainties in our measurements of RR, PP, and v​sin⁡iv\sin i. Given that measurements of v​sin⁡iv\sin i are typically made from a star’s spectral absorption lines and require that broadening from rotation be distinguished from other sources, including turbulence in the stellar atmosphere or instrumental resolution, the projected rotational velocity method is often subject to systematic uncertainties. Therefore, we adopted stellar inclinations previously determined using more accurate methods such as interferometry (Vega and β\beta Leonis), asteroseismology (β\beta Pictoris), and starspot tracking (ϵ\epsilon Eridani) whenever possible. Interferometry and asteroseismology also allow us to expand our sample to early-type stars with weak, often undetectable rotational modulation.

We conducted a literature search for disk inclinations (idi_{d}), selecting values that were the most well-constrained, typically corresponding to images with the highest spatial resolution. Most of these images were taken using ALMA, HST, and GPI, although the uncertainties on the inclinations vary widely as the spatial resolution is highly dependent on instrument configuration and distance. Inclinations can also be determined more precisely for edge-on disks than face-on disks.

To better understand whether the star and disk might be misaligned, we calculated the difference between the disk and stellar inclinations (Δ​i=id−is\Delta i=i_{d}-i_{s}), the absolute value of which gives the minimum star-disk misalignment; because we are unable to determine the position angle of the stellar rotation axis or the direction of the disk and stellar angular momenta, we are unable to calculate the full obliquity. For systems with stellar inclinations determined using the projected rotational velocity technique, we assumed the MCMC posterior distribution; for the systems with archival measurements, a sample of stellar inclinations were drawn from Gaussian distributions. Similarly, we drew a sample of disk inclinations using either uniform or Gaussian distributions when appropriate. We then took the differences between our samples of disk and stellar inclinations and adopted the median value along with lower and upper uncertainties representative of the 68%68\% credibility interval. These differences, along with the stellar and disk inclinations, are given in Table 4.

Refer to caption
Figure 2: Stellar parameters for the systems in our sample. The color of each point corresponds to the absolute value of the median of Δ​i=id−is\Delta i=i_{d}-i_{s}, where blue indicates a well-aligned system and red indicates a large misalignment. The top left figure shows mass versus TeffT_{\mathrm{eff}}, the top right shows radius versus TeffT_{\mathrm{eff}}, the bottom left gives v​sin⁡iv\sin i versus TeffT_{\mathrm{eff}}, and the bottom right gives the rotation period versus TeffT_{\mathrm{eff}}.

3 Results and Discussion

3.1 Comparing Disk and Stellar Inclinations

25 systems appear to be closely aligned with disk and stellar inclinations consistent of being within 10​°10\degree of each other (although large uncertainties mean that some of these systems could still be misaligned). There are several exceptions; most notably, HD 10647, HD 138813, HD 191089, HD 30447, ϵ\epsilon Eridani, and τ\tau Ceti all have misalignments ranging roughly between 30​°30\degree and 60​°60\degree. If stars and their disks are well-aligned, we would expect to see a monotonic, increasing relationship between disk inclination and stellar inclination in Figure 1. We test how well-aligned systems tend to be by calculating the Spearman rank-order correlation coefficient (rSr_{S}) for our data set. Using the median values for our inclinations, we find a coefficient of 0.62 with a p-value of 0.0002; however, this does not reflect the broad uncertainties on some of the inclination measurements. For each disk and stellar inclination, we drew a random sample and calculated a new coefficient and the corresponding p-value 10410^{4} times. The 68% credibility interval for rSr_{S} was .54±0.08.54\pm 0.08 with p-values of 0.0008−0.00069+0.00360.0008_{-0.00069}^{+0.0036}. These values for rSr_{S} are notably lower than the coefficient of 0.82 found by Watson et al. (2011) and indicate that while there is a positive correlation between disk and stellar inclinations, they are not always well-aligned.

It is important to keep in mind that disk and stellar inclinations can only put a lower limit on misalignment and that a full analysis requires knowledge of both the disk and stellar position angle on the sky plane. Further, inclinations do not indicate the directions that the star is rotating and the disk material is orbiting; if they are moving in opposite directions, the misalignment between the disk and star would be much greater than calculated. Given that systems such as K2-290—a strong candidate for primordial misalignment—have co-planar planets in retrograde orbits, this may be a significant bias (Hjorth et al., 2021).

While Watson et al. (2011) and Greaves et al. (2014) did not find signs of star-disk misalignment in their sample of debris disks, Davies (2019) observed misalignment of protoplanetary disks at a rate slightly higher than seen in our analysis (∼​33%\mathord{\sim}33\%); however, we note that they observed much smaller misalignments, typically less than 30​°30\degree. This indicates that the star-disk misalignment may not decrease as the disk transitions, as suggested by Davies (2019), and raises the question of whether misalignment increases as the system evolves. It is possible that mechanisms such as stellar flybys can incline debris disks (Moore et al., 2020) while processes such as accretion onto the star are unlikely to realign the system.

Figure 2 shows the mass, radius, v​sin⁡iv\sin i, and rotation period of each star in our sample versus the effective temperature. Figure 3 shows the difference between the disk and stellar inclinations as a function of system parameters. In these plots, we see most of the star-disk systems are well-aligned aside from the 6 mentioned above. The misaligned systems are not clustered around any specific TeffT_{\mathrm{eff}} or mass, suggesting that misalignment may occur regardless of stellar type, although there are not enough stars to make definitive conclusions. We also do not observe misalignment occurring more frequently with the presence of known planets; yet, many substellar objects in these debris disk systems may easily be undetectable. Finally, the 6 significantly misaligned systems span a wide range of ages (∼\mathord{\sim}7 Myr to 5.8 Gyr; Mamajek & Hillenbrand 2008; Bell et al. 2015; Pecaut & Mamajek 2016; Shkolnik et al. 2017; Nielsen et al. 2019); this is not surprising given that primordial misalignment is expected to occur during the protoplanetary disk stage, well before debris disks form.

Refer to caption
Figure 3: The difference between the disk and stellar inclinations (id−isi_{d}-i_{s}) plotted versus different system parameters. The color of each point corresponds to the median value of the minimum obliquity. The top left shows TeffT_{\mathrm{eff}} on the bottom axis while the right has the mass, the bottom left shows v​sin⁡iv\sin i, and the bottom right the number of confirmed planets in the system.

3.2 Implications for Primordial Misalignment

If magnetic warping were responsible for spin-orbit misalignment, Spalding & Batygin (2015) argue that misalignment should occur more frequently around stars with masses greater than 1.2 M⊙M_{\odot}; this is because lower-mass, young stars would be able to realign their stellar spin axes with the surrounding disks due to their stronger magnetic fields. As seen in Figure 3, 2 of the significantly misaligned systems (ϵ\epsilon Eridani and τ\tau Ceti) have stellar masses below 1.2 M⊙M_{\odot} while 2 (HD 10647 and HD 191089) have masses very close to this limit, suggesting that magnetic warping alone is not a viable mechanism for disk misalignment.

If chaotic accretion were at play, subsequent accretion of disk material onto the star is expected to reduce the misalignment to values lower than 20​°20\degree by the time planets begin to form (Takaishi et al., 2020). Not only does this fail to describe the distribution of obliquities observed for exoplanets, but it does not match the ∼​30​°−60​°\mathord{\sim}30\degree-60\degree misalignments shown in Figure 3. We do see systems with small potential misalignments near or below 20​°20\degree, including HD 107146, HD 129590, HD 145560, HD 202917, HD 206893, HD 35650, HD 377, and β\beta Leonis, but the large uncertainties on our obliquity measurements make it difficult to determine whether low-obliquity systems are truly misaligned. Additionally, without knowing the position angles of each star, we cannot definitively comment on whether star-disk misalignment commonly falls near 20​°20\degree.

While the significantly misaligned disks could have been torqued out of alignment by an inclined stellar or planetary companion, this mechanism is unable to explain the observed distribution of spin-orbit obliquities (Zanazzi & Lai, 2018; Albrecht et al., 2022). Ultimately, it is unclear what mechanisms can misalign disks around their stars; further, because we do not know of many planets in these systems, we are unable to determine whether the same mechanisms could be responsible for spin-orbit misalignment. As discussed in Section 3.1, mechanisms such as stellar flybys may incline debris disks in addition to planetary orbits, and the obliquities measured in this work may not reflect a system’s primordial architecture.

4 Conclusions

We investigate the alignment of resolved debris disks with their stars, placing a lower limit on their obliquities by comparing stellar and disk inclinations. With recent resolved images of disks taken by ALMA, HST, and GPI, along with rotation periods measured using TESS, we were able to include 31 systems in our analysis, more than 3 times as large as the samples included in previous studies of debris disks.

While there formerly was little evidence for misalignment between debris disks and their stars, we find 6 systems with disk and stellar inclinations separated by ∼​30​°−60​°\mathord{\sim}30\degree-60\degree. This indicates that these evolved disks are frequently misaligned with their stars; although, systems are more often well-aligned than not. Given that we observe such large minimum obliquities, some mechanism other than chaotic accretion needs to be at play. We also see misaligned systems with stellar masses below or near 1.2 M⊙M_{\odot}, suggesting that magnetic warping alone cannot be responsible for misalignment. Because resonant processes that could torque the disk out of alignment fail to explain the distribution of spin-orbit obliquities, it remains unclear what role primordial misalignment could play in shaping planetary systems. Further, it is unknown whether these disk obliquities truly reflect the structure of the preceding protoplanetary disk.

Future work needs to expand the number of debris disk hosts with inclination measurements, helping constrain the characteristics of misaligned systems. Few stars in our sample have known planetary companions and no confirmed hot Jupiter systems are currently known to contain circumstellar debris; searching for dust in confirmed planetary systems could help better understand whether the mechanisms that misalign disks with their stars are also responsible for spin-orbit misalignment.

Existing methods to measure stellar position angle cannot be applied to the vast majority of debris disk hosts (Le Bouquin et al., 2009; Lesage & Wiedemann, 2014), meaning the full obliquity between a disk and its star cannot be measured. As mentioned by Watson et al. (2011), a full Bayesian analysis accounting for this limitation could place more useful upper limits on the misalignment, similar to the framework presented in Fabrycky & Winn (2009) for spin-orbit angles. Regardless, the lower limits on misalignment presented in this work help better understand the geometry of debris disks, and future observations will improve our understanding of the mechanisms that shape and misalign these systems.

We thank the referee for thorough and insightful feedback that greatly improved the quality of this paper. We also thank Ruth Angus and Megan Bedell for a helpful discussion on how to measure stellar rotation periods and Ann-Marie Madigan and Carolyn Crow for thoughtful conversation about our results. M.A.M. acknowledges support for this work from the National Aeronautics and Space Administration (NASA) under award number 19-ICAR19_2-0041. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This work made use of the SIMBAD database (operated at CDS, Strasbourg, France), NASA’s Astrophysics Data System Bibliographic Services. The TIC data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute and can be accessed via https://doi.org/10.17909/fwdt-2x66 (catalog 10.17909/fwdt-2x66). This research has made use of the VizieR catalog access tool, CDS, Strasbourg, France (DOI: 10.26093/cds/vizier). The original description of the VizieR service was published in A&\&AS 143, 23. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.
Table 1: Sample of Disk Hosts and Stellar Properties
References
Name SpT TeffT_{\mathrm{eff}} Mass Radius v​sin⁡iv\sin i ProtP_{\mathrm{rot}} NplanetsN_{\mathrm{planets}} SpT TeffT_{\mathrm{eff}} Mass Radius v​sin⁡iv\sin i ProtP_{\mathrm{rot}}
(K) (M⊙M_{\odot}) (R⊙R_{\odot}) (km​s−1\mathrm{km\,s^{-1}}) (days)
61 Virginis G6.5V 5562±1105562\pm 110 0.98±0.120.98\pm 0.12 0.984±0.0450.984\pm 0.045 2.2±0.32.2\pm 0.3 29.0 3aaPlanets around 61 Virginis detected via radial velocities and inclinations are unknown (Vogt et al., 2010). 1 2 2 2 3 4
AU Mic M1VeBa1 3500±1003500\pm 100 0.66±0.020.66\pm 0.02 0.698±0.0210.698\pm 0.021 9.5±0.29.5\pm 0.2 4.8366±0.00754.8366\pm 0.0075 2bbPlanets follow edge-on orbits around AU Mic and are well-aligned with star and disk (Plavchan et al., 2020; Addison et al., 2021; Martioli et al., 2021). 1 5 2 2 6 7
GJ 581 M3V 3396±1603396\pm 160 0.31±0.020.31\pm 0.02 0.33±0.010.33\pm 0.01 ≤2.1\leq 2.1 130±2130\pm 2 3ccPlanets around GJ 581 detected via radial velocities and inclinations are unknown (Trifonov et al., 2018). 8 2 2 2 9 10
HD 104860 G0/F9V 6000±1506000\pm 150 1.11±0.151.11\pm 0.15 1.007±0.0541.007\pm 0.054 16±216\pm 2 2.9493±0.00312.9493\pm 0.0031 0 11 2 2 2 11 7
HD 10647 F9V 6151±1506151\pm 150 1.17±0.161.17\pm 0.16 1.096±0.0571.096\pm 0.057 3.8±0.43.8\pm 0.4 9.22±0.069.22\pm 0.06 1ddPlanet around HD 10647 detected via radial velocities and inclination is unknown (Marmier et al., 2013). 1 2 2 2 12 7
HD 107146 G2V 5873±1105873\pm 110 1.06±0.141.06\pm 0.14 0.958±0.0410.958\pm 0.041 4.9±0.64.9\pm 0.6 2.35 0 13 2 2 2 14 15
HD 129590 G3V 5897±1305897\pm 130 1.07±0.141.07\pm 0.14 1.689±0.0791.689\pm 0.079 32±232\pm 2 4.5291±0.00614.5291\pm 0.0061 0 16 2 2 2 17 7
HD 138813 A0V 10543±81010543\pm 810 2.72±0.432.72\pm 0.43 1.72±0.121.72\pm 0.12 97.9±2.297.9\pm 2.2 1.07 0 18 2 2 2 19 20
HD 141943 G2 5963±1205963\pm 120 1.09±0.141.09\pm 0.14 1.348±0.0621.348\pm 0.062 38±238\pm 2 2.283±0.0622.283\pm 0.062 0 21 2 2 2 22 7
HD 145560 F5V 6865±1406865\pm 140 1.49±0.251.49\pm 0.25 1.423±0.0611.423\pm 0.061 43±343\pm 3 1.40473±0.000611.40473\pm 0.00061 0 23 2 2 2 17 7
HD 166 G8 5489±1405489\pm 140 0.96±0.120.96\pm 0.12 0.89±0.0520.89\pm 0.052 4.1±0.44.1\pm 0.4 6.3265±0.00826.3265\pm 0.0082 0 24 2 2 2 25 7
HD 181296 A0V 9760±1409760\pm 140 2.49±0.352.49\pm 0.35 1.617±0.0421.617\pm 0.042 62±362\pm 3 5.4±1.25.4\pm 1.2 0 26 2 2 2 27 27
HD 191089 F5V 6487±1106487\pm 110 1.33±0.211.33\pm 0.21 1.31±0.0531.31\pm 0.053 43±643\pm 6 0.488±0.0050.488\pm 0.005 0 16 2 2 2 27 28
HD 202628 G5V 5831±1305831\pm 130 1.05±0.141.05\pm 0.14 0.97±0.050.97\pm 0.05 2.65±0.112.65\pm 0.11 14.215±0.09114.215\pm 0.091 0 21 2 2 2 29 7
HD 202917 G7V 5541±1405541\pm 140 0.98±0.120.98\pm 0.12 0.887±0.0520.887\pm 0.052 15.4±0.115.4\pm 0.1 3.3739±0.00363.3739\pm 0.0036 0 21 2 2 2 21 7
HD 206893 F5V 6554±1206554\pm 120 1.36±0.221.36\pm 0.22 1.311±0.0551.311\pm 0.055 32.7±5.732.7\pm 5.7 0.966±0.0030.966\pm 0.003 2eeThe two planets around HD 206893 have a mutual inclination of 15°\degree at most and could be misaligned from the disk by ∼​20​°\mathord{\sim}20\degree (Hinkley et al., 2022). 30 2 2 2 31 32
HD 23484 K2V 5182±1405182\pm 140 0.88±0.110.88\pm 0.11 0.804±0.0540.804\pm 0.054 ≤4.2\leq 4.2 10.32±0.8310.32\pm 0.83 0 21 2 2 2 21 7
HD 30447 F3V 6786±1106786\pm 110 1.46±0.251.46\pm 0.25 1.397±0.0531.397\pm 0.053 55±655\pm 6 0.88±0.020.88\pm 0.02 0 16 2 2 2 27 27
HD 35650 K6V 4220±1304220\pm 130 0.66±0.0810.66\pm 0.081 0.672±0.0630.672\pm 0.063 4.0±0.24.0\pm 0.2 9.43±0.039.43\pm 0.03 0 21 2 2 2 21 7
HD 35841 F3V 6493±1306493\pm 130 1.33±0.221.33\pm 0.22 1.231±0.0511.231\pm 0.051 36±336\pm 3 1.849±0.0191.849\pm 0.019 0 18 2 2 2 27 7
HD 377 G2V 5895±1405895\pm 140 1.07±0.131.07\pm 0.13 1.034±0.0551.034\pm 0.055 14.6±0.514.6\pm 0.5 3.601±0.0463.601\pm 0.046 0 21 2 2 2 25 7
HD 53143 G9V 5440±1005440\pm 100 0.95±0.120.95\pm 0.12 0.864±0.0390.864\pm 0.039 4±14\pm 1 9.592±0.0279.592\pm 0.027 0 21 2 2 2 33 7
HD 61005 G8Vk 5503±1105503\pm 110 0.97±0.120.97\pm 0.12 0.878±0.0390.878\pm 0.039 8.9±1.58.9\pm 1.5 5.1639±0.00785.1639\pm 0.0078 0 30 2 2 2 27 7
HD 92945 K1V 5105±1505105\pm 150 0.86±0.110.86\pm 0.11 0.791±0.0560.791\pm 0.056 6±36\pm 3 7.18±0.317.18\pm 0.31 0 21 2 2 2 34 7
TWA 25 M0.5 3899±1203899\pm 120 0.6±0.0840.6\pm 0.084 1.06±0.121.06\pm 0.12 12.9±1.212.9\pm 1.2 5.0318±0.00795.0318\pm 0.0079 0 35 2 2 2 36 7
TWA 7 M2Ve 3509±1203509\pm 120 0.46±0.0860.46\pm 0.086 0.92±0.120.92\pm 0.12 4.4±1.24.4\pm 1.2 5.41±0.375.41\pm 0.37 0 21 2 2 2 21 7
Vega A0Va 9660±909660\pm 90 2.15±0.122.15\pm 0.12 2.726±0.0062.726\pm 0.006 20.5±0.720.5\pm 0.7 0.67±0.070.67\pm 0.07 0 37 38 38 38 39 40
β\beta Leonis A3Va 8502±458502\pm 45 1.93±0.011.93\pm 0.01 2.28±0.112.28\pm 0.11 118±12118\pm 12  ⋯\cdots 0 41 2 42 42 43  ⋯\cdots
β\beta Pictoris A6V 8143±678143\pm 67 1.8±0.041.8\pm 0.04 1.54±0.041.54\pm 0.04 124±3124\pm 3  ⋯\cdots 2ffPlanets around β\beta Pictoris detected via direct imaging and appear well-aligned with the disk (Feng et al., 2022). 30 44 44 44 45  ⋯\cdots
ϵ\epsilon Eridani K2V 5065±1005065\pm 100 0.9±0.10.9\pm 0.1 0.755±0.0380.755\pm 0.038 2.17±0.252.17\pm 0.25 12.3±0.0612.3\pm 0.06 1ggOrbital inclination of planet around ϵ\epsilon Eridani has large uncertainties, may be misaligned with the disk (Llop-Sayson et al., 2021; Benedict, 2022). 1 2 2 2 6 46
τ\tau Ceti G8V 5333±995333\pm 99 0.92±0.110.92\pm 0.11 0.833±0.0370.833\pm 0.037 1.8±0.11.8\pm 0.1 34.0 4hhPlanets around τ\tau Ceti detected via radial velocities and inclinations are unknown (Feng et al., 2017). 1 2 2 2 3 47

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\startlongtable
Table 2: Disk and Stellar Inclinations
References
Name idiski_{\mathrm{disk}} Disk Imaging Facility istari_{\mathrm{star}} Stellar Inclination Method Δ​i\Delta i idiski_{\mathrm{disk}} istari_{\mathrm{star}}
(°\degree) (°\degree) (°\degree)
61 Virginis 77±477\pm 4 HSO 77.5−13.0+8.777.5^{+8.7}_{-13.0} v​sin⁡iv\sin i 2.7−8.9+13.02.7^{+13.0}_{-8.9} 1 2
AU Mic 89.4±0.189.4\pm 0.1 GPI 87.3−2.8+1.987.3^{+1.9}_{-2.8} v​sin⁡iv\sin i 2.2−1.9+2.82.2^{+2.8}_{-1.9} 3 2
GJ 581 [30.0,70.0] HSO 60.0−28.0+21.060.0^{+21.0}_{-28.0} v​sin⁡iv\sin i −9.0−23.0+29.0-9.0^{+29.0}_{-23.0} 4 2
HD 104860 54±754\pm 7 HSO 71.0±13.071.0\pm 13.0 v​sin⁡iv\sin i −11.0−13.0+14.0-11.0^{+14.0}_{-13.0} 5 2
HD 10647 [53.0,90.0] HSO 40.6−5.6+6.440.6^{+6.4}_{-5.6} v​sin⁡iv\sin i 30.0−13.0+14.030.0^{+14.0}_{-13.0} 6 2
HD 107146 18±218\pm 2 HST 14.2−2.3+2.414.2^{+2.4}_{-2.3} v​sin⁡iv\sin i 5.8−2.7+2.65.8^{+2.6}_{-2.7} 7 2
HD 129590 74.56±0.0574.56\pm 0.05 SPHERE/VLT 84.9−5.4+3.684.9^{+3.6}_{-5.4} v​sin⁡iv\sin i −10.3−3.6+5.4-10.3^{+5.4}_{-3.6} 8 2
HD 138813 29.0±0.329.0\pm 0.3 ALMA 79.7−11.0+7.379.7^{+7.3}_{-11.0} v​sin⁡iv\sin i −50.5−7.3+11.0-50.5^{+11.0}_{-7.3} 9 2
HD 141943 87±187\pm 1 GPI 84.1−6.2+4.184.1^{+4.1}_{-6.2} v​sin⁡iv\sin i 3.7−4.1+6.23.7^{+6.2}_{-4.1} 3 2
HD 145560 43.9±1.543.9\pm 1.5 GPI 59.9−7.5+11.059.9^{+11.0}_{-7.5} v​sin⁡iv\sin i −14.9−11.0+7.5-14.9^{+7.5}_{-11.0} 10 2
HD 166 21±2421\pm 24 HSO 36.1−4.5+5.436.1^{+5.4}_{-4.5} v​sin⁡iv\sin i 1.0−12.0+18.01.0^{+18.0}_{-12.0} 5 2
HD 181296 [70.0,90.0] Gemini South 74.0−16.0+11.074.0^{+11.0}_{-16.0} v​sin⁡iv\sin i 6.0−12.0+17.06.0^{+17.0}_{-12.0} 11 2
HD 191089 59±359\pm 3 HST 19.9−3.6+20.019.9^{+20.0}_{-3.6} v​sin⁡iv\sin i 41.3−19.0+4.241.3^{+4.2}_{-19.0} 12 2
HD 202628 57.4±0.457.4\pm 0.4 ALMA 51.2−4.6+5.551.2^{+5.5}_{-4.6} v​sin⁡iv\sin i 6.5−5.6+4.66.5^{+4.6}_{-5.6} 13 2
HD 202917 68.6±1.568.6\pm 1.5 HST 84.5−5.4+3.884.5^{+3.8}_{-5.4} v​sin⁡iv\sin i −14.7−3.8+5.4-14.7^{+5.4}_{-3.8} 14 2
HD 206893 40±340\pm 3 ALMA 29.8−5.6+6.029.8^{+6.0}_{-5.6} v​sin⁡iv\sin i 12.6−6.3+5.812.6^{+5.8}_{-6.3} 15 2
HD 23484 [50.0,90.0] Herschel 57.0−26.0+22.057.0^{+22.0}_{-26.0} v​sin⁡iv\sin i 13.0−23.0+28.013.0^{+28.0}_{-23.0} 16 2
HD 30447 83±683\pm 6 GPI 45.2−6.2+7.645.2^{+7.6}_{-6.2} v​sin⁡iv\sin i 42.3−8.1+7.542.3^{+7.5}_{-8.1} 3 2
HD 35650 89.0±2.589.0\pm 2.5 HST 80.1−9.4+6.980.1^{+6.9}_{-9.4} v​sin⁡iv\sin i 10.8−6.9+9.610.8^{+9.6}_{-6.9} 17 2
HD 35841 84.9±0.284.9\pm 0.2 GPI 79.2−9.7+7.479.2^{+7.4}_{-9.7} v​sin⁡iv\sin i 5.8−7.4+9.75.8^{+9.7}_{-7.4} 18 2
HD 377 8585aaNo uncertainties reported. Standard deviation of 5​°5\degree assumed. HST 79.1−8.9+7.479.1^{+7.4}_{-8.9} v​sin⁡iv\sin i 9.9−7.8+9.39.9^{+9.3}_{-7.8} 17 2
HD 53143 56.23±0.3756.23\pm 0.37 ALMA 67.0−18.0+16.067.0^{+16.0}_{-18.0} v​sin⁡iv\sin i −10.0−16.0+18.0-10.0^{+18.0}_{-16.0} 19 2
HD 61005 85.6±0.185.6\pm 0.1 ALMA 73.0−14.0+12.073.0^{+12.0}_{-14.0} v​sin⁡iv\sin i 12.0−12.0+14.012.0^{+14.0}_{-12.0} 20 2
HD 92945 65.4±0.965.4\pm 0.9 ALMA 65.0−23.0+18.065.0^{+18.0}_{-23.0} v​sin⁡iv\sin i 1.0−18.0+23.01.0^{+23.0}_{-18.0} 21 2
TWA 25 75±675\pm 6 HST 79.0−10.0+7.679.0^{+7.6}_{-10.0} v​sin⁡iv\sin i 1.0−8.4+11.01.0^{+11.0}_{-8.4} 17 2
TWA 7 22±2222\pm 22 HST 37.0−11.0+17.037.0^{+17.0}_{-11.0} v​sin⁡iv\sin i 0.0±19.00.0\pm 19.0 17 2
Vega [0.0,40.0] ALMA 6.2±0.46.2\pm 0.4 Interferometry 14.0−14.0+13.014.0^{+13.0}_{-14.0} 22 23
β\beta Leonis 33±733\pm 7 HSO 21.5±5.021.5\pm 5.0 Interferometry 16.8−5.6+6.916.8^{+6.9}_{-5.6} 24 25
β\beta Pictoris 85.3±0.385.3\pm 0.3 GPI 87.8±1.687.8\pm 1.6 Asteroseismology −2.0−1.5+1.6-2.0^{+1.6}_{-1.5} 3 26
ϵ\epsilon Eridani 18±1318\pm 13 SMA/ATCA 69.95−7.6+5.669.95^{+5.6}_{-7.6} Photometry + Spectroscopy −42.6−9.5+11.0-42.6^{+11.0}_{-9.5} 27 28
τ\tau Ceti 35±1035\pm 10 HSO 81.6−8.6+5.981.6^{+5.9}_{-8.6} v​sin⁡iv\sin i −38.4−8.3+11.0-38.4^{+11.0}_{-8.3} 29 2

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Appendix A TESS Light Curves and Measured Rotation Periods

A description of the light curve modeling approach is given in Section 2 while the derived rotation periods and 1​σ1\sigma uncertainties are found in Table 4. We additionally calculate Lomb-Scargle periodograms for each light curve and the false alarm probability (FAP) associated with the rotation signal (Zechmeister & Kürster, 2009). Several stars display double dipping, where two opposing star spots create a false signal at P/2P/2 (Basri & Nguyen, 2018); in several instances, including HD 377 and HD 92945, we find that phase dispersion minimization periodograms (Stellingwerf, 1978) better capture the true rotation period and use them in place of Lomb-Scargle periodograms. Figures 4 through 21 show a periodogram, phase-folded light curve, light curve from a single TESS sector, and the rotation period posterior for each object showing quasiperiodic variations in TESS data.

Refer to caption
Figure 4: Top left: The Lomb-Scargle periodogram for the AU Mic TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 1 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 5: Top left: The Lomb-Scargle periodogram for the HD 104860 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 14 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 6: Top left: The Lomb-Scargle periodogram for the HD 10647 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 2 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 7: Top left: The Lomb-Scargle periodogram for the HD 129590 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 11 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 8: Top left: The Lomb-Scargle periodogram for the HD 141943 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 12 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 9: Top left: The Lomb-Scargle periodogram for the HD 145560 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 12 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 10: Top left: The Lomb-Scargle periodogram for the HD 166 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 17 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 11: Top left: The Lomb-Scargle periodogram for the HD 202628 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 1 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 12: Top left: The Lomb-Scargle periodogram for the HD 202917 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 1 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 13: Top left: The Lomb-Scargle periodogram for the HD 23484 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 31 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 14: Top left: The Lomb-Scargle periodogram for the HD 35650 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 5 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 15: Top left: The Lomb-Scargle periodogram for the HD 35841 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 5 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 16: Top left: The phase dispersion minimization periodogram for the HD 377 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 5 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 17: Top left: The Lomb-Scargle periodogram for the HD 53143 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 1 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 18: Top left: The Lomb-Scargle periodogram for the HD 61005 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 7 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 19: Top left: The phase dispersion minimization periodogram for the HD 92945 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 9 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 20: Top left: The Lomb-Scargle periodogram for the TWA 25 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 10 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.
Refer to caption
Figure 21: Top left: The Lomb-Scargle periodogram for the TWA 7 TESS PDCSAP light curve is shown in black. The dashed grey line marks the 1%\% FAP level while the shaded red region denotes the 1​σ1\sigma confidence interval for the rotation period posterior. Top right: The phase-folded light curve using the peak period from the Lomb-Scargle periodogram. Bottom left: The black points show data from TESS Sector 36 while the red line and shaded region mark the mean and 1​σ1\sigma confidence interval for the GP model. Bottom right: The histogram shows the rotation period posterior derived from the GP model while the dash red lines mark the median and 1​σ1\sigma interval.

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